Gate Two: Matter and Form — The Thing in Itself and Its Appearances
From the book Two Wagons and a Hot Air Balloon by Rabbi Michael Avraham. Translated from Hebrew using gpt-5.4 (reasoning_effort=high, batch API).
Matter and Form: The Thing in Itself and Its Appearances
This gate contains four chapters:
- Chapter 1: Matter and Form: The Principle of Individuation
- Chapter 2: Form and Definition: Essential and Accidental Properties
- Chapter 3: Thinking and Cognition
- Chapter 4: The Linguistic Layer: The Problem of Reference
Introduction
In this gate we will propose an expansion of the Kantian distinction between the world of things as they are in themselves (noumena) and the world of appearances (phenomena), which was presented briefly in the previous gate. As noted there, this Kantian thesis underlies the human ability to say something about reality a priori—that is, prior to sensory experience—and thus underlies the existence of synthetic a priori propositions. The issue of phenomena and noumena will be linked to a question that was very popular in ancient and medieval philosophy, though it lost much of that popularity in the modern period: the question of matter and form (or substance and accident). At the end of the gate I will point to a further connection between these questions and a third issue, much more modern, namely the problem of reference, whose systematic philosophical discussion began at the beginning of the twentieth century and continues to this day.
The previous gate dealt with the distinction between the analytic and the synthetic, and in the present gate we shall see how that distinction naturally gives rise to different attitudes toward the thing in itself as well. It should be noted that in Kant’s own thought there is indeed a clear connection between the issue of the thing in itself and the issue of the synthetic a priori, a connection to which we briefly pointed already in the previous gate. It is important to note, however, that these are different kinds of connections. The purpose of this book is not to clarify Kant’s doctrine as such. We will make use here of Kantian concepts and ideas in order to formulate the arguments presented below. Kant’s terminology provides a convenient framework for this, but it is important to clarify that the connections drawn here will at times differ from those found in Kant’s own philosophy.
The purpose of the present gate is to point to the existence of two ways of apprehending the world around us, ways that are expressed primarily in relation to abstract concepts. In doing so we will expand the two positions presented at the logical level in the previous gate—the analytic and the synthetic—and connect them to the epistemological level, that is, the level of cognition. The main claim is that those who adopt the synthetic approach and those who adopt the analytic approach, as they were presented at the end of the previous gate, are usually divided not only on the logical plane—with respect to the concept of truth and the manner of rational argumentation—but also with respect to modes of perception and cognition, that is, on the epistemological plane as well.
In the next part we will continue to develop this claim in contexts that are less philosophical and more topical. In Part Four we will see an important implication of the picture presented in this gate. There we shall see that the very distinction between thinking and cognition is, in many respects, artificial.1
Chapter 1: Matter and Form: The Principle of Individuation
Introduction
In ancient philosophy the pair of concepts “matter” and “form” was widely used. These two concepts served in several different senses, and it is important to distinguish among them. For example, different views in antiquity and the Middle Ages disagreed over whether matter is “higher” than form—more spiritual, or more abstract—or “lower” than it. Such polar disagreement appears mainly because the terms “matter” and “form” were used in different ways. Since our aim here is not to survey the whole issue of matter and form, but only to make use of this pair of concepts for our own purposes, I will now define the sense in which these terms will be used in the present discussion.
In the Hebrew Encyclopedia, under the entry “Matter,” Hugo Bergmann writes:
In classical Greek philosophy the pair of concepts “matter-form” took shape to mark the difference between an undetermined element and a determining element in general. Matter and form are correlative concepts: matter is the content of form. The thing that has form, when we abstract the form from it, is matter. Hence “matter” denotes anything capable of receiving form, and in this broad sense one may speak of the matter of a proposition, of a cognition, of a story, and the like.2
Even in the sense of the term “matter” described here, two meanings may be distinguished: matter as the basic component from which concrete objects (or concepts, or propositions, as we shall see below) are formed—for example, in the case of a chair or a table, the block of wood from which they are made; and matter as the material object itself—the finished product—once abstracted from its form. I will use the term “matter” in the second sense: matter is the thing itself without its form. In similar contexts people sometimes use the concept of “substance,” as opposed to “accident,” but for various reasons we shall prefer the terminology of “matter” and “form.”3 Form, in this context, is the dual, complementary concept: the set of characteristics of the object or concept itself—that is, of its matter.
At this point the connection between the two issues begins to emerge: the ancient one concerning matter and form, and the more recent, Kantian one concerning phenomena and noumena. The distinction between form and the content that fills it also reminds us of the difference between analytic thinking, which is formal, and synthetic thinking, which deals with contents. We shall return to these connections after clarifying the distinction between matter and form more fully. To do so, we will briefly describe the problem of individuation and Aristotle’s formulation of the principle of individuation in response to it.4
The Problem of Individuation
Let us begin with the following claim: it is possible for there to be two entities that are completely equal in all their properties, and yet still be two different entities—that is, not one and the same entity. This Aristotelian claim appears, at first glance, quite simple, but it has been the subject of a long-standing philosophical dispute. A fairly common view among philosophers holds that such a thing is impossible. The best-known denier of this claim is Leibniz, who argued that no two drops of water are entirely alike. Leibniz did not even accept Locke’s view that two such drops could differ only by their location in space and time.5 According to Leibniz’s well-known “principle of the identity of indiscernibles,” any two things that do not differ from one another in any of their properties are identical—that is, they are one and the same object.
Leibniz even offered a “logical” proof of this principle: if there really were two individuals, A and B, equal in all their properties, and yet they were still regarded as two, then the very distinction from A would itself be a property that exists in B but not in A. We would then have found that they do, after all, differ in at least one property, contrary to the assumption that there is no difference between them in any property.
As Bergmann remarks there, this attempt at proof, which tries to establish a metaphysical principle by logical means, does not withstand criticism.6 Clearly, the claim that these two individuals differ from one another means that some difference does indeed obtain between them, but not in any property or attribute they possess. Leibniz’s apparent proof rests on the assumption that difference between entities can only be a difference in properties, and from this he concludes that the difference itself is therefore a property. Here, of course, Leibniz has begged the question. If there is no difference beyond difference in properties, then it is obvious that indiscernible entities are identical. There is nothing remarkable in that. What is disputed is the assumption itself, and therefore it is pointless to use it in order to prove the conclusion.7
The content of Leibniz’s claim—that two completely identical beings cannot exist—may be true on the metaphysical plane. Some thinkers, especially religious ones, have indeed argued this for theological and other reasons.8 Here, however, we are concerned only with the logical level of Leibniz’s claim, which in effect says that there is nothing in an object beyond its properties. That certainly has not been proven, and in my opinion it is also false. We have a clear sense that the identity of a thing is not determined by its attributes, and I do not think Leibniz gave any significant reason that should lead us to ignore this intuition.
We therefore return to the Aristotelian view, according to which it is not the properties, but some other special principle, that makes an entity the entity it is, a person the person he is, and in general an individual the individual it is. This is the principle called “the principle of individuation.” Two objects can differ from one another in their intrinsic identity, simply by the fact that they are two, and yet possess identical properties—that is, be indiscernible.9 This factor—the intrinsic identity of the object, abstracted from all its properties, and therefore, precisely because it is abstracted from its properties, not describable by any property—is Aristotle’s concept of “matter.”
The concept of “matter” stands in contrast to the concept of “form.” Form is the totality of all the properties of that entity. Everything we can know about an entity, and everything we can say about any entity, concerns only its properties, its form, which faces outward. About its intrinsic identity it is very difficult for us to speak—though not impossible. I will return shortly to the question of what can be said about the intrinsic identity of an entity, that is, about its “matter.”
It is important to emphasize that properties always define groups of entities—those that possess or bear the property. The property “red,” for example, describes or characterizes various garments, the sky at sunset, and so on. Therefore a property does not, in principle, single out one specific entity. True, a collection of properties may in certain cases fit the description of only one entity, but that is accidental and not essential. A genuine and essential individuation of an entity is accomplished only by its matter, which it shares with no other entity.
Let us now try to clarify further the claim that the distinctness of personality on the logical plane is not established by its attributes or properties.10 Gottlob Frege, an important logician of the late nineteenth century, distinguished between a predicate, which in his terminology is unsaturated, and an individual, which is saturated. A predicate is like a template containing a variable; without assigning a value to that variable, it says nothing. For example, the predicate “round” says nothing until we state which object is round. Thus in a template of the form “_ is round,” one must always insert some subject characterized by the predicate “round” in order to obtain a claim or a meaningful utterance. By contrast, the individual, designated for example by some proper name, requires no addition in itself in order to have content or meaning—or, in the language customary in analytic philosophy, in order to refer to something.
If we continue along this line of thought, then every kind or species also functions as a predicate in this context, and in order to saturate it we must add a subject of which it will be said that it belongs to that kind. For example, the kind “Jew” requires supplementation in order to be saturated: “Jacob is Jewish.” Usually, without that supplementation, the kind is a candidate for several possible subjects. Even when the kind contains only one individual, it still is not saturated until we add that subject. For example: “the youngest brother of Reuben, son of the patriarch Jacob” is a kind that has only one subject—it applies only to one entity, Benjamin. Nevertheless, its logical status remains unsaturated until we say, “Benjamin is the youngest brother of Reuben,” or alternatively, “The youngest brother of Reuben is kind-hearted.” In other words, there is a logical distinction between individuality and attributes, even in a case where those attributes fit that one individual and no other. This is what Bergmann writes in his book Introduction to Logic (p. 103):
If we descend from genus to species, and from species to ever lower and more determinate species, we shall eventually arrive at the lowest species. Even this lowest species is “determinate in every respect.” If, for example, we descend through the series: mammal, human being, youth, thirteen-year-old youth, and so on, we shall eventually reach a maximum of determinacy. But is this the same determinacy that marks the individual as an individual? To this one may answer: this ever-increasing determinacy nevertheless remains within the domain of predicates, and even when determinacy has reached its maximum, we are still dealing not with individuality, but with a general concept, which from a purely logical standpoint can serve as a predicate for many subjects.
We therefore cannot, by multiplying predicates, leap across the abyss that separates predicate from subject.
Let us summarize. Our cognition of an entity is always through its properties—or in our terminology, through its form—and not through its intrinsic identity, that is, not through its matter. Our cognition has no access to the matter of any entity, only to its form.11 Grammatically, in the sentences of language, form is expressed by predicates or attributes, while matter is expressed by a name serving as the subject of the sentence.
More on Human Cognition
In the formulation at which we have now arrived, the connection between the issue of matter and form and the issue of noumena and phenomena becomes clear. The thing in itself—the noumenon—which is not exposed to our cognition, is what Aristotle calls “matter.” The form of the thing, as it is termed in Aristotelian language, is what Kant calls the appearance, the phenomenon.
It should be noted that the link we are drawing here between these two issues involves a particular interpretation of Kantian philosophy. Some interpret Kant’s claim regarding the limits of human cognition—that it cannot grasp the thing in itself, but only its appearances—as a limitation of us, human beings with a particular cognitive structure, and not as an essential limitation. According to this interpretation, the things themselves do have properties, but we cannot know them as they are, only as they appear to us. A simple example would be someone viewing the world through a sheet of yellow cellophane: he would see all objects in that color, even though their “real” color might be different.
We argue here that this is true of cellophane placed over the eyes, but not of the eyes themselves. Our claim is that apprehending the thing in itself is impossible not because of some physical, psychological, or other limitation, but because such apprehension is not even logically well-defined, and is impossible on the epistemological level.12
To illustrate and clarify this claim, let us quote an example from Bertrand Russell’s The Problems of Philosophy:62
Sometimes people say: “Light is a kind of wave-motion.” This is misleading, for the light that we directly see, the light that we know immediately by means of our senses, is not a kind of wave-motion but something quite different, something which all of us, if we are not blind, know, although we cannot describe it so as to convey our knowledge to a blind man. Wave-motion, on the contrary, can be described very well to a blind man, since the blind can acquire knowledge of space by touch, and can feel wave-motion almost as we do when traveling on the sea. But what the blind man can understand is not what we mean when we say “light.” By the word “light” we mean precisely something that a blind man can never understand and that we can never describe to him.
By way of explanation of Russell’s claim, one might say that there is no principled obstacle to the possibility that the eye-brain visual system could have been built from sensors sensitive to electromagnetic waves that would be translated in our consciousness into sounds, rather than, as in our actual case, into sights. In such a world we would hear electromagnetic waves rather than see them. There would be no light in that world, only sound. The physical world itself, of course, would not change at all: it would contain acoustic waves as well as electromagnetic ones, exactly as it does now.
To put the point differently: one can imagine a completely different creature whose sensory system translates these waves into entirely different forms of consciousness—not light and not sound, perhaps even forms entirely unfamiliar to us. A blind person is one example, though only one particular example, of such a creature. The difference between us and such imaginary creatures could lie either in the senses themselves or in the brain-system that processes the sensory data and translates them into the form in which they appear in consciousness.
A similar distinction applies to each of the human senses. It is therefore clear that color, light, sound, smell, and the like are forms of perception determined by the perceiver—in this case, human cognition. Reality itself, which exists independently of the observer or perceiver, is the acoustic or electromagnetic waves themselves. These waves have no characteristics of their own. Only when cognition and consciousness observe such objects or phenomena are forms generated within consciousness: in the case of an electromagnetic wave encountered by a human cognitive system, light; in the case of an acoustic wave, sound.
This is true not only of waves. The same applies to material objects that have mass. These too, in themselves, have no properties. Characteristics such as roundness or color are generated only in the human cognition that observes them; they do not exist in the world itself.
This also lets us answer that old—and fundamentally mistaken—question: when a tree falls in a forest, and no human being is present to observe it, can one still say that a sound is heard there? According to what we have explained, the answer is self-evident: there is an acoustic wave there, but there is no sound. Sound is a phenomenon that exists only in the cognition of a human listener, which translates the acoustic wave in the world into sound within cognition. When such a cognition is not present, no sound is heard.13
If we now ask what the true color of the table before us is, in itself—that is, not as it is reflected to our eyes but as it “really is”—we are guilty of asking a meaningless question. The table itself has no color at all. The meaning of the question “What is the color of a given object?” is: “What color will appear in the consciousness of a normal human observer who looks at this object?” And so it is with all the properties of the various objects and persons we perceive with our senses. Form is the object as it appears to us, in the parameters we define—color, sound, and so forth.
The necessary conclusion is that our inability to grasp the thing in itself is not a human limitation, as those who adopt the interpretation mentioned above believe. This inability follows from the fact that the thing in itself has no form at all. The term “form” means: the object as it appears within the cognition that observes it. To know something in the world means to create a sensory translation of it within our cognition, not to enter into contact with its “objective” form. There is no such thing as an “objective form.” As noted above, the inability to grasp the entity in itself is not an a posteriori physiological or scientific claim. It is an a priori logical and epistemological claim, derived from the very definitions of the concepts of “cognition” and “form.” In light of what I have described, it would be more accurate to say that cognition does not “touch” form; rather, it “creates” it—out of contact with the thing in itself, that is, with the matter of the entity.
And Yet: Characteristics of the Thing Itself — The Apprehension of God
This picture of the distinction between matter and form, as parallel to the distinction between the thing in itself and its characteristics, still requires sharpening and clarification. For despite everything said so far, there is undoubtedly an ontological root for the sensory representation formed in human cognition. We can clarify this through a discussion of the apprehension of God.
Let us begin with a statement that appears many times in works of philosophy and religious thought: God cannot be apprehended in the same ways in which we apprehend other objects. According to this view, one can apprehend only God’s manifestations, for God Himself transcends ordinary apprehension.
In light of what we have seen above, a troubling problem arises: the same statement is equally true of every other object. No object can be apprehended in itself; what can be apprehended are only its manifestations—its form, or its phenomenon. If so, what is meant when it is said that God, unlike ordinary objects, cannot be apprehended and known in Himself?
A significant addition to the picture described above is concealed here. We have seen that a predicate has no meaning outside the consciousness that knows and observes it. As we saw in Russell, “color” is defined only in consciousness and not in the world itself. But one must notice that two objects that are completely identical in their structure in the world as it is in itself must be perceived in identical ways—we earlier called this, in paraphrase of Leibniz, the principle of the indiscernibility of identicals. If we see two apparently identical tables of different colors, then clearly something in their reality as it is in itself is causing this difference. That is, there is an intrinsic difference that expresses itself as a difference in form. The description of the difference can always be given in our system of terms—color, height, geometric shape, and the like—but the difference itself, in some sense, exists in reality itself.14
We must therefore qualify the simplistic picture drawn above, according to which matter is abstracted from all properties, while all such properties exist only within the cognition that observes the object. We now see that there is, in the matter of the thing—or in the thing in itself—a source for the predicates by which we observe it. The correct formulation is that the terms in which we describe the predicates—color, sound, brightness, and so forth—belong to our conscious world, but there are also “characteristics” in the world of things in themselves. The language of description is certainly subjective, and the concepts themselves, such as “color,” describe phenomena that exist only in consciousness. Yet the causes of these descriptions, or of these phenomena, certainly do exist in reality. Thus, contrary to what was said above, even in the world of the thing in itself there is an aspect to which one may refer as “characteristics.” Of course, one can refer only to their existence, not to any concrete description of them, since every such description belongs by nature to the phenomenal realm. In that sense, these “characteristics” are part of the world of things in themselves. They are the causes of the phenomenal appearances formed in the cognition of the observer. In reality there is no “color,” no “roundness,” no “sharpness,” and the like; there are only abstract factors attached to the thing, which, when they appear before our eyes, do so in these forms. It is indeed true that color, sharpness, and roundness are forms or phenomena that belong only to the world of our cognition and not to the world as it is in itself. These are the parameters by means of which we describe and classify forms—something like “categories,” in Kantian terminology.
In this sense, the apprehension of divinity differs from the apprehension of ordinary objects. The source of descriptions of God is not in the divine essence itself, since we have no access to it. God’s attributes do not arise from any factors within Him Himself, except perhaps indirectly, if at all. Their source is what Rabbi David Cohen, the Nazir, calls “metaphorical imagination.”15 He means a description or image whose root is not found in straightforward reality; in that sense such apprehension resembles imagination, for imagination is an image with no root in present reality. Of course, this image is not a hallucination, nor is it entirely rootless. Unlike an ordinary image, which is obtained by observing an object that is its source, here God implants this image in the prophet or sage without a material source in reality. It is a kind of “visual parable.”16
Connection to the Ontological Proof
There is another interesting point worth noting here. We have seen that we have no ability to speak about the matter of a thing, or about the thing in itself. All speech, description, and reference concern form. An attribute of the thing itself is found in its form as it appears in cognition, not in the thing itself. It is important to note that there are a few exceptions to this rule. There are claims or references—not descriptions—that can indeed relate to the thing in itself and not to its form. One of these exceptions is the claim that a certain thing exists. This claim concerns not the thing’s form but its matter.17
One interesting implication of this undermines what is known as the ontological proof for the existence of God.18 A concise formulation of one version of this proof runs as follows: the concept “God” is defined as a being possessing all perfections. One of the perfections is existence—an existing being is more perfect than a nonexisting one. Hence, if the concept of God is well defined, one may move from the conceptual level to the ontological level and conclude that God exists.
There are many objections to this proof. A large number of them derive from one basic claim: to say of a being that it is perfect is to make a claim about its attributes. But existence is not an attribute, and therefore one cannot say that existence is one of the perfections—or at least one cannot infer the existence of the perfect being, God, from the claim that existence is a perfection.19
This claim sounds rather vague. It is not clear how it refutes the argument itself, nor is its meaning obvious. What exactly is the criterion for classifying some statement as a description, and why is a statement asserting that something exists not a description of that thing? There is no place to elaborate on this issue here, but in light of what we have seen, it is worth noticing that the natural definition of an “attribute” is: a statement that concerns form, that is, a description. What concerns matter, or the thing in itself, cannot be called an attribute. As we have seen, a claim about the existence of something refers to its matter and not to its form.20 We may therefore say that such a claim is not a description of the thing. It seems that in this way one can better understand the objections to the ontological proof.21
Let us return to the course of the discussion and summarize. What has been proposed here is an interpretation of the Kantian claim about the inability to grasp the thing in itself. We have seen that this is not a human limitation but an a priori logical claim. The observing consciousness is what defines and determines the form of the entity. More than that: this consciousness also determines the parameters by which that form will be examined and described—that is, the characteristics we shall use to describe the entity: geometric shape, color, smell, sound, or even parameters wholly unknown to us, which appear—or at least may appear—in the consciousness of beings whose consciousness and cognition differ in kind from our own.22
Matter and Form of Concepts
I will now continue and extend the distinction between matter and form, following Aristotle himself, from objects to concepts as well. This immediately raises the following question. Objects are apprehended by the senses and the brain-based perceptual system inseparable from them; that is what we have discussed up to now. Concepts, by contrast, are apprehended by the intellect and by means of the tools of the intellect.23 Is it also the case here that the structure of the intellect defines the form of concepts, just as the senses do with objects? Or do concepts have characteristics in themselves, prior to the form they receive in our intellect, with the intellect functioning only as a passive apprehender or observer? In fact, there is room here for a third possibility, one that did not arise at all in our earlier discussion of objects: do concepts have matter and form at all, or are they all form? According to this last possibility, concepts exist only in our consciousness or intellect, and therefore it makes no sense here to speak of the matter and form of a concept, because a concept, by its very nature, belongs wholly to the world of phenomena.24
A discussion of this question seems to draw us into questions such as the existence of ideas, universals, or spiritual entities. Many philosophers have dealt with such questions, from Plato down to modern philosophy of science in its discussions of the existence of theoretical entities. The formulation of such questions is problematic in itself, for one must try to characterize what concept of existence is intended here. Clearly there is no occupation of space here, nor do concepts have mass, and so forth. We will therefore treat existence here as a basic and self-evident term, without trying to define it in terms of other concepts.
Certain worldviews, generally not popular today, treat concepts too as actually existing.25 If one begins from such an assumption, the Aristotelian distinction between matter and form can be applied not only to objects but also to concepts. It should be noted, however, that although the assumption that concepts exist makes matters easier to understand, we have no real need to enter the question of actual existence in order to use the distinction between matter and form with respect to concepts. One may say that concepts have matter and form without claiming that concepts exist in the world. There is the concept in itself, and there is its form, or its characteristics, as we apprehend them.26 To illustrate this point, let us now consider an example dealing with the matter and form of the concept of ownership in halakha (Jewish law).
Note 3: The Concept of Ownership — Matter and Form27
The concept of “acquisition,” or “ownership,” is understood in simple legal thought as the owner’s rights of use in an object, together with the prohibition on others using that object without the owner’s permission. This view raises several difficulties. First and foremost, there is an approach in halakha that holds that a person can own an object from which all benefit is halakhically forbidden. At first glance, what is ownership if not the possibility of use? This problem can indeed be resolved by noting that the owner may in fact use the object in terms of property rights, even if halakha forbids him to do so. No other legal entity can prevent him from doing so. For this reason he can also prevent others from using the object he owns. Thus it seems possible to live with the claim that in terms of property law he is considered the owner of the object even if he is forbidden to use it, and this even according to the simple conception of ownership.
From several other halakhic discussions, however, it appears that the concept of ownership is not exhausted by rights of use alone. Let us bring one example.
Halakha contains the category of a “Canaanite slave.” This is a non-Jewish person who sold himself to become the slave of a Jew. As a slave he is acquired by his master, who may make use of him as he wishes. When the master frees him, he becomes fully Jewish. There is a case in which the master renounces all his rights of use over the slave. In such a case the slave regains independence and ownership of his own body, yet his halakhic status remains that of a slave. In legal terms he does not become Jewish until his master, after renouncing those rights, also gives him a deed of release. In this intermediate state, before the master has given him that deed, the slave is apparently free in property terms, since the master has no right of use in him. Yet the Babylonian Talmud, Gittin 42b, says that one who injures such a slave pays damages to the master.
Rabbi Yehoshua Falk, in his Penei Yehoshua on tractate Gittin, explains that the master is still considered the owner of the slave’s body, even though he has no rights of use over him whatsoever.28 This is a case in which the master retains a status-based proprietary bond in the slave without ordinary property rights. We thus see that even in such a state, the relation between the slave and his former master is still called “ownership.” It follows that a situation can exist in which a person has ownership over an object in which he has no right of use whatsoever. More than that: this can be so even when that right belongs to someone else—to the slave himself, in our case.
On that same page of tractate Gittin, the Talmud discusses a similar case in which the slave’s master is a priest. In halakha, certain foods are defined as priestly offerings. Only priests may eat them, as well as members of their household and their property—animals and slaves. When the slave is not the priest-owner’s possession in the ordinary property sense, but only by virtue of this status-based bond, there are still opinions in halakha according to which he may eat priestly offerings. Again we see that such a slave is called the priest’s property even though the priest has no rights of use in him at all.
What is the meaning of such ownership, which is unaccompanied by any right of use? In Gate Thirteen I will argue that at the foundation of halakha stands a metaphysical system, and not merely a system of norms like any ordinary legal system. For our purposes here, let us say that the concept of ownership is not exhausted by rights of use in an object. It is a metaphysical relation between the owner and the object that is his property. True, the primary implication of such a relation is rights of use for the owner and prohibition of use by others without his permission, but that is only an implication and not ownership itself. The concept of ownership, or acquisition, is a metaphysical concept—regardless of the question whether the concept exists in actuality or not. This is, in our terminology, the concept in itself, or the matter of the concept. The form of the concept, as it appears to us, is rights of use and prohibition of use by others.29 The halakhic-legal consequences of ownership are the properties or attributes of this concept when one observes it—not with the eyes, of course, but with the “eyes of the intellect.”30
The metaphysical bond between owner and property is expressed not only in living property such as a slave, but in ordinary property as well. One could say much more about the implications of this distinction between the concept of ownership itself—the matter of the concept—and its halakhic consequences—its form. One could also discuss the matter and form of other halakhic concepts. For further elaboration on this subject, see my article “What Is ‘Legal Effectuation’?”31
Let us now bring another example from the world of halakha. This time we will discuss a concept that is not legal, like ownership, but distinctly halakhic: the sukkah (festival booth).
Note 4: What Is a Sukkah
In the Babylonian Talmud, tractate Beitzah 30b, the Talmud says that sanctity rests on the wood from which the sukkah’s covering—perhaps also its walls—is made. Most commentators understood the Talmud to mean only that it is forbidden to use this wood for other purposes. By contrast, Rabbi Shlomo ben Aderet, one of the greatest early Talmud commentators and legal authorities, in his commentary there, understands the Talmud to mean actual sanctity, namely that this wood is a sacred object. The Talmud later says that one cannot stipulate that the wood not become sacred. From this Rabbi Shlomo ben Aderet inferred that intrinsic sanctity cannot be made conditional. That is, one cannot cause it to lapse merely by a verbal stipulation; an actual act is required. In Talmudic language: “Intrinsic sanctity does not lapse for nothing.” The simple explanation is that if this is real sanctity inhering in the wood itself, and not merely a prohibition on using the wood, as the other commentators held, then this is a reality, and reality cannot be altered by mere words alone.32
At first glance, Rabbi Shlomo ben Aderet’s position is very puzzling. If, according to him, this is genuinely real sanctity, and therefore it cannot lapse by speech alone without an act, then surely it also cannot lapse by itself without speech. In halakhic terminology, intrinsic sanctity or full bodily ownership cannot be limited in time. If so, how would he explain the law—about which there is no dispute—that the sanctity of the sukkah wood lapses once the festival of Sukkot is over? At that point the wood may be used for any purpose one wishes; that is, it has no sanctity at all. This seems to prove that at the end of the festival’s eight days the sanctity departs of itself from the wood of the sukkah. If so, it would appear either that intrinsic sanctity can lapse even without an act, or else, contrary to Rabbi Shlomo ben Aderet, that the wood of a sukkah does not possess real sanctity in itself.
The explanation of Rabbi Shlomo ben Aderet’s view seems to be that after the festival the structure of the sukkah still exists, but it is no longer a “sukkah” in the halakhic sense. The halakhic concept “sukkah” does not overlap with the empirical concept “sukkah.” After the festival there is indeed a structure here that provides shade from the sun, but the halakhic sukkah is no longer present. If so, this is not a case of sukkah wood lacking sanctity because its sanctity has lapsed. It is not the sanctity that disappeared here, but the sacred object itself that vanished from the world. In other words, the sanctity that rests on the wood of the sukkah never lapses; rather, the sacred object is only the halakhic object and not the empirical one.33 “Sukkah” does not mean simply a collection of boards and branches assembled in the particular way required by halakha. That is certainly a necessary characteristic, but it is not sufficient. A sukkah is an object used to fulfill the commandment of sukkah. The concept “sukkah” has matter—the metaphysical sukkah—and form—the way it appears to our eyes. Again we see that the concept must not be identified with its form.34
To conclude the chapter, I will bring another example, which may sharpen both the distinction between matter and form and the principle of individuation, from a different angle.35
Note 5: Color and Individuation — The Chessboard and Domino Puzzle, and Quantum Physics36
On a chessboard-like board there are 8 rows and 8 columns, for a total of 64 squares. If we take domino rectangles, each of which covers exactly two squares of the board, then the whole board can be covered with 32 such rectangles. Now let us remove from the board two squares at the two ends of one of the main diagonals. In that case, 62 squares remain on the trimmed board. The question is whether this board can be covered by 31 dominoes of the same size. I suggest that the reader, before reading the solution below, think for a moment about the puzzle and try to cover the board in different ways.
The answer is that it cannot be done. One should now ask how this can be proved. Whoever struggled a bit with attempts to prove it will be surprised to find that the proof is much simpler than expected.
The trimmed board has 62 squares colored black or white, but the number of squares of each color is not equal. The two removed squares were of the same color, since they lie on the same diagonal. Therefore there are 32 squares of one color and 30 of the other, depending on which diagonal’s endpoint squares we removed. It is obvious that every domino placed on the board covers one black square and one white square; there is no other possibility. Therefore, when we place 30 such dominoes, they cover 30 white squares and 30 black ones. The two remaining squares will be of the same color, and thus they cannot be covered by the one domino we have left. This proves that such a covering is impossible.
Beyond the amusement of this puzzle, it is worth considering it in a somewhat different context. Clearly, the color of the squares is not really relevant. Even in formulating the puzzle I used the expression “a chessboard-like board,” because for purposes of the puzzle the squares could be colorless. It seems that we have introduced an irrelevant factor into the puzzle in order to solve it by a trick. The color of the squares seems completely inessential, and yet introducing it into the picture helped us solve the puzzle. This phenomenon is well known to mathematicians, who use similar devices in many contexts.
As in other cases of this sort, although the color is not relevant to the puzzle, it is still true that there are two different kinds of square here. All the squares may look uniform if we use an uncolored board, but in this case the appearance is deceptive. The difference between the groups exists at the topological level. For example, one can think of the group of squares diagonally connected to the two missing squares, and the second group as all the other squares not diagonally connected to them. This is a definition equivalent to the use of color on a chessboard, and it may be the relevant one here. In any event, there are two different kinds of square here, even if the board is not colored at all.
Because of the context of chess, coloring the board naturally suggested itself and helped us discern the uniqueness of these two types of square by characterizing them through a property that is, ostensibly, utterly irrelevant. We added a special form to each square—its color—merely in order to mark it, but the proof does not rest on the color. It rests on the different essence of the two kinds of square. This is an example of our inability to act and think at the level of things in themselves. In order to grasp them we must make use of their properties, even though it is not the properties that individuate them, but simply the fact that they are different. We color things to identify them, even though it is obvious that they possess individuation even without the color.
On the other hand, in this example we see something even more extreme. Not only is there individuation of the squares as they are in themselves; there is even a classification into types that we cannot discern without coloring them. This is an example of “characteristics” that exist in the thing itself prior to their formulation, or apprehension, in the terms of the apprehending consciousness, as we saw in our earlier discussion.
Here we see an example of the claim made in the text: it is the conferring of form that enables us to refer to or apprehend the thing in itself. Matter, or the thing in itself, cannot be specifically apprehended or referred to beyond its bare existence or its individuation. The word “to color” often serves as a metaphor for conferring identity on objects. Physics too speaks of a property of elementary particles called “color,” though it has no connection at all with color in the ordinary sense. It is the imposition of form in order to make identification possible. We are forced to “color” identical particles in order to mark and classify them.
It is interesting to note in this connection that in quantum physics there are particles that satisfy Leibniz’s principle of the identity of indiscernibles. These particles are called fermions. Their defining property is that no two particles can be in exactly the same state. By contrast, there are particles called bosons, which do not satisfy Leibniz’s principle, that is, they can indeed be found in identical states. A single type of such particle is enough to refute the Leibnizian principle. In order to distinguish such particles we must “color” them artificially.
One can continue this discussion at the level of quantum physics and show that the statistical properties of such particles differ from those they have in classical physics. In quantum physics, particles lack distinct individuality and are not distinguishable. One cannot refer to a particle as an entity with a continuous self-identity—that is, one cannot track the motion of such a particle along a space-time path. The particles are not defined at all as bodies with sharp individuation. All one can say is that there is one particle at location X and another at location Y, and there is no way to know whether the first is the particle that a moment earlier was at location Z while the second was at location R. At any given moment, all that can be said is that there is a certain number of particles at each point in space.
Failure to understand this statistical difference gave rise to the well-known paradox in statistical mechanics called Gibbs’s paradox. This can be illustrated by the simple case of two particles distributed between two places. If they are identical, there are three possible states: one particle in each place, both in place A, or both in place B. By contrast, if they are different, and we mark the first by the number 1 and the second by 2, then there are four possible states: particle 1 in place A and particle 2 in place B; the reverse arrangement; both in A; and both in B. This difference has important statistical consequences, leading to different thermodynamic properties in systems with many particles. It should be noted that “different particles” in this context does not mean particles with different properties—the “place” in this example is their property—but particles with an individuation that makes each one different from the other. Numbering them is merely a device of identification that expresses individuation and not a property, exactly like the coloring of the squares in the chessboard-and-domino example, and exactly like the name of a person or object in the earlier discussion. Giving a name is a kind of “coloring” of an object. Genuine properties of particles are not artificially added by us; they truly characterize them. Still, the form these properties take in our cognition is also derived from the structure of cognition itself, as we saw in the body of the chapter.
At first glance, this last passage appears to undermine the principle of individuation itself that we established in the body of the chapter, following Aristotle. We seem to see objects without individuation. Here, apparently, the question arises of the existence of theoretical entities. But if they do not exist, then our argument against Leibniz’s principle of the identity of indiscernibles, based on the existence of bosons, collapses as well.
It seems to me that the simpler explanation is that here too, as in our puzzle of the squares, individuation belongs not to the individual particle but to the group as a whole. That is the basic entity in this case, and the individual particle is indeed no more than a useful theoretical fiction.
The form, or property, relevant to each kind of square in the chessboard puzzle is not a property of the individual square but a property of the relation of the whole group to the missing squares. Therefore, in this case too, it is incorrect to refer to the square as it is in itself; rather one must refer to the group of squares of a certain type as it is in itself. The same applies to quantum particles.37
Such a perspective has very interesting implications for the relation between the individual and the group, or the whole within which it is contained. On this, see Note 15 below.
Chapter 2: Form and Definition: Essential and Accidental Properties
Introduction
In this chapter I wish to discuss the component of form, and especially the form of concepts. I shall then present two epistemologies with respect to concepts: one conventionalist—arbitrary and agreement-based—represented here through the thought of the analytic philosopher Hilary Putnam, and the other essentialist.
Later we shall see the connection between these two epistemologies and the two positions, analytic and synthetic, as they were defined in the first gate.
Form
In Note 3, brought at the end of the previous chapter to illustrate the terms matter and form with respect to the concept of “ownership,” we saw that the concept of ownership itself is a metaphysical concept, whereas its characteristics are the properties that accompany it—namely, rights of use and the like. We saw this by pointing to a case in which, despite the existence of a proprietary relation in reality—that is, ownership of a slave—these “properties” do not appear. Such a case shows that properties belonging to form do not characterize the concept in every case. Some always accompany it, while others describe it only at times. In Note 4 the situation was the opposite. There we saw that the characteristics—the material, in its everyday sense, from which the sukkah is made—are indeed essential to the concept of sukkah, but the converse is not true: there cannot be a sukkah without those characteristics, but there can be situations in which those characteristics are present and yet this is not a sukkah.
From these examples we arrive at the conclusion that, in addition to the distinction between matter and form, one must further distinguish within form itself between two parts: the accidental and the essential. The latter is that part of form which always characterizes the concept, and is sometimes confused with the concept’s intrinsic identity. The former is the accidental part of form, which sometimes characterizes the concept and sometimes does not.
Using this terminology, we can now see that in Note 3 we said two different things about the concept of ownership:
1. Rights of use are not the intrinsic identity—the matter—of the concept of ownership, but only part of its form.
2. They belong to the non-essential—that is, accidental—part of that form.38
Some medieval biblical commentators attribute the distinction between matter and form to the terms “chaos” and “void” at the beginning of Genesis.39 In the language of Sefer HaBahir, section 2:90
And what is “chaos”? Something that leaves human beings wondering. And what is “void”? Chaos existed and returned to void. And what is “void”? Something that has substance; the word hints, “it is in it.”
The meaning is as follows: “chaos” is a state about which one can only wonder, but regarding which we have no tools to ask or answer anything at all. This is matter, or the thing in itself. “Void,” interpreted as “it is in it,” is form, which pours content into the primordial matter and gives it substance.40
Continuing along this line,41 Gersonides writes in his commentary to Genesis there:[^93]
“Chaos” and “void” are matter and form, which are the principles of coming-to-be, as explained in the first book of Aristotle’s Physics. They are prime matter and the final form—that is, the form which prime matter first receives before receiving the other forms, for example the elemental forms.
It seems that what Gersonides intends here is to distinguish between the concept of form in general and what he calls the “final form,” which is the basic part of form first given to prime matter. This is apparently the part of form that we are calling here “essence.”
From another point of view, one may say that essence, precisely because it is the necessary part of a concept’s or object’s form, is that part of a concept’s properties without which it is no longer itself but another concept. This is the constitutive part of the concept. If taken in an unrestricted way, this formulation leads to the conclusion that there is nothing in a concept beyond its form, essential and accidental alike. It is with this approach—represented for our purposes by Hilary Putnam—that I now wish to engage.
Putnam’s View: The “Conventionalist” Approach
Hilary Putnam, a well-known contemporary analytic philosopher, proposes a principle that establishes a necessary condition for redefining any concept: in order for a thing that is redefined to remain the same thing previously defined in another way, the definition must preserve elements or characterizations belonging to the thing’s essence. Putnam argues that without this condition—namely, if one changes essential components of the definition—one is not redefining a concept but inventing a new one.42 Even a redefinition, if it refers to the same concept, must preserve the core of the previous concept if it is to count as a redefinition of that same concept. The concept of “definition” itself has not yet been clarified in our discussion, and it will be treated below (see also Gate Ten).
An interim remark: this perspective has implications for many issues, including topical ones. Consider, for example, contemporary attempts to redefine a nation, or a person, as “Jewish” without the religious component that was part of the definition accepted throughout history. Usually such attempts are devoid of substantive content and often involve circularity. But even if a truly contentful and meaningful definition were offered, one could still argue that the religious component in the previous definition was certainly essential. If so, it is difficult to see how one could refer to the concept “Jew” in such a new definition—whatever it may be—as the continuation of the concept “Jew” in its previous, classical sense. By contrast, if the intention is indeed to create a new concept, there is no justification for calling it by the name of the old one. This is especially true in the present situation, in which some still use the term “Jew” in its classical sense.
There is a fundamental problem in Putnam’s argument. In our terms one can say that the definition of a concept is in fact a verbal description of its essence. A definition should give as precise and exhaustive a description of the concept as possible. Clearly there is no point in including in a definition characteristics that are not necessary—features that may also fail to appear in certain instances of the defined concept. If so, as I noted above, in the terminology used here, the definition of a concept is really a verbal description of the essential part of its form.
If this claim is correct, then it seems at first glance that logically speaking one cannot change the definition of a concept at all. Such a change would in fact be the definition—and thus the creation—of a new concept. This problem arises because the components of a definition always belong to essential form, and if they can be changed in whole or in part, that shows that their appearance as features of the concept is not necessary—which contradicts their belonging to its essence.43
In the following note we shall sharpen further the distinction between the two parts of an entity’s form as defined here: the essential and the accidental.
Note 6: A Theological Difficulty
A believing person often feels, in relation to his Creator, a sense of injustice. Why were all human beings not given equal starting conditions—talents, economic circumstances, traits of character, and the like? The Sages say, for example, that when Moses our teacher was born, “the radiance of his face shone,” meaning that he was endowed from birth with exceptional gifts and chosen by God from birth. By contrast, every other person was not so privileged, and can therefore feel deprived.44
For those to whom it matters to wrestle with such questions—that is, those who believe in the existence of a Creator to whom such complaints can be addressed—there is a tendency to feel that this problem belongs to ethics, as though God appears to act in a way that is not moral. In light of our discussion here, this feeling seems plainly mistaken. At the present stage of the discussion, and especially according to Putnam’s view, this appears to be a logical problem. If God were to create Reuben as Moses, then there would be two Moseses—not Moses and an “improved Reuben.” A change of that kind entails changing Reuben’s essential characteristics, and therefore, according to Putnam, it does not leave him as a being that has undergone alterations but turns him into someone else. Such a change is, at first glance, impossible if one wants to preserve continuity of identity.
By way of analogy: suppose the number 2 came and complained to the Holy One, blessed be He, asking why it was not created as the number 1. Such a complaint reflects a logical misunderstanding. If it had been created as the number 1, then there would be two ones—not 1 plus an “improved 2.” In other words, such an act would not amount to changing the complaining being—the number 2, or Reuben—but to eliminating it and creating a new, different being.45 Such an act would also not help in any way with the frustration felt by the complainant, who would no longer exist. A request to change non-essential characteristics is the only kind that satisfies the demands of logic and remains relevant on the moral plane. Such a request, of course, does not involve a logical misunderstanding, unlike the examples above.
Later I shall explain the point at which, in my opinion, Putnam is mistaken. It will then become clear that demands to change essential characteristics are not necessarily devoid of logical foundation.
At this stage of the discussion, the impression is created that one cannot change an existing definition of a concept at all. Earlier we saw that the minimum requirement for this is that the change not damage essential components. Now our conclusion seems to be that no change at all is possible while preserving continuity. According to Putnam, the essential parts of a concept’s form cannot be changed if one wants to preserve the continuity of the concept’s identity. The parts that are not essential do not count as a principled change, since they do not constitute a change in the definition of the concept.
If we take as an example the concept “Jew,” mentioned in the interim remark above, then omitting the religious component from its definition is impossible if one still wishes to regard the result as the continuation of the previous concept. On the other hand, leaving the essential components intact while changing peripheral or accidental ones does amount to some change in the concept as it has been known until now, but not a change in its definition, which includes only its essential properties.
Despite everything said above, it seems impossible to ignore the feeling that such a claim does not fit our ordinary intuition. This is especially so in light of the claim to be presented below, according to which the root of the synthetic position is intuitive apprehension and common sense (see the next chapter, and more fully in Part Four).
The claim that one cannot change a definition of a concept at all, but only at most cancel the concept in its previous sense and create a new one in its place, rests on the assertion that there is nothing in a concept beyond its content—or, in our terminology, beyond its form. Therefore, since a definition contains only essential components of form, it is obvious that the new definition cannot be seen as representing the continuation of the previous concept. This is the view we will call “conventionalist,” that is, a view that understands definition as an arbitrary act representing nothing beyond convention or agreement. Conventionalism sees in the concept nothing beyond the collection of its characteristics.
The Essentialist Approach
According to the essentialist approach, a definition represents a concept and not a collection of properties. The concept exists even without the definition and is independent of it, or of any act of social agreement—we will later describe this, following Kripke, as the “baptism” of a concept. According to essentialism, the definition of a concept is not arbitrary or based on agreement, nor is it a fiction of the intellect. The definition attempts to grasp and present the form of a concept that exists in itself, while its matter—its intrinsic identity—cannot be directly grasped. The definition is a verbal expression of the collection of essential properties of the concept, but through them it represents the concept itself.
We saw a similar process in relation to objects. As noted above, cognition cannot apprehend the properties of the object as it is in itself, because they are too primordial and have no direct expression for us. Cognition produces from the object an image that exists within the intellect, and for that purpose it uses parameters drawn from human cognition and thought—such as color, geometric shape, and the like.
So too, the apprehension of a concept—as it is in itself, the matter of the concept—takes place through its form, or more precisely through the essential part of its form. The result of this process of apprehension, when expressed in words, is the definition of the concept. At the beginning of the gate we mentioned that a person “looks” at a concept with the eyes of the intellect, analogously to looking at an object with the physical eyes. Both kinds of observation generate a form within the observing cognition. The description of the essential part of the result of this observation is the definition of the concept.
According to this view, which may be called essentialist,46 one can speak of changing the definition of a concept in a way that preserves continuity, so that the new definition still refers to the old concept—to its “matter.” This is contrary to Putnam’s view, which, as we saw above, leads to the conclusion that it is impossible to change the definition of a concept. According to the essentialist conception, the change does indeed create a new mode of reference, but the concept itself—the matter—remains the same concept to which the previous definition referred. Such a conception solves the problem of continuity, but Putnam’s difficulty regarding the alteration of essential properties still remains. The claim that a concept has an essence really means that continuity is required not only for the matter but also for the form.
This problem requires detailed treatment, and this is not the place for it. Briefly, I would say that the solution lies in our earlier claim that form is a function of the observer. As we have already noted, this is true of concepts no less than of objects. A change in the definition of a concept, assuming the essentialist view that continuity is preserved—and therefore that it is the same concept—results from a change in the cognitive system of the being who “observes” the concept with the eyes of the intellect. That is, essential properties are preserved, but receive description in different parameters according to the new cognitive categories. If even such continuity is not preserved, then there seems to be no escape from concluding that we are indeed dealing with a new concept. My purpose here is only to point to a theoretical model that allows for change in the definitions of concepts. It is difficult to provide criteria by which to decide whether continuity of the concept’s identity is preserved, because that is a question whose answer lies at the intuitive level, prior to analysis and definition. For some elaboration on this, see Gate Eleven.47
With respect to the example mentioned earlier—the proposal to change the definition of the concept “Jew”—the possibility of a change that preserves the continuity of this concept depends on the claim that it has matter, or intrinsic identity, and not form alone. On this point, let us bring the illuminating words of Gershom Scholem, which should be interpreted in this way as well:[^100]
It is clear that in the eyes of many, among them some scholars as well, Judaism is a closed system of defined concepts. In my opinion, this view is no longer tenable. With the return of the Jewish people to its history and to its land, Judaism has become—for most of us—an open, living, undefined organism. It is a changing phenomenon, shedding form and taking on form in the course of its history.
According to the conventionalist Putnam, one might determine that there can be no real argument over the meaning of a concept, because such an argument is actually discourse about two different concepts. Any such dispute can supposedly be solved quite simply by coining two terms, each serving the different purposes of the two sides in the dispute. For example, in the dispute over “Who is a Jew?” one could propose the simple solution of using two terms: “Jew,” meaning someone born to a Jewish mother or converted according to halakha, and “Israeli,” meaning an Israeli citizen who identifies with the state and is willing to fulfill his obligations toward it. Splitting and distinguishing these two definitions would answer most of the concrete ideological problems. The proposal to redefine the concept “Jew” would be satisfied if we called the new concept “Israeli,” or any other name, while the term “Jew” could remain in its previous sense. And if, for sentimental or other reasons, someone nevertheless wanted specifically to use the term “Jew” to describe what we earlier called “Israeli,” or vice versa, then one could simply exchange the words used to represent the two concepts.
In short: if there is nothing in a concept beyond agreement on its definition, then there is no point in wrangling over definitions and words. One can choose another word and solve all the problems. Whoever feels that there really is a genuine dispute over the definitions of concepts, such as the dispute over “Who is a Jew?”, then regardless of his particular position in that dispute, necessarily assumes the existence of the concept in itself and does not apprehend it in a conventionalist way. For him, the concept “Jew” is fixed and standing, even if there are disagreements about its characteristics and definition. He feels that despite the dispute, the two sides are still speaking about the same concept, and only because of this does the argument have meaning.
For this reason the essentialist will oppose the proposed solution that says one should coin two different words and thereby solve that dispute. The essentialist will say that a dispute about a concept is a real dispute, not an illusory one, between two cognitions observing the same concept in itself; therefore it cannot be resolved by coining two different terms. In the case of “Who is a Jew?”, the essentialist grasps that there is a concept in the world designated by the word “Jew,” and that the dispute is not about agreements but about the description and definition of the intrinsic identity of that concept as we apprehend it. The dispute concerns the question: What is the correct description of the concept?—not, What is the relevant terminological agreement? Accordingly, the two terms proposed above, even if the semantic proposal were adopted, would still, according to the essentialist, be two terms pointing to the same concept. Such a solution would be of no help at all from the essentialist point of view.
The basic claim of essentialism is that the continuity of a concept does not depend on its definition—that is, on its form—but on the simple factual question whether we are indeed speaking about the same concept. Just as we argued above against Leibniz that the distinction between two objects is not rooted in the plane of their properties but in the question of their intrinsic identity, their individuation, so too here we establish something like a principle of individuation for concepts.
No criterion can be offered for determining this, because the issue concerns the matter of the concept and not its form. As we have seen, every criterion and definition concerns form, and therefore cannot address a question of this type. The new proposals regarding the concept “Jew”—even if I personally do not agree with them—are indeed alternative proposals that reflect a real dispute, and not merely a stubborn quarrel over rights to use a particular term or word. A dispute over a conventional term does not justify so stubborn a struggle, at such a high social and cultural cost. If this were not a genuine dispute, it would be simpler and more natural just to agree on changing the disputed terms.
It should be noted that in the last few paragraphs not only was the essentialist approach to the existence of concepts described. We also pointed out that this is the approach that accords with common sense. All participants in disputes such as “Who is a Jew?”—regardless of their position in the debate—implicitly assume an essentialist approach. At times they do not admit this, and very often they make conventionalist claims such as, “Everyone has his own Judaism,” or “No one has a monopoly on Judaism.” But underlying such claims are alternative definitions of the concept “Judaism.” Anyone who tries to change the definition of a concept thereby demonstrates, by that very fact, that his approach is essentialist. The arguments against analyticity and conventionalism—the connection between which we will see in the next chapter—are the main subject of Part Three. Here we have merely anticipated them.
Summary
Let us now summarize the chapter. We have seen that every concept is divided into three components: its intrinsic identity (its matter), its essence (its necessary form), and its accidental form. Form is the result of the activity of cognition as it observes the concept. Definition is the verbal expression of the essential part of the concept’s form, as obtained through that observation. A change in the definition of a concept is possible only according to the essentialist approach, and only as a result of a change in the cognition that observes the concept.
At this point one may ask: how is this act of observing a concept carried out? How does the cognition that observes translate the concept itself into a picture—an understanding—within us, whose verbal expression is the definition? What is the nature of this act according to the analytic interpretation, and according to the synthetic one? These questions are the subject of the next chapter.
Chapter 3: Thinking and Cognition
The Transition from Thought to Cognition
In the previous chapter we encountered two approaches: conventionalism and essentialism. Conventionalism is an approach that treats concepts as agreed-upon abbreviations among language users. These abbreviations arise from agreement and not from observation, because there is nothing there to observe. For the conventionalist, a concept has no matter, only form. Essentialism, by contrast, treats concepts similarly to objects. Concepts too have matter and form. In concepts, as in objects, form is the result of observing the concept—its matter, or the concept as it is in itself. In this chapter we shall see that these are two different worldviews in a deeper sense than merely their attitude toward concepts.
When we dealt with matter and form at the beginning of the gate, we spoke of cognition apprehending the concept by creating its form in consciousness. At that stage of the discussion, we did not enter at all into the mode of apprehension itself. Conventionalism does not recognize the existence of the concept in itself. “Concept,” on this view, is no more than a shorthand for a definition agreed upon in the community of its users. Such a view usually stems from an unwillingness to recognize the reality of things that cannot be observed by the senses. Such an approach is prepared to deal only with sensory data and with their analysis. Things that do not arise from sensory cognition or from analytic treatment of it and its findings are not subjects for discussion. Essentialism, by contrast, claims that there are things whose existence does not depend on their always being observable. Therefore the “concept” in itself—the matter of the concept—can, according to this approach, exist even though observation always shows only its form, that is, its attributes.48
In a similar way—though with respect to objects rather than concepts—the idealist approach in philosophy claims that because we cannot directly observe the object in itself, we should give up the assumption that it exists and instead identify the object with its appearance in our minds. According to this approach, there is no external world at all, and everything we see is rooted inwardly in our consciousness. Idealism is an approach that denies the existence—and in our terms, the matter—of objects as they are in themselves. Conventionalism, for very similar reasons, denies the existence—the matter—of concepts as they are in themselves. Both approaches are usually based on denying the reliability of the means of cognition relevant to the domain in question: the senses with respect to objects, and intellectual cognition—the “eyes of the intellect”—with respect to concepts.
A similar dispute takes place concerning the existence of mystical or spiritual phenomena. These too cannot be directly observed, and therefore many in the Western world tend to deny their very existence, at least on the objective plane. Such phenomena receive attention or recognition mainly as experiences undergone by those who report them.
It is important to notice that the discussion is now moving from the logical plane, with which thought is concerned, to the epistemological plane, which concerns perception and cognition. The distinction we made in the previous gate between two modes of thought, analytic and synthetic, belonged to the plane of thought, that is, the logical plane. The two positions based on these two modes of thought, the analytic and the synthetic, are positions regarding the question “What is a true claim?” and not regarding the question “What really exists?” The distinction between conventionalism and essentialism belongs to the plane of epistemology—and perhaps, more accurately, to ontology.49 My aim is to point to the implications, on the epistemological and ontological levels, of the two modes of thought presented in the previous gate at the logical level, that is, to connect these planes.
The analytic-synthetic division is made wholly within the human intellect, as a characterization of thought. It deals entirely with the world of forms, in Aristotelian terminology, or phenomena in Kantian terminology. The division between conventionalism and essentialism concerns the ways in which cognition creates the world of forms of concepts out of the world of concepts as they are in themselves—the noumena. The dispute turns on the question whether cognition invents concepts, creates them, and defines their use arbitrarily, or whether it attempts to know concepts that exist in themselves independently of the cognition that observes them.
In light of this distinction, it is clear that one cannot even ask whether the process of observing or cognizing a concept is analytic or synthetic. The terms “analytic” and “synthetic” describe attitudes on the logical plane of thought, not on the plane of cognition. Despite this, I wish to argue that there is a connection between these two planes of discussion. That is, there is a connection between one’s mode of thinking—analytic or synthetic—and the way one’s cognition operates—conventionalist or essentialist. Someone characterized by a certain mode of thinking will, in all likelihood, also have a corresponding epistemology. It should already be emphasized that this claim is, to a large extent, parallel to Kant’s claim about synthetic a priori judgments. His claim too links these two planes to one another.
At the most basic and simple level, the connection is that according to the synthetic approach it makes sense to deal also with things that are not the result of sensory observation or the analysis of such observation.50 Beyond that, synthetic thinking claims truth for certain contents expressed in propositions—or at least their superiority to rival contents—and not merely the consistency of arguments, as analytic thinking does. The analytic thinker’s objection to this approach is: why are these propositions more justified than their opposites, when they cannot be logically justified on the basis of known and accepted premises, nor on the basis of observation of the world?
A detailed discussion of this question is the main purpose of Part Four. Here I only wish to point out that in order to ground knowledge of specific cognitive contents—and not merely logical relations of entailment between them—a proponent of the synthetic approach must embrace an additional mode of confirmation or “seeing,” besides the analytic mode of thought, a mode that also yields certainty. My claim is that cognition of contentful propositions is based on immediate apprehension of the concept or subject under discussion—a kind of cognition directed toward the matter, the intrinsic identity, of the concept, and not only toward its form, its characteristics.
This operation is indeed carried out by a certain part of the intellect, but this is an intellect that observes and cognizes, not one that analyzes and thinks. This part of the intellect functions here as a kind of additional sense. The axioms, or contentful knowledge, adopted by those who hold the synthetic position are the product of cognition and not of thought. The analytic limitations, which show that thought deals only with relations of entailment and not with the contents themselves—with formulas and not their contents—do not apply to our capacity to know reality, whether factual or conceptual. Cognition does not require grounding in more fundamental propositions.
Maimonides, at the beginning of his Guide of the Perplexed, explains that every biblical use of the verbs “to see,” “to behold,” or “to gaze” refers to seeing with the intellect and not with the eyes. Beyond the linguistic claim that Maimonides is making, one may derive from this a substantive conclusion as well: the intellect functions also as a cognizing faculty, not merely as a thinking one. We will expand on this central issue in Gate Eleven.
Such a conception seems to contradict the entire modern mode of thought—and still more that which preceded Kant. For Aristotle, the intellect was indeed classified as a sixth sense. In our culture there are only five senses, as a result of the analytic-conventionalist conceptions dominant in the world today. In Gate Eleven we shall see that the sharp distinction between cognition and thought, which is a cornerstone of modern philosophy, is not always correct. It is itself mainly a product and characteristic of analytic thinking.
We have now reached the point where it becomes entirely clear that the synthetic thinker also requires an epistemology different from that of his analytic counterpart. As we saw in the previous gate, certain truths—synthetic a priori truths—are said about the world, yet apparently do not arise from sensory observations. If so, besides a different mode of thought and a different criterion of certainty, there is also a different epistemology here from the analytic one. A more detailed discussion of this point will appear in Part Four, mainly in Gate Eleven.51
A parallel picture emerges with respect to the analytic thinker. One who does not claim the correctness of contents or propositions but only the consistency of arguments—that is, the analytic thinker—does not employ epistemology with respect to concepts at all. His epistemology is, at most, the use of the senses alone, directed, of course, only toward objects.
As we saw at the end of the previous gate, the analytic thinker too admits that objects observed by him do indeed exist. We saw that his criterion for accepting a proposition as true is that it either arises from empirical observation or has a logical-analytic proof. By contrast, on the plane beyond the senses, the analytic thinker employs only thought and not cognition. Concepts are treated only against a conventionalist background. Observation, in the full sense of the word, exists only in relation to objects and not to concepts. According to the analytic thinker, the use of the term “observation” with respect to concepts can only be metaphorical. It really amounts to observing accepted patterns of usage of words in a language—or, in effect, looking at a dictionary—and not observing the concept represented by those words, as the essentialist claims.52
One may of course ask why sense-data deserve more trust as representations of external reality than does the intellect observing concepts. In both cases we apprehend only the form, and from it we want to infer the existence of the thing itself, that is, its matter. There are two analytically consistent answers to this question: idealism, which claims that there really are no things in themselves; or a milder idealism, in Kant’s style, according to which there is indeed a world as it is in itself, but even when we are dealing with “things in themselves,” we are not really doing so. The objects of our discourse are their reflections in cognition.
Even the Kantian assertion of the existence of objects in themselves, abstracted from their properties, is in fact unjustified, since it does not arise from experience. One can only say that it is an unavoidable assumption of reason—a transcendental argument. As we shall explain in Part Three, especially in Gate Seven, this does not elevate it beyond the status of an assumption lacking justification. The conclusion is that an approach which claims that only sense-data, and nothing else, are trustworthy is no less mystical than the views it labels as such.
Differences Between Eastern and Western Conceptions
We have seen that according to the analytic position, beyond the senses there is only thought and not cognition. According to the synthetic position, by contrast, there is also cognition that does not occur through the senses. Sensory cognition is directed toward the properties of the object or concept—that is, toward their form.53 Non-sensory cognition is directed straight toward the thing in itself, that is, toward its matter. This difference between the two modes of cognition of objects—sensory, which is indirect, and direct—is one of the foundations of the difference between conceptions common in the Eastern world, meaning the Far East, and those of the West. Cognition, as understood by various Eastern conceptions, often operates by “connecting” to the world outside it—not necessarily through the senses—rather than by sensory reception of the characteristics of that world. Eugen Herrigel, in his book Zen in the Art of Archery, gives a striking description of this phenomenon through Western eyes. Among other things, he recounts the way his teacher shot an arrow at the target: his teacher would shoot straight into the center without looking at the target at all.54 This is a form of connection to the surrounding world that does not proceed through the senses. Our discussion, to be sure, concerns connection to concepts and not necessarily to objects. But it is enough to point to a mode of connection that is not sensory in order not to dismiss such a possibility out of hand. We plainly see here an epistemology that is not mediated by the senses. If so, we need not reject out of hand the claim that there is also a non-sensory epistemic process that we use in order to know concepts—to “observe” them.
Western rationalism treats such phenomena with great skepticism—even though they are apparently facts—and classifies them, as well as many other non-Western approaches, as “mysticism,” or else tries to explain how the senses are involved after all, or to show that the matter is fraudulent. This is also the reason that essentialism, which claims the objective existence of concepts, has not been a common approach in Western philosophy over the past century.55 Such views do indeed count as mysticism in the usual Western sense. Yet the negative connotation attached to the term “mysticism” is not nearly as well founded as it appears at first sight. In the next part we shall try to examine these cultural and philosophical differences. In Parts Three and Four we shall try to take a position in this debate and, for entirely rational reasons, support specifically the Eastern-essentialist-synthetic approach, which in the West is usually classified as mysticism.
Some describe this “Eastern” way of looking at the world, when directed toward concepts, as looking inward rather than outward. That is, a person looks inward into himself and not outward at the world. It is indeed plausible that concepts do not exist in the same sense in which ordinary things exist, as we already noted above. A claim that lies at the basis of Kabbalah (Jewish mysticism), as well as other mystical traditions and also Plato, is that there is a correspondence between the human being and the world. Therefore, looking inward, which is easier, can teach us about the structure and properties of the external world. This inward gaze seems subjective, but it has objective significance. This claim is simply another way of saying that there are synthetic a priori propositions—that is, propositions grounded in human reason while their subjects, whether objects or concepts, are found in the external, objective world.
Gershom Scholem writes in several places, when defining mysticism, that it is not merely some subjective matter to which no one but the mystic himself has access. Significant mysticism is a doctrine that also has meaning for a wider public. That is precisely what characterizes a mystic of real stature. A mystic is someone who succeeds, out of himself and his experiences, in exposing the objective within the subjective, the inward truth shared by a wide public of people. This definition, of course, assumes that there is such a layer within every human being, and also that this layer is common to all human beings.56
Let us conclude this discussion with a quotation from Agnon’s Sefer Ha-Maasim.57 He testifies of himself that when he was shown Samaritan writings “that had been offered to him in the house of the depths of his being,”
I read them and marveled that I was reading and understanding, and I marveled that everything written here was already known to me: some of these were things that I myself had written and that had been copied into their script, and some were things I had wanted to write but had not written because the pen had not grasped them.
The author of those writings is a mystic, a master of formulation and inner observation. He succeeds in looking within himself and giving outward expression to things that others also see or feel. Although these things sound deeply familiar to them, they are unable to give them verbal expression. Once the mystic formulates and describes them, the listeners or readers too are able to find them within themselves and identify with them.
The Essentialist Mode of Cognition
I will now bring two notes that illustrate the essentialist mode of cognition of the matter of a concept or of a phenomenon.58 The first, from philosophy and halakha, illustrates the apprehension of a phenomenon rather than of a concept, and through it we shall discuss the concept of “process” in general. The second, from moral philosophy, illustrates the apprehension of the concept “good.” Neither example is connected in any way with the domain of mysticism, and for that very reason both illustrate especially well the differences between the approaches. In my view they also reveal failures in the conventionalist conception. More detailed discussion of this point will appear in Parts Three and Four. Let it also be noted that these examples can serve as illustrations of the existence of the matter of concepts, in addition to the two examples in the earlier halakhic notes—the concepts of “ownership” and “sukkah,” in Notes 3 and 4.
Note 7: The Giving of a Bill of Divorce and Zeno’s Arrow — Process Versus Change of States59
The Talmud tries to characterize what is required of a husband divorcing his wife in order for the giving of the bill of divorce to effect the divorce. This characterization is made through many varied examples in tractate Gittin. The commentators tried to summarize what emerges from those examples in the form of general principles and proposed a number of definitions. For example: a valid delivery of a bill of divorce is the transfer of monetary ownership of the bill from the husband to the wife. Or alternatively: its physical transfer from the husband’s hand to the wife’s hand. These two definitions, like others, were rejected because they did not fit the examples appearing in the Talmud. At the end of these discussions, the commentators propose a definition that tries to satisfy all the constraints arising from the various Talmudic passages. A striking phenomenon is that this definition is very vague and usually fails to clarify the halakhic requirements beyond what is already found in the examples themselves.
My claim is that the failure to provide an explicit definition of the act of giving the bill of divorce stems from the fact that this is a process and not a state. The attempt to define a process is always made through its boundary states—that is, what was before it, when the bill was in the husband’s hand or ownership, and what is after it, when the bill is in the wife’s hand or ownership. The attempt to characterize a process through its boundary states is doomed to fail. To illustrate this phenomenon, let us use the famous Zenonian paradox of the flying arrow.
The Greek philosopher Zeno of Elea presented the following paradox: let us observe a flying arrow. At every indivisible instant of time, it appears to stand in a different place. The question therefore arises: at what instant does it change its position—when, that is, does it move?
The solution I proposed to the paradox of the arrow rests on the distinction between motion and change of states. By way of illustration, let us examine the relation between the velocity of a body and its change of position. In elementary mechanics, the “velocity of a body” is defined as the ratio between a certain distance traversed by the body and the amount of time it takes to traverse it. When the velocity of the body is not constant, one can define instantaneous velocity, that is, its velocity at a given instant. This velocity is calculated by determining that ratio over an arbitrarily small interval around the moment in question. In other words: if you wish to know the velocity of a given body at time T, take two moments very close to each other around T and examine the body’s position at those two moments. The ratio between the difference in positions and the difference in times, taken over intervals that get smaller and smaller around T, yields the instantaneous velocity at that point. In mathematics, this ratio is defined as “the derivative of position with respect to time.” It should be noted that the derivative describes rates of change of states in many contexts, and not only velocity, which is merely a particular example of a process of changing states, when the states in question are spatial locations.
From this description it might seem that a body has velocity only over a time interval and not at a point in time, since at every indivisible instant the distance it traverses is zero. But that is a mistake. The result of the procedure described above is the velocity of a body at a point in time. It is true that the way one computes velocity is by using intervals that get smaller and smaller around the point T, but a time interval is required only in order to calculate velocity, not necessarily in order to define it as such. A body has velocity at an indivisible instant, even though it cannot change its position at such an instant. Mathematically as well, the derivative of a function exists at a point and not only on an interval. The consequence of the fact that a body has velocity—namely, the fact that it changes its position—occurs only over an interval of the time axis and not at a single point on it.
It follows that velocity and change of place are not identical concepts. One exists at a point in time, while the other exists only over a time interval. In other words, change of place is not velocity itself, but only its result or implication.
An amusing illustration of this distinction between process and change of state may be seen on a computer screen. The pointing dot called the cursor appears to move across the screen. In fact, of course, it does not move at all; it merely changes location. The “process” is carried out by extinguishing the previous dot on the screen and immediately lighting a nearby dot instead. A sequence of such operations appears to the user’s eye as continuous motion. In field theory in modern physics, the motion or change of state of particles is described by “field operators.” This is a description that represents the movement of a particle by annihilating it at its present location and recreating it at the next one, exactly like the cursor. These are examples of changes of state without a process, or changes of place without velocity.60
Let us now return to the paradox of the flying arrow. A body has velocity at every instant, but it changes its position only over an interval of time. At every moment the body is moving and not standing still—that is, it possesses velocity. The other side of the same coin is that at every moment the body is located at a given place, but in no sense is it standing still there. At every moment of its flight the arrow is moving while at the same time being located—not standing—in a definite spatial point.
The delivery of a bill of divorce can be understood in the same way. The Talmud is trying to tell us how to carry out a proper process, while the commentators try to characterize it through the boundary states altered by that process. The main problem here is that boundary states are an indication that a process exists, or a way of detecting its existence, but certainly not the definition of the process itself.
The root of the confusion between velocity and change of place, or between process and changes of state, lies in the conventionalist approach. According to that view, the concept is identical with the way it appears to us. Velocity, therefore, is nothing more than change of place, since all that appears to us is change of place. Velocity as such cannot be seen.61
Essentialism, by contrast, claims that there is a concept such as “velocity”—or more generally, “process”—that precedes change of place or change of state. Change of place or state is the form in which we observe the process itself. One must not identify the intrinsic identity of the concept with the way it appears to us. The mode of appearance is only the concept’s form and not its matter, the phenomenon and not the noumenon. We have no direct access to the noumenon of concepts, just as we have none to the noumenon of objects. This is a condition that follows from the very fact that human perception is an external interaction with the object or concept, as explained in the previous chapters. But this constraint should not lead us to become conventionalists and altogether abandon the existence of the concept in itself, just as the impossibility of knowing the object in itself does not lead most people to become idealists.
In a similar fashion one can explain that the Talmud is trying to convey to us an immediate sense of what constitutes a valid delivery of a bill of divorce. It does so by means of examples and not by means of an all-encompassing definition—and this is always its way—because only in this manner can it convey the concept without reducing it to a definable form. Definitions deal with forms, not with concepts themselves, and therefore do not always exhaust them. For this reason definitions are uncommon in the Talmud. A further discussion of this matter will appear below (see Gates Ten and Eleven).
Note 8: What Is “Good”?
The basic problem of philosophical ethics is the question of the content of the concept “good.” Different people who say that someone is doing a good act often mean entirely different things, and sometimes even opposite things. By way of example: some view abortion as a woman’s elementary right over her own body, and therefore, at least in cases of need, as a good act. Others see it as an actual act of murder (see Note 26 below). It does seem that there are certain values—some of the content of the concept “good”—about which there is almost universal agreement across human societies, but even this claim is disputed among anthropologists.
In light of this bleak picture, it seems that the concept “good” has no objective meaning, but is open to interpretations dependent on context, society, and so forth. But even if this is true, does it show that the concept “good” has no matter? That is, is it merely a convention that changes from one society to another? Suppose someone wishes to persuade his friend to do some act by arguing that it is a good act. Does the statement “Do this because it is good” have any meaning beyond the statement “I think you ought to do this”? In other words, is “good” nothing more than an abbreviation for the predicate “an act that ought to be done”—without any agreed criteria for what characterizes or defines such an act? According to this view, the statement “You ought to do this because it is a good act” really means: “You ought to do this because you ought to do this.” Or in other words: “You ought to do this,” without any justification.62
The context that concerns us here will become clearer if we formulate the question differently: is the term “good” an abbreviation for the set of criteria it represents in a given society, or does it have some objective meaning? I want to emphasize that our concern here is not the relativity of moral principles. Even if we agree that all moral principles are relative and change from one society to another, there is still room for the question: is the term “good” itself used in the same way in all human societies, while only its interpretations or concrete appearances vary from one to another?
Underlying the dilemma as formulated at the beginning of this note is the assumption that there is indeed nothing in the concept beyond the collection of ways in which it appears to us. The content of the term “good” under discussion here is merely the collection of moral principles it represents. Since, therefore, different societies have different principles, the conclusion that this concept has no objective content seems unavoidable. But this is simply to assume what one is trying to prove—the very failing of all the approaches described here.
Our claim is that in the essentialist approach the concept “good” is grasped as a concept in itself, while moral principles are only the form in which it is expressed in the world of phenomena. Our claim here is that the concept “good” is used in exactly the same way in every human society. The form in which it is expressed may change according to circumstances and from one society to another. The intrinsic identity of the concept can be felt by a person who looks inward into himself and tries to experience the feeling that accompanies his judgment that a certain act is good or moral. That feeling, in my opinion, is common to all humanity.
If this claim is correct, then one may go further and say that there really is meaning to the statement that a certain act ought to be done because it is good, beyond merely expressing a desire that it be done. In my opinion, every person clearly senses that there is such a meaning, even if the analysts among us try to suppress this sense and define it as a fiction. This approach stems from the prior assumption that the intrinsic identity of a concept is identical with its content, as claimed above.
The meaning of the concept “good” is that feeling or inner insight that accompanies each of us when we use this concept. Two people who describe opposite acts as good are still using the concept “good” in the same sense, for otherwise there is no disagreement between them. They could simply define two different terms and solve the problem that way, just as we saw above in the discussion of the concept “Jew.” Clearly, they are “observing” the same concept itself, but the form of the concept changes according to the observer, and therefore they see a different picture and also act according to different principles. I refer the reader to Russell’s quotation at the beginning of this gate regarding the concept “light,” and to the dispute with Putnam that we conducted above.
Let us sharpen the point and generalize it. It makes no sense to discuss the relativity of the good or of morality without first assuming that the concept “good” itself is being used in the same sense by both disputants. If they are speaking about two different concepts, then there is no disagreement between them. This is true of every argument: agreement lies at its basis. The same is true, as we saw, of the dispute over who is a Jew, and of many other discussions as well. If the secular person and the religious person use the concept “Jew” in different senses, then the whole discussion is semantic and can be easily resolved by coining a new term. But clearly that is not the case. Both sides speak about the same concept, even though a significant part of its components—including essential ones—differs between the two outlooks. All are observing the matter of the same concept—the concept in itself—but they see different forms. This phenomenon follows from the fact that the cognition observing the concept is different. That was also the point of dispute with Putnam above, where we saw that according to his method one cannot change a concept in an essential way—in fact, one cannot change concepts at all—without thereby simply creating another concept.
Since in this gate our purpose is only to point to the differences between the two modes of thinking and apprehension under discussion, we will suffice with this brief treatment. In Part Three we will begin systematically to take a position in this dispute. There we shall try to show and support the claim about the essentiality of the concept “good” in a more substantial way, as part of our overall support for the synthetic-essentialist approach. The discussion of the concept “good” is only one example of the more general analysis that will be undertaken there (see also Note 23 below, which will deal with the relation between a concept’s extension and its content).
Exceptions in Western Thought: Plato and Husserl
This is the place to note briefly certain exceptions in Western thought that speak of ideas very close to what we are here calling essentialist epistemology. The first to be mentioned, of course, is Plato, whose world of ideas was abandoned by modern philosophy—without justification, in my opinion. Many of the ideas raised here could, with considerable justice, be called a return to Plato.
In a more modern period, the phenomenological approach appears, especially that of Edmund Husserl. Husserl speaks of “contemplation of ideas,” or, as he calls it, “eidetic evidence,” meaning contemplation of abstract concepts through concrete objects. His claim is that abstract concepts—or in his language, general concepts—like individual objects, are given to us through cognition, that is, epistemologically, and not by generalization from the particular to the universal, which is an act of thought rather than cognition. According to Husserl, there is a way to contemplate an individual object and through it contemplate the concept hidden within it or behind it. The individual becomes transparent, until we see the universal through the particular.63
At first glance, this position resembles the one proposed here, and with some justice. Nevertheless, it seems that the resemblance is only external. When Husserl tries to ground this claim, he resorts to considerations similar to Kant’s. He uses transcendental considerations that turn the universal concept into a subjective entity, in the sense that it exists only in consciousness, and thereby turn eidetic seeing into transcendental thinking. Note thoroughly: not cognition but thought; not outward but inward. Thus Husserl too did not cross the “Western” boundary line toward an approach that recognizes the possibility of immediate cognition of ideas existing outside the cognizing spirit.64
In the synthetic position proposed here, by contrast, we speak of the concept as really existing in the objective world. The way to behold it, like the thing in itself, is not through transcendental methods. This will be clarified in more detail later, beginning with Gate Seven. Here I wish only to emphasize that even if our method here can be called phenomenology, it is certainly not transcendental.65
Essentialism and Conventionalism with Respect to the Concepts of Quality and Quantity
Let us conclude the chapter with a note that gives an example of the differing implications of essentialism and conventionalism with respect to the meaning of the concepts “quality” and “quantity,” and with respect to the difference between them.
Note 9: Quantity and Quality
In this note I wish to present one possible implication of the distinction between a conventionalist and an essentialist approach with respect to the difference between quantity and quality. The note is long, and is therefore divided into subsections.
A. The Difference Between Quality and Quantity — A Conventionalist and an Essentialist Approach
In ordinary language the terms “quality” and “quantity” are used quite frequently, and they are usually understood as describing different forms of measurement. Some properties describe qualities of a thing or things, while others are described as quantitative. In halakha too, the distinction between quality and quantity arises in several contexts.
Let us begin with a halakhic example. According to halakha, an ordinary court consists of three judges. Not all of them need have the same level of expertise and wisdom. One can have a court composed of one learned scholar together with two laymen. The ruling is determined by majority opinion, as derived from the verse, “Follow the majority.”
There are opinions among the legal authorities—for example Sefer HaHinukh, commandment 78, following Rabbi Hai Gaon—that the majority in question is not a numerical majority of judges but a majority of wisdom and expertise. Therefore, when the learned scholar disagrees with the two laymen, the ruling follows him. By contrast, Nahmanides, in his novellae to tractate Yoma, holds that the decisive majority is always the numerical majority of judges.66
At first glance, this seems to be a dispute over whether what matters is the quantity or the quality of the judges. According to Sefer HaHinukh, quality is decisive, whereas according to Nahmanides one follows the quantitative majority.67
Upon deeper reflection, however, this description is not so unambiguous. According to the author of Sefer HaHinukh, it indeed seems at first glance that the quality of the judges, rather than their quantity, is what matters. Yet one can formulate the matter differently. One might say that Sefer HaHinukh too requires a quantitative majority rather than a qualitative one, but the majority he requires is a majority of the quantity of wisdom, not a majority of the number of judges. We initially assumed that what is required is a majority of judges, and the question was whether to assess that majority by the number of judges or by their quality. According to the alternative understanding suggested here, the required majority is not a majority of judges but a majority of wisdom. On this definition, Sefer HaHinukh too holds that quantity is decisive; the only dispute with Nahmanides concerns which magnitude is to be quantified in order to determine the majority. What we earlier called “the quality of the judges” we would now call “the quantity of their wisdom.” If so, everyone could apparently agree that the required majority is quantitative, and the dispute would concern only which quantity must be measured in order to determine the halakhic ruling.
Up to this point we have assumed that the concepts “quality” and “quantity” are well defined, but that their application to reality is unclear. Thus, if for some reason it is clear that the required majority is a “majority of judges,” then the dispute is clearly over how to measure that majority: through the number of judges or through their quality. In such a situation it seems obvious what quality and quantity are, and the only question is how to determine that this is indeed the dilemma, and not the alternative formulation I proposed.
But one can formulate the question more radically and say that the concepts “quality” and “quantity” themselves are not well defined, and indeed are not really different from each other. The quality of something can always be described as the quantity of something else. The quality of a judge is always the quantity of his wisdom. In this formulation there is already a challenge to the very distinction between the concepts “quality” and “quantity,” and not only to their application to concrete problems. But precisely for that reason, this formulation is problematic, because there is a clear intuition that when one is referring to the judge, wisdom is defined as his quality, whereas when one is referring to wisdom, its degree is a quantity. If so, the question is not only about the difficulty of applying the concepts “quality” and “quantity.” The more basic dilemma is: are “quality” and “quantity” in fact identical concepts, whose difference is fictitious, or is there a real difference between them?
Shlomo Maimon, in his Giv’at HaMoreh on Guide of the Perplexed, Part I, chapter 74, discusses this issue and writes that by a quantitative addition, quality does not increase. In the context of our example, the natural tendency to refer to the wisdom of the judges as a quality rather than a quantity stems from the fact that if we add a number of judges whose level of wisdom is X, we still obtain—roughly speaking—the same level of wisdom. That level is lower than the level of wisdom possessed by the one learned judge. This is a case in which the quantity of the judges changed, but their quality did not. So, apparently, we have a definition of the difference between quality and quantity: the parameter that does not change when quantities are added—wisdom—is called a qualitative parameter. The parameter that does change—the number of judges—is called a quantitative parameter.
A further example: adding water at a certain temperature to more water at the same temperature does not change the quality of the water—its temperature—but only its quantity, that is, the total mass.68
This definition seems at first glance intuitively clear. Obviously it does not solve the first question we raised, concerning the way the question about judges is posed: is the dispute about what quantity is required—wisdom or judges—or is it about whether a qualitative or quantitative majority of judges is required? But with respect to the second question—the more radical formulation challenging the very distinction between the concepts—it seems, at first glance, to provide an adequate answer.
And yet, a careful examination of this definition shows that the problem has still not been solved. If, for example, I were somehow to add wisdom rather than judges, then it would be the number of judges that remained unchanged, while wisdom would increase. It may be hard to imagine how to do this in reality with judges, but with the example of water one can certainly think of heating the same quantity of water further. This is an addition of heat without a change in the quantity of water. According to the definition of Giv’at HaMoreh, such a description would imply that heat is actually the quantitative parameter, while the water is the qualitative one. Something similar can be imagined in the case of judges: we might teach them and thereby make them wiser and more skilled, without changing their number, that is, their quantity. If so, even according to the definition given above for the concepts “quality” and “quantity,” there is no clear distinction between them. Everything depends on what the process of addition is. That process determines what will be called quality—what does not change in the process of addition—and what will be called quantity—what does change in that process.
But despite all this, it seems perfectly obvious that “quantity” and “quality” are understood by every reasonable person as two different concepts. It seems clear, at least intuitively, that wisdom is a quality, while the number of judges is a quantity. The question is whether these concepts can be clearly defined.
Some might say that the difference lies in the type of things being measured. When one measures an abstract concept, such as wisdom, one says that this is quality. By contrast, when one measures concrete objects, such as judges, one says that the result is quantity. According to this, one cannot speak of quantities in the context of abstract concepts.
But if we accept the essentialist position, then there is apparently no essential difference between abstract objects—predicates, or concepts in general—and ordinary physical objects. These too “exist,” in some sense, no less than ordinary objects.
B. Abstract Concepts and Concrete Objects — Essence and Convention
Here we enter the question of conventionalism versus essentialism: what is an abstract concept, as opposed to a concrete object? Clearly, one can speak of quantities of abstract concepts—for example, how many new ideas there are in an article. Grammatically, it may still seem possible to formulate the distinction by saying that when one counts subjects one gets quantity, whereas when one measures predicates or attributes one gets qualitative parameters. But to make the distinction between the concepts we must move to the question of what is subject and what is predicate in reality, not merely in the grammatical sentence—unless, of course, we accept that “quality” and “quantity” are just linguistic terms that do not represent reality. In analytic terminology, we would then say that they have only correct use, and not essence, meaning, or “matter.” As we have seen, this is precisely the conventionalist position.
In Gate Eleven we shall see that it is implausible that fictitious concepts arise out of nothing. If they exist, are understood, and can be used, then it is highly likely that they have matter—that is, a dimension in reality. The same applies to the concepts “quality” and “quantity.” If they can be used, and members of the linguistic community who use them understand one another, then clearly they have roots in reality as two separate and different concepts.69 This critique of conventionalism applies to these concepts as well. It closes the door on attempts to be even partially conventionalist—that is, to believe that only some concepts have an essence while others are merely the result of agreement.
In any case, it seems that the distinction between abstract concepts and objects plays a role in defining the concepts “quality” and “quantity.” From the essentialist point of view, this difference is more problematic, though even conventionalism does not entirely escape the difficulty. It may be that specifically the intuitive understanding of the difference between quantity and quality can help us distinguish between abstract concepts and non-abstract ones. That is, according to the essentialist, although these two types of entities are similar in many respects, there is still a difference between them: one is measured in qualities and the other in quantities. The question is how we can sharply define this pair of concepts.
C. Problems in the Distinction Between Quality and Quantity
In Gate Ten we shall sharpen the point that no basic concept can be precisely defined. One may say that the concepts “quality” and “quantity” are basic, and therefore cannot be reduced to more fundamental concepts. It may be that they can help us understand ontological distinctions—between abstract and concrete entities—or that they themselves may perhaps be understood on the basis of those distinctions.
Pirsig, in Zen and the Art of Motorcycle Maintenance, speaks of his unsuccessful attempt to define quality. His conclusion is that it was the Greeks who implanted deeply in our culture the assumption that every concept must be precisely defined. If one frees oneself from this demand and allows the intuitive understanding of concepts to function without analytic direction and criticism, one reaches better insights. In Note 14 below we shall discuss in detail the role of the Greeks as the historical fathers of the analytic position.
The problem of distinguishing between quality and quantity seems to be connected also to another problem concerning them: the problem of quantity turning into quality.70 The question is: from what point does quantity become quality? The answer, in simple terms, is that this occurs when the object that changed quantitatively simply becomes another object, and not merely a greater quantity of the present object. No definition can be offered, because becoming another object is a statement about the matter of things, whereas definitions deal with their form.
This claim also recalls Putnam’s claim, discussed above at the beginning of Chapter 2, regarding the impossibility of changing the definition of concepts because such a change creates another concept. The objection raised there against Putnam was that according to his view, a concept’s becoming another concept cannot happen at all. We therefore suggested there that a different definition does not always change the concept under discussion, even if essential properties change. A concept becomes another when its matter is different. Similarly, a person whose body parts are systematically replaced and transplanted one by one—including the head, whose replacement is only a technological problem—will at some stage become someone else. The question is what that stage is. The answer cannot be defined, because it belongs not to the plane of forms but to the plane of individuation. In the world of things in themselves, things cannot be defined. There we must rely on a feeling or intuition—sometimes called “common sense,” on which see Gate Eleven—and in fact on cognition, which discerns whether we still have before us the same object or concept, or whether it has become another.
It seems, then, that in the question of quality and quantity as well we must rely on a similar intuition. When the object changes in its essence, this is a qualitative change; when we merely have more of the same thing, this is a quantitative change. As we have seen, the answer to the question when it is the same thing and when it is something else cannot be defined. There is here a certain parallel to the attempt to define a sharp and general criterion for the essentiality of properties, which, as we explained, is necessarily doomed to fail.
Quality and quantity, then, can serve as another example of the existence of matter in concepts that grounds them, even when we have no clear definition of their form or characteristics.
D. The Real Distinction Between Quality and Quantity: Ordinal and Cardinal Numbers
After a long period of wondering about quantity and quality, whose main stages have been described up to this point, it seems to me that I have finally succeeded in clarifying for myself the difference between them. I will describe that conclusion in the present subsection. The exposition up to now followed my earlier hesitations, and I have presented it here because I thought it might help clarify the difference between a conventionalist and an essentialist approach. I think that a reader who followed these hesitations has also learned something about that distinction. I now wish to present the solution to the problem, whose basis lies in a mathematical distinction between two different functions of the numerical system. The solution itself is not directly related to the issues that concern us here, but after the shared struggle with the problem of quality and quantity, I feel obliged to share the solution with the reader as well.
Perhaps I may begin the explanation with a halakhic question. There is a prohibition against measuring various things on the Sabbath. Some legal authorities hold that one may measure temperature with a thermometer on the Sabbath. At first glance, the basis of the permission is that heat is an abstract concept, and therefore measuring it is not considered the kind of measurement forbidden on the Sabbath. It should be noted that the original prohibition against measurement on the Sabbath is rooted in weighing merchandise, that is, measuring concrete physical objects.
I once heard a halakhic decisor wonder why time, which is no less abstract a concept, is forbidden to measure on the Sabbath. When I reflected on this question, the distinction between quality and quantity suddenly became clear to me. Let me preface this by noting that in mathematics two different counting operations are defined, or perhaps more accurately, two kinds of use of numbers. When we count objects and say that five objects lie before us, we mean the quantity of the objects: more than four and less than six. One may say that here numbers function as cardinal numbers.71 Every additional object counted adds one to the total count. An object removed from the count lowers its value by one. Each unit has a meaning, and the sum of the units gives the total count.
By contrast, when we measure intelligence, in intelligence tests for example, the number that represents intelligence is not formed by adding units. One cannot take one unit of intelligence and add it to the total accumulated so far, or subtract it. In this case the numbers are ordinal numbers. That is, the total number representing the level of intelligence represents a certain level, and the individual units within it have no distinct meaning. An intelligence score of 100 is a level of intelligence lower than 110 and higher than 90. One cannot add 10 units of intelligence in order to change the level. Even if someone becomes more intelligent, in one way or another, we say that he has reached a level of 110, not that 10 units of intelligence have been added to him. No one can distinctly point to those units that were added to him.
If so, in this example each number represents a particular level of intelligence, and the function of the hierarchical numbering is to arrange the levels one after another in some order, not to represent how many units have accumulated in total. The numbers that represent intelligence are a scale (whose units are arbitrary in certain respects) intended to provide a quantitative measure for qualities, and to arrange and classify them according to that measure.
If we apply this distinction to our purposes, we will understand that time is counted by cardinal numbers: we count how many seconds have passed, each second being a unit added to the total count. Temperature, by contrast, is measured by ordinal numbers. The number here is not an aggregate of units that together constitute a total count. It has a holistic significance, not the significance of a collection of units. A temperature of 50 degrees is hotter than 40 degrees and cooler than 60 degrees.72 It is meaningless to think in terms of adding one degree in order to obtain a larger total number of degrees of heat. We thus learn that although time and heat are both abstract parameters, there is a difference in the way numbers are used in relation to them. Measurement forbidden on the Sabbath is measurement whose result is expressed in cardinal numbers, such as measuring an amount of merchandise or measuring time, and not measurement of a parameter that is measured in ordinal numbers, such as temperature or intelligence.
One may infer from this more generally that “quality” is a parameter measured by ordinal numbers, whereas “quantity” is a parameter measured by cardinal numbers. The question of greater wisdom versus greater numbers with regard to judges is now also better understood. Wisdom parallels intelligence, and as we have seen, it can at most be ordered, not counted. Wisdom is therefore a quality, whereas the number of judges is a quantity.
This distinction is connected to the insights above, though it modifies them somewhat. Concrete concepts can always be counted in the sense of tallying. We count how many concrete objects there are in a collection. Among abstract concepts, some can be counted (the number of ideas in an article, or an amount of time), while others can only be ordered qualitatively. In other words, the intuition is correct that a qualitative parameter is always an abstract concept, but it is not correct that every measurement of an abstract concept is a measurement of qualities.
This explanation too does not yet place the concepts of “quality” and “quantity” on a completely distinct and fully defined footing. It still remains to clarify what characterizes those abstract magnitudes that can only be ordered and not counted. My earlier claim about the impossibility of defining primitive concepts still stands. Phaedrus, the hero of Pirsig’s book, will have to continue his ceaseless—and apparently futile—pursuit of a definition of quality.
Let us now summarize the conclusions that emerged from this chapter. Concepts, like objects, have three components: matter, essential form, and contingent form (accidental, non-necessary form). Just as we argued with regard to the thing-in-itself that the inability to know it is not a human limitation but a logical impossibility, so too the attempt to define or describe the concept in itself (the matter of the concept) is logically impossible. The reason parallels the one given above regarding the world of objects in themselves: every definition or description is the result of a consciousness perceiving the concept, and therefore it relates to the concept’s form rather than its matter. One may add that any proposed criterion for determining which properties of an object or concept are essential does not, on its face, seem possible. The decision about the essentiality of a property, of an object or a concept, is the result of immediate observation of the matter of the concept. This process too cannot be formulated verbally, for the same reasons.73
Chapter 4: The Linguistic Layer — The Problem of Reference
Introduction
In this chapter we will briefly point to the implications of the discussion thus far for a philosophical issue that has stood, since the beginning of the twentieth century, at the center of intense debate among analytic philosophers. This is the problem of reference, or “naming.”
A person untrained in philosophical thought—especially analytic philosophy—may feel that this issue does not concern a real problem, and that all the entanglement surrounding it is nothing more than an artificial phenomenon of linguistic hairsplitting. It seems that this feeling is accurate. It is precisely professional philosophers, many of whom today (at least in the Anglo-American world) are analytic to one degree or another, who are accustomed tacitly to assume conventionalist premises; the problem therefore troubles them, and they fail to find an adequate solution.
This chapter seeks to suggest that the healthy intuitive feeling of the ordinary person is based on a hidden essentialist assumption, and that it can be philosophically grounded without sinking into analytic complications. Naturally, I cannot enter into all the details of the problem and its solutions (including the essentialist one proposed here). Still, it is of great importance to understand the principle that underlies the proposed solution. Its importance for our present purposes lies in the fact that it provides a sharp and elegant illustration of the connection, which this gate has been discussing, between an analytic stance and conventionalism.
The Problem of Reference
Systematic discussion of this issue began toward the end of the nineteenth century with the German logician Gottlob Frege, and gained momentum at the beginning of the twentieth century with the well-known article by the English mathematician and philosopher Bertrand Russell, “On Denoting.”74 The presentation of the issue and the discussion of it will be brief, since it serves us more as an illustration than as part of the argument itself.75 We will see here the importance and uniqueness of the name of a thing as a linguistic device that serves human cognition in its relation to the thing-in-itself. Beyond illustrating the linguistic implications of analyticity, this also marks a transition from the essential plane to the linguistic one. We will stand here on the linguistic expressions of the distinctions made in the previous chapters.
Russell’s basic question was: what is a name, or more precisely, what is the meaning of a name? A view attributed to the philosopher John Stuart Mill says that the meaning of a name is the object of which it serves as the designation, or which it indicates. The meaning of the name “Abraham our forefather” is the man, or object, Abraham our forefather himself. Frege too espoused this position.
Philosophers raise many objections to this claim. For example, it is not clear, on this account, what the meaning of the sentence “the Festival of Unleavened Bread is the Spring Festival” would be. If the meanings of names are the objects they designate, then this appears to be a claim identifying Passover with itself.76 Russell himself raises additional claims, such as: what is the meaning of the statement “the present king of France is bald,” when there is no object at all designated by the description that serves as the subject of this sentence? (That is, according to Mill’s definition, this statement would be meaningless, rather than, as we might have said, simply false.) Russell further argues that if we examine the set of all bald people on the one hand and the set of all hairy people on the other, we will not find the king of France in either set. This, of course, follows from the fact that France currently has no king. In other words, this interpretation of the meaning of names is vulnerable to the emergence of contradictions and various logical problems. Another problem in this context is the meaning of a sentence such as: “Job never was and was never created; he was only a parable.” If Job did not exist, then there is no object to which this name points. If so, who is the subject of the sentence above?
Russell coined the term “denoting phrase” for names or definite descriptions. For example, “David Ben-Gurion” is the name of the man whose possible definite description is “the first prime minister of the State of Israel.” Both expressions are denoting phrases for the same person, except that one refers to him through his name and the other through a definite description. In this context Russell introduces Frege’s distinction between the meaning and the reference of a denoting phrase. The reference is the object to which the phrase refers, while the meaning changes with the denoting phrase. The meaning may be complex, whereas the reference is always a single simple object. The expression “the center of gravity of our solar system in the first second of the twentieth century” is an expression with a complex meaning, requiring understanding of many concepts (“center of gravity,” “solar system,” “second,” “the twentieth century,” and so on). By contrast, the object to which this expression refers is exceedingly simple: one defined point in space.
Note 10: The Simplicity of Reference and the Complexity of Meaning — Halakhic Implications
In halakha (Jewish law) there are several examples in which we have a complex description that at first glance appears to be a combination of several concepts. Our claim here will be that this is a complex description that points to a concept that is itself single and simple. This perspective also has various halakhic implications.
Let us begin with an example from Tzofnat Pa’neach, the responsa of Rabbi Yosef Rozin (the Rogatchover), responsum 2. The author there discusses a situation in which a festival falls on the Sabbath. The law determines that there are labors done for the preparation of food for the meals that may be performed on a festival, whereas on the Sabbath they are forbidden. The question discussed there is whether one who performed such labor on a festival that falls on the Sabbath—and therefore violated the prohibition of labor on the Sabbath—also violated the prohibition of labor on the festival, even though on an ordinary festival such labors are permitted. The author discusses this question from angles other than the one that interests us here. Our claim is that there is strong reason to think that in fact both prohibitions were violated.
To clarify this mode of perspective, let us look at an example that may be clearer. The law determines that the sacrifices of the Day of Atonement in the Temple must be offered by the High Priest. Rabbi Meir Simcha HaKohen, in his book Or Sameach,77 Laws of the Day of Atonement Service, chapter 4, law 1, points to the fact that Maimonides holds that all sacrificial service on the Day of Atonement, even though it includes sacrifices not uniquely associated with that day—such as the additional Sabbath offerings, if the Day of Atonement falls on the Sabbath—is performed by the High Priest. Rabbi Meir Simcha argues that from this we see that Maimonides conceives of the Day of Atonement as a single essence, such that all sacrifices offered on it, even if only ostensibly by accident (simply because in that particular year it happened to fall on the Sabbath rather than on a weekday), possess the sanctity of the Day of Atonement, and therefore all must be offered by the High Priest. He brings another example there from the Passover offering, certain parts of whose service may be performed on the Sabbath that falls on the following day. From this it is proven that this offering is considered a “Sabbath” offering, even though when Passover falls on the Sabbath this is an accidental rather than essential occurrence.
As a conclusion from the discussion there, Rabbi Meir Simcha writes that when the Day of Atonement falls on the Sabbath, and a sick person must eat because of danger to life, he need not recite the sanctification blessing over wine beforehand (even though, on its face, eating on the Sabbath normally requires such sanctification first). This is because the character of that Sabbath cannot be severed from the fact that it falls on the Day of Atonement. The sanctity of that Sabbath finds expression in the fact that one fasts on it. The combination of Sabbath and Day of Atonement is not accidental, but creates a new essence: “the Day of Atonement that falls on the Sabbath.”78
In light of this example, the claim at the beginning of our remarks now appears clearer. A festival that falls on the Sabbath is likewise not an accidental combination of two concepts, but a new concept with a new essence: “a festival that falls on the Sabbath.” Therefore, if someone performed labor on such a day, it is reasonable to say that he desecrated all of its aspects.79
In fact, this is an excellent example of the claim made in the main text: even if the definition offers a complex meaning, the reference is simple. The reference is always something definite and delimited; only the definition requires us to combine several concepts with one another. In our case, there is an entity called “a festival that falls on the Sabbath” that is no less simple than the entity “Sabbath,” but its description—or its meaning—is composed of the fusion of several properties.
Additional examples of this perspective, somewhat different in kind, may also be seen. There are concepts in halakha that always include within themselves—not merely accidentally—broader parent concepts. Tosafot on tractate Nazir, Babylonian Talmud 49a, state that every High Priest is, in particular, also an ordinary priest. And the Rogatchover discusses, in light of this determination, a case in which a High Priest violates a prohibition that applies only to him and not to an ordinary priest: did the “ordinary-priest aspect within him” also violate this prohibition?
We find a similar explicit discussion in the Talmud regarding an ox that gores. An ox that gores for the first or second time is called an “innocuous ox,” and from the third time onward it is called a “forewarned ox,” with different laws applying to it. The Talmud (Babylonian Talmud, Bava Kamma 45a) discusses whether every forewarned ox that gores is also an innocuous ox, except that an additional layer of forewarning has been added to it, or whether it has become something entirely new (in Talmudic terminology: does “the aspect of innocuousness remain in place”?).
Likewise, in tractate Shevuot 13a, the Talmud discusses whether priests are also Israelites—that is, whether they are an entity with “two tiers”—with respect to the atonement of their sins on the Day of Atonement through the same sacrifice that atones for all Israel (the scapegoat), or whether they attain atonement through a separate sacrifice (a new entity, with a single tier that differs from the “Israelite tier”).
In all these examples, a complex concept is under discussion, and the question is whether it still contains components of the simple concepts that compose it, or whether it is a different, new essence.
This phenomenon of regarding the combination as something non-accidental may be understood by means of an analogy from a point located in three-dimensional space. If we try to describe such a point in a given coordinate system, we will obtain three different numbers representing different aspects of it—in mathematical terms, projections of the point onto the three different axes. So too, a day on which both a festival and the Sabbath occur is one single, simple point. The complex description we give this point results from the fact that we are equipped with a conceptual system—a coordinate system—on each of whose axes this day has a projection. On the axis of festivals, this day has a projection, and therefore it is called “Passover,” while its projection on the axis of Sabbaths also yields a positive result, and therefore it is also called “Sabbath.” The essence of the concept to which this expression points is simple and unitary, even though the description by means of the collection of projections may be quite complex.80
This is a consequence of the fact that there can be infinitely many halakhic concepts, while human reason can analyze them only if they can be reduced to a finite number of basic concepts. That is, complex halakhic concepts are obtained as a combination of atomic basic concepts. For example, the concept “a festival that falls on the Sabbath” is a composition, or combination, of the concepts “festival” and “Sabbath.” When these two coexist, a complex concept emerges. The basic concepts of halakha are the coordinates mentioned in the previous paragraph, and there is a finite number of such concepts. The number of complex concepts is, in principle, infinite, since there are infinitely many ways to combine a finite number of concepts. In mathematical terms, this is a description of an infinite space (of combinations and situations) by means of a finite basis (a basic array consisting of a finite number of primitive concepts).
It is clear that on the practical plane there still remains a difficult question: how are we to determine the laws that apply to complex concepts, if not through analyzing their projections? One might say that the laws of the Day of Atonement that falls on the Sabbath should be determined by the Sabbath, or vice versa. The decision in this matter cannot be verbally described, just as we saw that no criterion can be offered for the essentiality of properties. The question here concerns clarifying which feature is more essential in the complex concept for the matter under discussion.81
Such a perspective in halakha is plainly essentialist. There is a matter of the concept (or its very self), which exists beyond all its forms of description. A conventionalist perspective in halakha would say that this concept is truly complex, that it is simply the sum of its descriptions, and therefore it has no reference, only meaning. From such a perspective there is no room to wonder whether one who cooks on a festival that falls on the Sabbath also violates the festival prohibition; each feature is judged on its own. From an essentialist perspective, we consider the object (or concept) represented by the description, and not the collection of components of the description itself. The characteristics are derived from the essence.
A simple observation indicates that there is a difference between definite descriptions and names. Names usually have no meaning, only reference, whereas definite descriptions have meaning, but do not always have reference (as in the example above, “the present king of France”).82 In light of the discussion in the previous chapters, let us now add that meaning is the form of the object or concept, and reference points to its matter. Let us further add that even names that appear to be names of objects may be interpreted as names of concepts. For example, even if there is no object to which the expression “the present king of France” refers, we can still speak about it. We speak about a concept, not an object. Nor is the concept identical with its meaning. That is, the claim is that there is an additional component to the concept—one usually ignored—and that is its matter. This is the subject of the sentence “the present king of France is bald.” The ignoring of this component, the matter of concepts, stems from opposition to essentialism. As stated in the introduction, the problem of reference arises chiefly from a conventionalist conception, whether explicit or implicit.
For example, the problem Russell raises regarding the meaning of sentences like “the Festival of Unleavened Bread is the Spring Festival” is resolved on its own. The meaning of a concept is not the object to which the name points, but the matter of the concept. We can now understand that the matter of the concept “the Festival of Unleavened Bread” is different from the matter of the concept “the Spring Festival.” As stated, the problem of reference disappears here of itself.
In his article, Russell discusses in various ways the question of what the reference points to. He shows that the meaning cannot be the reference, and tacitly ignores the possibility that the matter of the concept is the object to which its name points. This gives rise to the question: what, then, is the reference? As a result of this difficulty he proposes his own theory of meaning and reference, which, even if it is free of logical problems, is undoubtedly convoluted and contrary to common sense. It is not the concept of “meaning” to which any reasonable person refers.83
Frege’s distinction between reference and meaning solves all the problems—at least all those known to me—in the problem of reference, provided one recognizes the existence of a matter (or very self) of a concept. The reference of an object relates to the thing-in-itself (the matter), and the reference of a concept relates to the concept-in-itself. By contrast, the meaning of a concept relates to the way it appears to us (the form), that is, to its properties.
Kripke’s Solution
In his book Naming and Necessity, Kripke discusses the various approaches to the problem of reference, such as the cluster theory of descriptions, which holds that the referent of a name is not a single description but an object that satisfies a substantial part of a collection (a cluster) of descriptions. Later on there, Kripke raises the thesis he himself supports: the concept or name as a social mode of usage that comes into its role through a process of “baptism.” This is a supposedly objective dimension of the concept that creates its reference.
In this way, Kripke tries to add an objective dimension to the concept from within the conventionalist system (that is, without really acknowledging the objective existence of a matter of the concept). In fact, the process of “baptism” is the very essence and foundation of conventionalism, for what is described here is social agreement concerning the use of a concept. Ironically, Kripke takes the foundation of conventionalism—which is the root of the problem—and tries to construct it itself as an objective dimension of the concept, and thereby solve the problem. This is a characteristic move in analytic entanglements that twist within the thicket they themselves have created. It was of this that Berkeley spoke when he said that philosophers raise dust with their feet and then wonder why nothing can be seen.
I do not enter into all these theories in detail, because they run into all kinds of difficulties and pressures, and this, as noted, chiefly because they fail to distinguish the existence of a matter of concepts. This is something every reasonable person perceives (even if sometimes only implicitly), and the ignoring of it stems from analytic tendencies—that is, from the desire to reduce every concept to a logically consistent definition that will capture its essence. Here again we see the correlation between analyticity and conventionalism.
An Essentialist Modal Description: Names and the Principle of Individuation
Later in his discussion, Kripke also arrives at the question of identifying certain properties as essential.84 His discussion pertains to various understandings in modal logic,85 which translates this question as follows: which properties remain attached to the object in every possible world we can conceive of.86 One of his conclusions is that the object’s name is such a property: it is a rigid designator. We, by contrast, will argue that the name has a special status that no other property possesses. It points to the matter of the object, or of the concept, and in that sense it is rigid. It is meaningless to speak of a world in which this would not be the name designating the concept under discussion. Such a world would not differ at all from the present world, since the entire content of that name is the pointing to this object. In another possible world, even if we had chosen a different combination of letters, essentially it would have been the same name, because it would point to the same object. The entire content of a name is the object or concept to which it points. Therefore, a name, generally speaking, is not a property, since properties deal with describing the thing, not pointing to it (in this sense).
A property, by contrast, may characterize the object in one world and fail to characterize it in another. A property has a meaning beyond this specific object, and therefore one can also speak of its absence under other circumstances with respect to the object in question. An essential property is one that accompanies the object in all the possible worlds of modal logic. The identification between a name and essential properties is characteristic of the analytic approach, which refuses to recognize the difference between them—that is, the fact that the name points to the matter of the concept, whereas a property (even an essential one) describes its form. In contrast to the analytic approach, my claim here is that a concept has matter as well and not only properties, and this is the reference of the name.87
According to the argument presented here, the name of a thing, or of a concept, is our means of relating directly to its matter and not to its form. The difference is not between a rigid designator and a non-rigid one, but between a designator (or pointer) and a descriptor. As stated, the designator relates to the matter of the thing or concept (its very self), whereas the descriptor relates to its form.
In chapter 1 of this gate we spoke about the principle of individuation, which is not a property, yet it is precisely what individuates the object. The name is in fact a linguistic expression of this principle of individuation. Any definition that uses various properties is always on the plane of form, not matter, and this is exactly the “unbridgeable gap” between the individual and its descriptions of which Bergmann speaks in the quotation at the end of the first section of that chapter. For this reason, the search for an explicit definition of the meaning of names is an act that is logically impossible. Definition deals with form, whereas names relate to matter.
Here we encountered the linguistic expression of the picture described throughout this gate up to this point. We saw that concepts have three components: matter, essential form, and accidental form. We saw that those of the analytic approach tend to ignore the possibility of a matter of concepts (essentialism), and to treat them conventionally. Here we encountered the linguistic expression of all this. We saw that the name is a referral to the matter of the concept or object, whereas descriptions relate to its form, and definition to its essential form. We saw that analytic thinkers tend to become entangled in various logical-philosophical problems because of their conventionalist tendency, and therefore they identify the concept with its properties (its form). It is this ignoring that creates the problem of reference. This is a clear product of the analytic-conventionalist approach, and the solutions proposed for it, all of which are concentrated in the layers of the properties of concepts, remain on the same plane. The problem of reference is one of the strongest indications of the connection between analyticity and conventionalism, and of the many failures latent in those approaches.
Note 11: Names in Torah and Halakha
In Torah literature one not infrequently encounters the assertion that the name of a thing, or of a person, is its essence. In Genesis 2:19 it is said:
And the Lord God formed from the ground every beast of the field and every bird of the sky, and brought them to the man to see what he would call it; and whatever the man called each living creature, that was its name. And the man gave names to all the cattle, and to the birds of the sky, and to every beast of the field, etc.
Already Adam gave all things their names, and several commentators explained there that the name of a creature is its essence. In light of what we have said here, the naming arose from contemplation of the object itself, of its matter and not its form. In this description, names acquire meaning, and the connection between them and the objects is not arbitrary as it is usually perceived. Their use as names points to the matter of the creature so called, and not to its form.88
At the beginning of Shnei Luchot HaBerit by Rabbi Isaiah Horowitz, in the section of the introduction called “Beit Hashem,” the author discusses the meaning of the names of the Holy One, blessed be He, and cites Rabbi Moses Cordovero from Pardes Rimonim (gate 19, the Gate of the Four-Letter Name, chapter 1; the quotation is from Shnei Luchot HaBerit):
The name of the Infinite One—that is, it indicates His very essence. By way of analogy: the name Isaac is a handle attached to that man, through which speech can grasp him. If we did not associate him with a name, we could not speak about him, for we would not know him. So too the Infinite One: through emanation there is a handle and a name for Him that indicates His essence, so that we may engage with Him, etc.
Rabbi Moses Cordovero here explains the meaning of a name and its relation to the object. It is an attachment between a word and an object that allows one to engage with it not through its properties but through its very self. The analogy is to the handle of a vessel, by means of which we can grasp the vessel—even one that would be difficult to grasp without a handle.
Later, Shnei Luchot HaBerit writes that the divine name differs from other names in that this attachment is not arbitrary:
The four-letter name for Him, or the other names, are not like a proper name among human beings, for their names are conventional—that is, Abraham our forefather agreed to call his son Isaac for one reason or another, but not because the name Isaac is related to some attribute at all, nor because his name indicates his essence. But His blessed names are not so, for all of them indicate the attribute of the thing designated by them, etc.
Here a picture is presented according to which all names are created in a process of arbitrary attachment to the objects they represent (as opposed to definite descriptions), something akin to Kripke’s “baptism.” But the divine name is not so, and nevertheless it is still a name and not a definite description. This follows from the fact that with God there can be no change, and therefore a meaningful name can be used with respect to Him. That is, the relation between God and His attributes and names is not similar to the relation that exists in other objects.
We see that there is a deeper layer in the relation between name and object, one that can arise from a relation between them and not from arbitrary stipulation. Yet the terminology remains “name” and not “description,” because the relation is to the matter of the object and not to its form. The correspondence that turns a name into a definite description is a correspondence to form and not to matter. Contemplation of the matter of an object, or concept, is a process difficult to define, yet we have demonstrated its existence, directly or indirectly, in the previous examples.
Rabbi Yosef Rozin (the Rogatchover) explains the properties of the divine name in a similar way.89 He argues that the divine name has no parts, just as God Himself has no parts and is simple. This determination rests on a resemblance between the name and the object it describes, meaning that there is a non-arbitrary relation between them. The practical implication of this concerns writing two letters from the divine name on the Sabbath. The Rogatchover explains that such writing does not have the same law as writing two letters from another name—such as “Shm” from “Shimon”—a matter on which opinions differ in the Jerusalem Talmud, Berakhot 5:1. This is because the divine name has no parts, just as God Himself has no parts. In this context it is interesting to note that the expression we use to refer to God is “the Name.”
In the context of the divine name, a distinction is made between appellations and names. The simple explanation of the distinction is that appellations are definite descriptions, whereas names are pure designators. Only the explicit name of God (the four-letter name), which is called “the name of the essence,” is considered a non-arbitrary designator. Some of the names themselves acquired meaning retroactively—that is, after they had been chosen arbitrarily as names of God (for example, “Elohim” is also used as an appellation for important people or for judges). All these distinctions have halakhic implications, some of which are disputed among legal decisors, but this is not the place for them.
Another example of the intimate relation between a name and the one who bears it, as distinct from the relation between a name and various properties of its bearer, may be found in Mikhtavei Torah, which presents an exchange of letters between Rabbi Yosef Rozin (the Rogatchover) and Rabbi Mordechai Kalina. There, in sections 193–194, the following question is discussed: when one writes a bill of divorce, halakha requires that it be written for the sake of the woman being divorced—that is, the one who writes it must think that this bill is being written for her sake. The question is whether one must think of the woman’s very self, or of her name. It is entirely clear that it would not help to think of her properties, even the most essential among them. Here too, then, there is a halakhic distinction between the matter of the object and its form, even in its essential aspects.90
Russell, who in the eyes of many marks, more than any other philosopher (perhaps together with Frege), the opening of the analytic age of the twentieth century, also opened the systematic discussion of the problem of reference. It is no accident that he presents a complicated and unreasonable understanding of the concept of reference, as did many after him, and this because of their analytic stance. Russell tried to grasp the thing in itself—the matter of the thing or concept—by means designed for dealing with its form.
It is worth noting that this is a case in which Western thought struggles over a question that Eastern thought is not troubled by at all. When we apply Western analytic methods in a domain of this sort, we fail, because this is a domain in which they are inapplicable. It has already been said that most important philosophical problems remain in the same condition in which they were when first raised. Analytic philosophy does not truly succeed in solving them, because the attempts to solve them are made with unsuitable tools. Even the formulation of the problems is done in such a context, and therefore it itself already carries within it the seeds of failure. If there is success in solving some problem, it is clear that some dimension of synthetic thought is also involved in the judgment, or else that this success tacitly presupposes what it seeks to prove.91
Summary of the Discussion in This Gate
In the second gate, we linked three philosophical problems that arose in three different eras in the history of philosophy: the problem of matter and form from the Greek era, the problem of the thing-in-itself from the Kantian era, and the problem of reference from the modern analytic era. In the terminology we are using, the three problems represent, in different ways, the same perplexity: how to say something about the world in itself and about what happens within it (about the matter of things), and not only about the ways in which they appear to us (their form). We saw that when analytic means are used in order to treat synthetic issues, one arrives at solutions very far from common sense, and sometimes one also sees problems in places where they do not necessarily exist.
In the course of the discussion, we saw that there is a distinction between the matter and the form of objects, and also of concepts. Within form, we distinguished between the essential part, which is reflected in the definition, and the contingent part. Following this, we discussed the possibility of changing a concept’s definition. We saw that every dispute and every claim regarding the relativity of a concept’s interpretation and definition (which relate to its form) tacitly and implicitly presupposes the objectivity of its matter.
We saw here that the two logical positions presented in the previous gate—the analytic and the synthetic—have an epistemological expression. Those of an analytic position will generally hold a conventionalist epistemology of concepts, and those of a synthetic position will generally espouse an essentialist epistemology with respect to concepts.
Following this distinction, I argued that the problem of reference, which intensively occupied the philosophers of the twentieth century, does not arise at all. The broad discussion and entanglements surrounding this problem in the analytic era stem chiefly from the assumptions of analytic philosophy, which usually represents an analytic philosophical stance, and not merely a method of philosophizing (as mentioned in the previous gate). The claim that analytic philosophy generally expresses a philosophical stance—analyticity—and not merely a method of philosophizing, will also be discussed in the next two sections.
Footnotes
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In light of the reliance on Kant, the question arises where Kant himself stood on the analytic-synthetic map that we are proposing. At the end of the previous gate we saw that he belongs to the analytic wing of the philosophical map. The question of Kant’s place on the map drawn here will be discussed in greater detail in the third section. ↩
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It is interesting to point to a similar connection mentioned above in Note 1 regarding Rabbi Chaim of Brisk’s expansion of the Talmudic concepts of the legal object and the legal subject. Rabbi Chaim treated prayer as a kind of object, and spoke of its characteristics (“the object-character of prayer,” in his language), as distinct from the characteristics of the one praying. On this, see Rabbi S. Y. Zevin, Ishim VeShitot, Bitan HaSefer, 1952, chapter 3. ↩
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A distinction between “substance” and “accident” is often used to describe the difference between two kinds of form of the thing itself. There are properties essential to the thing, called “properties in the thing itself” (intrinsic or essential to it), and properties that are not essential to it and are present in it accidentally and may also be absent from it. Later in my remarks I distinguish between these two kinds of properties, and therefore I do not wish to use here the terminology of “substance” and “accident.” The reader should note the definitions given here and remain attached to them in the continuation of the reading. ↩
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See Bergmann, Introduction to Logic, from p. 97 onward. See also Bertrand Russell, Human Knowledge: Its Scope and Limits (1948), cited by Bergmann in a note on p. 101. ↩
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Leibniz’s claim was that space and time are expressions of other differences that exist between objects. Where those do not exist, space and time likewise do not distinguish between them, since, as stated, they cannot be the source of the differences. Although I do not agree with Leibniz’s claim as such, Locke’s claim does not seem correct to me either, but for another reason: the impossibility of two drops of water, or any two objects, occupying the same space at the same time is a physical problem, not a logical one. It cannot be that the location of the drop of water in space has a constitutive logical status for it. In the absence of a repulsive force between the two objects, they could theoretically occupy the same space at the same time. In that case they would still count as two different drops. In quantum mechanics this state is not even merely theoretical. In that theory, the location of a drop of water is a concept that must be redefined, and there it is possible for two particles to occupy the same place. Alternatively, there are situations in which the location of a particle has no meaning at all, and yet one still speaks of the number of different particles. There are particles called bosons (after the Indian physicist Bose) that can have entirely identical physical properties and nevertheless be counted as a collection of different particles. They lose their personal identity, but their number has physical significance. Let us also note that even particles that are not of this sort (called fermions, after the physicist Fermi) are today regarded in physics as identical particles, meaning that they lack continuous personal identity. They adopt different physical properties and exchange them. So even with respect to these particles it would not be correct to claim that their characteristics are what constitute their logical status. This claim, which at first glance seems merely semantic, has measurable consequences in thermodynamics. The interested reader is referred to any elementary book on statistical mechanics that discusses Gibbs’s paradox in quantum statistics. See a brief discussion of this below in Note 5. ↩
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Here too there is an implicit critique of Leibniz, who in effect tries to argue that the analytic is not empty. Leibniz tried to make a claim with metaphysical content and to bring an analytic proof for it (see the next note). Leibniz himself, in my opinion, is in a position in which he feels that metaphysics is a legitimate and important domain in philosophy, but he tries to ground it by analytic means. In this he precedes Kant and others, an interesting expression of whose approach is found in Yuval Steinitz’s book Etz HaDa’at. See the critique of Steinitz’s remarks in the appendix. That critique is valid for Leibniz as well. ↩
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This is a classic example of an analytic proof whose conclusion is a strong claim about the world. In such a case, a reader aware of the emptiness of the analytic immediately begins to look for where the conclusion was already hidden in the premises, for, as noted, the analytic cannot add new information beyond what is already known in the premises. After a brief examination it becomes clear, as explained in the body of the text, that the conclusion was indeed tacitly assumed already at the stage of the premises. This example again illustrates that one cannot add knowledge about the world by analytic means alone. See the previous note. ↩
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Their arguments were of the following type: if two objects have the same characteristics, then one of them is superfluous. Why would the Creator create a superfluous object? This is, of course, a metaphysical-theological argument, not a logical one. That is, in principle, from the standpoint of the logical definitions of objects and properties, two different objects that have the same properties are possible. It is only on the theological plane that we know facts about the will of the Creator, namely that He does not create such pairs. ↩
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It is clear that the opposite principle, the one that determines the “indiscernibility of identicals”—that there is no difference between two identical objects (which are in fact one and the same object)—is accepted by every rational person. ↩
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See Bergmann, Introduction to Logic, p. 102 and following. ↩
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Schopenhauer qualifies the statement above and determines that human cognition has access to one object as it is in itself. This object is the knower, or cognition in itself. For a description of this claim, see Shalom Rosenberg, “Rabbi Kook and the Blind Dragon (Schopenhauer),” in Be’Oro, World Zionist Organization—Department for Torah Education and Culture in the Diaspora, Jerusalem, 1986 (edited by Chaim Y. Hameiel). ↩
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Epistemology is the theory of knowledge or cognition—the branch of philosophy that deals with human cognition. ↩
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I am not entering here into this problem at the level of quantum theory, but only at the conceptual level. In quantum theory it may be that without an observer even the acoustic wave does not exist in the accepted sense. ↩
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This is not the difference of which Leibniz spoke in his “proof” cited above for the principle of the identity of indiscernibles. A difference of this sort also concerns the source of form in the thing itself. Leibniz spoke of the very fact that this object is defined as an individual, and in this it differs from another object. This difference certainly concerns only “matter,” and therefore cannot count as a property, as claimed in our main text. ↩
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See Rabbi David HaKohen, Kol HaNevu’ah, Mossad Harav Kook, Jerusalem, 1975, at the beginning of the third essay of the first part. The philosophy of Rabbi HaNazir will be discussed below in the eleventh gate. ↩
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The description that appears here has a deep connection to the issue of the negative attributes of the Divine, and to the question of how Kabbalah relates to the Divine through positive attributes. This is not the place to expand on the subject; the wise reader will understand further. ↩
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It may be that there are further exceptions, such as the number of things. To say that there are three things is, seemingly, a statement about the thing itself (the matter) and not about its form. Another such exception is the difference between objects that stems from the mere fact of their being two, of which Leibniz spoke in his aforementioned “proof.” That difference too, as stated, concerns the thing itself and not its form. An interesting exceptional case is love for a particular person. It is hard to suppose that the object of love is a collection of that person’s properties. It is more plausible that one loves the person himself and not his properties. My thanks to Hamutal from Be’er I for this idea. ↩
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This proof was proposed by the Christian Anselm and further developed by Descartes. See the discussion in the first part of Steinitz’s Etz HaDa’at, which will be discussed in the appendix to this book. It is also worthwhile to see Abraham Tzvi Braun, Chapters in Ontological Analysis: The Issue of Being, Magnes, Jerusalem, 1977, chapter 3; and also the reader edited by him, From Parmenides to Contemporary Thinkers, Magnes, Jerusalem, 1977, part 2. ↩
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Openly or implicitly, all the objections to the ontological proof can be mapped onto this claim—at least all those of which I am aware. ↩
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One might say that existence relates to “characteristics” of the sort found in the world in itself, in light of the previous discussion. Here that seems implausible. Determining the existence of something is a statement about the matter itself, and not about characteristics, neither in the world nor in cognition. ↩
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I clarified here precisely the objections to the proof, and did so as an example of the distinction between statements that concern matter and statements that concern form. Nothing should be inferred from these remarks as to my view of the proof itself or of the objections to it. ↩
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Russell himself, although he brings the example of light quoted above, does not understand the limitation of perception as we describe it here, as becomes evident from reading the continuation of chapter 3 of his The Problems of Philosophy. He regards it as a cognitive limitation, and therefore, in my opinion, much of the discussion conducted there is mistaken. This is not the place to discuss the matter. ↩
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It is not by chance that I use here the term “intellect,” which belongs to the mental side of a person, and not the term “brain,” which is an organ belonging to his physiology. ↩
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Even in the discussion of objects there is a philosophical approach that holds that they have no existence at all outside our consciousness. This is the philosophical idealism briefly mentioned above. ↩
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Quite a few philosophers have claimed the existence of entities other than material ones. I do not intend at the moment to claim that there is a dispute between analytic and synthetic thinkers on this question. Still, I will say that there is a clear correlation between positions on this question and the thinker’s place on the analytic-synthetic axis. The analytic thinker is more inclined to deny the existence of non-material entities. See further discussion of this question in the third section. ↩
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In the logical argument above we presented, following Bergmann, matter as the individual grammatically represented by the subject of the proposition, in contrast to form, which is represented grammatically by the attribute or predicate. According to this division, it is clear that one may also speak in concepts of the concept itself appearing as the subject in propositions, as opposed to its form appearing as an attribute or predicate. This distinction is related to the accepted distinction in logic between the use of a term in quotation marks, where we deal with the concept as such (and sometimes with the word representing it), and its appearance without quotation marks, which points to an object in the world represented by the concept. A sentence whose subject is ball deals with the object represented by the word “ball,” whereas a sentence whose subject is “ball” deals with the term or word “ball” itself. See, for example, the beginning of Avron Polakow’s Logic for Thinkers and Computers, Akademon, Jerusalem, 1980, where he distinguishes between mention and use of concepts. I will return to this point below. ↩
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The subject is discussed in my aforementioned article “What Is ‘Legal Effect’?” ↩
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This explanation is not sufficient. One must add to it the assumption that payment for damage is not compensation for the loss of work-value, but rather a payment to the owner akin to a penalty imposed on the damager, whose measure is somehow the value of the lost labor. Evidence can be brought for such a claim, but this is not the place for it. ↩
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Here one actually sees more than that. The form of ownership as rights of use is not necessary and does not always accompany ownership. Here we are already entering the concept of essence, which will be discussed in the next chapter. ↩
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This metaphor is based on Maimonides, who at the beginning of his Guide of the Perplexed explains the various verbs used in the language of the Torah for seeing with the eyes as opposed to those used to describe seeing by means of the intellect. On this, see further in the eleventh gate. ↩
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A further discussion of the meaning of matter and form in halakhic concepts may be found in Mefaneach Tzefunot by Rabbi M. M. Kasher, published by the Tzofnat Pa’neach Institute, Jerusalem, 1976, in chapters 1 and 14. This book contains halakhic connections to many philosophical questions, though nearly all of them belong to ancient and medieval philosophy. Such connections characterize the method of study of Rabbi Yosef Rozin, known as “the Rogatchover genius,” and Mefaneach Tzefunot serves as a kind of encyclopedia and introduction to his method. ↩
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This principle—that bodily sanctity does not lapse on its own—is the subject of a dispute among the Amoraim in Babylonian Talmud, Nedarim 29a. In the course of the passage one sees similar conceptions regarding ownership of the body itself (as distinct from usufruct, which is mainly rights of use without absolute ownership of the body), which also does not lapse on its own and cannot be made time-limited (see Rabbenu Nissim’s commentary there). This is an indication that the understanding really underlying this determination is the principled one that reality cannot be changed by speech alone. ↩
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A similar determination appears in Rabbi Elchanan Wasserman’s Kovetz Shiurim on the above Talmudic passage. He brings there a difficulty from Oneg Yom Tov, which asks: when rain is falling, and everyone is therefore exempt from the commandment of the sukkah, why is it still permitted to remain inside it? For, as we saw, there is a prohibition on using a sukkah for purposes other than the commandment. He explains that when rain is falling, there is no commandment to sit in the sukkah, and therefore this is not a sukkah at all. His intent is exactly what we are saying here: there is indeed a “sukkah” in empirical reality, but not a halakhic “sukkah.” ↩
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One may argue that this is the matter and form of the sukkah object, and not of the concept “sukkah.” In my opinion, since we are discussing the sukkah in general and not a concrete sukkah, the simple understanding is that we distinguished here between the matter and form of the concept “sukkah,” and not of a particular object designated by the word “sukkah.” ↩
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Later, further examples will be brought dealing with the concepts “good” and “process” (Notes 7 and 8), and these too will sharpen the relation between the matter of a concept and its form. ↩
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On this riddle, see the book by the well-known American mathematical puzzle writer Martin Gardner, The Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, New York, 1959. See puzzle 3 there, p. 24. The solution also appears there on p. 28. ↩
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See in the next note a similar case concerning the properties and essence of numbers. ↩
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There is a tendency to see rights of use as an essential part of the form of the concept of ownership, and not an accidental one. This tendency stems from the view that rights of use are a central expression of ownership, and it is difficult to call them an accidental feature. In our schematic division here we classified the rights as part of the accidental component, because they do not always appear. Still, there is certainly room for the claim that properties that usually characterize a concept cannot be called accidental with respect to it, and some philosophers do indeed argue so (see, for example, Millot Higgayon by Maimonides, at the beginning of gate 11). If I recall correctly, Kripke claims in his Naming and Necessity (mentioned in the last chapter of this gate) that a person’s having five fingers is an essential property, even though it is clear that a person can be born missing some fingers. Such a person is a defective human being, because a normal human being has five fingers. The same applies to the concept of ownership. Ownership without rights of use is defective ownership. In this way one may perhaps preserve the essentiality of certain properties even when there are (pathological) situations in which they do not appear. Since this is only an example, I see no need to go into further detail. ↩
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See the above-mentioned Mefaneach Tzefunot, in the introduction to chapter 1. ↩
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This is how Nahmanides explains the words of the aforementioned Sefer HaBahir in his commentary on the beginning of Genesis. ↩
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Let us note that on the semantic plane it seems from the words of Gersonides that he conceived the concepts of matter and form in the opposite way to what we presented above: “tohu” is the form and “bohu” is the matter. ↩
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Hilary Putnam, “The Refutation of Conventionalism,” in Mind, Language and Reality, Cambridge, 1975. See Steinitz, Etz HaDa’at, note 158. A discussion of the implications of such an approach for the relation between morality and religion appears in Daniel Statman and Avraham Sagi, Religion and Morality, Bialik Institute, Jerusalem, 1993, p. 48 and following. ↩
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There is here a connection to the note above regarding the essentiality of properties, even though in pathological cases they may fail to appear in the object or concept. ↩
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Since this is only an example, I do not intend here to enter into a detailed presentation of the approaches in religious thought that discuss the question whether this is indeed truly the case. There are claims that all human beings were created with the same capacities and the same spiritual potential. It seems that on the plane of intelligence, and certainly in the economic sphere, this is not true. Of course, one who understands the human being as a random creation of nature does not struggle with these questions at all, unless he has proposals for improving the situation (such as communism, socialism, genetic engineering, and so forth). ↩
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It is interesting to note in this context that in field theory in modern physics, the motion of an object or a change in it is represented by its destruction in the previous place or state, and its creation in the new place or state. An example of this is the movement of a cursor on a computer screen. The observer thinks it is moving, but in fact it is extinguished or destroyed in the current square and relit in the next square, and so on. In the scientific picture of the world there is no difference between a change in an object and its destruction and recreation in a new state. There is no treatment there of conceptual continuity, or of the question whether it is the same object or a new object. In the discussion here we distinguish between these two concepts. For a more detailed discussion of this issue, see Note 7 below. ↩
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This is the use of the foreign word that describes this approach: essentialism. The terms conventionalism and essentialism are not entirely precise. I hesitated here whether not to use “nominalism” and “realism,” which in certain respects seem more suitable. Later we shall see that my definition of these terms is broader than the accepted one. I identify nominalism with idealism and claim that they have the same root. Both express analytic skepticism. By contrast, conceptual realism will be identified with metaphysical realism and described as derived from a synthetic outlook. Therefore I chose, in the context of concepts, the terminology of conventionalism versus essentialism. The term “essentialism” itself is not at all precise, since, as I will note below, it itself derives from a conventionalist conception. I chose it because it is the closest available term for our purposes. See below, Note 101. ↩
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It is very important to note that, according to what we have said, concepts are brought into the intellect, and understood by it, through a process of cognition and not only through processes of thought. The relation between thought and cognition, especially with respect to concepts, will be discussed at length in the next chapter and below in the eleventh gate (it will be elaborated more fully in the second book of the trilogy). ↩
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The correct Hebrew translation of essentialism is “mahutanut.” It should be noted that even this terminology itself points to the conventionalist conception that underlies it. Essence, as defined in the previous chapter, is part of the form of the concept or object—the necessary, as opposed to accidental (contingent), part of it. The object itself is the very selfhood of the individual, the matter, or the thing-in-itself. The identification latent in the term “essentialism,” between essence and the selfhood of the object or concept itself, itself stems from a conventionalist conception. This is the conventionalist’s description of the opposing approach described here. We will use this term because it is the closest among the accepted terms in the philosophical world. One might have thought of “selfhood-ism” as a more accurate name for this approach. ↩
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As noted, Kripke criticizes the accepted claim that there are no analytic-a posteriori propositions. His claim is that the analytic-synthetic division lies on the logical-linguistic plane, whereas the a priori-a posteriori division lies on the plane of cognition. Therefore, for him, all four theoretical categories are possible. As an example he brings analytic propositions that a person learns a posteriori, and I have already remarked that this is a different concept of apriority from the Kantian one. In any case, it seems that Kripke did indeed put his finger on an important point in the Kantian division. The divisions do in fact lie on different mental and cognitive planes (thought and cognition). Therefore, already in Kant’s doctrine there is this link between thought and cognition, and in fact Kant’s statement about a connection between these concepts (the impossibility of analytic-a posteriori) constitutes a basis for the form of his transcendental argument, which is precisely this: a projection from thought to cognition. One of Steinitz’s claims in his Etz HaDa’at (see the appendix) against analytic philosophy is that the assumption that concepts containing an internal contradiction cannot exist is also a connection—apparently unjustified on their own terms—between logic and cognition and the world. To this problem, however, Kant apparently offered a solution: cognition will not grasp such a concept, even if it exists. In the third section we will see that this is no solution at all, because there is no necessary connection between the constraints of thought and the constraints of cognition. Despite this lack of connection between the constraints of thought and cognition, we will see below (and even more in the eleventh gate) that the very distinction between these two planes, thought and cognition, is itself rather shaky. ↩
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As we shall see in chapter 1 of the third gate, the analytic approach does indeed deal with synthetic philosophies, or with metaphysics, but only from an analytic point of view. That is, it asks what one who holds such-and-such an approach must think. It is not willing to claim the correctness of one approach as against another. In the same way, the analytic thinker is prepared to discuss a given concept as it is used in different contexts, but not to claim a meaning for that concept beyond the forms of usage that arise from agreement among the users of the language. Analytic philosophy deals mainly with problems of language. Some analytic thinkers claim that all philosophical problems have their root in incorrect use of language. There have indeed been a number of analytic philosophers who do not fit exactly under these definitions, and these usually regard analyticity as a method of philosophizing and not as a philosophical position (as I mentioned above). In the next two sections we will elaborate more on this subject. ↩
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As stated, there is here a clear echo of Kant’s innovation, which posits the existence of synthetic-a priori propositions. The combination “synthetic-a priori” is also a combination of an epistemological concept (a priori) and a logical one (synthetic). The “a priori” here serves as a code-name for that additional mode of confirmation of which I spoke in the body of the text, by means of which we come to recognize the synthetic determinations that are the content of such propositions. In the twelfth gate I will distinguish between a priori and analytic in a manner different from Kant, and then the connection—and also the difference—between the approaches will become clearer. ↩
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See Encyclopaedia Hebraica, under the entry “Nominalism,” where Bergmann states as a self-evident matter that positivism, which in the next gate we will identify with the analytic position, is a continuation of nominalism (conventionalism, in our terminology). This is a claim exactly parallel to what I argue in the body of the text. ↩
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The intention here is to characteristics as they are in themselves. Above, in chapter 1, we saw that every cognitive picture has a root in reality itself. Differences between objects also exist in reality itself, and only their descriptions in cognition are shaped within parameters that are human-subjective, products of the structure of our cognition. Thus the form of objects is created in our cognition, but it has sources and roots in reality itself. These are the characteristics in themselves, to which sensory cognition relates. ↩
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Eugen Herrigel, Zen in the Art of Archery, Dvir, Tel Aviv, 1990. See also Lidia Aran, Buddhism, Dvir, Tel Aviv, 1993. In the book Philosophy in the East and Philosophy in the West, by Ben-Ami Scharfstein, Shlomo Biderman, Dan Daor, and Yoel Hoffmann, Yahdav, Tel Aviv, 1978, one can also see the philosophical dimension familiar in the West as it appears in the East. ↩
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The term “extra-sensory perception” arouses in a Western person very skeptical connotations. Certain scientific attempts made in order to confirm such phenomena have met with torrents of mockery and contempt. Although I do not agree with the principled Western approach to such matters, the scientific attempts, and certainly the pseudo-scientific ones, do indeed deserve such treatment. The main problem with these attempts is that they try to apply Western tools of thought and research to an elusive subject. The insistence on doing so sometimes yields distorted interpretations of findings and ignores essential problems in the research. See, for example, Arthur Koestler, The Roots of Coincidence, Sifriyat Afikim, Am Oved, Tel Aviv, 1975. ↩
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In the eleventh gate we will discuss this at greater length. ↩
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Samukh VeNireh, Schocken, 1962. The passage is also brought by Gershom Scholem at the end of part 1 of his book Devarim BeGo. ↩
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Here we encounter a term of a third kind. Beyond concepts and objects, one can also apprehend phenomena or events. With respect to the cognition of these too, we shall see the difference between the two approaches described here: conventionalism and essentialism. ↩
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I discussed this subject at length in two articles that I published in the past. The first deals mainly with the halakhic aspect of giving a bill of divorce, and appeared in the Department of Basic Studies bulletin of Bar-Ilan University, on the weekly Torah portion Ki Tetze, year 1995. The second deals with the philosophical aspects, especially the philosophy of science and various aspects of the uncertainty principle: “Zeno’s Arrow and Modern Physics,” Iyyun 46, Tishrei 1997. The discussion here is extremely partial and concise. A reader interested in more expansion and detail on the subjects discussed in this note is referred to those articles. ↩
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This discussion also touches on problems of continuity and identity of changing objects, and this is not the place for it. ↩
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Perhaps what is called in physics the “Doppler effect” makes it possible to observe velocity itself not through changes of location. There are relativistic and quantum problems here, and this is not the place for them. ↩
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See, for example, Chaim Perelman, The Realm of Rhetoric, translated by Yosef Or, Magnes, Jerusalem, 1984, p. 27 and following. ↩↩
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See Bergmann, Introduction to Logic, chapter 4, section 19, p. 334. A more detailed discussion can be found in Bergmann’s Hogei HaDor, which also discusses Husserl’s doctrine, and in Abraham Tzvi Braun’s introduction to his translation of Husserl’s Cartesian Meditations, Magnes, Jerusalem, 1991. And, of course, in that book itself. ↩
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Husserl himself calls his method “transcendental phenomenology,” and not for nothing. ↩
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Perhaps one could use the expression “non-transcendental noumenology.” ↩
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On this matter see the Minhat Hinukh commentary to Sefer HaChinukh there, and Sha’ar HaMishpat on Shulchan Arukh, Choshen Mishpat, section 18, and what he brings there from Shevut Ya’akov. ↩
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Rabbi Yosef Engel, in his book Lekah Tov, section 15, discusses the question of quantity versus quality in halakha in various contexts, and it is worth noting that he does not address this issue at all. ↩
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See a discussion and additional examples in Mefaneach Tzefunot by Rabbi Menachem Mendel Kasher, chapter 11, section 9. ↩
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Later in the book we will expand this argument and call it (following Descartes) an “anthropological proof” for the existence of concepts. ↩
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See the discussion of the heap paradox at the end of the eighth gate, and in the books Mefaneach Tzefunot and Lekah Tov mentioned there. ↩
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In set theory, the terms “cardinal numbers” and “ordinal numbers” are used in a somewhat different sense, with respect to infinite cardinals. To the best of my understanding there is a connection between those two uses, but this is not the place to elaborate. ↩
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Heat as energy, which is measured in calories, is a cardinal magnitude and not an ordinal one. And for those versed in esoteric matters I will add: there is a connection between this distinction and the physical distinction between intensive and extensive magnitudes, though they do not overlap. ↩
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One can of course propose various formulations for the essentiality of a property, of an object, or of a concept—for example: “a property that characterizes the concept in all its appearances is essential to it.” This is an entirely correct criterion, but at the same time also an entirely useless one on the practical plane (see the joke of the hot-air balloon). The whole question of the essentiality of a property comes down to the question whether it appears as a characteristic in all the appearances of the concept or object. Whoever determines that a certain property is essential thereby determines that it appears in all the appearances of the concept. Thus, this definition—which we too used here—is usually not helpful in a discussion of the very essentiality of the property with respect to a concrete object or concept. ↩
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This article is important for our purposes also historically, since many regard it as opening the analytic era in twentieth-century philosophy. The article was translated into Hebrew by Dorit Bar-On in the anthology Philosophia, edited by Leo Rauch, Yahdav, 1983. ↩
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A more detailed discussion in Hebrew may be found in Saul Kripke’s Naming and Necessity, and in the introduction and notes to the book by the translator, Avishai Revah. ↩
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It may indeed be that this is only an indication that the same object is being referred to in two different ways. This claim does not seem particularly problematic to me. See further below. ↩
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This book is a commentary on Maimonides’ Mishneh Torah. Rabbi Meir Simcha was rabbi in the city of Dvinsk in the same period in which the Rogatchover also served there as rabbi, in the first third of the twentieth century. ↩
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The Rogatchover calls an accidental combination of this sort a “juxtapositional combination,” that is, a case in which the two components are neighbors of one another (a physical mixture). An essential combination that creates a new entity he calls a “blended composition,” meaning that the combination fuses the two components into a new entity (a chemical compound). It is interesting that in his discussion of the question above he does not use this distinction, even though it is very common in his thought. ↩
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One might specifically say, precisely because of this approach, that he committed only one prohibition: he desecrated the “festival that falls on the Sabbath.” But within the traditional conceptual system used to analyze such situations, this concept does not exist. This prohibition is expressed by saying that the person violated two prohibitions, that of the Sabbath and that of the festival. ↩
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One might say that these projections should also determine the laws, meaning that one who performs labor of food preparation on a festival that falls on the Sabbath would violate only the Sabbath prohibition. But then there is no meaning at all to viewing the combined concepts as projections of a single concept. It is clear that Maimonides (at least according to Rabbi Meir Simcha’s interpretation) did not understand the joining in this way, since for him even the laws of the Sabbath are affected by the fact that it falls on the Day of Atonement. ↩
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On this matter, see my article “Two Types of ‘What Do These Cases Have in Common?’: Conceptual Construction,” Meisharim 2, Yeshivat Hesder Yeruham, 2003, in the discussion of the dispute between Rabbi Asher ben Jehiel and the leading authorities in the issue of Babylonian Talmud, Bava Kamma 6a. There the discussion concerns a law learned from two primary categories that have different characteristics. The dispute concerns the question which characteristic is the essential one and which is secondary (accidental). ↩
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Kripke brings an example of a name that has meaning: the city of Dartmouth, which lies at the mouth of the River Dart. He argues there, rightly, that the historical process led to the selection of a meaningful name, but once the name Dartmouth was established, the meaning is no longer relevant to the way it is used. Even if the River Dart were to dry up completely, we would continue to call that city by the same name. Thus the word Dartmouth now functions linguistically as a name and not as a description. ↩
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The formal problem that Russell raises in his article against Frege requires separate and detailed treatment, and this is not the place for it. ↩
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See above in chapter 2, in the discussion of Putnam on essence, and in the note there. ↩
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Modal logic is a logical theory that deals with the truth of claims in different possible worlds. A “necessary” claim in the modal sense means a claim that is true in every possible world. ↩
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Kripke’s very linking of the two problems—names and necessity—indicates that his line of thought was very close to the one described here. In my opinion he was caught in the cords of his analyticity, which did not allow him to find a reasonable escape from the tangle he discerned. Another example of this we saw above in Leibniz, and yet another we will see at length in the appendix at the end of the book. ↩
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It seems to me that this is Meinong’s conception. ↩
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See the note above on the name of the city Dartmouth. ↩
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See the book Mefaneach Tzefunot, and Rabbi Moshe Shlomo Kasher’s introductions to the Rogatchover’s commentary Tzofnat Pa’neach al HaTorah. ↩
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After writing this note I saw that there is a discussion of the relation between the problem of names in analytic philosophy and the interpretation of the divine names in the article: Y. Gellman, “Names and Divine Names: Kripke and Gikatillia,” in Sefer Higayon, M. Koppel and E. Merzbach (eds.), Zomet Institute, 1995, pp. 51–60 in the English section. ↩↩
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See my remarks (following Bergmann) on Leibniz’s attempt to prove his principle of the identity of indiscernibles at the beginning of this gate. ↩