On Platonism (Column 383)
In Column 376 I discussed the limits of a priori thinking. At the end I said I intended to continue dealing with non-verbal cognition (and the limits of linguistic representation), which occupied the following columns, and with Platonism, to which I now turn.
What is Platonism and what is an Idea (Form)?
In his Republic, Plato uses several images to explain his conception of forms, i.e., the Ideas. In Book VI he likens the soul to eyes that can see only things illuminated by the light of the sun, and writes in Plato’s name (d508):
Apply this comparison to the soul in the following way. When it is fixed on the place where truth and reality shine, the soul apprehends and understands them, and appears as if it possesses reason; but when it turns to a place mingled with darkness, the world of things coming-to-be and passing away, it only forms opinions and its edge is blunted, and it moves in its views from here to there and again seems as if it lacks reason.
According to Plato, there is a place where truth and reality shine—where our soul grasps them fully, purely, and in a refined way. This is the world of Ideas, which contains pure forms rather than material, fashioned objects like those in our world. Such clear understanding is not possible in “the world of things coming-to-be and passing away,” namely our world, for here reality does not appear in its purity. As they descend into the world—that is, as they become instantiated in material objects—Ideas are mixed with various dross (darkness), and therefore our grasp of them becomes less clear.
A little later, at the beginning of Book VII of the Republic, Plato presents the famous “Allegory of the Cave”:
Human beings live in an underground cave, whose mouth opens toward the light that spreads throughout the cave. They have been there since childhood, and their legs and necks are chained so that they cannot move, and they can see only what is in front of them, because the chains prevent them from turning their heads. Above them, at a distance, a fire burns, and between the fire and the prisoners there is a road that ascends upward, and if you look closely you can see a low wall built along the way, like a screen in front of which puppeteers display their dolls… [And those people] see only their shadows, or the shadow of others [chained beside them], cast by the fire onto the wall before them… For them… truth will be nothing more than the shadows of the passing figures.
The prison [the cave] is the world of the senses, the light of the fire is the sun… and the journey upward [along the steep path out of the cave] is the ascent of the soul toward the world of contemplation… the world of the Idea of the Good appears only at the end [after extended habituation], and can be seen only with effort… and it is the immediate source of reason and truth for the thinker, and it is the power upon which a person acting rationally in his public or private life must fix his gaze.
Plato explains that the tangible world is an illusion, or a kind of projection of ideal forms in a world of pure universals. One who wishes to understand the real world must focus his gaze on the Platonic world of Ideas, for only there can full understanding be achieved. There lies true reality. He takes for granted the existence of such a world, and our ability to behold it through the power of thought. The objects in our world are instantiations (a kind of projection) of the relevant Ideas.
A Platonic outlook, or Platonism, is a stance that believes in the existence of abstract Ideas, of which objects in reality are concrete realizations. Thus, in our world there are horses, but in the world of Ideas there is the Idea of horseness, which is a kind of concept. According to Plato, the Idea is not merely a concept, but an abstract entity that contains the information about horses. The information included in the Idea is not all the information that exists in concrete horses, but only the information essential to something’s being a horse (if you like, the information common to all possible horses). There is a particular horse whose height is 2.10 meters. In the Idea there is no information regarding the height of the horse, since a horse’s height is an accidental datum not tied to its being a horse, and therefore it varies from horse to horse. It may be that some information exists there regarding the range of horses’ heights (a horse cannot be five meters tall, nor ten centimeters), but the height of a concrete horse is not essential to horseness. Thus the information contained in the Idea is the essential information that defines a horse as a horse—that is, everything without which the horse ceases to be a horse.
Between the Idea of Horseness and the Perfect Horse
People sometimes speak of the Idea as a perfect horse, but for our purposes this is a double error:
- The Idea of horseness is not a horse, not even a perfect horse. This Idea has no tail and no cells. According to Plato, an Idea is an abstract entity that, in some way, contains all the information that exists in concrete objects. Therefore it is incorrect to see the Idea as a perfect horse, since it is not a horse.
Note that for the same reason the Idea cannot be imagined—at least not visually. The Idea has no body and no bodily form. It is, in essence, a complex of information (including visual information; in the computer age it is easier to grasp this as a kind of file of information), but this information is embodied in an abstract entity that can be contemplated, from which one can understand the essence of concrete objects (the disk).
- Beyond that, the information included in the Idea is not information about a perfect horse but about a pure horse. For example, suppose the perfect horse in your eyes is one whose length-to-height ratio is the golden ratio. The Platonic Idea, in its ordinary sense, does not speak of such a specific horse (even though sometimes it is used that way). The Idea is information about a pure horse, namely a horse that has only properties essential to horsehood and not accidental properties. The ratio between its height and length is not essential information about a horse, and therefore it is not included in the Idea. The Idea includes information about pure horseness without the accompanying, non-essential features that appear in concrete horses. The criterion that determines which information is included in the Idea is not perfection but essentiality.
These two clarifications sharpen the meaning of the Idea in the Platonic picture. Since, in Plato’s conception, the Idea is also an entity, it is therefore useful, for what follows, to define two distinct objects: is the Idea of horseness, whereas is the pure horse (not necessarily perfect). The first is an Idea, and the second is an ideal object—that is, an object endowed only with essential properties and no additional ones. I do not intend to say that such a horse actually exists. This is a Platonic definition, but it differs in essence from the Idea. It is a different kind of Platonic entity that is not an Idea. An Idea is a collection of properties, and the ideal horse is a horse (even if abstract). If we suppose that the information in the file is information about the equation 2+3=5, then the information is the concept, the disk that contains this information is the Idea, and some representation of the equation (for example, a formula describing it on paper) is the pure equation. The instantiations of the Idea are different cases in which two objects join with three to form together a collection of five objects. Each such situation is an instantiation of the Idea.
We have seen that the Idea of horseness is not a horse, while the pure horse is. But there is also an inverse difference between them: the pure horse does not exist in any sense (it is an abstraction of a horse), whereas the Idea does. It has, of course, no mass and no position in space, but it exists in some sense.[1] Plato’s description of this sounds quasi-geographical: the Idea is located in the world of Ideas. But “the world of Ideas” does not describe any location in the universe; rather, it is a different mode of existence. Below we shall see the implications of this distinction.
The Dispute Between Plato and Aristotle[2]
It is commonly thought that there is a philosophical dispute between Plato and Aristotle regarding Ideas. Aristotle did not believe in the existence of Ideas, even though he too used categories—that is, a partition of objects in the world according to certain abstract properties. But Aristotle saw categories as abstractions we perform in our minds, not as existing entities. Plato, by contrast, held that Ideas are a kind of real entities; thus what Aristotle saw as an intellectual process of abstraction Plato saw as a kind of observation.
As an example, consider the Idea of horseness again. A person encounters many horses throughout life. At some point an understanding arises in him that there is some abstract Idea that defines the concept of a horse—the Idea of horseness. Aristotle sees this process as a mental process: abstraction and generalization performed by the human intellect. Out of the concrete horses, the person constructs for himself an abstract concept of horseness. Plato, by contrast, sees the crystallization of this insight as the result of observation. A person manages to behold (not with his eyes, of course) the Idea and to understand from it what horseness is and what is common to all the objects we classify as horses. From then on, the diagnosis of some object he encounters as a horse is made by comparing the object with the Idea of horseness that he beholds with the eyes of his mind.
The Basis of the Dispute
At first glance there is no reason to espouse a Platonic position. It looks like baseless mysticism. Why invent worlds and entities that no one has encountered and no one can encounter?! It is seemingly clear that this is an intellectual process of abstraction and not observation. So what, nevertheless, causes people (like me) to sail to the mystical realms of Plato? It seems to me that one of the main considerations underlying this stance is the question of taxonomy.
Throughout our lives we encounter many objects—non-living things, animals, or people—and we partition these objects into groups according to various categories. The question is how we should relate to these partitions. Thus, for example, we define the groups horses, donkeys, fish, birds, human beings, stones, liquids, and so forth. These partitions themselves are arranged on a hierarchical tree that determines a taxonomy of objects. For example, we may divide all objects in the world into four types: inanimate, vegetative, animal, rational; and each of these is divided into species, which themselves are divided into subspecies, and so on.
The question is: whence did these partitions arise? We could have divided objects quite differently. We could, for instance, have divided them according to their height, or according to the letters with which their names begin, or according to ARMA (compositions in different proportions of fire, air, water, and earth, as in the Kabbalah and Greek philosophy), or even simply collected them into arbitrary groups. In fact, why isn’t the partition I described above itself an arbitrary partition into categories? In what sense are these partitions “more correct,” or less arbitrary, than others? Do they claim anything about reality at all, or are they merely our subjective definitions—the manner in which it is convenient for us to regard the various objects in reality?
Aristotle would probably answer in terms of efficiency and intellectual effectiveness. The partition that helps us think about things and discover some kind of lawfulness in them is by sorting them into genera, species, subspecies, etc. This sorting is chosen for reasons of convenience and fit to our mode of thought, and perhaps also fruitfulness (we choose partitions that allow us to arrive at interesting laws). Our partitions are not truer than others in any essential sense. They are simply the most effective form for us.
By contrast, Plato sees these partitions as “natural,” that is, not something arbitrary. Reality is truly divided according to these categories. In other words: we did not invent them but drew them from reality. When I say that the object before me is a horse, I have said something about reality and not merely assigned it to a subjective definition born of my fevered brain. To be sure, to the same extent one can draw different categories from reality, like height or ARMA, and it is hard to see why we think that precisely these partitions are correct. Here Ideas enter the scene. Plato argues that the correct partition is one made according to categories determined by Ideas. Therefore, on his view, these are partitions that exist in reality itself and not only in our overactive minds. We contemplate the Ideas, and from comparing them with the objects before us we understand that among them are horses, donkeys, animals, liquids, inanimate objects, human beings, fish, and more. In this way we also see the relations and the taxonomic hierarchy among all these.
In the Platonic conception, all this is not our invention but the product of observation of the world of Ideas. It is forced upon us. Hence we all treat these partitions as natural and correct rather than arbitrary. For this reason, a contemporary Platonist would claim, our chemistry views all materials and objects as compositions of the elements of the periodic table, and not as blends in various proportions of the four Greek elements—fire, air, water, earth—or of Kabbalistic sefirot.
Our common feeling that there is a partition of objects that is more natural and correct than other partitions is the basis for adopting the Platonic picture and believing in the existence of Ideas. Without this we would have to regard all partitions as equally possible, and the adoption of one partition or another as arbitrary (perhaps stemming from our mode of thought and not anchored in reality itself). Therefore, in my opinion, this is not mysticism, but a demanded interpretation of our most natural and basic intuitions.
The only alternative to this “mysticism” is to relinquish those intuitions and to adopt an instrumental view that hangs these partitions on our accidental brain structure and on the explanatory effectiveness they have for us (because of that structure). This is Aristotelianism. According to Aristotle, other creatures constructed differently from us would likely use entirely different partitions, and they would be no less correct than ours. On his view there are, in truth, no horses or fish in the world. They exist only in our overactive minds. The objects of course exist, but the fact that they fall under the headings horse, fish, or rock is merely an arbitrary matter that derives from our mode of thought.
What Would Borges Say About This?
The Argentine writer Jorge Luis Borges was a one-of-a-kind literary and intellectual genius.[3] His wild imagination, vast and comprehensive erudition, and philosophical and intellectual understanding were truly extraordinary, and unfortunately he does not receive his due. In his collection Ficciones there is a story called “Tlön, Uqbar, Orbis Tertius,” which deals with the dispute between idealists and realists. Idealism (more precisely here, solipsism) is a view that does not believe in the existence of an external world. The solipsist sees all our impressions and understandings of the world as things that occur within us. For him there are no other people and no other objects, living or inanimate, besides ourselves. All events and objects are experiences that occur within our consciousness. Even if we are not idealists, we must admit that what we actually encounter are only cognitive impressions and not the things themselves. If so, says idealism, there is no reason to assume that there exists “out there” anything beyond these cognitive impressions. Occam’s razor is the solipsist’s totem, for it instructs us to make the fewest assumptions and posit the smallest number of entities possible. Solipsists use this principle consistently to the end (to a fault?).
The story describes a fictional planet named Tlön, which has been taken over by a group of idealists led by Bishop Berkeley (the well-known Irish idealist philosopher of the eighteenth century). Borges describes what transpired on that planet through literature (which he of course invented for the story) that documents it, and mainly through linguistic phenomena. It is one of the most brilliant depictions of this dispute, and the literary-linguistic illustration helps one understand it and its significance in depth (and above all the absurdity of the idealist view and its distance from our intuitions as reflected in our language).
Among other things, Borges describes the vernacular in one of Tlön’s hemispheres, in which there are no nouns at all. Instead of speaking of a moon rising over the river, they say: it-moons over the continuous flow. It is a language without nouns but only verbs and their inflections. The reason, of course, is that in the idealist/solipsistic worldview there are no objects; everything is mental occurrences within us. Therefore there is no moon, but there is the phenomenon of moon-ing (what we experience as the moon rising or dawning). There is no river, but only a phenomenon of continuous flow. From this you can understand that one cannot speak of a moon rising above a river, but of a moon-ing experienced above a phenomenon of continuous and persistent flow.
But Borges has further innovations, again presented through various linguistic expressions. He argues that in the language spoken in Tlön’s other hemisphere there are indeed nouns, but everyone knows they are a fiction. Therefore any collection of properties can serve as a noun. Thus, for example, when we speak of a ball, we mean the conjunction of the following properties: a round object, made of leather and filled with air. Alternatively, in our language, a bird is a living creature that flies in the air and has wings. By contrast, in idealist Tlön (regarding the prevailing philosophical views there) there are no objects; hence there is no impediment to defining nouns composed of a completely arbitrary collection of features—for example: the scream of a bird in the distance together with the color of the cloud that passed over my house at seven in the morning. That object can be called “Moses,” or, if you prefer, “Tzriḥanan.” In an idealist world there is no preference for objects defined “naturally” in our thought over these arbitrary objects. Our ordinary objects are, in their eyes, nothing but arbitrary constructions as well, so if arbitrariness is the order of the day, why limit ourselves to a “natural” set of properties?! No wonder, then, that any collection of properties can receive the status of a noun in Tlön’s language. There are countless “objects” (linguistic fictions) that arise and disintegrate instantly at the speaker’s breath.
Back to Platonism
The analogy between the dispute over objects and our discussion of Ideas is obvious. In an Aristotelian worldview there are no real Ideas. They are constructions of our thought with no anchor in reality itself. If so, there is no necessity to adhere precisely to the “natural” Ideas (or categories). In principle there could be an infinite number of Ideas and categories, and any creature or group can create categories for themselves at will (for example according to efficiency and fruitfulness) and use them—much like what happens among the idealists on Borges’s planet Tlön. Thus Aristotelianism arises. Platonism, by contrast, maintains that Ideas exist in reality (just as realists hold that objects exist), and therefore there are Ideas that exist and are correct, and other Ideas are arbitrary and do not reflect any truth, and hence it is not correct to use them. Natural intuitions reflect some truth and are not merely arbitrary constructions derived from the structure of our thought.
Incidentally, one could draw another analogy with the dispute between conventionalism and essentialism regarding concepts. The conventionalist sees a concept as our arbitrary and free creation, whereas the essentialist, by contrast, understands that the concept is formed through observation of the Ideas. A concept is essentially a kind of Idea, and so this is almost the same dispute as the one described above. For example, the concept democracy includes several features: a state with separation of powers, an elected government and a change of government every few years, civil rights, and so forth. The conventionalist sees this concept as arbitrary: one collects several features and assigns a general name to that collection. In his view one could also define the concept plutkoverbatzia (just a coinage of mine, of course) to describe states that are on a seacoast, cultivate peaches, and have more than five million inhabitants. However, that definition is neither useful nor fruitful, so he will not adopt it. The essentialist, by contrast, sees the concept democracy as a kind of reality. It is a natural concept, even though it was not known in the past. It was not created in modern times but discovered in modern times—or realized then. But the Idea existed somewhere in the world of Ideas even earlier (at least since the blessed Plato created it). Concepts that do not exist in the world of Ideas are not natural. Of course, in his view one can define an unnatural concept like plutkoverbatzia for practical and fruitful purposes, but it is an arbitrary definition.[4]
The Third Man Paradox[5]
In one of the later Platonic dialogues, Parmenides, Plato describes an encounter of the young Socrates with the old Parmenides. By means of a logical argument and a series of questions, Parmenides attacks the idea of a pure world of forms (a world of Ideas) as opposed to our world, which, according to Plato, is populated by shadows and imitations. He asks about the relation between the form and its appearances in our world. One of his main arguments is called the “Third Man Argument” (TMA), which to this day receives elaborate logical and philosophical treatment and arouses not a few disputes.[6]
I shall present here one formulation of it, following more modern analyses:[7]
We observe a set of objects, {x, y, z…} of the same kind. They all possess the same set of essential properties, for example, human beings. We denote the set of human beings by {H}. There are different people who belong to this set: x, y, z ∈ H.
What defines this set? Anything endowed with the essential properties (the form) of human beings belongs to the set. It has a brain and a heart; it recognizes, speaks, remembers, and thinks; it laughs and wills, etc. We denote this set of properties as: {}. This is essentially the definition of the concept “human being.” Beyond this, of course, each person has additional accidental properties that do not enter our account (such as height, gender, or skin color).[8]
Thus our real objects have the following properties:
x() ; y() ; z()
Each of them has all the properties of a human being, and in addition it has accidental properties that may differ from one to another.
Let F be the Platonic Idea of a human being; according to Plato, the form F is an existing entity. What are this entity’s properties? Parmenides argues that they are precisely the essential properties listed above: {}, and only those (because it is an Idea—recall the purity criterion mentioned above).
But if the Idea F has those properties, then it too belongs to the set of human beings (since any object that possesses those properties belongs to the set): F ∈ H. Assuming we had two human beings in the original set, we now have a third man (hence the name of the argument). According to Aristotle this of course does not happen, since in his view the Idea is not an entity but a mental abstraction.
Now we have before us a new set of entities: {x, y, z, F…}, all of which form the set of human beings. We repeat the process for this new set. The properties that characterize it are the same properties: {}. The new Idea (Parmenides presumes in Plato’s name that each distinct set has its own Idea) of this set is F′. Clearly this Idea too has the same properties, and therefore it belongs to the set, and we obtain a new set: {x, y, z, F, F′…}.[9] And now the process is repeated again, and so on ad infinitum.
This means that there cannot be a single Idea of a human being. There are infinitely many distinct Ideas, all of which have the same properties. Moreover, the set of human beings is also infinite. What is the problem with this? Some see the problem in the conclusion that the Idea of the set of human beings is not unique (Plato presumably assumes it should be unique). Others see the problem in the very assumption that there are infinitely many human beings (or infinitely many entities in general, which itself is problematic).[10] Still others see the problem in the fact that there are countless different Ideas that have exactly the same features. In what, then, do they differ from one another?[11]
I note that Aristotle himself saw the Third Man as one of the essential pitfalls in the Platonic doctrine of Ideas, and thus one of the proofs for his own position.[12]
Several Problematic Assumptions in the Third Man Argument
In light of the picture we described above, this argument appears completely refuted. First, Parmenides assumes that every set of objects uniquely and unambiguously defines a single Idea. It is not clear on what this assumption is based. On the contrary: the Idea of human beings describes every set of human beings—those who were here a thousand years ago as well as those who are here now, human beings living in Haifa, or human beings living in eastern Tokyo. All these have the same Idea as human beings. Of course they also have another Idea (with further specific properties beyond being human) as residents of Haifa or Tokyo. Any object can be included under several Ideas (and this is usually the case; it is hard to think of an object with only one property). Thus, for example, a table is also red, also has four legs, and is also made of wood. Each of these properties is an Idea: redness, being made of wood, having four legs. The concrete table is an instantiation of each of these Ideas, not just one of them. Therefore, even if we add the Idea F to the set of human beings, the process ends there. The Idea F′ is not different from F. It is the very same Idea.
But beyond this, the entire strange argument rests on a major error, and that is why I brought it here. Parmenides assumes that the Idea is also a human being, since it has the properties that define humans. Yet above I noted that horseness is not a horse (pure or ideal) but something entirely different. So too the Idea F is not a human being, and hence it cannot be added to the set of human beings. It may seem that it has those properties, but it does not have matter of the human sort. The set of human beings is a set of objects that have human matter, and each has the collection of essential properties of human beings. The Idea has only the properties of human beings but not the matter (it is not a material entity). Although for Plato the Idea is an existing entity, its “matter” is not biological, and therefore it is not a human being.
Even this is too generous a formulation. One can see that Parmenides’ mistake is far more egregious: he is not correct in assuming that the Idea F has the properties of a human being. The properties are features of human beings, but the collection of properties that constitutes the Idea did not produce a human being. Therefore the properties contained within this collection are not properties of the Idea (i.e., properties that characterize it), but properties contained by it. Think of the set of properties that generates the Idea “tableness”: {red, made of wood, having four legs}. We have already seen that this set of properties is not itself a table; hence it is also clear that it is wrong to say that this set of properties is made of wood or that it is red. The properties contained in it are not its properties. Thus the Idea of size is not big, and the Idea of horseness has no four legs (and cannot be ridden). The form/Idea of a triangle has no angles. The property “having three angles” is one of the features contained in it. By the same token, the Idea of “human-ness” has no intellect. This Idea includes the property “having intellect,” but that property itself has no intellect. The Idea of “human-ness” does not think; it includes the Idea of thinking (=having thought).
More generally, properties characterize objects, not Ideas. The most basic error underlying the Third Man is a conflation between (which is the Idea of a human being) and (which is the pure human being—one endowed only with the essential properties of human beings). These two things are “objects” in a certain sense, but the first is an Idea—an existing object that is not a human being—while the second is an abstraction of a concrete object; it is indeed a human being, but it does not exist.[13] The first does not have the properties of a human being (rather, they are contained in it), but the second does (it is characterized by them).[14]
[1] To sharpen the point I add here that even a photon (a single quantum with a defined and unique wavelength) exists in a physical sense although it has no position in space and no mass. Therefore not every object that lacks position and mass is an Idea. The converse, however, is true. The photon interacts with other entities and affects physics; Ideas do not. They exist in a parallel world (of which our world is a projection).
[2] Important disclaimer: I am not an expert in Greek philosophy and have hardly dealt with it. As is known, the only place in the world where one currently tramples the Sages’ injunction and studies Greek wisdom is in the yeshivot (when studying the philosophy of Maimonides or Saadiah Gaon), and I, a small person, am exempt from the urge that leads people to this “transgression.” From this you will understand that everything I write here about Plato and Aristotle is not authoritative information but the product of my limited acquaintance with their ideas. But I am not much concerned to verify the precise views of these righteous figures. I merely use them here to present, side by side, two positions that are the subject of my interest. Platonism and Aristotelianism in this column are positions defined by me, not necessarily what Plato and Aristotle actually thought. I am fairly sure it is close, but I do not wish, and cannot, to commit to how close.
[3] I recommend reading his stories, and also reading about him in Leo Corry’s book, The Literary World of Jorge Luis Borges, in the “University on the Air” series.
[4] One could also say that if such a concept is fruitful, this is an indication that it is a natural concept with an existing Idea. An artificial concept will not be fruitful. I am not sure this is correct, though it is not implausible to me.
[5] The subject is discussed in Part III of Volume 11 of our “Talmudic Logic” series, The Platonic Character of the Talmud.
[6] 131the–132in, in the Libes translation, vol. 3, pp. 17–18.
[7] See: Pelletier, F. J., Zalta, E. N., 2000. “How to Say Goodbye to the Third Man.” Noûs 34, 165–202. For a broad survey see Palmer, John. “Parmenides.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. Summer 2012. http://plato.stanford.edu/archives/sum2012/entries/parmenides/ and the sources cited there, especially in chapter four.
[8] You can immediately understand that there can be views that see skin color or gender as essential properties, and therefore see the set “human beings” as an arbitrary combination of other natural sets: black-skinned, yellow-skinned, and white-skinned. From here discussions of racism, chauvinism, etc., may grow. The connection between Platonism and all these will be discussed below.
[9] By Leibniz’s identity of indiscernibles, the two entities F and F′ are one and the same. They have the same properties, and two entities that do not differ in their properties are the very same entity. But in several places I have argued that Leibniz is mistaken, and therefore here too we assume these are two distinct entities with the same properties.
[10] If there are infinitely many existing entities, then we are dealing with an actual infinity and not a potential one. But philosophers and mathematicians usually assume that the notion of infinity must be potential and not actual; otherwise paradoxes arise. See the Wikipedia entry “Hilbert’s Hotel.”
[11] This is, of course, a Leibnizian view, but in the previous note we already saw that this formulation of the argument relies on an opposing conception.
[12] See his statements in Metaphysics (trans. Chaim and Hannah Rosen, Magnes, 5747) VII–IX 1039a2, p. 65, and also XI 1059b6–10. The label “the third man” comes from his description in Aristotle’s words. See Metaphysics XI 1059b6–10:
They place the intelligible objects as a kind of third things, in between the forms and the perceptible things—some particular third items in addition to the forms and to what is here-before-us; but there is no third man and no third horse in addition to the form itself and those in each case.
[13] About it one can certainly say that it has the properties of a human being, even though it does not exist—just as one can speak of the properties of fairies or of any literary beings. There is no impediment to discussing the properties of Raskolnikov, the protagonist of Dostoevsky’s Crime and Punishment, even though such a person never existed in reality.
[14] In the aforesaid book we formulated the Third Man paradox for instead of , since for it one can indeed formulate the argument as presented above (for the pure human being does have human properties), and we showed that even there the regress does not arise. It is quite easy to see that in this case the Idea F′ is the Idea F; and, of course, here too F should not be added to the set of human beings, for it is a pure human being and not a concrete, existing person (this is in contrast to the Idea, which does exist in the world of Ideas).
Discussion
The opposite, Guta.
In Judaism, the “spiritual” (the divine, etc.) can be embodied only through the concrete text, which consists primarily of practical commandments and was given to a particular people within a real history. Exactly as Aristotle’s form can exist only insofar as it is embodied in concrete matter.
And the test: take the material substrate away from the formal-spiritual thing (the Torah), and it becomes meaningless.
Have I weakened?
Correctionette: the formal-spiritual thing (the divine).
Doron
The Torah belongs (at least in the hava amina) also to the angels; the proof is that they argued with Moses about it. So when you take the materiality and concreteness away from the Torah, the Torah remains in its purity, only without the expressions of this world.
Dvir
From what you’re saying, I understand that if I argue with you about the Ferrari you bought with your own money, then it’s mine too. Works for me.
Besides, I have no idea what hava amina means.
Plato’s ideas are the shadows of psychological processes.
Whoever believes in ideas is chained in the cave of ideas, not understanding that these are shadows and that there are other things causing them.
Hava amina = initial assumption.
If you argue with me about my Ferrari, that means there is, by definition, no problem with your having a Ferrari. Otherwise the argument is foolish.
The fact that the angels argued with Moses means that Torah is not something that belongs specifically to this world by definition. Rather, Torah can also belong to angels.
Now everything is clear. I’m convinced.
A. According to you, an idea is the common denominator of all horses. But seemingly there could also be an idea of objects that have no common denominator among them (a necessary and sufficient one), for example an idea of a creature of the type “horse or dog.” You referred to the fact that there are many horses (“I encounter quite a few horses”); the question is whether, if there were only one horse in the world, there would be no idea, or only that people would have a harder time identifying it (separating the essential from the accidental). It’s not clear to me why one needs to deal with many horses and define the common denominator; seemingly one could/should deal with the idea of horseness even on the basis of a single horse.
B. What is a pure horse? A horse has a height of between 10 and 500 cm; what does a pure horse have? This abstraction is not clear. I also didn’t understand what is meant by the words that the pure horse is a horse. But since according to you the pure horse does not exist, maybe there’s no point in dealing with it.
D. You lean heavily on abolishing the partition between thinking and cognition. But the idea that consciousness receives information coming from abstract objects is itself hard to grasp: how, when, and why certain abstract objects appear before the eyes of the intellect. This idea of horseness—how does one examine it, and what is the meaning of the connection between it and examining a concrete Rocinante? This does not seem like an intelligible thing to me (though I still haven’t managed to form a stable opinion on the matter). And this is what bothers me most in the whole idea of Platonism.
E. At the end you hinted that realism has an implication. First of all, I like implications (as long as they’re not in the psychologistic sense). I understand that the intention is that, for example, everyone agrees that human life is important, and they ask whether a fetus is a human being or not; that is, the moral question depends on a conceptual question. I heard something like this from you in connection with the moral question regarding targeted killing. But I think that categorically this conceptual-ontological discussion is *incapable*, under any normal and sensible conception of morality, of producing moral directives. The question is whether the life of a fetus is important, and one cannot smuggle the moral claim under the cover of the ontological claim; it is simply irrelevant. Even if it is a “human being,” the moral question will remain whether the life of a human being who is a fetus is important. As far as I can think, I see no possibility of deriving a normative implication from a realist view. Therefore realism functions only as an explanatory matter, without implications (normative or even predictive) regarding unknown things. I seem to recall that in another answer on a different matter you called a unique explanatory proposal for something not under dispute “a practical difference in retrospect,” and if you indeed think so then I’ll continue (unless things will be clarified in the next post, in which case I’ll wait and see).
C. I haven’t begun to understand the argument from taxonomy. And I also don’t understand (and I also didn’t understand in Two Carts) what Borges wants from life. My intuition (her name is Yocheved) does not say that there is an idea of horse, but that there are many animals in all sorts of shapes and with all sorts of properties, and some of them I group under the name “horse” for considerations of similarity in their properties and relations to one another. True, what I said here is only a declaration, but let it be on the record.
V. I still need to think more about the Third Man issue.
Z. Who has kept us alive, sustained us, and brought us to this time :). Too bad there wasn’t a Telegram update about this post.
With God’s help, 1 Iyar 5780
If Aristotle recognizes only tangible beings—does he then not accept the existence of God? And if he does accept the existence of an abstract God—what prevents him from assuming that the abstract God also created abstract entities?
With blessings, I-Don’t-Know
A-B. I didn’t understand. “Horse or dog” has no idea, because that is an artificial creature like Borges’ creatures. It is an invention and not something from reality. If there were one horse in the world, there is no obstacle to there being an idea, except that then we would not arrive at it. When I say the common denominator of all horses, I mean all the horses that can be conceived of or could exist, not only those that actually exist. Therefore the pure horse is also a horse in that sense.
C. If you don’t have an intuitive feeling like the one I described, then indeed you are Aristotelian. If in your eyes I am not a human being but a collection of molecules, and my definition as a human being is arbitrary because it is convenient for you, then we have a disagreement. If you do not see the difference between a chariot-horse and a bird beyond my subjective matter, then again we have a disagreement.
D. I didn’t see a question here, and I also don’t understand your difficulty.
E. I don’t remember what hint you are talking about. I agree in principle, and I even wrote this in my article on organ donation (what practical difference does it make whether brain death is death or not? The question is whether it is proper to kill such a person for the sake of another). But still, the definition of the concepts reflects the moral implication; that is, if it is not proper to kill such a person, this will be expressed in the ideational view through the fact that I will “see” that such a person is not alive.
Z. I didn’t understand about Telegram.
As I said, I am not an expert on Aristotle. But I do not see the difficulty. Aristotle does not claim that abstract entities cannot exist. He only claims that there is no reason to assume their existence if there is no necessity for it.
A. If I understand correctly, you claim that there cannot be an “or” in an idea (a horse is condition A and condition B and also “a spot on the nose or a long ear”), because then there is nothing common to all of them. If that is indeed what you are claiming, then why?
B. I’ll drop (with a sigh) the matter of the pure horse.
C. Conscious entities like a person, a horse, and a bird are a bit different, because consciousness really is one thing that presides over a collection of particles. Let’s talk about a bottle cap. Is there a separate essence called cap-ness that somehow rests upon a certain collection of particles, and that is what unifies them (I don’t understand what I’m writing here), or are there just some particles here that together behave in a certain way, and therefore it is convenient to think of it and call it a cap? That’s regarding a single cap, and the same applies to a collection of caps.
E. Indeed, not “at the end” and not “hinted.” I wanted to refer to the end of note 8 regarding a possible connection between racism and Platonism. What you wrote I either do not understand or do not agree with. Maybe one can extract morality from contemplation of the concept of the good and the right, but not from contemplation of the concept of life. It may be that a brain-dead person is “alive,” and yet there is still no moral problem in ending that life. What creates that dependence?
Z. There is a “Telegram channel for post updates” through which I keep updated on new columns. For this column (and the previous one), for some reason no notice arrived, and I only learned it existed when I saw a comment on it in the list of recent comments. The last notice is for column 381.
A. It seems to me that you too understand perfectly well the difference between “or” ideas that have no real basis. But one cannot give an answer to your question. The only answer is that I “see” (in my intuition) that there is no real idea here. This is exactly what Borges describes.
C. I tend to think there is an idea of cap-ness.
E. I answered. In principle one can say that his definition as a human being contains within it the prohibition against killing him. But as I wrote, I agree with the substance of your words (I referred you to my article in Techumin).
Z. I passed it on to Oren.
With God’s help, 1 Iyar 5780
Even a person who skillfully creates some work of art acts out of an idea standing before his eyes, which his action in matter comes to realize. All the more so it stands to reason to say this about the Creator of the world, whose material creations come in order to actualize an idea, a thought that precedes its execution.
An additional indication that physical being is a tool for realizing a spiritual idea is that material bodies undergo a constant process of “metabolism,” “one generation goes and another generation comes,” yet humanity as a whole remains and develops. The rivers go to the sea, but the sea is not full. Some of its waters evaporate and return as rain, once again channeling water to the sea. The molecules of the rivers and the sea are constantly being replaced, yet the water cycle remains stable.
Another indication of the existence of an “idea” underlying physical reality is brought by Plato from the fact that souls find incomparably greater satisfaction in spiritual values—wisdom, goodness, justice, beauty, etc.—than in the fulfillment of any material desire. And as our Sages say, the soul finds no satisfaction in all the pleasures of the world because it is a “king’s daughter” from the heights above.
With blessings, Ami’oz Yaron Shnitzer
A. Let’s leave aside the example of horse or dog. You claim that in all ideas there is no component of “or.” I do not understand why such a component could not exist, and why you need such a claim at all—that the idea is the intersection of all horses.
In note 13 you ascribed properties to literary entities. Do you mean that the entity was suddenly created in the abstract world by the power of the writer’s thought? The alternative non-Platonist view is of course self-evident, and it is not clear to me whether you departed from it, and if so, why. This interests me especially because of a certain personal twist, as follows. When I was a child I read many books (stories), and in every book, every night, there came a stage when I already wanted to sleep but found it hard to fall asleep from curiosity. One night I realized that it made no sense that the author got to decide the continuation more than I did. I too could decide the continuation exactly as he did! So in no time I imagined a continuation in which all the plot threads were severed in an optimal and wondrous way and everyone was happy and content. Then, calm and satisfied, I went to sleep. And since then I kept using this miracle cure every time. It may sound ridiculous, but psychologically it really did soothe my curiosity. A childish thought that affected me very, very deeply over time. Among other things, within a few years (not immediately, for some reason), sadly my capacity for enjoying stories and films was badly damaged. I can’t stop thinking about the screenwriter and the author and feeling the arbitrariness, and reshaping things by the power of thought and imagination. As a matter of direct feeling, I stopped “immersing myself” in books (literature), and the experience changed significantly into that of a curious observer from the outside (much less fun). I classify this matter under the category of thoughts that should be suppressed and repressed, but that doesn’t really work for me, and somewhere I’d be glad to get rid of it (whether rightly or not). My nose tells me that from the connection you drew between Platonism and the properties of literary characters I might derive something.
First, regarding Telegram, you need to contact the channel administrator there. It is his initiative, and we have no connection to it.
I did not state categorically that there is no “or,” only that usually, if there is no essential connection, then there is no idea. For example, a democratic state can be seen as an “or” or an “and” (there are several models of democratic states): the intersection of all horses is not a definition but a result. If these are the essential properties that characterize horses (without which they are not horses), then they will appear in all horses.
Literary entities are further examples of realizations of the idea, but not in the real world but in an imaginary world. A pure horse is an imaginary entity, but it is a horse and is characterized by the characteristics of horseness. I didn’t understand what you are asking about this..
A. You say that you did not state categorically that there is no “or,” and while saying so you return and state exactly that. What is the principled problem with the essential properties that characterize (and only characterize) all horses being, say: 1. four legs 2. a drooping belly 3. a spot on the nose or a long ear. If these are the essential properties, then this will not come from the intersection of all horses. I don’t know why you returned to the pure horse, but I don’t understand what that means at all and cannot deal with it.
Maybe you can share with me what your experience is in reading a storybook or watching just an ordinary movie that tells a story. How do you free yourself from the little voice that everything is completely arbitrary? If in the story the character failed to catch the train and is disappointed, one can simply think that he did catch it. From the idea that the author does not control the story one arrives at the idea that there is no “story” and no “character,” and the whole literary thing simply dissolves.
A. Now I understood the objection. In principle you are right; I do not accept an “or,” because otherwise it is not one idea but two. True, you can define the idea of animals, which includes within it two-legged and four-legged creatures. In such a case there is an idea of a two-legged animal and an idea of a four-legged animal, and the idea of animal as a whole is “or” this or that.
I experience no difficulty at all. I do not need to think it is real in order to enjoy it. A situation has been painted for me and I enjoy it. So what if it could have been otherwise? And in general, it seems to me that one should free oneself from the detached intellectual gaze in order to enjoy. If you enter the situation and forget that it is a story, the question will not bother you.
There is enjoyment in the situation, like seeing a beautiful picture or eating Bamba. But there is no curiosity and no sadness and no joy and really no emotions at all. Only the beauty of the picture remains, and a collection of interesting reflections that good writers always scatter along the way. Because when relief comes from the fact that the sick person recovered, the thought immediately attacks that “just as easily” he could have remained sick. Curiosity about what will happen next becomes completely meaningless. This is a very significant (negative) change in the reading experience. Clearly one ought to free oneself and forget that it is a story; that is the whole problem, and it turns out that this is not easy. I thought that perhaps a Platonic philosophical conception of literary characters might help in this matter.
Platonism believes in the existence of ideas, but not in the illusions of inventing ideas where there is explicit fiction.
What is meant by discussing the properties of a literary character like Raskolnikov? To say that if there were a person who behaved like the character, then he would probably have the property of psychopathy? To say that the property of psychopathy is a successful first-order approximation of what the author had in mind when he created the character? To say that the author, with great talent, hit upon an abstract character that already existed before him and has those properties (which is something I do not understand, but let’s assume it)? Why is the subject of properties of literary characters in a column titled Platonism? By the way, about that book itself there is a lot to discuss, and perhaps its day will come.
It was an example for the claim that even nonexistent objects have properties, as distinct from an idea, which is an object that does exist and has no properties.
Ugh. Please delete.
Could I get an explanation for the statement that even objects that do not exist have properties?
I don’t know whether that is a statement. Maybe it is a claim and maybe a definition. I have nothing to explain about it beyond the obvious. A character in a book has properties. That is obvious, no? You assume that properties characterize only existing objects, but I don’t see why to restrict things that way. And again, it seems to me that this is a definition, and therefore one should discuss the implications and not the definition itself.
What implications could this have? I still haven’t read the article on organ donation, but for the time being I understand in general that the question of realism yes or no has no normative implication, and no other implication either. An interesting ontological question and no more. But if there are implications, by all means. (If the character did exist, then there could be a psychological implication for the reading experience.)
A sentence like “Peter Pan is mischievous” I understand roughly as follows: “The actions attributed to the character Peter Pan are actions characteristic of people with the trait of mischievousness.” A sentence like “Peter Pan wears a green shirt” means “The author wrote that Peter Pan wears a green shirt.” Do you interpret these sentences differently?
Regarding the Third Man there are implications (whether one can quantify above it). But later I will address possible implications, such as, for example, what the commandment to love one’s fellow or to hate the sin/sinner is directed at. Is there such a commandment if there are no sinners at all (to hate the sin and the idea of the sinner), or if there are no Jews at all?
To the nice and mysterious person who manages the Telegram channel for updates about posts from this site (the channel “Rabbi Michael Abraham RSS”), if by chance you see this message—it seems you send messages manually when you notice a new post comes out (which is why the last two columns were missed). If so, that’s a shame. It is very easy and convenient to send automatic messages on Telegram. If you happen to read this message, please respond here and we can automate it together (a matter of minutes).
With God’s help, ערב יום העצמות 5780
R. Joseph B. Soloveitchik distinguishes, in the existence of a nation, between a “covenant of fate,” based on the shared fate of the members of the nation—a fate that brings the collective to the need to unite in order to provide for the existential needs of all the individuals—and, by contrast, a “covenant of destiny,” in which the nation coalesces for the sake of an idea that the nation is going to bring into effect.
Similarly, Rav Kook distinguishes between the conception that the state is a “great society of responsibility,” whose purpose is to promote the welfare of individuals, a welfare that cannot be achieved without cooperation; and, by contrast, the conception of the “State of Israel” according to the Torah, as a state whose destiny is to be “a kingdom of priests and a holy nation,” to proclaim the name of God in the world and spread the faith of the Torah and its values in the world by creating a model society that will be “a light unto the nations.”.
As we conduct our “annual soul-searching,” the conception of the state as “the foundation of God’s throne in the world” places upon us a far greater demand: not only to examine whether what is being done here is “good for the Jews,” but to examine to what extent we are advancing toward the destiny of providing an example to the nations of the world.
At one point this year we merited to provide a positive example to the nations of the world: in our ability to recognize quickly the seriousness of the danger of corona, and in the relatively rapid protective response through the vaccination campaign that vaccinated the vast majority of the state’s residents, an achievement that one can only wish other countries would come close to.
With blessings, Ayin-Sham
There is a WhatsApp group for updates on posts and lessons only (no discussions). Recommended—
There are likewise, among the wedding blessings, two parallel blessings that ask God to gladden the groom and bride,
The first blessing emphasizes the existential side. Here there are two “beloved companions,” whose joy lies in the sense of a person and his wife as being “in the Garden of Eden of old,” when each saw in his or her spouse his or her entire world, the lost rib completing him into one flesh.
But after it comes the blessing that sees married life as the realization of great ideas, ideas of “joy and gladness… love and fraternity and peace and companionship.” Ideas that the marital bond comes to bring into effect in real life. For the building of peace and unity in one Jewish home is not only their personal-private joy, but the laying of foundations for the building and redemption of the whole nation, toward the state in which “the cities of Judah and the streets of Jerusalem” will once again be built, and there will again be heard “the voice of joy and the voice of gladness, the voice of the groom and the voice of the bride..
The natural existential joy, combined with the deep insight that personal joy is one brick in the rebuilding of the love and fraternity of the whole people of Israel—these are what make couplehood deeper..’.
With blessings, Ayin-Sham
With God’s help, 4 Iyar 5780
It seems that Plato’s words—that the reality perceived by the senses is only a “shadow” of something abstract—are close to Kant’s statement that a person cannot know “the thing in itself,” but only its phenomena.
With blessings, Yaron Fishel Ordner
Thank you very much, an interesting article. I just wanted to say that I did not understand a fairly basic point in Borges.
As I understand it, the claim Borges presents is that idealist conceptions do not really accord with our most basic intuitions, to the point of absurdity, and therefore we have no reason at all to accept them. (He does not present a better proof, though it is not clear that one is needed or possible).
But I could not understand how he deals with the simple difficulty presented by Berkeley following Kant, that in truth all that is revealed to us is only sense data, not the phenomena themselves, given that we are the ones perceiving.
And so, finally, why is it not true that the mind does not experience the object as such, but only its appearances *in verbal form*.
So that indeed the language appropriate for us to speak should not be one with nouns but only with verbs and their inflections, like the phenomenon of “moon-ing”? Or other verbs that are carried out in our sensation in a mental form.
We simply assume that behind those phenomena stands a real object represented through them, but this is an axiom that the mind translates for linguistic use.
I will allow myself to answer.
If everything is in “verbal form,” then that means our discourse too is only “motion” or “becoming.” This is a return to Heraclitus and the paradoxical idea that nothing has stable and fixed meaning, since “everything flows” (including this statement itself).
In short, it is an idea that cancels itself on the spot.
Therefore in practice no one really holds this idea seriously.
But in terms of truth, isn’t that formulation the one that reflects most correctly the idea of perception?
And perhaps it is not either Plato or Aristotle, but rather like a continuum between them? The process begins in our head, but after all we are a portion of God above.
Thus language can be both conventional and essential, and there is no contradiction in that.
The whole fun is precisely the opportunity to be exposed to what passed through this particular creator’s mind. That’s what is intriguing. You really get into a person’s mind..
Therefore, in my opinion, one must not detach the work from the creator, otherwise everything really is arbitrary.
In my opinion, following Plato, it is impossible to make claims at all that do not rest on the assumption that there is an absolute fixed foundation in reality (more accurately: a fixed foundation that exists beyond revealed reality).
It follows that all our perceptions are a mixture of a temporary and changing element found within us (and perhaps also in the phenomena) and an eternal element beyond what is revealed.
Any other claim immediately loses its internal coherence (that is, it becomes meaningless).
Why “following Plato”.. Plato merely managed to formulate partially what we already knew before him..
Einstein too, with that relativity thing of his, only managed to formulate partially what everyone who opened a chumash with Rashi already knew before him
Through sense data we encounter reality itself. One can of course raise skeptical claims, but that is how one understands things with common sense.
Now I just saw it, N. This matter troubles me quite a bit. Obviously the creator knows how to paint more interesting and beautiful situations than I can fantasize. But curiosity about what the creator will decide to write is not the kind of curiosity (“what happens to the character”)—gripping, electrifying, and absurd. Great writers, of course, still pad the whole book with little gems of interesting human observations and rounded, magnificently built characters even without there being interest in the complete plot as a whole. There are many examples, but for me, for instance, The Death of Ivan Ilyich is a prime example that is all fragments of little reflections. The shift from focus on the whole (in the naïve period) to mushroom-picking between the paths (in the current period) is, truth be told, a bummer.
And by the way, regarding the general theme of evil actions for the sake of a utopia (the road to hell is paved with good intentions, in the follow-up column to Platonism), I have a sense that it is a common theme. Right now I only remembered—and let the בעלי תריסין forgive me—that in Harry Potter, in the last book, it is told that Dumbledore, the admired wizard, flirted in his youth with a dark wizard friend who preceded Voldemort, whose slogan was “For the Greater Good,” which he engraved on the huge prison he built to imprison all his opponents. And in the book there, Dumbledore’s repentance from justifying local evil deeds for a globalist utopia is presented as a sharp decision between evil (that wizard, and the early Dumbledore) and good (the later Dumbledore).
Regarding what you wrote about the proof from taxonomy:
“The only alternative to this ‘mysticism’ is giving up these intuitions, and adopting an instrumental conception that hangs these divisions on our accidental mental structure and on the explanatory effectiveness they have for us (because of that structure).”
I wanted to ask in what way these intuitions differ from other intuitions—for example, the intuition that what I see in the world really exists there. That is, I do not understand how the mere existence of intuitions leads you to conclude that there must be some idea in the world that justifies them. It is simply true, that’s all. Without any ideas.
The question is what the basis is for the fact that certain classifications seem to all of us to be ‘correct,’ and in what sense they are correct. This is simply how we are used to thinking. When some claim seems to us ‘correct,’ the meaning is that it corresponds to some state of affairs in the world itself (this is what the statement “claim X is correct” means = it correctly describes the state of affairs in the world). Do you have criticism of someone who would classify animals differently and not agree with your classifications? I certainly would criticize him, and I would say that he is not grasping something in reality.
I agree with everything you wrote; I just don’t understand how what you wrote yields the conclusion that ideas exist. This intuition can be correct even without ideas existing. Just as my intuition that my eyes are reliable is correct without there being something in the world that must exist as a result.
The question is whether concepts like fish or mammals exist in the world, or whether these are our mental categories?
With God’s help, 15 Iyar 5780
According to R. Tzvi Yehuda Kook (cited in ‘Wikipedia,’ entry ‘The Course of the Ideas in Israel,’ note 7), the words of the Zohar that there are among the sages of Greece those who are ‘close to the path of faith’ refer to Plato, who believed in the spiritual foundation within creation.
With blessings, Yefa’ur
It may be so and it may not, but how does that connect to the matter of the intuition regarding taxonomy? That is, this intuition may be correct, and yet there is still no existence of such concepts as abstract “entities.”
Does the creation story, which says that they were created before man, change anything about this question? At least according to that myth, if one accepts it, their existence does not depend on man. Therefore it is possible that they are not only mental categories. At the same time, man is called upon to give them names. Taxonomy. The midrashim that accompany this story speak about names that coincide with existing ideas.
In the end, the existence of entities and ideas is a question of faith in some creator and in creation, no?
I hope I managed to clarify myself. Sorry for bursting into this dialogue.
With God’s help, 15 Iyar 5780
To 39 — Greetings,
To strengthen your words: from the Torah’s words “And God said, Let there be light,” it is proven that the concept of “light” preceded its actual existence. The end of the deed is first in thought.
With blessings, Yaron Fishel Ordner
Oren,
I do not know what more I can add. I explained what I had to explain.
Taxonomy,
I did not understand your claim. Are you claiming that if the ideas were created before man then they exist? That is a tautology.
Yaron,
I assume you know Rabbi Zevin’s article, “According to the Views of Beit Shammai and Beit Hillel.” One of the examples he brings there is the Vilna Gaon regarding “Creator of the lights of fire” / “light of fire.” His claim is that “the lights of fire” is fire in actuality, and “the light of fire” is singular because it refers to the power of fire as such (the idea).
I thought that perhaps this is the message of the creation story. There are ideas, there is a world, and there is man. So in the end this too boils down to a matter of faith.
Following Oren’s words, an innocent question: is it correct that the argument from taxonomy does not recognize “similarity” but only “identity”? That is, two things are similar if and only if they have an identical common component. Therefore, in order to identify that two objects are both “fish,” there has to be something identical shared between them (namely the idea), and it is not enough that they simply be similar in various respects.
I think that is true even apart from what I said
You wrote above:
“Do you have criticism of someone who would classify animals differently and not agree with your classifications? I certainly would criticize him, and I would say that he is not grasping something in reality.”
I claim that I could criticize him even without there being some idea of correct classifications existing in the world (that is, he is not grasping something, but it is not something that exists in reality). That is, for something to be correct and open to criticism, there need not be some existing entity in reality to give it an anchor or validity. For example, I claim that one should trust our intuitions. And if some person were to claim otherwise, I would criticize him. And yet I do not claim that those intuitions must exist in reality in order for us to trust them.
But your intuitions speak to you about reality; otherwise there really is no basis for criticism. Against what are you comparing the taxonomic claim in order to know whether it is correct or not? Classification is a subjective matter, and there is no correct or incorrect here unless there is an idea.
It is an understanding that I intuitively understand to be objectively correct, without comparing it to something in reality. I am trying to understand why you assume there must be an idea or a comparison to something in reality in order for something like this to be justified. After all, there are many other intuitions of yours that you accept as correct without their being compared to something in reality. For example, the intuition that accepts your tools of thought as correct. Is there in that intuition some comparison to something in reality? Or some existing idea that backs it up?
In my opinion there is no such thing without comparison. If you think your senses or your tools of thought are reliable, that is based on comparison to reality as such. “Reliable” means they correctly reflect reality.
Let me sharpen the point: even if in practice I am not relying on observation when I reach the conclusion that my senses are reliable, my claim is that the very meaning of the claim that they are reliable is that if I compare their data to reality, it will come out identical. If there is nothing to compare to, there is no meaning to the statement that something is ‘true.’ At least in that sense every truth-claim is grounded in comparison; otherwise we are dealing with a subjective statement.
With God’s help, 32nd day of the Omer 5780
To Haver and Dvir — Greetings,
The angels indeed have a correct line of reasoning that the ideational element in the Torah is “larger than life,” but Moses too is right in his answer to them: the Torah was not intended only for the upper spheres, but was intended to elevate and refine those who dwell in the world of matter and impulses, and to raise them little by little to a more noble reality.
Therefore, with Plato’s ideas the Rambam cannot “go to the grocery store.” In this world he needs the scientist who describes nature and its laws in the most precise way, and in his time that was Aristotle. And above him the Rambam needs the Torah and its detailed laws, whose purpose is to shape the personality of man so that he may be a faithful bearer of the divine ideals, as the Rambam explains in detail in the third part of The Guide of the Perplexed
With blessings, Lipa Feivish Sosnovitsky Dehari
Line 1
To strengthen your words, …
“But the fact that they fall under the heading of horses, fish, or rocks is just an arbitrary matter that stems from our mode of thought”
I didn’t understand what is so difficult about Aristotle’s view. Suppose F is black and G is white.
Let us take the shared properties of the objects we call “horses,” say QWERTYU for the sake of the argument. Let us take the shared properties of the objects we call “rocks,” say ZXCVBNM.
Adam walked in the Garden of Eden and saw QWERTYU+F QWERTYU+G ZXCVBNM+F ZXCVBNM+G — he called F black and G white, QWERTYU horse, and ZXCVBNM rock.
The question is why he did not give names to other collections of properties. For example, countries that are close to the sea and grow figs and have fewer than ten million residents could be called blipkamic countries.
And according to Plato’s reasoning? Is the answer that those countries have no special idea?
Indeed. I explained this.
My intention was that a person gave names to the physical objects he saw visually several times; clearly he has no interest in giving names to certain essences or to things composed of several objects (which he saw visually) unless he intellectually sees that there is something here worth giving a name to—that is, some particular essence or some particular collection of objects that has content.
What about ideas of objects that change according to the use made of them—did they exist before the invention of their mode of use? Likewise, there can be different uses for different people for the same object, so the number of ideas is supposed to be infinite, like the number of potential uses. The trouble is that an actual infinity of ideas runs into Hilbert’s Hotel paradox (unless you say that the person who uses the object in a certain way creates the idea of that use).
I didn’t understand a thing.
The idea of an object is derived from the way it is used (there is no additional common denominator between a plow and a winnowing fork in the category of farming tools). Therefore the question arises whether the idea of the plow existed before the plow was invented. After all, there could be a person or group for whom a plow would serve for scratching the back, and therefore the uses are infinite (assuming the future is not fixed in advance and there is no way to know how human beings will actualize their infinite potential possibilities for using objects), and they are even subjective to some degree. Therefore, if you say that the idea of the plow preceded its invention, it turns out that there are infinitely many actual ideas, which leads to Hilbert’s Hotel paradox. If the idea is created only with the invention of the plow, it turns out that the inventing person did not contemplate the idea in order to invent the plow, but created it—which is similar to the Aristotelian approach.
What does all this have to do with uses and objects? You are talking about the idea versus its realization in our world. By the same token you could ask whether the idea of democracy existed before the first democratic state was created. In my opinion, yes. And this really does not depend on the question of whether human beings would never have created a democratic state.
I did not understand what bothers you about an infinity of ideas. And what does it have to do with Hilbert’s Hotel?
In short, I did not understand your pilpul.
I’ll explain again, with your permission,
Unlike a horse, whose essence does not depend on man’s relation to it and therefore the number of essences of its type can be finite (horse, donkey, etc.) and exhaustive, the essence of objects is derived from the use man makes of them. Since the number of uses a person can make of any object is infinite, the number of ideas of objects according to your view (from what you answered in the previous response) should be infinite. Thus, using a piece of colored cloth to sew a garment would create for it the idea of a piece of clothing (which could also be shared by a piece of nylon), whereas over the years people might get used to using exactly that same piece of cloth as a handkerchief, thereby creating for it a different idea (shared with a piece of paper). It is also possible that they might get used to using that same piece of cloth as a color sample, and thus we would ascribe to it a third idea together with a piece of wood painted that same color. The point of the matter is that the possible uses one can invent are infinite, and therefore if the ideas exist before the uses are invented, then at every given moment we have an actual infinite number of ideas. Let us metaphorically house each of the infinitely many ideas in the infinitely many rooms of Hilbert’s Hotel, and the rest go and learn…
You are right that the same question could be raised about ideas of notions like democracy, but it seems to me that ideas of objects illustrate it better.
I didn’t understand a thing. The idea of a plow is a tool intended for plowing. If someone wants to use it as a comb, that is the idea of a comb. So what is the problem? And why is an infinite number problematic? It is not actual but potential. If you have no problem with an infinite number of uses, why should an infinite number of ideas be problematic?
I am not sure you see a problem here. I certainly don’t.
A. I used existing ideas so that it would not be too difficult to explain unfamiliar ideas, but clearly human beings can invent uses that did not exist in the past, and these are ideas that were not in use in practice.
B. The uses are potential (it is not certain that a use will be invented), whereas according to you the ideas exist in actuality even if the use will never be expressed in the world; therefore they are an actual infinity.
B. There is no connection. A potential infinity is something entirely different. There is no problem here at all.
This is not clear to me; could you explain or refer me to sources, please?
If we take as an example the idea of companies that manufacture cars, it is clear that there is no limit to the number of companies that can be established and named by the infinite combinations of existing letters; this is a potential infinity, since in practice infinitely many companies will never be established. By contrast, if you claim that the ideas of all those companies always exist, since it is not fixed in advance which companies will be established, there must be an actual infinity of ideas.
By contrast, I think one could solve this question if we assume that the person who founded the company is the one who created the idea. Likewise, the idea of parenthood that you mentioned in column 497 did not exist before there was sexual reproduction, and the idea of the Jewish people was created only when there was such a people in actuality. None of this requires that the idea does not exist (but perhaps it rules out the notion that it was created through contemplation of it), and therefore it can also have legal validity (as you argued in column 497).
You do not understand at all what a potential infinity is as opposed to an actual infinity. It has nothing to do with the question whether the objects actually exist or not. There are actual and potential infinities of objects and of ideas. There is no connection at all.
Besides, there is not an idea behind every piece of nonsense and nuance. The idea of a tricycle is not the idea of a car with four wheels.
All this is just pilpul. You can read a bit in HaMatzui HaRishon, second conversation.
I wonder why the Rambam was drawn after Aristotle? There is something that seems so “Jewish” about Plato’s philosophy. I was strengthened 🙂.