Gate Ten: Who Is Rational? Is There a Pure Analytic Thinker?

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).

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Who Is Rational: Is There Such a Thing as a Pure Analytic Thinker?

This gate contains four chapters:

1. Chapter One: Analyticity: Model and Reality
2. Chapter Two: Between Philosophy and Theology
3. Chapter Three: Who Is Rational?
4. Chapter Four: On Definition

Introduction

In the previous three gates we dealt with the attack on the analytic stance on several parallel planes. The present gate, which concludes the third part, addresses an important parenthetical remark. In the last three gates, the analytic stance has been exposed in all its nakedness, to the point that the question naturally arises whether there are, in fact, any people who hold a pure analytic stance. Therefore, before we turn to the next part, in which the synthetic stance will be presented, we shall discuss this question and its implications.

Chapter One: Analyticity: Model and Reality

Is There a Genuine Analytic Stance?

In light of what was said in the previous three gates, the question arises whether there are people who truly hold an analytic stance. We saw that every analytic consideration, including the analytic stance itself, is itself based on hidden synthetic assumptions. Therefore, anyone who is not a genuine skeptic cannot hold a pure analytic approach. In fact, one may say that our discussion implies that there is no one who does not hold a synthetic stance—some explicitly, others implicitly. In the previous gate we saw that even the most analytic domain, mathematics, cannot seal itself off within a world of formal-analytic proofs, that is, within an axiomatic system.

At first glance, it may therefore seem that defining the analytic stance is nothing more than setting up an artificial dummy at a shooting range so that we may attack it. It appears that, in practice, not all those who hold secular and left-wing views are as skeptical as they ought to be according to our description.

Postmodernism is indeed skeptical in many senses, or at least it seems to rest on a skeptical outlook. But secular liberalism, and left-wing thought, apparently are not. We have seen that when an analytic thinker attacks the synthetic stance, he himself is making a synthetic claim. If so, it is not clear against whom all the arguments in this book are directed.

In the introduction to the previous part, we noted that every human being is a complex creature, and that the one-dimensional types defined here—the analytic and the synthetic—are merely theoretical constructs. This is a typological description of two extreme types of stance, solely for the sake of discussion. The views and positions of real human beings are located somewhere between the analytic pole and the synthetic one. Even so, analytic characteristics do exist in the real world as well. The purpose of every typological analysis is to provide a basis for understanding the complex reality that blends the types it describes in varying proportions.

For example, we noted that the position that advocates tolerance as a value usually conceals an analytic stance behind it (see the prologue at the beginning of the book, and Gates Four and Six). How are we to explain the fact that among those who identify with arguments about the obligation to be tolerant, many hold positions that are called “modernist”?

The answer is, as we have already mentioned before, that sometimes the analytic stance is implicit, and perhaps even unconscious to the very person who holds it. The modernism underlying some of the prevalent positions in our world is, to a considerable extent, counterfeit—or at least partial. A person generally tends not to be tolerant regarding values that truly matter to him, whereas the other values—the ones toward whose opponents he adopts a tolerant approach—apparently do not really matter to him.

What distinguishes those who hold analytic positions in our real world from those who hold the synthetic outlook is the number and nature of the values in which they truly believe, and for which they are indeed prepared to coerce. These liberal modernists usually believe in a very small number of values, and what characterizes them is that these are only passive framework-values (see above, Gate Six). A total absence of certainties and values, or total analyticity, is found only in extreme postmodernism, and even there only with reservations. Therefore, postmodernism is an extreme pole in whose light one can understand the liberal-modernist phenomenon as well, and trace it to its analytic roots. It is not wholly analytic, and therefore it is willing to argue in favor of certain values.

Beyond that, if one observes the processes around us, one sees at least a clear trend. Postmodernism is steadily taking hold among those with left-wing and secular positions. This indicates, at least symptomatically, that skepticism really does lie at the base of both of these outlooks. This is in fact the process Nietzsche foresaw (see Gate Three). Postmodernism already lies latent within the prevailing modernist worldview. Most adherents of secular left-wing outlooks are unwilling to draw the radical skeptical conclusions that their positions require, because those conclusions are painful and difficult to implement in practical life, and also because, despite what they say, inwardly they are not genuine skeptics, and so they still advance synthetic claims. This creates a kind of limping between two positions. A person is a skeptic when he wants to be, and a dogmatist when he wants to be. Toward the religious person, or the right-winger, he asks (like Achilles in the prologue), “Where do you get your dogmatic beliefs from?”—yet toward his own values he adopts that very same dogmatic attitude. We saw important examples of this process in Gate Five (in Chapter One), where we called it “Bokononism.”

Yet despite all this, it is important to see—especially in light of the discussion in the previous part—that on the ideological-social plane there are still many analytic statements in our world (some of which I pointed to in the previous paragraphs). They are uttered because a person tends to ignore the abstract philosophical assumptions that underlie his ideological statements. For this reason, when people conduct a debate about religious coercion, for example, it appears as though there are two equivalent positions here, and perhaps the religious one even seems inferior. Usually it is specifically that side that is asked to provide proof that it is right, since it claims the right to impose its positions on others. Of course, it fails to provide such proofs (see the prologue). But then, on the abstract philosophical level, it suddenly becomes clear that it is almost impossible to be an analytic thinker, and that the synthetic stance has a clear advantage over the analytic one. On that description, it is specifically analyticity that bears the burden of proof.

This is why the analytic type is not merely a dummy. The arguments raised in the present gate against analyticity are directed also at partial analytic thinkers. If they are willing to acknowledge synthetic statements, at least in the sphere of social frameworks, why are they unwilling to recognize a priori the validity of such truths with respect to the contents of those same frameworks? There does not seem to be any logical basis for distinguishing between granting validity to framework-values and granting validity to substantive values.

The Importance of Logical-Philosophical Examination

When the analytic stance is examined at the abstract meta-ideological theoretical level, it really does seem utterly unconvincing, and perhaps even nonexistent. To the extent that it tries to go beyond mere skepticism, it immediately turns out to be inconsistent as well. This is precisely the advantage of examining ideologies and cultures at their abstract philosophical, meta-ideological level.

This is probably also the reason why those who hold such positions do not tend to examine them on the philosophical plane. Usually the discourse deals with cultural, artistic, and value questions, but not with questions of validity and truth-values on the abstract logical plane. The clarity of logical discussion is covered over by a dense veil of verbiage—sometimes impressive, but usually empty of content—when we deal with more concrete planes.

But precisely for that reason, one must insist on conducting the discussion specifically at the abstract level. We must discuss what proof is, what truth is, and how each side reaches any certainty at all, if it does. Only afterward can one return to the plane of practical-ideological discussion. On the abstract plane, the balance of power is completely reversed. The confidence in the righteousness of the way that characterizes the analytic side (secular-left-postmodern) stems from the fact that it does not trouble itself to clarify for itself the philosophical basis of its views and ideologies. Clarifying that basis is one of the main aims of this book.

Zionism as a Parable

An example of a process marked by the kind of internal contradiction described above has been occurring in Zionist society (mainly the secular part, though not only there) over the last several decades. First, we must note that Zionism is plainly a modernist outlook. There is some truth that lies at its base, beyond empty liberal-secular universality.

The generation of the parents rebelled against Jewish tradition (at least in its accepted sense), but despite that it possessed a firm Jewish national foundation. Yet suddenly, out of that worldview, there grows an estrangement in the generation of the children. As we already explained above, we have here a generation that “dares” to draw the conclusions required by views that were in fact already the possession of the parents’ generation.

This process is described with terms like “disintegration of values” and “selfishness,” but in fact it is a more intellectually honest approach. In a situation in which “God is dead,” in Nietzsche’s terminology, there are no longer any absolute truths—religious, traditional, national, Zionist, social, or otherwise. In such a situation, just as there is no religion, there is no nation either. The analytic rebellion against religious tradition leads to an expansion of the analytic circle—and makes it more consistent—by refusing to accept any absolute values whatsoever.

The post-religious components within a society in which God has “died” produce post-Zionism, which is nothing other than a particular case of postmodernity. This is the clear direction of the historical process. It is no accident that those who lead the postmodern process also lead post-Zionism. All of these have one root: analyticity—meaning recognition only of truths, or positions, that are “empty” (such as equality, pluralism, and the like). The direction in which the secular-liberal-left avant-garde is now moving is plainly postmodern. This process indicates the expected direction of development for the entire movement. We are witnessing a long process in which the younger generations are prepared to continue, more courageously, the process their parents began, and therefore they draw closer and closer to genuine skepticism. As noted, they are only exposing something that was already hidden in the earlier generations. This is the meaning of the slow spread of postmodernity. The Nietzschean scenario, according to which modernism turns by a kind of metamorphosis into postmodernism, has been taking place over the last decades right before our eyes.

Is Analyticity a Straw Man?

Let us now return to the question with which we opened this gate. The analytic model is not a shooting-range dummy. It is the basic idea that lies at the root of the prevailing views in the modern Western world. True, sometimes it is well concealed within supposedly modernist views, for the reasons mentioned above.

The answer, then, to the question raised at the beginning of the gate—who is the analytic person against whom the attacks of the previous gates are directed?—is given here on three levels:

1. A human being is complex, and indeed there is almost no such thing as a pure analytic thinker. Yet there is an analytic side in all of us. Our arguments are directed against that side.
2. Sometimes a person is an analytic thinker even though he himself is unaware of it. That was the purpose of the arguments that sought to expose the analytic layer behind common claims (mainly in the second part). Their aim was to show that the analyticity that will be presented in the present part as an empty vessel is not a dummy. It is an idea borne by—or within—many of the ideas and values that appear in our world.
3. Sometimes the situation is the reverse: a person feels himself to be an analytic thinker, and our aim here is to prove to him that he is not. That is, to bring the synthetic element to consciousness and give it legitimacy. Its repression often stems precisely from the fact that it lacks legitimacy in our society. If indeed we all hold a synthetic stance, it is proper that we recognize this. Many misunderstandings stem from failure to recognize the synthetic side within us.

Chapter Two: Between Philosophy and Theology

From Philosophy to Education: Rationalist Repression¹

From the description of the historical progression toward postmodernism, another important point emerges, one that serves as a motivation for the present discussion. One of the aims of this discussion is to point out the hidden analytic assumptions that underlie modern and postmodern thought—something that may also help halt the continuing spread of postmodern skepticism. Many of those who carry this banner are, in their inner being, not really analytic thinkers at all (see the end of the previous chapter). They feel that they must be such in order to be regarded as belonging to the “rational” and “enlightened” public in our world. Why accept value-laden or ideological assumptions without justification and argument?

This feeling causes them to repress the beliefs that exist within them. As we have seen, almost all human beings hold a synthetic stance. Perhaps not everyone believes in the same things, or in the same certainties, but almost everyone believes in some certainty. It is very worthwhile for each person to be aware of this when examining positions opposed to his own.

Not infrequently I have spoken with students—and this is really a variation on conversations I had with myself at that age—who felt that nothing in the world is really true. Many of them argued that a person acts on the basis of first assumptions that are, as everyone knows (!), arbitrary. Such students expect one to show them, or prove to them, what we have here called “the synthetic stance.” Alternatively, they ask that their analytic arguments be refuted.

In such situations, one must do exactly what is done in this book. There is no possibility of refuting a genuine analytic stance, because it is pure skepticism. One cannot contend with consistent—perhaps better, resolute—skepticism. But who among us is really a resolute skeptic? What must be done in such a situation is to show that skepticism is not the only rational solution—to help them mature out of adolescent rebellion into the third stage of synthetic maturity. One must get the youth to give up the assumption that rationality requires relinquishing unproven beliefs. One must show him that rationality means holding beliefs that are not grounded, because otherwise no rationality at all is possible.

It is important to try to get them to examine whether they themselves really hold an analytic outlook. Do they really believe and act as though nothing at all is true in the world? Does not the very demand for proofs itself tacitly presuppose that there is such a thing as “proofs,” even if there are no specific proofs for what one of them is seeking?

It seems that the only possibility in such a discussion is a sharp and clear presentation of the two stances, the analytic and the synthetic. Such a presentation makes clear that a person can be either a synthetic thinker or a skeptic. All other positions are merely a superficial cover for one of these two, and nothing more. Once the positions have been presented and sharpened, each person must examine where he himself stands. Does he really see himself as a total skeptic? From considerable experience, I can say that after such a conversation, and after explaining that nothing in the world has “proofs” in the analytic sense, and yet every person has things he truly believes in, most people identify within themselves some synthetic point or core. As stated, most of us—and perhaps all of us—hold synthetic stances. Analyticity is syntheticity under repression, in order to preserve “rationalism.”

In practice, there exists in the world an “analytic feeling,” which is merely apparent, illusory analyticity—but not an “analytic stance” or “analytic worldview.” If people look within themselves and notice that they are not genuine skeptics, that is, that they too believe in certain truths and certainties, perhaps it will be possible to halt the great drift that may carry them—and the generations that follow them—into intellectual nihilism, or toward the predicted end of the Nietzschean scenario.

True rationalism lies specifically in the synthetic approach. One need not be “a believer in the god of doubt,” like Achilles in the prologue, in order to be rational. Such a belief is no less dogmatic, and perhaps even more so, than belief in the old and good God.

In the following excursus we shall try to develop this important point and show that in the course of the present part we are in fact employing a different sort of philosophical argument. Someone might call it a “theological argument,” as distinct from a “philosophical argument” (these terms will be clarified in the excursus itself). It is strongly recommended not to skip the excursus, because it is one of the focal points of the argument of the entire book. The logical infrastructure of nearly all the arguments in this book lies in the distinction between “theological” (= as a method of argument and philosophizing) and “philosophical.”

Excursus 25: The Existence of God: Between Philosophy, Theology, and Religion

Let us begin with a striking definition that I once heard of the difference between theology and philosophy:

Philosophy assumes premises and derives conclusions from them, whereas theology assumes the conclusions and derives premises from them.

This distinction is meant to claim that theology’s conclusions are known in advance. So far as I know, no theologian has ever, following his arguments, reached the conclusion that God does not exist. He assumes God’s existence, and afterward tries to find an argument that proves it.

Yet from this perspective, it seems that almost no philosopher—or anyone else—has denied God’s existence as a result of philosophical reflection. Usually one first felt that he did not accept the belief, and only afterward arrived at philosophical arguments that justify that position—if there are any such arguments at all.² This observation is probably symptomatic of discussions about the existence of God, on all sides.

At first glance, this definition is attractive. Theology is not a matter of proofs, and if proofs exist, they come only after the worldview has already taken shape. Philosophy, by contrast, appears as a rational structure leading from plausible premises to the required conclusions that follow from them. Wonderful rationality.

But when one examines philosophy somewhat more deeply, one sees that even the philosopher who draws conclusions from his reflections cannot do so solely on the basis of analytic considerations. For if he derives a conclusion from some premises by means of an analytic argument, then—as we have seen—the conclusion was already hidden in the premises. If so, which came first here: the premises or the conclusions?

Since Kant, the difference on this plane between theology and philosophy has almost ceased to exist. As we saw above, Kant too did not ask whether synthetic a priori judgments are possible, but how such judgments are possible. He assumed their existence and only afterward sought arguments to justify it. One may say that this is the main difference between him and Hume, who wonders about these same questions and is not willing to assume necessarily that they have answers. The answers Kant proposed to Hume’s difficulties—for example, the system of transcendental arguments—even if they had been satisfactory answers (in Gate Seven we saw that they are not), do not constitute proof of the validity of such arguments, but rather an after-the-fact excuse for one who decided to adopt them despite the Humean difficulties. Thus, remarkably, Kant too, and transcendental philosophy, have a “theological” character: they assume the conclusions and only afterward find a way—dubious as it is—to anchor them.

One should note that after Hume’s rejection of empiricism, the only route proposed in the history of philosophy for arriving at confidence in synthetic conclusions about the world is the transcendental route. But this route, in the terminology proposed above, has a purely “theological” character.

In the example of the train to Scotland (see Excursus 21 above), we saw how Taylor reverses the direction of the physico-theological proof, in Kant’s terminology. The classic argument from design claims that it is improbable that a world so complex and purposive arose by chance. From this it infers the existence of a factor that planned and assembled the world. From the existence of such a factor, one may also infer that there is a basis for trusting our senses, and thus solve the fundamental problem of epistemology.

The sting that Taylor adds to the physico-theological argument is a reversal in direction. Even if we do not dismiss out of hand the possibility that such a thing could in fact happen by chance, his claim is that in that case we could not believe our senses. There is no logical possibility of trusting our senses while simultaneously claiming that they arose by chance. He therefore begins with the assumption that the senses must be trusted, and from it derives the existence of a factor that would provide a logical basis for that trust. This is exactly the reverse of the usual direction. In the terminology proposed here, Taylor moves from an argument of “philosophical” character—from the premise that God exists to the conclusion that one may trust the senses—to an argument of “theological” character, in which from the conclusion, prima facie unjustified, that one must trust the senses, he derives the premise that will ground it: the existence of God as a coordinating factor.³

In Gate Seven (see especially Excursus 21 and the main text before it), we broadened Taylor’s argument from trust in the senses to trust in human cognition in general. We argued that the “philosophical” basis for our epistemological trust in our cognition is belief in the existence of God as a coordinating factor. One may call this “the argument from epistemology.” Put differently, one may say that whoever believes in an essentialist epistemology, and in synthetic thought in general—and in the last gates we have learned that most human beings do—probably tacitly assumes the existence of God as a coordinating factor.

Let us emphasize that belief in God as a coordinating factor is the only possible guarantee, after rejection of the two other possibilities, the empiricist and the Kantian ones (see the previous two gates), for our trust in our cognition. Since we believe that our cognition does in fact work, we are forced to infer that there exists a coordinating factor that ensures the proper functioning of cognition, so that it corresponds to reality in the world as it is in itself. In Gate Eleven we shall continue to discuss the “argument from epistemology,” and sharpen its importance as a basis for the synthetic stance (which will there be called “the logic of hearing”).

In the terms defined here, the reversal in the direction of the argument presented by Taylor—and by us following him—is precisely the move from the “philosophical” direction to the “theological” one. Taylor means to tell the reader that if he in fact assumes the reliability of the data of the senses—and of epistemology in general—then he thereby discovers that, implicitly, he also believes in a factor that coordinates him with the world. One can therefore understand the term “theological proof,” because it does not convince one who does not believe in God; rather, it tries to show that whoever believes in his senses has in fact always already believed in God.

This is exactly the form of argument we saw here in the body of the chapter. We are trying to show a person that he already, in any case, holds a synthetic stance; we are not trying to persuade him to become such a person. A genuine analytic thinker (= a resolute skeptic) is of course not open to persuasion. With one who believes in nothing, we have no way to break through the shell of his monad and prove to him that he is mistaken, if only because the very methods of proof are, for him, also in doubt. Only one who possesses some synthetic core can be helped to sharpen that fact within himself, and perhaps to expand the boundaries of that core and its sphere of application.

In another formulation:

1. Not to trust his senses—and, as we broadened the argument, not to trust his cognition and reason either.
2. To go on trusting the senses and cognition, and thereby commit himself to rejecting the possibility that they arose by chance.⁴

Even one who chooses the second option, that is, to trust his senses and cognition and therefore to assume the existence of a coordinating factor, will have to explain to himself why he does so. That is: in the “theological” direction of the argument, trust in the senses indeed presupposes belief in the existence of a coordinating factor. But why choose the second option rather than the first? Why not reject both trust in the senses and belief in the existence of the coordinating factor together?

At this point the “philosophical” direction enters the “theological” picture. A person decides thus because he simply apprehends God through essentialist contemplation. The conclusion that God exists is not a metaphysical speculation, as it is usually perceived. It is simply an immediate awareness that He exists. The grounding for this is cognitive rather than discursive, just as the grounding for the claim that objects exist depends on the fact that I see them before me. There is no point in looking for any other grounding. A purely rational grounding for any fact in the world—and certainly for the existence of God—apparently cannot be given (Kant himself, in his Critique of Pure Reason, showed this). At the basis of faith, as at the basis of every synthetic belief about the world, lies cognition and not thought. The transition from thought to cognition, and the absence of a sharp boundary between them, will be discussed in the next gate.

So far, we have distinguished—or more precisely, erased the distinction between—philosophy and theology. This is the place to continue and discuss the relation between both of these and religion. The God whose existence we are discussing is philosophical. He makes no religious demands, and He is not involved with the world. His “role” is to ensure the coordination between us and the world, and thereby make cognition and thought about the world possible. This conception resembles Kant’s instrumental understanding of God. After in Critique of Pure Reason he rejected the three theoretical possibilities for proving God’s existence, in Critique of Practical Reason and in the Groundwork of the Metaphysics of Morals he presents a “proof” of “theological” character from morality.

The course of Kant’s “proof” is this: he brings evidence from the very existence of moral principles as an indication of God’s existence. Superficially, this is a “theological” move parallel to the one here. But from Kant’s words it appears that he is trying to claim that God really has a “role.” Kant “manufactures” God in order to ensure that human beings will be moral.

But such a thought is not even theology; it is simply opium for the masses. The question whether God exists or not is a question about reality. It cannot be answered according to convenience and the consequences that follow from it. It is no surprise to find that Kant anticipates postmodernism in this matter as well, by producing values according to convenience. We saw a similar production of values in Gate Six when we dealt with democratic modernism and American pragmatism. Ahad Ha’am also tried to do this with the values of halakha (Jewish law), saying that one should preserve the character of the Sabbath as a national, cultural, and social glue.

If the existence of moral values is an indication of the existence of God, then the God in question is a philosophical God. One cannot derive from this any proof that God has practical demands, “religious” in character. Of course, this also does not rule out the existence of such demands. The same is true of the conclusion of the argument here regarding the nature of God: if trust in the senses is an indication of belief in God and not its basis, then the door is opened to ask further: does God have additional characteristics as well? That is, is God “religious,” or only “philosophical”?⁵

There are two points that can be drawn from the proofs of the existence of the philosophical God that may also be relevant to the question of the religious God.

A. In the course of the present proof one can extract some of His characteristics as well, and not only His very existence.⁶ For example, He appears to be rather sympathetic—perhaps compassionate and gracious? The basis for this is that we hold an implicit belief that He preserves the proper coordination between us and the world, and that He has no intention of confusing us (unlike Descartes’s famous “demon”).

B. The second point is much more significant. Claims about the existence of the “religious God” are often rejected on the grounds that such an existence is simply implausible. Typical statements are: we have never seen such entities, and inventing them is mere mythology. Even if there is an argument from design—or order—that shows that the probability of the world’s having come into being by chance is extremely low, the one who insists on not believing will answer that the plausibility—not the probability—of God’s existence is even lower.⁷

Now this very claim requires examination: how does one determine such plausibility? On this our sages said:

“Not having seen something is no proof.”

But beyond that, if one can show such a person that he himself already believes in the “philosophical God”—for example, following the “argument from epistemology” presented here—then the philosophical “price” he is “forced” to pay if he assumes the existence of a “religious God” is much lower. If he is already compelled to admit the existence of a transcendent entity of which he has no experience whatever, then even on his own terms the transition to religious belief is no longer so implausible. When he now comes to discuss a “religious” question—for example, whether the revelation at Sinai took place or did not—he can no longer simply dismiss the claim, without further thought, as mere mythology. If there is such a transcendent entity, is it really so implausible that it also revealed itself at Sinai and gave the Torah to the inhabitants of the world? How can it be so obvious that the philosophical God does not have religious characteristics?

We are now required to return once again to the issue of the burden of proof, discussed above. It now appears that the burden of proof—whether the philosophical God has religious characteristics or not—falls on the secular person who believes in the philosophical God, not on the religious believer who believes that the philosophical God is also “religious.”

In this excursus we have expanded and sharpened the distinction between an argument of “theological” character and an argument of “philosophical” character. We then continued to discuss the relation between the two and the implications this has for the religious discussion.

Summary and Conclusions

We have therefore reached the conclusion that within the worldview of the analytic thinker there exists a basic synthetic core, and the entire dispute concerns only its size and its nature. In such a situation, the debate is conducted on the same plane, and on both sides of the barricade stand synthetic positions. In such a case there is room for an open, non-academic discussion, an attempt by each side to persuade the other and even to arrive at conclusions. Both sides already recognize that there is truth; the only question is what that truth is. As we saw in Gate Four (in Chapter Three), analyticity seals off openness and the very possibility of discussion. Once everyone is already aware of his own syntheticity, it no longer seems so simple to accuse specifically the religious stance of ossification, dogmatism, or irrationality. In the eyes of plain common sense, as I tried to show in Gates Six and Seven, it is specifically secularity—and certainly analyticity, whether full or partial—that appears more dogmatic, and less plausible and rational. In any case, that at least is something about which one can now argue.

Chapter Three: Who Is Rational?

We now come to the question of questions: who is rational? This question is highly complex. The definition of rationality is not at all as clear as it may seem at first glance. If rationality is simply acting according to guiding principles, then it seems that every person acts according to some principles—except that each acts according to different ones. We have already seen that there are no general principles that are of analytic origin, that is, principles that can be proved.⁸ Another characterization of rationality seems to lie in the source of the principles themselves—for example, whether that source is external or internal. In other words: does the person act autonomously, or are his actions dictated from outside—social influences, family, education, and the like?

Here too, the distinction is not simple. What is an autonomous decision? Is adherence to humanistic moral principles more autonomous than the decision to adhere to God’s commandments, or even to obey rabbis—or other sages? Is it more plausible to make decisions by ourselves—“from the gut”?—about what ought to be done, or is it perhaps more rational to obey a divine command, assuming there is such a command? This, on the basis of the very plausible assumption that if there is a God, then He presumably knows better than I do what is right to do. Does a religious worldview stem more from brainwashing, as many tend to think, than a secular worldview? This is not the place to elaborate on that discussion, mainly because its character would be more journalistic and empirical and less philosophical. I shall therefore suffice with an excursus that addresses one issue among many. This discussion will illustrate and sharpen the dilemma before us better than any abstract and general statements could do.

Excursus 26: Induced Abortions and a Woman’s Right Over Her Body

A very common slogan in the secular Western world today is “a woman’s right over her body.” In the name of this right, people support the right of a woman—perhaps together with her partner—to kill a fetus if she does not wish to give birth to it. The reasons for not wanting to give birth may vary—social, psychological, medical, simple lack of desire, and others—but in principle many people today see no essential difference among them. The reason for this is the belief that a woman has a right over her body.

A similar argument is heard regarding a person’s right over his body when he wants to die. The question of euthanasia arises when a person asks a physician, or any other person, to put him to death in order to spare him suffering, or for any other reason that is supposedly for his benefit. We dealt briefly with this discussion in Gate Five (mainly in Chapter Two), following the citation from Yeshayahu Leibowitz’s book dealing with the subject of values. Here we shall focus on abortions, because through that issue it is easier to show the irrationality and brainwashing that exist not a little specifically on the secular-liberal side.

Here too one can argue, as in Leibowitz’s discussion mentioned there, that the criterion for when a fetus is already considered alive is unclear. Even if there is some intuition that a fetus is not regarded as a living person in every respect, it is still difficult to see how anyone could justify that on any objective plane. There is no clear objective criterion for when a fetus becomes a living person.

No one intends to argue that it is permissible to kill a person who lives in my house because I have a right over my house. Even the greatest champions of abortion rights do not claim that I have the right to kill my son or daughter if I do not want—or am unable—to support them. Even the killing of a fetus is permitted only under certain lenient circumstances, the scope of which is under dispute. It follows, then, that the argument for abortion is based not only on a woman’s right over her body—for I also have full rights over my house—but also on defining the fetus as an object that is not fully a human being.

But here the question immediately arises: where is the boundary between a human being and one who is not? From when is it permissible to kill such an object, and for the sake of what needs? specifically from within a religious worldview one can understand the claim that God established a boundary line—for example, a certain age of the fetus or a certain stage of development. But from a secular point of view it is difficult to understand how people can have such great confidence in this definition, to the point of permitting killing.

The Nazis in the Holocaust exterminated people with intellectual disabilities, Roma, and Jews because they did not view them as human beings, or at least not fully human. Everyone condemns those acts. In what way are those acts different from the induced abortion of fetuses? There are many reasons to support a position that sees a severely intellectually disabled person as “less human” than a fetus. A fetus at least has the potential to grow and become a complete person. In modern life we place so many restrictions and boundary-lines in order not to violate the rights of man, the citizen, and the child, or the sanctity of life, and we are willing to bear very grave consequences so that these rights will not be infringed.⁹ On the other hand, with respect to the most elementary right, the right to live, we infringe without any fear that perhaps we have crossed the line. There is some unclear sense of certainty that the fetus is not a human being; on this issue, modernist skepticism—more precisely, postmodern skepticism—somehow disappears. The prevailing norm today in modern society is that if a woman does not feel like bringing the child into the world, she simply kills it. The absurdity grows when one notices that the person who kills the child is specifically the physician, who is committed, among other things, to the principles expressed in the physician’s oath.

If there really is a family, or a parent, suffering from problems that interfere with the healthy raising of the child, then a society that truly worried about the child’s fate ought not to murder him, but rather establish shelters and care for him there properly and humanely. Liberalism, true to form, chooses the easier solution—we have already seen the connection between analyticity and pragmatism. It is simpler to define a value called “a woman’s right over her body,” a slogan of no small charm in our times. Once this magical slogan has been fixed in place, one can whitewash the fact that it is nothing more than a fig leaf legitimizing murder. In this way one can murder those children with a quiet conscience, provided one finds suitable wording. Postmodernity has always tended to see every philosophical or moral problem as a problem of language, and therefore was satisfied with solutions of wording. We also saw a similar characteristic in analytic philosophy in Gates Two and Three. It is interesting that the attempt to fight this phenomenon is described by the knights of humanism with the clerical and benighted term “religious coercion.”

It should be noted that the purpose of the discussion here is not to persuade anyone of the existence of a moral prohibition against performing abortions, though that too is a most lofty goal. Here our purpose is only to point out that the liberal argument in favor of a woman’s right over her body is a classic example of demagoguery in argument and of brainwashing.

The problematic assumption in the discussion of killing fetuses is not a woman’s right over her body, but the determination that the fetus is not a human being. That is the focal point of the dispute, and the weak point in the argument for killing fetuses. As is well known, the demagogue tries to present his argument while omitting the problematic premise, and pointing instead to the premise that expresses a principle accepted even by his opponents. That makes it very easy to persuade your rival that he really ought to agree with you.

Opponents of abortion generally do not deny a woman’s right over her body. What is in dispute is the claim that this right grants her moral permission to kill a fetus that is in her body. Waving the slogan “a woman’s right over her body,” although it is irrelevant to the dispute, is very effective. It casts abortion’s opponents in a negative light—as irrational and unenlightened. Beyond that, it may even persuade the opponents themselves, because they too completely agree with that claim. One should notice this demagogic brainwashing of “liberalism,” and the fact that it operates so effectively.

Another reason for its effectiveness is the convenience of adopting such a value-claim. As noted, the values of liberals are usually tools for attaining comfortable lives without disturbance. The foundations of analyticity and pragmatism are intertwined all along the way. In this manner they adopt negative-passive values, as we defined them at the end of Gate Six. But when it is more convenient to kill, one can easily arrive at permission even in this matter.

There is another important point here. Many times I have raised this simple argument before supporters of “a woman’s right over her body”—or, more precisely, supporters of induced abortions. To this day, as far as I remember, in most cases my interlocutors were persuaded. The interesting question, and no less important, that I usually continue to discuss with them is this: how does an intelligent person fail to think on his own of such a simple argument? In other words, how is it that those same people who were persuaded in conversation with me did not themselves think of such a simple implication of the moral principles and human rights in which they themselves believe, and sometimes even fight for?

This question should also be asked by someone who is not convinced by this argument. He too should ask himself: how is it that those who are convinced by so simple an argument do not think of it on their own? He should ask himself whether he had already asked himself those questions and rejected them earlier, or whether he is encountering them here for the first time.

The answer is very simple, and symptomatic of our discussion here. There is an intensive secular, analytic brainwashing that does not allow people to weigh their position using straightforward and honest judgment. People place the arrow—being “rational,” “enlightened,” and in favor of “a woman’s right over her body”—and around it they draw the target, that is, the moral justification.

This conception also stems from the fact that an analytic approach does not seriously believe in the correctness and validity of values, and therefore is more easily swept along by the various demagogic winds and fashions blowing through the world. If values are adopted for pragmatic reasons, why should reasons of convenience or fashion fare any worse? The values can then be manufactured afterward, ad hoc, in order to justify retroactively the outlook one wanted in the first place. In our analytic world, as one hears quite often today, values are a matter of fashion.

In fact, in present-day Israel there is no public debate at all about abortions. One would expect at least a split of public opinion, dividing the public between supporters and opponents. But the wider public, as a result of the brainwashing called “politically correct,” is entirely of one mind. There is complete consensus regarding an act for which it is very hard to see why it is not murder. Until not very long ago, broad public agreement on this point prevailed as well.

The concept of the “politically correct” is often vilified in our circles, but it still has enormous power. Liberal society feels itself open to every direction of argument, but very often it is not at all so. One may perhaps voice arguments that are not politically correct, but almost no one listens to them or considers them seriously.¹⁰ The reader is invited to return to Gate Four and examine the discussion of the “academic openness” of the liberal-analytic world.

On this issue, specifically the religious person appears to act in a more rational direction. He acts according to the command of One who knows exactly—at least according to his worldview—where the line passes between a human creature and one who is not. Very often he will oppose abortions also on moral grounds, for he does not have the pragmatist bias that erases the simple considerations pointing in that direction.¹¹

We therefore return to the question posed in the main text: which of the two is more rational? Or, alternatively: who is it that acts and is persuaded in ways that resemble brainwashing?¹²

Chapter Four: On Definition

Introduction

In this chapter I wish to touch on a more specifically defined question, though it too is difficult to define systematically: what is scientific rationality? Naturally, this question has received more attention, and it is clear that it is not detached from the more general question raised above. Here I shall present an abridgment of Rabbi Zaini’s incisive article, which deals with precisely these problems.¹³

Rabbi Zaini’s Description

Rabbi Zaini describes the beginning of a course that he himself teaches in the Mathematics Department at the Technion on set theory. Within that framework he begins with a definition of the concept “set”: “A set is a collection of elements.” But the concept “element” also requires a definition, and so the repertoire is enriched by another definition: “An element is a member of a set.” As he describes there, he has never seen even an eyebrow raised by any student on hearing this pair of circular definitions. In his words:

The aura of sanctity that envelops and crowns every word issuing from the mouth of a senior academic is accepted by them more readily than anything of God. Before this “cultural wonder,” I cannot rid myself of the feeling that perhaps something remains here of the spirit of devotion that so characterized ancient idolatry, now clothed in a new form.

Rabbi Zaini then goes on to describe the stage at which he defines the “empty set”: “An empty set is a set that contains no elements.” Here too all the students diligently summarize in their notebooks, and not one of them is stirred to ask how this accords with the definition of the concept “set,” which was just now defined as a collection of elements. How can a collection of elements contain no element at all? Here too the halo of sanctity surrounding the temple of academia demands idolatrous devotion and absolute trust.

Rabbi Zaini continues in his article and describes how, to one’s astonishment, despite all the difficulties and circularities—this one and many others—the “method” works. It is possible to build sophisticated and powerful mathematical theories, all based on circular definitions of this kind. The difficulties remain in place and admit of no convincing solution, as the “priests” of those “academic temples” know very well. Obviously, these difficulties do not come to the knowledge of the “masses of believers,” who cling in their naive faith to the absolute perfection and rationality of academic knowledge.

The article continues and presents a long list of concepts that cannot be given a non-circular definition, such as “collection,” “union,” “object,” “point,” “line,” “plane,” and so on. Finally the discussion reaches the concept of “definition” itself, which is perhaps the most basic of them all. A basic assumption in all the sciences and in mathematics is that there is room for such a concept. Rabbi Zaini points out that this concept has not received significant treatment, and that the assumption—usually implicit—that everything can be defined has never been examined, justified, or grounded. He goes on to argue that reality—sadly?—shows exactly the opposite: no concept, not even the simplest and least abstract, can be defined in an absolute and independent fashion.¹⁴

On Definition

At this point it is difficult to accept Rabbi Zaini’s sweeping approach. Clearly, no basic concept can be defined, precisely by virtue of being basic. A basic concept is one that serves us in defining concepts that are not basic, and whose definition rests on it (see the discussion of the heap paradox and similar concepts, above in Gate Eight, Chapter Four). From that point on, however, one can define complex concepts out of the basic set that itself admits of no definition. This situation is similar to one we have pointed out several times already: every justification of some principle rests on first assumptions. “Justification,” in this context, means mathematical reduction to those first principles. There is no doubt that those assumptions themselves cannot be justified.

In the same way, concepts such as “line,” “plane,” “collection,” and the like cannot be defined non-circularly, and therefore they serve as basic concepts. One who tries to define them as well will be forced either to surrender their basic status in favor of other concepts—which will serve to define them—or to use circular definitions. Ultimately, the purpose of definitions is to clarify the picture, and it is therefore clear that one should not become enslaved to them. On the other hand, there is no doubt that they help greatly in clarifying and illuminating many situations.

In light of the foregoing, a meaningful definition does not constitute the concept—as mathematicians usually think—but only clarifies it. A concept that we cannot understand even before the definition, that is, one that is not present within us in some way—or that we do not “observe”—also cannot be clarified by means of a definition (see the discussion of this at the beginning of the next gate). In Gate Two we saw that the material of the concept is present within us and also in the world, and that it is the description of the concept that takes on form only within the consciousness that observes it. The definition, as we saw there (in Chapter Two), is merely a verbal description of the essential part of the concept’s form.¹⁵

Excursus 27: The Usefulness and Meaning of a Mathematical Definition: Convexity and Concavity

Let us now discuss a fine and simple example that will illustrate the power and importance of a mathematical definition. A “convex” geometric shape is a shape all of whose boundaries bulge outward, with none of them indented inward. A “concave” shape is the opposite, that is, one that also has boundaries that bend inward. There are several ways of defining convexity and concavity mathematically. Here we shall make simple use of one of them.

There is a theorem in mathematics stating that the intersection of any two convex shapes is itself a convex shape. That is, if we draw two convex shapes on a sheet of paper, so that there is some overlap between them, then for any two convex shapes, and in any manner of overlap between them, the overlapping region will always also be convex—that is, all its boundaries will bulge outward.

This theorem may seem fairly obvious on the intuitive level, but on a somewhat less superficial look it is not so easy to prove. One has to take account of all the ways in which two convex shapes can overlap, and make sure that in none of them is there even one case in which the intersecting shape has a concave boundary. For example, if a certain side of the boundary is created by a combination of two boundaries of the intersecting shapes, perhaps a concave line of boundary is formed there. The reader is encouraged to try to think of a mathematically precise way to prove this theorem before continuing.

The ordinary reader probably did not succeed in proving it. Here we can see how the definition comes to our aid. First we must define, in a precise way, the concept that is intuitively clear to us, “convex shape.” Let us define it thus: a “convex” shape is a shape such that if we take any two points inside it and connect them by a straight line segment, that entire segment passes inside the shape—in other words, there are no points on the segment that are not inside the convex shape. A reader who reflects a bit on this definition will see that it is simple and corresponds intuitively to the concept of a convex shape in our cognition. We now continue and use this definition in order to prove the theorem above.

Let us define the shape C as the one obtained from the intersection of the two convex shapes A and B. We take any two points in C and connect them by a straight line segment. These two points are inside shape A and also inside shape B, because they belong to the intersection of those two shapes. Therefore, if A and B are convex, the segment connecting those points lies wholly within A, by virtue of A’s definition as convex, and wholly within B for the same reason. It follows, then, that the segment lies inside each of the two shapes, and therefore it lies also in their intersection—that is, in C.

We have thus proved that if we take any two points whatsoever lying within shape C, the straight line segment connecting them also lies wholly inside it. From the definition of convexity it follows that shape C is convex, because for any two points lying within it, the straight line segment connecting them lies wholly within it.

It is worth noting that we did not use our visual intuitions here at all, nor did we try to survey the full range of possible convex shapes and possible modes of overlap between them. Even so, all of these certainly stood in the background. They served us at the stage of defining convexity itself, and only at that stage. Once we arrived at a definition that exhausts the whole concept of convexity, all that remained was to work on an abstract logical plane, without any visual dimension.

The reader who is not mathematically trained has received here a small lesson in mathematics. Our purpose was to show that by means of a good definition we manage to reach things that without a definition would have been very difficult for us to reach—or else we might make mistakes. On the other hand, one cannot reach by means of such a definition things that it would be impossible to reach without it.

There is no doubt that such a definition would not be possible if we had not already been equipped beforehand with the concept of convexity in an intuitive way. One who wished to teach someone not equipped with that intuitive understanding what convexity is, and to do so through the abstract definition, would probably be unable to succeed. The definition only translated the intuitive concept into a more precise formal form, but in no way does it replace the intuitive understanding that precedes it.

We have seen here that although a definition is seemingly an act that does not in principle add to the existing knowledge, it greatly helps us analyze and understand the meanings folded into that knowledge. The formulation of the definition seemed self-evident to us, and from it we obtained, by an analytic process, a theorem that was far less obvious to us beforehand. That theorem was already latent within our prior knowledge of convexity, but only implicitly. This is exactly how mathematics works, and analytic reasoning in general. Analyticity extracts from the premises what is already present in them.

We once again see that from a definition one cannot learn anything new, but only sharpen and clarify knowledge that already exists within us beforehand. This, as stated, is the emptiness of the analytic. Obviously, if concepts like “the boundary of a shape,” or the concept “shape” itself, were not clear to us intuitively, we could not extricate ourselves from such a problem by means of formal definitions. For example, we could find ourselves defining a convex shape too narrowly, so that it would be easier to prove the theorem above, but thereby we would lose knowledge that could have been at our disposal. For instance, if we defined a convex shape as a shape with straight boundaries, we would obtain a true theorem—but one that is too narrow. We would not know that the theorem is also true of shapes with boundaries that curve outward. In short: a definition is not a substitute for intuitive understanding, but only a highly important aid to it.

It is also worth noticing that the definition relied on our intuitive understanding of what convexity is, and therefore it is not arbitrary at all. This is in contrast to conceptions according to which assumptions that are not proved—and likewise definitions—are arbitrary. A definition must contain within it the intuitive information that stands at the basis of the proofs in the theory built upon it. The advantage of the definition is that all the non-analytic stages have been removed from the proof stage and concentrated within the definition. From that point onward we use only analytic operations.

It is thus clear that one cannot dispense with syntheticity completely. There are no miracles; therefore there are no analytically proved results where syntheticity is required. Analyticity cannot teach us anything new about the world beyond what is already present in the premises. Therefore all the knowledge required for the proof must be hidden in the definitions. This is exactly what mathematics does: it hides all the synthetic parts of inference within the definitions—and hence their circularity—and afterward uses only analytic inferences. This creates the illusion of purely analytic thought, because the synthetic residue is well hidden within the premises. By contrast, synthetic thought also accepts synthetic rules of inference as legitimate, and therefore it is less constrained by definitions and is not necessarily exposed to circular considerations and definitions.

This second mode of approach brings the synthetic element to the surface, but it exists also in the first mode of presentation. As we have seen, there are cases in which the definition specifically hinders and narrows the understanding and learning of a concept when the concept is intuitively clear to us. In such cases, the second mode of operation seems more reasonable. Mathematics and analytic thought are efficient in those domains in which a sharp separation can be made between the synthetic and analytic parts, and all the synthetic part can be inserted into a system of definitions that will then serve us throughout the rest of the inquiry and thought.

A definition in this sense is a kind of axiom, which likewise stands at the base of the system. The formulation of the definition hides much information about the concepts under discussion, and therefore it functions as a kind of axiom. Above we saw that one generally arrives at the overarching axiom—the major premise of the argument—through synthetic thought, that is, by induction or analogy. There lie all the synthetic stages of the inference. From the axiom one proceeds onward to the theorems by means of derivation rules, which are of a logical-analytic character.

Is a Definition Always Helpful?

Rabbi Zaini’s description shows that enslavement to the search for definitions does not always clarify the picture. Sometimes, in order to have a coherent definition, we narrow the concept, and thereby we lose part of what the real concept tells us. This resembles Russell’s proposal—preceded by Leibniz—discussed in Gate Three (Chapter One), to solve philosophical problems by changing ordinary language into a formal language free of paradoxes and ambiguities. There we saw that even if such a language were found—and Gödel’s theorem, discussed in the previous gate, casts very great doubt on that—it would simply avoid problems by narrowing the ability to express things in language. That narrowing would prevent one from expressing the problems, but certainly would not solve them.

Anyone familiar with the Talmud knows that it consistently avoids all-inclusive definitions and generally proceeds instead by discussion through particular examples. The generalization of the examples into rules is done by the learner, and is not regarded as possessing binding and objective validity. Different houses of study disagree among themselves on questions of generalization, as do the different methods of Torah study. Each has his own mode of generalization and his own conceptual system. Rabbi Zaini, later in his discussion, points out that this approach does not stem from deficiency or primitive thought, but on the contrary: it stems from recognition that defining basic concepts only narrows them and does not clarify them (see also Excursuses 3, 4, 8, and 9).

In Pirsig’s book Zen and the Art of Motorcycle Maintenance, there is described a desperate attempt by its hero, Phaedrus, to arrive at an exhaustive definition of the concept “quality.” The conclusion of that desperate and impossible chase is that it was the ancient Greeks who implanted so deeply in Western culture the belief that everything must have a definition. This deep basic assumption is what entangles thinkers in impossible pursuits and absurd logical loops, as we saw above. In Gate Four we described the development of this idea, up to its exhaustion in modern twentieth-century positivism and its end in postmodernism.

Such an approach can be helpful and useful, but not true. With an approach that is wholly positivist, one cannot advance toward new horizons of knowledge. Basic concepts cannot be defined, just as basic principles cannot be justified. In Gate Six, when we dealt with the concept of “value” (and also in Gate Seven), we noted that the rules of justification themselves—the basic laws of logic—cannot be justified, at least not analytically.

One should notice the parallel here between definition and inference. There is a set of basic concepts, and there are derived concepts that are defined by means of the basic set. Likewise, in an axiomatic system, as we have seen, there are basic propositions that are not proved—axioms—and there are derived propositions that are inferred from them. Positivism relates to both planes: it wished to deal only with well-defined concepts and only with propositions that can be proved formally-analytically. It follows that analyticity—and likewise the postmodernity that grew out of it—undermines the existence of both: the existence of concepts that have objectively fixed and sharply defined meaning, and the existence of propositions that are objectively true or certain. The first challenge, which denies that concepts have sharply fixed meaning, is a form of conventionalism; the second is analytic skepticism.¹⁶ Let us recall that in Gate Two we saw the connection between analyticity and conventionalism, though from a somewhat different angle.

In the next part we shall focus on the opposite connection, namely the connection between syntheticity and essentialism. There we shall continue to examine how, according to the synthetic stance, it is in fact possible to advance, acquire knowledge, and understand new concepts—or more generally, how one can learn in a non-circular fashion. For this purpose we shall make use of essentialism, and of what the Jerusalem Nazirite calls “the logic of hearing.”

Summary of the Discussion in This Gate

This gate dealt with a seemingly side issue, yet one called for at this point in the discussion: is there such a thing as a genuine analytic thinker, and can a rational person at all be such a thing? The answer was that on the philosophical level there is no plausibility in the analytic stance. As we saw, this is the chief benefit of examining ideological questions on the logical-philosophical plane. On the more actual, or ideological, plane, reality is more complex, and people are sometimes unaware of the philosophical prices they must pay in order to hold ideological positions—such as the analytic one—which sound persuasive to them at first glance.

As we saw in the second part, many claims in the Western world are based, at least implicitly, on an analytic stance. Yet those who hold them are not always aware of this, and therefore they ought to examine their positions directly on the philosophical level as well, and at least to be aware that every ideological position must be examined on those planes too.

In this gate we noted that the figure of the analytic thinker is one component within the figure of the postmodernist, the secular person, and the liberal leftist. It is clear that this figure in its purity is only theoretical, but we already addressed that in the introduction to the second part. We tried to clarify somewhat the problem involved in defining rationality, and the way this bears on the question of which of the two stances is more rational, the analytic or the synthetic.

Footnotes

This itself is an analytic conception, for it holds that in the absence of decisive proof, mere plausibility carries no weight. Without proof, according to this approach, we may do whatever we please. Let us note that this is also a certain version of the American pragmatism we encountered in Gate Six, which judges values according to their convenience and practicality.

Equiprobability is generally a result of lack of knowledge, not of knowledge. From such a probabilistic consideration, all one can claim is that the probability of God’s existence is 0.5, since we have no information in favor of or against the side saying He exists as opposed to the side saying He does not. At this point plausibility enters in place of probability. Plausibility is an intuitive concept, of course open to various interpretations, and this is not the place to discuss it.

It is worth noting that experts in statistics or in the sciences are usually not experts in plausibilities but in probabilities. Plausibilities can be determined by anyone according to his own judgment.

One last important remark on this subject.

Even a statistical consideration does not determine the position I should adopt on a given issue. Only plausibility determines that. Even where a probabilistic consideration is relevant, all its persuasive force derives from the fact that it creates in the hearer a high degree of plausibility regarding its predictions. In other words, probability too is a tool for creating plausibility, but in the final analysis plausibility is what determines a person’s position on the issue under discussion. Sometimes there are cases in which plausibility will not go in the direction indicated by the probabilistic calculation. This can happen because a probabilistic calculation is made, as noted, under conditions of lack of knowledge. In the absence of knowledge, one may also decide on the basis of bare intuition rather than on the basis of probability theory. For example, regarding the result of a die throw—is it really so groundless to decide by some bare intuition rather than on the basis of probability? Let these remarks suffice.

I once heard from a friend a story about another friend of his who came to an interview prior to his acceptance into medical school. The interviewers, seeing before them a student wearing a skullcap, asked him what he would do if he found himself in a situation in which he would have to perform an induced abortion—obviously not in a case of danger to life. He replied that if they meant the halakhic question, there is always the possibility of selling the knife to a gentile. But from the moral point of view, he said, he had no idea what he should do in such a situation. The interviewers assumed that the problem here was a religious, technical problem, one that ought to trouble only observant Jews. A situation absurd to this degree can arise only through intensive brainwashing, as indeed is taking place all the time.