Front Matter

From the book A Presence and an Absence by Rabbi Michael Avraham. Translated from Hebrew using gpt-5.4 (reasoning_effort=high, batch API).

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A Presence and an Absence

On Science, Religion, and Myth

And not with you alone do I make this covenant and this oath;

but with whoever stands here with us today before the Lord our God, and with whoever is not here with us today.

— Deuteronomy 29:13-14

This book is dedicated to the memory of my father and teacher, Rabbi Nahman Mendel (George), son of Rabbi Shmuel Zenvil Avraham, of blessed memory.

Wittgenstein

Author’s Preface: Perhaps this book will be understood only by someone who has himself already had the thoughts that are expressed in it—or at least similar thoughts…. On the other hand, it seems to me that the truth of the thoughts presented here is absolute and cannot be challenged. In my opinion, I have, in essentials, finally solved the problems. And if I am not mistaken about this, then the value of this work lies, secondarily, in showing how little has been accomplished by the solving of these problems.

6.211 What we need in life is never a mathematical proposition. We use a mathematical proposition only in order to infer from other propositions, which do not belong to mathematics, a proposition that likewise does not belong to mathematics.

6.51 It is not that skepticism cannot be refuted; rather, it is plainly meaningless if it seeks to cast doubt on what cannot be asked.

For doubt can exist only where there is a question; a question exists only where there is an answer; and both exist only where something can be said.

6.54 These propositions of mine make something clear in that whoever understands me eventually recognizes that they are meaningless. Through them, and by means of them, he will climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)

He must overcome these propositions, and then he will see the world aright.

7. What cannot be spoken about must be passed over in silence.

— From the Tractatus¹

Frege

Since, by your own admission in the preface to the book, only someone who has himself thought the thoughts expressed in it will understand the book, the value of the book is not scientific-philosophical but merely artistic. It is not the thoughts themselves that matter most in it (for the reader who understands them is supposed already to know them), but rather the way in which they are expressed.

— From a letter by Frege to Wittgenstein, after receiving a copy of the Tractatus²

A Deadly Dilemma

While the bloody battle between Blues and Greens raged furiously in Byzantium, there lived there a scholar, far removed from every theological and political quarrel, living only for his beloved sciences: philology, grammar, and law.

He thought that thanks to his solitude and his abstract field of activity, he would be protected from any danger to his health, or even to his life.

One bright day the war of factions again broke out in the streets; a band of Blues, seized by rage, came to the street where the scholar lived and searched every house for sympathizers or enemies.

They burst into his room. He stood before them, his face radiant with great ideas and love of truth.

“Are you a Green?”

“No.”

And they already thought him one of their own.

“Then a Blue?”

“Not that either.”

“If you are nothing—you shall surely die!”

And they killed him on the spot.

— Popper-Lynkeus³

Contents

• List of Notes
• Introduction
• Prologue
• Gate One
• Introduction: The Analytic and the Synthetic
• Chapter 1: The Meaning of the Synthetic A Priori
• Chapter 2: The Analytic-Synthetic Confrontation in Science and on Other Planes
• Summary of the discussion in Gate One
• Gate Two
• An Analytic-Synthetic Analysis of Science: Characteristics and Methodology
• Chapter 1: The Naive Picture: Francis Bacon’s Inductivism and the Challenges to It
• Chapter 2: An Analytic Account of Science: Analytic Solutions to the Methodological Problems
• Chapter 3: A Synthetic Account of Science: Synthetic Solutions to the Methodological Problems
• Chapter 4: Two Planes of Analyticity and Syntheticity: On the Meaning of Scientific Equations
• Chapter 5: Between Science and Mathematics
• Chapter 6: The Social Sciences and the Humanities, or: Is Empiricism the Only Criterion?
• Summary of the discussion in Gate Two
• Gate Three
• A Priori Structures of Meaning: Myth and Science
• Chapter 1: Myth as an A Priori Structure of Meaning
• Chapter 2: Myth and Paradigm: A Priori Structures of Meaning in Science
• Chapter 3: Analytic and Synthetic Interpretations of the Status of A Priori Structures of Meaning
• Chapter 4: Two Conceptions of Historical Myths
• Summary of the discussion in Gate Three
• Gate Four
• Parallel Planes of Explanation
• Chapter 1: Presenting the Problem
• Chapter 2: What Is Explanation? The Problematic Nature of the Existence of Different Planes of Explanation
• Chapter 3: Simultaneous Adoption of Parallel Planes of Explanation
• Summary of the discussion in Gate Four
• Gate Five
• Science and Concepts: Weaknesses and Strengths Inherently Present in the Scientific Perspective
• Chapter 1: Degeneration and Elaboration of Concepts
• Chapter 2: The Scientific Process as the Treatment of Degenerated Concepts
• Chapter 3: A Concluding General View—Science and God
• Summary of the discussion in Gate Five
• Gate Six
• Religion and Science, or: Apologetics for the Advanced
• Chapter 1: The Nature of the Contradiction and the Principal Solutions to It: The Natural Sciences
• Chapter 2: Interpretive Dilemmas: Biblical Criticism
• Chapter 3: Interpretive Dilemmas: Criticism of halakha (Jewish law) and the Talmud
• Summary of the discussion in Gate Six
• Summary and Conclusions
• Science, Religion, and God
• Epilogue
• Bibliography
• Index of Subjects and Names

List of Notes

1. Testimony that cannot be refuted by alibi evidence
2. The theory of negative attributes: can knowledge be accumulated through negation?
3. Different levels of confirmation: halakhic and scientific attitudes toward variation in evidence
4. The raven paradox and material implication
5. The circularity underlying analogy and induction
6. The ontological status of a physical force field
7. The significance of Talmudic interpretive harmonizations: the purpose of study
8. Ockham’s razor
9. The purpose of Torah study
10. The force field and its sources
11. The dispute between Maimonides and Nahmanides over the thirteen hermeneutical principles
12. Logical and physical necessity
13. The ontological status of sets
14. The criterion of justiciability
15. Halakhic and other expressions of the ontology of species and genera
16. The brave bird
17. The mirror paradox
18. The Protestant thesis
19. A Kabbalistic-Hasidic perspective: the king and the garments
20. The psychological “myth”
21. Foundational and directive halakhic concepts
22. Two kinds of scientific explanation: teleology and causality
23. Vitalism and materialism
24. The parable of the blind man and the sighted man
25. From analyticity to syntheticity in Kuhn: the disciplinary matrix
26. Disputes among the sages concerning reality
27. Interpreting the Torah: Pardes, the fourfold interpretive method
28. Phenomenological and essential theories
29. The MIU system
30. Logic and reality
31. Definition and rationale
32. Do we think in the form of an axiomatic system?
33. Theories and models in mathematics
34. Cause and purpose in the creation of the world
35. Mathematical and physical correspondences
36. Theories of synchronicity
37. The logic of “two legal categories”
38. What opposites have in common
39. Continuity of identity
40. The principle of sufficient reason: the concept of emanation
41. Wonder at creation
42. The age of the world: between science and religion
43. Saving the life of a non-Jew on the Sabbath: moral aspects

Introduction

The Analytic and the Synthetic: A General Description

In my previous book, Two Wagons and a Hot-Air Balloon: On Judaism and Postmodernism (hereafter, throughout this book: the first book),⁴ I described a confrontation that has run throughout history between two philosophical positions: the analytic position and the synthetic position. The meaning of the title, Two Wagons and a Hot-Air Balloon, was explained there in the introduction. The “two wagons” are the empty wagon (the secular one) and the full wagon (the religious one), the wagons from the famous meeting between the Hazon Ish and Ben-Gurion. The “hot-air balloon” is a humorous image intended to express the emptiness of analytic thinking, which was the interpretation we proposed there for the Hazon Ish’s remark. We shall return to this emptiness later as well.

The terminology analytic-synthetic is borrowed from Kant’s philosophy (though in our usage it has been broadened), and it describes two forms of philosophical attitude toward certainty or truth. The analytic position is an approach that accepts as certainties only the results of empirical observation, experience, or the logical derivatives of such results. It relates only to principles that have been demonstrated formally and precisely (through the mathematical derivation of conclusions from premises), or that have been observed directly. By contrast, the synthetic position allows even principles that have not been proven or directly observed to be treated as true. In Gate One we shall elaborate somewhat further on this confrontation, insofar as is needed for understanding what follows.

In the first book these two positions were described from historical, ideological, philosophical, cultural, and other perspectives. A critique of the analytic position was presented there. It was portrayed as a position expressing emptiness—intellectual emptiness, not necessarily moral emptiness—and the synthetic alternative was also proposed. The foundation of syntheticity is a renewed trust in intuition, and a willingness to treat foundational assumptions as true even when they are not fully proven. Underlying the claim that foundational assumptions can be examined, and that unproven claims can therefore be accepted as true, is the thesis that the sharp distinction between cognition and thought should be canceled. This follows the teaching of Rabbi David HaKohen, known as the Nazir, who speaks of an auditory logic—that is, a kind of thought that is itself cognition. This is apparently also what the philosopher Edmund Husserl means when he calls it eidetic intuition. The central claim is that a person knows his foundational assumptions, and does not exactly think them.

The purpose of this book is to examine that same confrontation between the analytic position and the synthetic position in the context of the philosophy of science and scientific methodology. As we shall see, this confrontation also radiates outward into the relations between science, religion, and myth. Over the course of the book we shall draw some of the conclusions that follow from these two positions, the analytic and the synthetic, with respect to those domains.

A considerable portion of the discussion deals, ostensibly, with standard material in the philosophy of science, which we shall address, as concisely as possible, in Gate Two. But it is important to remember that we shall describe the problems and the various points chiefly from the analytic-synthetic angle. Our principal concern in this book is with additional perspectives that tend to be neglected in discussions of this kind. These perspectives are connected to the analytic-synthetic framework.

It should be noted that Ze’ev Bechler, in his book Three Copernican Revolutions,⁵ describes this very confrontation (in his terminology: actualism-informativism) in the narrower context of the philosophy of science. We shall mention several points raised in his book, but, as we shall see below, he goes only part of the way and does not offer a genuine alternative to analyticity (actualism, in his terminology). In this sense, his approach parallels those of Taub and Steinitz, discussed in the previous book. All three sense the analytic vacuum. All three cry out and protest against it, yet they do not offer a truly grounded alternative. They provide no solutions to the problems posed by analyticity (actualism), and from the force of those problems analyticity derives its absurd conclusions.

As we saw in the previous book, and as we shall see again here, the root of the matter is that these thinkers do not descend to the logical-philosophical root of the problem: the need to abolish the sharp dichotomy between cognition and thought.

The Trilogy

This is the place to note that, in the not-too-distant future, a third part will, God willing, be published, and it will complete this trilogy (hereafter, throughout the book: the third book). That part will deal with the human being and the relations between body and soul, and also between emotion, intellect, will, and choice, and between all of these and psychology in its various layers.

Originally, all three parts were written as one book, which was supposed to be published as a single unit. Once I realized the great scope of the material, and after receiving the opinions of several friends, I decided to split the book into three separate parts, to expand and elaborate each of them, and to establish each on an independent basis.

Thus, one may indeed treat the three books as a trilogy, but each of them is built as a book in its own right and is not directly dependent on the other two parts. Even so, a fuller picture can be obtained only through a detailed reading, in order, of all three parts. In truth, what we have here is one long line of argument, each stage of which depends on what came before it. In order to preserve the autonomy of each part, a summary of the relevant portions of the earlier books will be given here (and, God willing, also in the third part), insofar as that is necessary for understanding the matter. Beyond that, there will be references, not obligatory ones, to the other parts, so that anyone who wishes to broaden and deepen the discussion may do so as he chooses.

The Name of the Book

We shall conclude the introduction with a brief reference to the meaning of the book’s title and to the quotations on the second page.

The title of the present book, the second in the trilogy, expresses the fact that its contents deal with the question of the existence (“what is present”) and nonexistence (“what is absent”) of abstract entities, both in science and in myth. The discussion will proceed through a comparison between science and myth, and its conclusions are that the necessary foundation required for both of these domains is a synthetic position. We shall see the implications of these two approaches for the question of the existence of abstract entities in both domains. The matter will become clearer as we proceed.

The Three Quotations on the Opening Page

The first quotation on the opening page is taken from the book of Ludwig Wittgenstein, one of the greatest philosophers of the twentieth century and one of the fathers of the analytic school in philosophy. His first book, which expresses the doctrine of the “early” Wittgenstein and was the only one published in his lifetime, was titled by him Tractatus Logico-Philosophicus (= Logical-Philosophical Treatise), or in short, the Tractatus.

In this book Wittgenstein deals with an attempt to address the fundamental problems of mathematics and logic, and of philosophy in general, by analytic means. It is therefore important to note that the first sentence quoted above actually expresses the emptiness of the analytic: “how little has been accomplished by the solving of these problems.”

The closing sentence also expresses an analytic approach (proposition 7, “What cannot be spoken about must be passed over in silence,” is the final proposition of the book), but it is important to note that this is a moderate analytic version. Wittgenstein does not deny the existence of the things about which one must remain silent; he denies only our ability to speak about them usefully.

In Wittgenstein’s statements quoted above there is a description of mathematics as an analytic tool whose whole importance lies in clarifying synthetic claims. Once they have been clarified with the help of the mathematical “ladder,” we must throw it away, since it has no meaning in itself. This too is an expression of a synthetic position, though somewhat implicit.

Gottlob Frege, who wrote to Wittgenstein the disappointing letter part of which is quoted above in the second excerpt, is one of the greatest logicians and philosophers of mathematics of all time. His works, which were not sufficiently recognized in his own day, inspired many who came after him and continue to do so to this day. He too is considered one of the founders of the analytic approach in philosophy, although it seems that he was not an analytic thinker in the senses this term takes on in our trilogy. It is important to note that he also deeply influenced Wittgenstein himself.

In his letter, Frege rebukes Wittgenstein for clarifying only those things that the reader already knows in advance. He claims that a book of this sort has merely artistic value, not philosophical value.

It seems to me that, among other things, Frege is rebuking Wittgenstein for his analyticity. As we saw in the first book, and as we shall see again below, the analytic position regards philosophy, and thought in general, as a tool for clarifying foundational assumptions—but certainly not as a tool that reaches new truths, that is, synthetic claims, beyond what is already in our possession. Frege himself, despite his abilities, his work, and his lofty status as one of the fathers of analyticity, expresses a synthetic approach in several of his positions.

However, in the first book we already pointed out, and here we shall show in greater detail, that the principal role of philosophy, even from a synthetic conception of it, is to clarify what we already know. At first glance that may seem to be the analytic motto, yet those who hold the synthetic position accept it to a certain extent as well. The difference between the two approaches does not lie precisely in their relation to this question, but rather in the question of the arbitrary status of the assumptions, and therefore also of the conclusions. Can foundational assumptions be criticized, or can one clarify for someone an error contained in his positions, or not?

As we saw in the first book, and as we shall see again, the heart of the matter lies in the attitude toward intuition as a solid basis for acquiring knowledge of the world. This is the only foundation upon which the logical-analytic structure can be built, and therefore analyticity cannot offer any substitute for it.

It is worth noting here that these two figures in particular are examples of clearly analytic thinkers who did not necessarily express analytic positions, in the sense this term has for us. See below in Gate One. Their analyticity was a central tool of thought and analysis, but they were aware that it was only a partial tool, and that its use solves very few of the real problems, as Wittgenstein writes in the preface to the Tractatus.

The third quotation is taken from the book of Josef Popper, who called himself by the pseudonym Popper-Lynkeus. Popper—not Karl Popper, the philosopher of science, whose views we shall discuss in Gate Two—was a thinker active in the first half of the twentieth century who worked on social, technological, and scientific matters. He also set down his thoughts in short stories and fantasies, each dealing with a different subject.

The fantasy quoted here concerns a man of the humanities who feels detached from what is happening in the world and is convinced that everyone recognizes his value. When he encounters bitter reality, it becomes clear to him that his learned neutrality, empty of any political content and, in his view, above all such disputes, actually expresses opposition to both warring sides. From their perspective he does not exist at all, and they kill him.

This is an illustration of neutrality, or ideational emptiness, that focuses on the study of the abstract as such, ostensibly without connection to any political or practical consequences. Against this background it is interesting to note that philology, grammar, and law are three fields used in the study of the sources of Judaism. Here too scholars feel that they are dealing with matters without prejudices, and that their findings therefore reveal the failures of some traditional positions.

But this is an empty analyticity, which, when it meets reality, proves to be a position equally opposed to all positions alike. The very absence of assumptions—supposedly—constitutes a position within this discourse. The analytic thinker believes that he is merely a neutral scholar who takes no part in ideological power struggles, but it turns out that he most definitely represents a position opposed to all the others: the analytic position.

If we return to the previous two quotations, it is important to note that the disagreements between Wittgenstein and Frege also exist on abstract logical planes. Yet throughout the trilogy we repeatedly see that disagreements of this kind bear on very many value-laden and ideological questions, and therefore their practical consequences are decisive.

All these are only rough headings, intended to clarify the relevance of the quotations above and to provide a general introduction. Further elaboration will be given in Gate One, which is devoted to clarifying concepts we shall need later in the book, and also in what follows.

The Structure of the Book

The structure of the book is as follows:

• In Gate One we shall try to describe, in brief, what we need from the first book. This is an introductory gate.
• In Gate Two we shall discuss the philosophy and methodology of science, and present the central points in these issues from the analytic-synthetic angle. We shall see that science, usually presented as the foundation of analytic outlooks, is itself based on clearly synthetic principles and methodology.
• In Gate Three we shall examine the relations between science and various myths, and show that science itself also operates within a framework that can, in certain respects, be regarded as a myth. Already in this gate we shall see that, contrary to conventional religious apologetics, synthetic positions—mythic and religious ones—should not be built upon the ruins of science. This path will later be called the postmodern rehabilitation of religion and myth. Here we shall try to offer a synthetic, rather than an analytic, path to such a rehabilitation. Precisely through trust in science we shall understand the need for religion and myth, and for the supposedly “outdated” assumptions regarding their credibility.
• This synthetic position, as we shall see, requires us to regard several planes of reference and explanation as valid simultaneously.
• In Gate Four we shall discuss the problematic nature of such a position, and propose several ways of overcoming it. There we shall try to understand what explanation is and what description is, what the relation is between cause and purpose, and also address the question of how contradictory planes of explanation can coexist side by side. Several methods, or mechanisms, will be proposed there that make possible the simultaneous adoption of different planes of explanation.
• In Gate Five we shall introduce a new term: degeneration of concepts. By means of it we shall explain some of the successes and limitations of science, and propose some delimitation of its validity.
• In Gate Six, the last gate, we shall demonstrate these various methods through different issues concerning the contradiction between science and tradition—religion, or myth. Beyond the specific contents discussed there, this gate also serves as an illustration of the methods proposed in Gates Four and Five. It should be noted that the explicit discussion in this gate will deal more with questions of interpretation, connected with what are called the social sciences and the humanities, than with questions concerning the natural sciences. The latter are woven mainly through the discussion in Gates Four and Five, and to some extent also through the first chapter of Gate Six.

This book, like its predecessor, is interwoven throughout with notes that serve as local expansions. They were printed in a different font so as not to interrupt the flow of reading. Some are intended to clarify ideas that arise briefly in the main text, and some expand side issues or present examples and interesting implications of the discussion. Most of them can be skipped during a first reading, unless stated otherwise.

Apologies

A few apologies that are difficult to do without:

• First, the ideas for this book took shape over a long period of time. Therefore, I do not always remember their written and oral sources. I apologize to the originators of ideas if I failed to mention them by name.
• Here too I have continued the approach that characterized the first book, namely, that the book assumes no prior knowledge and addresses as broad an audience as possible. Such a decision carries the price of a certain expansiveness, which some readers may find unnecessary. My apologies to them. In general, I hope and believe that every part of the book contains something new for every kind of reader.
• The whole trilogy, and this book in particular, is a monograph. As such, it does not pretend to raise every possible option on every subject, or to present the full range of existing opinions. Nor do I claim that I have correctly understood the views of every thinker whom I cite in the course of my discussion. The interpretations given to different thinkers are given to the best of my understanding, but without the comprehensive research required of one who seeks to plumb the full intent of their words. As far as I am concerned, even if the venerable “Rabbi” Kant did not say what I have put into his mouth, that is not really important. The reader, in my view, should examine the arguments on their own merits, not according to the stature of those who said them. This book presents one particular position and recruits everything available in its favor. It is indeed tendentious, and I declare that openly in advance.

Thanks

At the end of the introduction, and before opening the gates, I wish to thank all who contributed to me in the subjects discussed in my books and in other fields. I will not repeat here the detailed list that appears in the first book, but this is certainly the place to mention those who contributed directly to the present book.

First, my friend Avi Warshavsky, who read the initial manuscript of this book as well, and who here too contributed from his wide knowledge and the sharpness of his thought. Some of his comments appear under his name, but I am certain that there are many others that also came from him.

Second, the devoted editor, Yitzhak Rekanti, from whom I benefited in counsel and resourcefulness in several areas, and for whose patience, responsibility, and professionalism I am grateful.

To my family members, and especially to my dear wife Dafna, to my sister Naomi, and to my brother Dani (who even read the first book…), and to my children, for not disturbing me too much.

The staff of the yeshiva in Yeruham has hardly changed since the publication of the first book, and I thank them all again here; but the students are mostly different now, and I wish to thank them as well, for their support and attentiveness, for their ideas and their interest. I wish them students like mine.

I also wanted to evoke the memory of my good friend Ze’ev Olami, of blessed memory, a senior researcher at the Weizmann Institute. Beyond several scientific works we did together, we exchanged very many thoughts and ideas in numerous and varied fields. Ze’ev passed away before his time from cancer, which battled him and could not overcome him for several years, until at last he was defeated. May his memory be a blessing.

As thanks to the One who made the principal contribution—the God of the spirits of all flesh, who assists me in all that I do—I shall conclude the introduction with the prayer of Rabbi Nehunya ben HaKanah, recited when a person enters the house of study:

May it be Your will, Lord my God and God of my fathers, that no mishap come about through me, and that I not stumble in a matter of Jewish law, and that my colleagues rejoice because of me. And may I not declare the impure pure, nor the pure impure, nor the permitted forbidden, nor the forbidden permitted. And may my colleagues not stumble in a matter of Jewish law, and may I rejoice because of them. For the Lord gives wisdom; from His mouth come knowledge and understanding. Uncover my eyes, that I may behold wonders from Your Torah.

— Shulchan Arukh, Orach Chayim 110

Prologue

Tortoise: Hello, Achilles. Nice of you to come down among the people once in a while.

Achilles (clearing his throat): Hello, hello. Here we meet again.

Tortoise (chuckling to himself): Yes. Tell me, do you remember our last meeting?

Achilles: I think the subject we discussed was analyticity and syntheticity. Back then you managed to do the impossible: to make me repent and turn from analyticity to syntheticity. As we saw then, that process itself involves an inherent logical paradox.

But to tell the truth, I am still troubled by some of the questions I asked you at that meeting. The fact that there is truth, and that it is not necessarily relative and subjective, still gives me no clue as to what that truth is. For example, is your traditionalism a necessary derivative of your synthetic position?

Tortoise: That depends on what necessary means for you. Logic? If not, then yes—I hold a traditionalist approach because of my synthetic position.

Achilles: But traditions are nothing more than primitive myths!

Tortoise: You pest! You yourself are a primitive myth! Tell me, how are Hector and Priam? When did you last meet Zeus?

Achilles (glancing, involuntarily, at his heel): What—just don’t tell me you’re post-Hellenic!

Tortoise: No. Absolutely not! I only wanted to show you that even the existence of a ridiculous, over-philosophizing creature like you is based on myth and tradition. So in fact you too are traditional, almost as much as I am. (pointing at Achilles) Here stands an enlightened philosopher with a traditionalist outlook.

Achilles: Well, you surely understand that myth is not measured by the degree of its historical reliability. The Trojan War may never have existed at all, yet Achilles as an idea, as an ideal form, does not depend on any historical Achilles.

Tortoise (sighing): So who is post-Hellenic here?

Achilles: A post-Hellenic person is one who undermines the Greek-Hellenic myth. I, on the contrary, believe in it. But belief in a myth does not mean trust in its historical occurrence. After all, myth is not history, and certainly not science. I think the Hellenic myths are a cultural framework, and also an important and meaningful medium for the transmission of ideas. I believe in them as such.

Tortoise (looking around anxiously and winking at the reader): Still, doesn’t it bother you a little that I am talking with an idea? They might forcibly institutionalize me for that.

Achilles (tears in his eyes, somewhat confused. Then he straightens his suit and draws himself up): But Thetis, my mother, always told me not to believe in superstitions. And my master and teacher Hephaestus, the one who forged my shield, who himself enjoyed the actual authority of a demigod, was endowed with a very rational approach to the world and to the entities operating within it. He was never prepared to accept claims about the real existence of a mythic figure or event. So I have no choice but to follow them and declare: I think, therefore I do not exist!

Tortoise: Actually, it would be more accurate to say that you do not think, and therefore you do exist. (chuckling to himself) Tell me, why is it that with regard to science you do insist on a realist approach? Have you ever seen a force field with your own eyes? Or perhaps you grow an electron tree in your yard? And what about the speculations of your historian friends, ancient or modern? Do they seem to you more real than the myths of the Zulu tribe—with all due respect to the Zulu, of course?

Achilles: You taught me to be synthetic. Science is based on synthetic a priori claims—that is, claims whose source lies in our thinking and not in experience, and yet they are claims about the world outside us. And I have already learned from you to accept them as true. But myth contains no claims at all. The “problem” with myth is not that it is based on synthetic a priori propositions, as science is, but that it has no factual content at all. But, as I already told you, that is not a problem. Myth is not judged on the plane of historical reliability.

Tortoise: Well, at least you are willing to learn something from a barbarian like me. But you know, it seems to me that there is room for improvement in your capacity to learn. Tell me, am I right in detecting that you still have remnants of analyticity in you? I strongly recommend that you purge the leaven. You would do very well to reexamine your relation to reality. You need to clarify for yourself what myths are, what sciences are, and also what the relations between them are.

Achilles: What McCarthyism! What exactly do you mean?

Tortoise (angrily): I mean to say that, in my opinion, you really do exist.

Achilles (in a forgiving, understanding, sympathetic tone): Oh, really! (after a pause) Tell me, Descartes…

Tortoise (interrupting impatiently): Don’t philosophize, and don’t be so stubborn. I am prepared to give you a candle.

Achilles: Mmm… I don’t understand! Would you mind expressing yourself like a civilized being?

Tortoise: I mean that I want to help you search out the leaven. Perhaps that way I will prove to you that you exist.

Achilles: That might perhaps be worth another race between us. Perhaps we could call it “the spring race.”

Tortoise (sighing, and thinking to himself: “So he agrees. We shall make one more attempt to save a little strength and time”): The spring race, or the charming race—everything with you is words, words, and more words. (And now he adds, with undisguised hope in his eyes): Tell me, it is a somewhat long story. Are you still willing?

Achilles: To tell the truth, after the previous race I expect greater consideration from you. After all, I do not possess athletic ability like yours. You remember that already in the first race we held, you won. Zeno of Elea already documented that.

Tortoise (beginning to crawl energetically): And perhaps a pest like you does not deserve consideration. In any case, follow me. And… try not to leave any gaps.

Achilles (beginning to take on flesh and blood as he runs): Wait a moment…

Footnotes