Sometimes out of boredom I pick off the shelves a book I wouldn’t read otherwise. So it was that leafing through Bertrand Russell’s History of Western Philosophy, chapter on Dewey, I came across this definition: A belief is true when holding it avoids surprises; if we end up being surprised by the facts, our belief was false. This struck me as wonderfully hilarious, my boredom suddenly vanished, which was, I suppose, proof of the falseness of my previous views of truth. I imagined King Solomon in Gibeon, when the Lord—not Russell; the biblical one—appeared to him in a dream and offered to grant him any boon. Solomon asked for wisdom and discernment, we are told, and the Lord was so pleasantly surprised that He granted the son of David honor, riches and a long life, on top of unparalleled wisdom. Yet had Jehova added, “But Schlomo, my boy, you should be warned; a perfectly wise man discerns all truth, hence he is never surprised, hence he’s perfectly bored: would one wish for a long life, even if filled with honors and riches, under such conditions?,” very likely Solomon would have settled for half-and-half, wisdom and folly.
Then I reflected that Jesus, witness to all truth, ought to have never been surprised: everything that happened was foreordained and he knew it in detail. Surprisingly, though, we read in Matthew 8.10 and in Luke 7.9 that Jesus “was astonished” (ethaúmasen) at the strong faith of the centurion, and in Mark 6.6 that he “was amazed” (ethaúmazen) at the lack of faith of the people of Nazareth. Thomas Aquinas interpreted this as a proof of Jesus’ humanity, for a purely divine being, a perfectly wise one, he argued, would not have been astonished or amazed. Thus, we see that the notion of truth as avoidance of surprise is much older than Dewey and Russell, older than Ogden and Richards, who proposed similar ones, and even older than Aquinas. Plutarch (Moralia, 44B) reports Pythagoras as saying that he had gained this advantage from philosophy, to wonder at nothing (tò medèn thaumázein), and Horace, ever the elegant echo of the Greeks, puts it thus in Epistles, 1, 6, 1-2:
Nil admirari prope res est una, Numici,
solaque quae possit facere et servare beatum.
(To marvel at nothing is perhaps the one thing, Numicius,/
the one and only thing that can make a man happy and keep him so.)
My intention is not to blaspheme against any of the Lords, but it must be pointed out that Christian dogma and positivistic, Russellian logic partake of the same essence, that is the denial of the main feature of time: to bear the new and the unexpected. The Christian god is omniscient, possessing past and future in something timeless Plato called aión and Augustine and the other Fathers called eternity, and has deigned to communicate his knowledge, at least in spurts and snippets, to prophets, evangelists and his Son. For their part, Positivists don’t claim to know everything, merely that only knowledge of eternal truths is possible. Thus Russell wrote somewhere: “The beginning of wisdom is to realize the unimportance of time.”
In this essay I don’t mean primarily to raise the tí esti, the “what is” of truth, or to define it, but rather to examine the question Pilate might have asked had he been a psychotherapist: “How does it feel to be a witness to the truth?” Thus reformulated, the question seems at first to have become empirical, hence more amenable to answers, but if we reflect a moment we discover that it isn’t so. For as soon as we say “feel,” and we say it next to “truth,” we hear Hegel’s sharp rebuke: “The unutterable—feeling or sensation (Gefühl, Empfindung)—far from being the highest truth, is the most unimportant and untrue” (Logic (Encyclopaedia), §20). Our new question, then, would be false from the start, the way questions may be false, by containing a contradiction. Truth, for Hegel, is the universal, that is, the abstract, the “permanent substratum” (Logic, §22); and if we read a little further, “Philosophy therefore advances nothing new.”
Listening carefully and comparing, we are forced to ask a further question: in Hegel’s “unimportant and untrue” of feeling, in his “universal,” “abstract,” and “permanent substratum” of truth, and finally in his proud “nothing new” of thought, aren’t we hearing the same metaphysical refrain we hear from Russell, the same song of eternity, moreover, we hear in Christian dogma? Perhaps Hegel, the Positivists and the Fathers of the Church are, if not spiritual brothers, first cousins? *1 Their grand uncle, in that case, is Aristotle. When the rules of thought were organized, at one and the same time the new and the unexpected were banished from the realm of Truth, exiled into the bogs of feeling and psychological motivation. At the beginning of the Metaphysics (I,2), Aristotle places wonder and surprise (tò thaumázein) at the beginning of wisdom in the same sense one places hunger at the beginning of hunting, cooking and eating: for him knowing is the activity by which one assuages wonder. In On Interpretation, 18a-18b, he offers the following argument: A proposition is either true or false and never both; but this applies, too, to a proposition whose verb is in the future tense, thus referring to some future event; it follows that whatever will happen is determined now (or at least as soon as the corresponding proposition is thought). All things, therefore, are necessary.*2 Yet Aristotle, never inclined to extremes, recognized that many things are contingent. Whether or how he got out of this mess is unclear.
It is easily understandable that the Fathers would not be open to the new, because of the dangers of heresy; as for Hegel’s and Russell’s animus against the new and the unexpected, one may argue that Hegel was reacting against the Romantic love for unmediated or immediate knowledge, spontaneity and communion with nature, Russell against Bergsonian intuition. Any honest person who attempts to teach anything not strictly formal or factual to college students, who therefore must constantly contend with their peevish “That’s the way I feel, anyway,” must sympathize with Hegel and Russell, if not with the Fathers of the Church, and might post upon his office door: “It marks the diseased state of the age when we see it adopt the despairing creed that our knowledge is only subjective, and that beyond this we cannot go” (Logic, §22). But beyond those understandable reactions, there is something more troubling, namely the question whether the new and the unexpected can ever become the matter of conceptual thought. Will philosophy keep open and free of brambles the path opened by Kierkegaard and followed by few *3? Will it be ever able to grasp the purport of Time’s speech at the beginning of Act IV of Shakespeare’s The Winter’s Tale,
“...Since it is in my pow’r to overthrow law, and in one self-born hour to plant and o’erwhelm custom”?
Will it be able to say what the Shepherd says in the same play,
“Now bless thyself: thou met’st with things dying, I with things new-born”?
Or will it forever remain decrepit, comical?
For when I say “witness to the truth” I do not mean a humdrum truth, 2+2 = 4, which has become ossified into a rule; I mean it in the sense of Shakespeare’s Shepherd, witness to the lifting of the bearing-cloth in which the baby is borne to baptism, the revelation before the giving of a name. But even 2+2 = 4 need not be humdrum; no truth exists in isolation, objectively: it all depends on our witnessing. Times have changed, mathematical science has moved far beyond the eternally fixed certainties of Hegel and the Positivists, surprise and the unexpected have gained a legal footing, the disastrous dialectics of freedom and necessity are crumbling and so are the political systems purporting to be based on them; History, as always, is ending—and it is just beginning. So let us reformulate our question once more: “How does it feel to be a witness to the truth in our time, 20 centuries after Jesus and Pilate?
Having written the above, in January 1997 I was in the audience when Caroline Walker Bynum, a medievalist, delivered her presidential address at the annual meeting of the American Historical Association. Her title was “Wonder,” and she began by saying that she keeps on her bulletin board a copy of a Paris wall slogan from the student rebellion of 1968: “Toute vue des choses qui n’est pas étrange est fausse.” We have here, concisely put, the opposite of Russell’s criterion of truth: truth must be étrange, a word for which Bynum offers the English “bizarre” or “foreign.” “Strange” comes first to mind, but I prefer the stronger “outlandish” or “uncanny.” In any case, the Parisian students were rebelling against an entrenched and very basic view of truth, going back at least as far as Aristotle and farther to Pythagoras; they were voicing the opposite view, at least almost as old, going back to Tertullian’s logically stricter “Credibile est, quia ineptum est.” *4
Which of these is a true view of truth? There seems to be four possibilities: (1) one and only one of these two views is true, (2) neither, (3) both, and (4) the question makes no sense, and there is no such thing as the truth of truth (a view maintained by Ogden and Richards in The Meaning of Meaning).
At the beginning of On Interpretation Aristotle states the obvious fact that there are different languages and that words, whether spoken or written, are not the same for everyone; but then he goes on to state something far from obvious and quite startling:
“However, those of which the words are signs (seméia) in the first place, those affections of the soul (pathémata tês psychês) are the same for everyone, and those of which these (the affections) are likenesses (homoiómata), namely the very things (prágmata), are also the same for everyone.”
Ever since, those rhyming neuter plurals—pathémata, homoiómata, prágmata—have been the three key words and refrain of our definitions of truth. And also of our theories of reference, typically threefold. The definition which was to have a brilliant future in the West is found in the 10th century Isaac ben Salomon Israeli’s Book of Definitions: truth is “adaequatio intellectus et rei.” Here pathémata tês psychês becomes intellectus, homoióma becomes adaequatio, and prágmata becomes res. On different interpretations of those three Greek words have hinged the various philosophies of the West, up to the 20th century when Frege denied that a definition of truth is possible and Heidegger gave an entirely different one. I have already noted, however, that our concern will not be primarily with the “what is” of truth; when it comes to the question of how does it feel to be witness to truth it seems better to start from an example, for which I must choose the truth that impressed me most. Sometimes I tell my math students that it was the proof of the following Euclidean proposition: The center of a circle is unique. But I’m afraid it is false, I mean, the claim that it impressed me most is not true. No: my most memorable experience with witnessing truth happened at age 6, when older cousins told me the “facts of life,” or “about the birds and the bees.” The revelation shook me to the core, and it may be philosophically worthwhile to inquire why.
In the first place, it dramatically involved my father and mother, the two beings closest to me, and it meant that there was something uncanny going on at home, in my world (this succeeds better in German: Etwas unheimlich im Heim; in English “outlandish” may be a better word). There was the announcement of a need, a craving (“But do they like it? Oh, yeah! They love it! It’s like a kind of hunger, you see...”), but it was a need, a hunger I did not feel—not yet. Secondly, and equally important, certain facts, already obvious to me, became linked, or rather aligned and pointing to the uncanny: “Have you noticed that sometimes it gets stiff? Right now it gets stiff only when you want to go pee, but later you’ll see...” plus my parents’ bed, larger than mine and my sister’s, on which they slept side by side, plus those parts of my younger sister’s body glimpsed through the shimmering water in the basinette, and the fact that people come in two types, boys and girls. Some kind of cognitive unity was achieved, by which I do not mean logical consistency but merely that alignment and pointing to the uncanny. Finally, it was clear to me that the revelation was not about what adults call natural science, but about my own origin and destiny—what was announced was a need that was bound to shape my destiny. The distinction is important, for ever since Galileo recanted before the Church, the truths of natural science have become more and more detached from ethical truths, the ones which regulate our behavior in life.
To fit this story into a theory of truth and reference of the Aristotelian type, one would have to come up with a proposition such as “Here’s how animals, including your parents, reproduce, etc.” Then one would have to find the references, the mental constructs of which some of these words are signs. The concept “penis,” for example, would include (in the set-theoretical sense) likenesses or copies of my cousins’ as well as mine, and for the sake of communication one would hope that even if perfect identity as postulated by Aristotle was not achieved, there was some overlap among the corresponding mental constructs in my cousins’ minds and mine. Finally, to decide on truth or falsity, one would have to compare the structures established by the proposition between those mental constructs with the structures of those things whereof they are likenesses (the referents) in the world out there. One would have looked at the pertinent “states of affairs” and checked if they were “like” what my cousins told me.
All this is plausible, even though one may point at problems with the meaning of “like,” “likeness” and “similarity,” of “mental constructs,” “overlap” and “structure,” to name but a few which have occupied keen minds. The most important problem, though, is that those operations have very little to do with the feeling of witnessing the truth. The model behind the above type of description is the puzzle: one assumes that there are identifiable, fairly stable pieces (the mental constructs), which may or may not fit with each other and with a frame (the outside world); each true proposition allows us to achieve a better fit. Now whether these pieces are given to all of us, as Aristotle seems to assert, or whether, according to more fashionable views such as Michel Foucault’s, some or all the pieces are arbitrarily cut so that, in the limit, each of us plays a different game at any given time, it does not matter much: truth is still the gradual fitting of a puzzle (all truth, that is, except this metaphysical one, that truth is the gradual fitting of a puzzle; but that’s okay, for a model cannot cover everything). If I am pressed to propose a better model, I would say that the revelation of truth effects something similar to what in physics is called a change of state: suddenly the whole mental reality is changed into something new, as when liquid water is changed into ice or into vapor. I mean to stress not the molecular mechanics, but the suddenness of the change and the phenomenological (if not chemical) newness. Charles Galton Darwin, in The Next Million Years, writes that “happiness does not come from a state, but from a change of state.” Gabriel García Márquez’ Cien años de soledad opens with Colonel Aureliano Buendía facing the firing squad and remembering the uncanniness of that distant afternoon when his father took him to discover ice. Perhaps I will remember my cousins’ story if I ever face a firing squad, for the uncanninness of one moment evokes the uncanninness of a previous one. Or, guns pointing at me, one second before that final “Fire!,” perhaps what I’ll remember will be that other moment when at age fifteen I came upon the theorem, “The center of a circle is unique.” It wasn’t any less uncanny than my cousins’ story; suddenly, I had discovered what is math: that, once remarked, the uniqueness of the center was obvious to my intuition, clear to my senses, was not the point; the point was that it had to be deduced, somehow, from the definitions and the axioms. Circles, radii and centers inhabit a world independent from the senses, a world with no birds nor bees, mercifully free from parents and beds, an uncanny world indeed which at that moment was revealed. I cannot say which revelation I’ll remember at the final juncture: we’ll have to wait and see.
In any case, theories of truth and reference of the Aristotelian type are unable to explain the wonder of the witnessing of truth. For the time being we’ll just keep those three features—uncanniness, organization of cognitive unity, and close connection to one’s origin and destiny—which I take to be characteristic of the witnessing of truth. It is already apparent that witnessed truth being uncanny, it cannot coincide with what is fully expected, but the notion of “uncanny,” too, is in need of elucidation, if the witnessing of truth is not to be dismissed as mystical. We must note immediately that the three features of witnessed truth are by no means independent: we must ask what is it that moves us to abandon the cozily familiar for the sake of a new cognitive unity, and we must also ask what is it that moves us to assume the uncanny and incorporate it into our destiny. For I could have rejected the lesson of my cousins, relegated it to some well-protected corner of my memory, or somehow or other minimized it.
The same John who told us about Pontius Pilate had Jesus admonishing the Jews that truth will make them free. The German Idealists inverted the relation: freedom is not (or not only) the result of truth but, according to Schelling and Hegel, it is at the very basis of truth. Heidegger, in Vom Wesen der Wahrheit (On the Essence of Truth), continues that tradition and takes freedom to be that essence. We may go along with him, if by freedom we understand not his Taoistic letting-be (Sein-lassen), but precisely that movement in us which assumes the uncanny even though it would be so much easier not to do so and stick to the familiar. Perhaps some day our freedom, in seeming conflict with all scientific natural laws, will be explained in terms of evolutionary biology; for the time being it remains a mysterious, irreducible but undeniable fact.
As soon as my cousins left, I asked my parents whether “that” was true. Somewhat shamefacedly (bless their souls) they acknowledged it was. Years later Mother told me I had been shaking all over. With time, “that” too became a familiar thought, part of the human rut, and so, having lost its uncanniness (well, to be truthful, not all of it), its truth became diluted—it was turned into a non-truth, we might say it became false. Such is obviously the fate of most truths, if not all; for how could we avoid the fatal dissolution into familiarity? This jejune psychological fact lies, I think, behind the Heideggerian contention that truth—alétheia—is a lifting of the veil, a revelation, but at the same time, or even prior, a re-velation, an occultation or dissimulation: the veil is lifted only to be replaced. Again, how could we avoid that? We could die right after the moment of truth, thus sealing it in the amber of nothingness. We could, like Oedipus (a far better example of truth, freedom and destiny than the birds and the bees, but less mine) gouge out our eyes, so that no new ideas, no familiar light, would be allowed to disolve the uncanniness of our truth and make it unwitnessed, that is, false.
Witnessing truth, then, puts us in a tragic predicament, and Nietzsche, who went far and mad trying to answer our questions, was right to insist that Greek tragedy and Greek philosophy were born at the same time. The three features of the witnessing of truth are always present in Greek tragedy: uncanniness, esthetic unity of organization, and ethical consequences. The chorus sings in Aeschylus’ Agamemnon the fundamental tragic axiom with respect to truth: “We learn through suffering,” where we must understand that what we learn (matheín) are strong truths (usually not the ones which were later to be called mathematics), and that matheín, learning, means not just the acquisition of truth but also the holding on to it, the saving it from becoming trivial. Nietzsche was also right in proclaiming Wagner’s Tristan und Isolde the modern equivalent of Greek tragedy. For Tristan and for Isolde, truth is that of their mutual love, made even more uncanny by its origin in the drinking of the love potion, and it was Wagner’s stroke of genius to make this truth unable to bear the sunlight, not because Tristan’s and Isolde’s love was disloyal and sinful, a betrayal better kept in the dark, nor, as in the traditional poetic conceit, because dawn brings the lovers’ parting, but because their strong truth could not abide the rut of the familiar. The sun, in fact, with its periodic, predictable setting and rising, is the primary source of repetition, and repetition is the source of familiarity, as well as the source of the old hope of rebirth. Hence sun and sunlight are repeatedly cursed: cruel, envious, garish, deceptive, liars.
It is time to elucidate what we mean by uncanny. But first, what do we mean by elucidate? Simply, that we move away from the domain of the birds and the bees (someone might dismiss it, “Oh yes, that’s a big thing with kids”), away from the personal and psychological, and into the domain of pure reason, whose strong citadel is logic and mathematics. We must meet Hegel, Russell and the other philosophers on their turf. For this, it will be useful to select another example of witnessing the truth, this time from the history of pure reason—naturally enough, the traumatic episode at the very beginning, when pure reason lost its innocence. Aristotle himself mentions this example when, at the beginning of his Metaphysics (983a), he insists that wonder, the beginning of wisdom, must be extinguished by wisdom: the incommeasurability of the diagonal of a square may seem a wonder (thaumastón) to the uninitiated, but “a geometrician would wonder at nothing so much as if the diagonal were to become measurable.” My aim in this essay is to argue against such superficial notion of “wonder,” “wonderful,” and “uncanny.”
Having secured the logical tools for mathematical proof, chiefly the principle of non-contradiction, and the most elementary properties of natural numbers (1,2,3, etc.), having proved that in a right triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides (for which, says Diogenes Laertius, Pythagoras offered an hecatomb to the gods), at some point—we do not know exactly when or how (perhaps some older cousins?)—the Pythagoreans discovered that the hypotenuse of a right isosceles triangle is incommeasurable with its side. In other words, if we construct a right triangle with two sides of unit length (say one yardstick), we will not be able to measure the length of the hypotenuse with any natural number of yardsticks or any natural number of sticks obtained by dividing the original yardstick into equal parts. For any modern student of math this fact is trivial, a commonplace, so we must show why and in what sense it was uncanny for the ancient geometers. At the same time, this will show the proper meaning of “uncanny.”
The Pythagoreans considered real being to reside in numbers (integral fractions) and their relations; this meant that anything in the world becomes present and abides in time, undecayed, only insofar as the thing partakes of number and numerical relations. Until this is so, we witness mere appearance. A free act, whether conscious or not, was at the origin of their predicament: for nothing necessitated lengths to be measured that way; for instance, the ancient geometers might have settled for measuring lengths of different types with different “sticks” (apparently ancient Egyptian builders did precisely that: they measured horizontal lengths by rolling a wheel and vertical ones by putting wheels atop one another)—but this, of course, would have made a shambles of what cognitive unity means now and for us. For the tenets of modern science are fundamentally the same, except that in the last 25 centuries the notions of number and numerical relations have been much expanded. Now, the discovery of the incommeasurability of the hypotenuse of the right isosceles triangle meant for the Pythagoreans that there was something (the hypotenuse) which had no real being, which nevertheless, for all intents and purposes, was as present to them and as stable—as really being—as the unit sides. In the language of modern mathematics, it meant that there were holes in the real number line. There was a sudden irruption of not-being into being.
We might say: it is this sudden irruption of not-being into being while and insofar as we are trying to hold on to being which merits the name “uncanny.”
But we must bear in mind that in so defining the uncanny we haven’t moved away from Hegel’s “work of the negative”: indeed, it would be hard to avoid the negative already at work in the “un” of uncanny or unheimlich, or in the “out” of outlandish. All we have added is the word “sudden,” and this adverb already points to an acceptance and a welcoming home of time, an effort toward the new.
This irruption of not-being into being was not a contingent event, but rather necessitated by what for the Pythagoreans were the very laws of being—the properties of natural numbers and the principle of non-contradiction: this is the second feature of witnessed truths, cognitive unity. As for the third, ethical consequence, let us recall that the Pythagoreans based a whole ethics on their numerical lucubrations.
So much for pure reason’s childhood trauma. Russell used to counter this sort of argument by pointing out that thanks to the progress of mathematics in the last couple of centuries, we are now in the secure and happy possesion of the system of real numbers (not to mention Cantor’s transfinite numbers), and that therefore the uncanniness of the Pythagorean truth and the resulting trauma were due to childish immaturity. Had they been wiser, more grown-up, had they been more modern, they wouldn’t have been surprised. Aristotle didn’t argue otherwise.
But the truth is the opposite. The modern real number system, a brilliant achievement of the human mind, is also the most uncanny. This means: if we liken the Pythagorean discovery of the irrationality of the square root of 2 to a pox that poked holes into the face of Being, the logical construction of the real number system might be compared to a flood of not-being, an ocean out of which only a few rocks of being end up showing forth. Let us see why. There are natural numbers, big ones, which will never become present to any human mind or any computing machine; this is merely saying that the natural numbers are infinite, and that the speed with which we or machines can think has an upper bound. But if we could count the first number in one second, the next one in half a second, the next one in 1/4 of a second, the nth one in 1/2n of a second... we would be able to think any natural number, or any fraction, in less than two seconds. Similarly, given this superhuman speed of thought, irrational numbers such as the square root of 2 would become present to us, and so would all numbers which are roots of algebraic equations with integral coefficients. Actually, we would be able to grasp many other numbers as well: to get the square root of 2, for example, it would be enough to add (in two seconds) the infinite series 4 - 4/3 + 4/5 - 4/7... But here we come against the most uncanny. Imagine some immortal gods, who can think that fast or arbitrarily faster, and who spend their godly lives only computing: even they could think only a negligible portion of the real numbers (technically speaking, a set of Lebesgue measure zero). Worse: even though these gods could come up with infinitely many real numbers never thought before, they could have no idea how to start carrying out computations that would result in bringing to their divine presence anything but a negligible portion of the real numbers between, say, zero and one. To summarize our discussion: being is presence, presence is thought, but thought requires time (arbitrarily short for gods, yet still time); consequently, only denumerably many numbers could come into being; but, as Cantor proved, the real numbers are not denumerable, therefore, even to a divine intelligence, most real numbers cannot be. This is why I likened the real number system to an ocean of not-being, although the metaphor —any metaphor—is unable to grasp the immense negativity of the flood.
Irruption of not-being into being while and insofar as we are trying to hold on to being is what we are calling (provisionally following Hegel’s style of thought) the uncanny or outlandish. How could Russell, and more generally the Positivists, deny such uncanniness? By the only possible tactic: a denial of time. If being, presence and thought “happen” independently of time, or in no time at all, then our argument breaks down. To posit a god like the Christian one, who resides in eternity, outside of time, amounts to the same thing. Both tactics, the Positivistic and the Christian, are, of course, unthinkable; we must call them (in the sense Wittgenstein used the word) mystical. There’s a difference, though. The Christian tactic stops there: God’s eternity is unthinkable, mystical; Positivists go further, one more twist, and this further twist overflows the category of the uncanny and falls into the comical. The Positivist takes the concept of the real number system, an ocean of not-being unless we deny time, and proceeds to identify it with time. It is of little moment whether time is thought of as an open line or as a circle (as Nietzsche did and as we are told religious thought always did); the important fact is that time is thought of as a continuum, which means that locally, regardless of the total picture, time is identified with the real number line. There is still another, deeper comical aspect, bringing to mind the reply, found somewhere in Francisco de Quevedo, to one who did not believe in demons: your unbelief shows that you’re possessed by demons, thereby proving they exist. Although time is denied by the positivist tactic, logic of course is avidly grabbed on; specifically, the principle of non-contradiction as the main and most certain rule of thought; but when we look it up in Aristotle, who was the first to formulate it, we read in Metaphysics, 1005b: “It is impossible for the same attribute at once to belong and not to belong to the same thing and in the same respect.” Time is present in the “at once,” thus time must be taken into account in the formulation of the logical principles which are then used to reject it. We find in Frege a striking use of that tactic: in common parlance a sentence, for example “It’s raining,” may be true at this moment but false one hour later; Frege will have none of that, so he insists that “Only a sentence with the time-specification filled out, a sentence complete in every respect, expresses a thought.” This means that only of such complete sentences, where time—and not only time, we may add, but space location too—has been filled out, we may say that they are true or false. And he concludes: “But this thought, if it is true, is true not only today or tomorrow, but timelessly.” (Gottlob Frege, Collected Papers on Mathematics, Logic and Philosophy, p.370). We may ask Frege and Aristotle about the truth of the sentence, “There’s a pi-meson here” (the average life of which is about 10 to the power -16 seconds, and there are physical events still more ephemeral), and how we could “complete it in every respect.”
Let us try to encapsulate the Positivist strategy: time is used to forge the weapons to deny it; then a logical uncanny construct is arrived at, the real number system, whose being is only assured by time denial; finally this construct is identified with time. Thus the being of time is guaranteed only by its not-being. Why call such strategy comical? The comical is an ethical category: when a human being, say A, takes not-being as the basis and justification of his being, the reaction elicited in another human being, B, who sees A’s behavior, and, while feeling quite safe, recognizes (or thinks he recognizes) the quid-pro-quo, is laughter, the comical. Note that it is not enough for A merely to take not-being for being or conversely; if A trips on the stairs and falls because he didn’t notice the being there of another step, this is not comical by itself, and even in slapstick it would require a whole pattern of such misses to make them comical. Not-being must be taken consistently as the basis for A’s being: this is what makes Don Quixote a comic novel.
I hope I have shown in what way pure reason’s notion of time is a case of witnessing the truth, exhibiting the three features of uncanniness, cognitive unity and ethical consequence. That the ethical consequence is comical in no way detracts from the strength of the witnessing and the truth; to feel otherwise would be like maintaining that Don Quixote is inferior to Madame Bovary. It still might be objected that the second feature, cognitive unity, is not clear enough, for our previous discussion points to possible logical inconsistencies in the identification of time with the real number line. But we must remember that cognitive unity is not the same as logical consistency. The positivistic notion of time has allowed for the application of the Calculus to the phenomena of motion and the basing of modern science on mathematical analysis; thus, a huge number of important facts are seen to fit together. Whether or not physics will go on relying exclusively on this notion of time is another question, which I am unable to tackle.
Having said this much about the Positivistic rejection of time and uncanniness—hence of the witnessing of truth, it remains to show how Hegel dealt with it. Irruptions of not-being into being are the bread and butter of Hegel’s logical system—not sudden irruptions, to be sure, for the dialectics progresses outside time, and even though it pretends to ride on History, it is a steed like Gonella’s, nothing but pellis et ossa. The flesh of contingency and the contingency of the flesh are gone, desiccated, rejected, for “all true thinking is a thinking of necessity” (Logic, §119). Hegel would have viewed the Pythagoric trauma as a typical case, in which a concept or conceptual frame encounters its limit of applicability, that is, its negation; measurability turns into incommeasurability, discrete into continuous magnitude, and so on and viceversa; there is nothing unfamiliar or uncanny in that, since it happens all the time and to all concepts. Secondly, Hegel would have shrugged at our calling uncanny the situation with numbers, and especially with the real number system. “Die schlechte oder negative Unendlichkeit,” the wrong, bad, negative infinity, he calls the numerical infinity in Logic §93-95, and describes it thus: “Something becomes an other, but the other is itself a something, therefore it likewise becomes an other, and so on ad infinitum.” This, he says, is tedious. For him not only is the situation not uncanny, but utterly uninteresting. And what is then the true, genuine infinity, die wahrhafte Unendlichkeit? This: since something is always an other with respect to another, it follows that all things have otherness in common; therefore, when something becomes an other it really becomes, or joins with, itself. This “genuine infinity,” where everything becomes itself, this radical rejection of the new, is “der Grundbegriff der Philosophie,” the fundamental notion of philosophy, and in it, Hegel insists repeatedly, “we feel at home.” So much for the unfamiliar, the wonderful, the uncanny and the outlandish: unfortunate errors of the unphilosophic understanding.
Should we call it comic, as before? I hesitate to do so because the sophism is too obviously false to be comic, and also because Hegel’s substitution of a philosopher’s worldly paradise in which he felt at home, for the lost, unwordly paradise of Christianity, has been the keystone of so many worldly hells in our century. Certainly from the Hegelian point of view this isn’t surprising: paradise turning into hell and both aufgehoben into a stately paradise that’s also hell, is something that should have been theoretically predicted from the start.
But let’s go back to my personal witnessing of truth about the birds and the bees, and let us show that, in spite of appearances, it bears some uncanny resemblance to my later witnessing of mathematical truth. “The birds and the bees” is a silly title for the story of sexual reproduction, the way a male and a female give birth to the new. If we called uncanny the fact that at most a few real numbers may become present to us (the way mathematical objects become present, by exhibiting beautiful relations to other mathematical objects), shouldn’t we also call uncanny the fact that only a few of our descendants may become present to us (the way human beings become present, by showing forth their cháris, their grace)? It is true that not all of us have the fortune of having children and grandchildren, but then not everybody becomes a great mathematician either. The potentially infinite chain of ancestors and progeny is no less wonderful and uncanny than the vastness of the real number system. To define this uncanniness as a sudden irruption of not-being into being seems now clearly perverse, a perversity that pervades Hegel’s dictum, “Something becomes an other, but the other is itself a something, therefore it likewise becomes an other, and so on ad infinitum—tedious.” There is a problem though: this wonderful chain of being, my children and grandchildren, was not in my mind when I was six; my cousins didn’t as much as mention it; should we therefore dismiss this later revelation as irrelevant? Logic and physics are strict about this point: no event can possibly influence a previous one. Incidentally, a point of great interest to historians, who must ask about the relation later interpretations bear to the truth of the past, and one of the main concerns of Kierkegaard in the Philosophical Fragments cited above. It is well known that Kierkegaard often spoke indirectly and with many voices; one of those voices says in mock professorial tone (p. 95):
“Unless it is assumed that the consequences (which, after all, are derived) gained retroactive power to transform the paradox, which would be just as acceptable as the assumption that a son received retroactive power to transform his father.”
Well, why not? Why can’t my children or my grandchildren receive retroactive power to transform me? I mean it in the strongest sense: why can’t my children and my grandchildren transform my original witnessing of the truth? We have already seen that logical and physical strictures about time are not to be taken too broadly, for they are based on a previous denial of time, and that should, after the inevitable fit of laughter, give us pause. I will use this pause, our final one, to declare that yes, my children and grandchildren may, and they should, I hope, transform me and my original witnessing of the truth in ways unforeseen. It was one of the set themes of Greek and Roman Comedy, sons making fools of their old men.
(I had written the above more than ten years ago and had forgotten about it. Now, recovered by chance, dusted but unpolished, I will let it seek its fortune through the threads and holes—the being and not-being—of the Net.)