On the Shoulders of Giants
Page 14
The fluctuating characters of fiction are made of the same stuff as the characters of mythology. Oedipus and Achilles were fluctuating entities like Anna Karenina or Pinocchio, except that the former were created in ancient times and the latter were born, as it were, as secular myths. And we feel entitled to say that it is true that Pinocchio was born from a piece of wood just as we feel authorized to say that it is true that Athena was born from the head of Jupiter.
It is not enough to say that the ancients thought that Jupiter and Athena really existed whereas anyone who thinks of Pinocchio as a fluctuating character knows that he never existed. I would say that these are psychological accidents, and I might add that a great number of believers have fairly fuzzy ideas about the degree of existence of their gods—that there have been young shepherdesses who say they have spoken with Our Lady; that some romantic girls killed themselves for love of Jacopo Ortis; that at the Sicilian puppet theatre, the audience used to insult the villain Gano di Maganza; that there are teenagers who are madly in love with a character, not a movie star; that there is no saying that Caesar believed in Jupiter; that Christian poets continued to invoke the Muses—and so we enter a universe of feelings, fantasies, and private emotions where it is difficult draw precise boundary lines.
The kind of existence we have allowed to fluctuating characters also explains their moral function. I know I have already written and talked about this topic, but I cannot overlook it in bringing this contribution to an end.
Although these characters fluctuate, they seem irremediably bound to their destiny. Of course, when we weep at their stories we hope sometimes that things might go differently, that Oedipus might take another path and not meet his father on the road to Thebes, that he might arrive in Athens where he could couple with Phryne, that Hamlet might marry Ophelia and live together happily ever after on the throne of Denmark, that Heathcliff might put up with a little more humiliation and stay on those wuthering heights until he can marry his Catherine and live with her as a perfect country gentleman, that Prince Andrey might get well, that Raskolnikov might not conceive the mad idea of murdering an old woman but finish his studies and become a respectable state official, that when Gregor Samsa is transformed into a horrible insect a beautiful princess enters his room, kisses him, and transforms him into the richest man in Prague. Today, computers could even offer programs that rewrite all these stories to our liking. But do we really want to rewrite them?
Reading fiction means knowing that the character’s destiny is ineluctable. If we could change the fate of Madame Bovary, we would no longer have the comforting certainty that the assertion Madame Bovary committed suicide is the model of every indisputable truth. Entering a fictional possible world means accepting that things went, and will always go, in a certain way, regardless of our wishes. We must accept this frustrating fact, and through it experience the thrill of destiny.
I believe that this lesson on fate is one of the main functions of fiction, and constitutes the paradigmatic value of fictional characters, saints of the secular community—and also of many believers.
Only the fact that Anna Karenina inevitably dies makes her fondly, imperiously, and obsessively present as the melancholy companion of our existence, even though she never physically existed.
[La Milanesiana, 2009]
7. Paradoxes and Aphorisms
We often hear people say things like “it’s paradoxical: he was the one who ran into me and now he claims that I should pay the damages,” or “it’s paradoxical that Raphael’s wife died on the very day of their wedding.”
Well, the first case is not paradoxical; it is merely an affront or, at most, absurd. And neither is the second, which is an unusual coincidence and a shocking departure from the norm, like the birth of a two-headed calf.
While both of these naive usages connect to an aspect of a paradox, that it runs counter to what was desired or expected, in neither case are we dealing with a genuine paradox.
If we were reducing paradox to mean something only curious or bizarre, we might even call it paradoxical that there are two distinct meanings of the word paradox. One of them applies in the realm of logic and philosophy, and the other in rhetoric.
Logical paradoxes ought more properly to be called antinomies. I saw someone on the internet claiming that the Greeks called them paralogisms, but that isn’t true. A paralogism is a simple error of reasoning that is easy to correct. For example, it is a paralogism to state that because all Athenians are Greeks, and all Spartans are Greeks, all Athenians are Spartans. In this case, sheer common sense tells us the conclusion is false, but sometimes it helps to diagram the paralogism to find its flaw:
All A’s are G’s
All S’s are G’s
Therefore, all A’s are S’s.
A paralogism is such because in this syllogism the middle term (G) is not quantified, and the lack of quantification of the middle makes the argument fallacious.
On the other hand, what medieval scholars called insolubilia are antinomies, which is to say expressions or arguments that cannot be said to be either true or false—because they are are susceptible to two mutually contradictory interpretations.
The most classic antinomy is that of the self-professed liar. The statement “I am lying” cannot be true or false: if it were true, it would mean that I am telling the truth and therefore it is not true that I am lying; and if it were false, then it would not be true that I am lying, and so it would be true that I am telling the truth, and therefore I would really be lying.
The most popular version of this is the paradox of Epimenides, the Cretan who maintains that all Cretans are liars.
St. Paul, a man with many good qualities but no sense of humor, took the saying seriously and, in the Epistle to Titus, he tells us that the Cretans certainly are all liars and the proof of this is that a man who knows them well, a Cretan himself, says so. But in that case it is obvious that, since Epimenides is a Cretan, he must be lying. But if he is lying, then it is not true that all Cretans are liars. Therefore, some Cretans tell the truth. But is Epimenides one of them, or not? If he is, then it is true that all Cretans are liars and it is false that some Cretans like Epimenides tell the truth. If Epimenides is one of those who lie, then we go straight back to square one.
But the paradox of Epimenides is not really a paradox, because we can escape that by concluding that Epimenides is the only liar among all the Cretans—in which case, the fact that he does not tell the truth is just normal.
The famous story of Achilles and the tortoise, attributed to Zeno, also passes for a paradox. Let’s say the tortoise is one meter ahead of Achilles. To overtake it, Achilles has to close that gap and, after the first half-meter, he has closed half of it. Then he must cover the remaining distance, and after gaining another quarter of a meter, he has accomplished half of that task. And so on ad infinitum, with the logical result that Achilles never passes the tortoise.
Or let’s imagine a path that is one kilometer long, from point P to point A. Then let’s imagine a runner, Achilles, who starts from point P and runs toward the finish—that is, toward point A. Achilles must first cover half the distance between points P and A, reaching the midpoint between them, which we shall call M. Achilles must therefore cover half of the remaining distance between M and the finish A, arriving at point S. This halving process continues ad infinitum, because regardless of how small the distance to cover may be, it can always be halved.
The story of Achilles is not a paradox and Aristotle had already seen the solution when he made a distinction between potential infinite and actual infinite: among magnitudes there is infinity by addition (I can always find an even number greater than the one before it) but not by division, because the infinity of the subintervals in which a unit of length is divisible is always contained within a limited totality (which is never greater than 1).
Although the process of fractalization (half of the whole, half of the half, half of the half of the half, and so
on) continues indefinitely, its result will never be greater than 1—as also happens with irrational numbers. So 3.14, as far as we can analyze it, will never be 4.
If this reasoning is applied to the fractal length of a coast, in which the potential division process could be infinite, at least insofar as we can always postulate smaller and smaller microbes, this takes nothing away from the fact that in real terms Achilles can cover this distance in a single step. Achilles will cover his unit of length in his unit of time.
There is also talk of topological paradoxes, and some have said that the Möbius strip is paradoxical. I find nothing paradoxical about it. It may seem improbable that a twist suffices to turn a two-sided surface into a single-sided one, but in fact it happens, and we have seen this; all this means is that topology is a little more complex than Euclidean geometry.
There are far more serious paradoxes, one of the most famous of which is the barber paradox proposed by Bertrand Russell.
It comes in an ingenuous version and a subtler one. The first is: “The village barber shaves all the men who do not shave themselves. Who shaves the village barber?” Obviously, he cannot shave himself because he only shaves those who do not shave themselves, and it is presumed that no others in the village are appointed to shave anyone. I put this paradox to my children when they were young and they suggested three solutions: perhaps the village barber is a woman; or the barber does not shave and has a very thick beard; or the barber does not shave but rather burns off his beard, no doubt leaving his face horribly scarred. Actually, the paradox should be stated like this: “Among the inhabitants of a village there is one and only one barber, a well-shaven man. The sign above his shop says, ‘the barber who shaves all those who do not shave themselves.’ The question at this point is: Who shaves the barber?”
Modern logic and mathematics have proposed many antinomies for the resolution of very subtle problems that I will not deal with here. Rather, I shall limit myself to mentioning some other successful antinomies—for example, this one, cited by Aulus Gellius. The story goes that Protagoras gave legal training to a promising young man, Evatlo, and he required Evatlo to pay only half the fee upfront, saying that the student could pay the rest when he won his first case.
Evatlo, however, did not go on to practice law, but went into politics instead, and so he never won his first case because he never actually had one. Therefore, Protagoras was not paid and finally called on Evatlo to settle the price of his training. The young man decided to defend himself, acting as his own lawyer and thereby creating the following situation of indeterminacy. The possible outcomes according to Protagoras were these: if Evatlo wins, he has to pay Protagoras on the basis of the agreement, because he will have won his first case; if Evatlo loses, he has to pay anyway, by virtue of the sentence. But now look at it from Evatlo’s perspective: if Evatlo wins, he does not have to pay Protagoras, thanks to the outcome of the case; but if Evatlo loses, he still does not have to pay Protagoras, because of the terms of the agreement and the fact that he did not win his first case.
This paradox has long served to demonstrate that both lawyers and politicians are untrustworthy people.
Another one is the crocodile dilemma, mentioned by Diogenes Laertius: a crocodile grabs a little boy playing on the banks of the Nile. The mother begs the crocodile to return her child. “Certainly,” says the crocodile, “if you can tell me in advance exactly what I’ll do, I’ll give you back your son; but if you guess wrong, I’ll eat him for lunch.” The mother, weeping desperately, calls out her prediction: “you’ll devour my baby.”
Now the crocodile is in a bind: “I can’t give you back the child, because if I do, it means you’ve guessed wrong, and as I told you, if you guess wrong, I devour him.” But the mother shrewdly objects, “It’s not like that at all! Quite the opposite, you can’t eat my baby, because if you devour him, that will mean I guessed correctly. You promised that if I did that, you would return the child, and I know that as an honorable crocodile you will keep your word.”
And finally here are some delightful logical paradoxes collected by Raymond Smullyan:
Of course I’m a solipsist, isn’t everybody?
Of course I believe that solipsism is the correct philosophy, but that’s only one man’s opinion.
Authorized parking forbidden.
This species has always been extinct.
You’ve outdone yourself as usual.
God must exist because he wouldn’t be so mean as to make me believe he exists if he really doesn’t.
Superstition brings bad luck.
What, on the other hand, is the rhetorical paradox?
Etymologically, it is only παράδοξος, that which goes parà ten doxan—that is, beyond common perception or opinion. So the term originally referred to a statement that was far from everyone’s beliefs—odd, bizarre, or surprising. This is the definition of it that we find it in Isidore of Seville; according to him, a paradox occurs when we say that something unexpected has happened, as when Cicero, in his Defense of Flaccus, wrote that “he who ought have been the singer of praises has become the one who begs for his release from danger.”
We can find rhetorical notions of paradox in various dictionaries, but the basic idea usually contains elements like these:
a theory, concept, statement or dictum that contrasts with widespread or universally accepted opinion, with common sense and common experience, and with principles and knowledge that are taken as read; but it can possess, in an apparently illogical and disconcerting form, a fundamental validity, which runs counter to the ignorance and the superficiality of those who uncritically follow the opinion of the majority.
So paradox in the rhetorical and literary sense would be a kind of maxim or saying, which at first sight seems to be false but which eventually reveals a nonobvious truth.
In this sense paradox almost always takes the form of a maxim or an aphorism.
There is nothing harder to define than the aphorism. As well as “something set aside for an offering” and “donation,” over the years the Greek term came to mean “definition, dictum, concise maxim.” Examples include the aphorisms of Hippocrates. According to the Zingarelli Italian dictionary, an aphorism is a “brief maxim that expresses a rule of life or a philosophical judgment.”
It has been said that an aphorism is a maxim in which the most important thing is not only the brevity of the form, but also the perspicacity of the content, which puts elegance or brilliance before the acceptability of the assertion in terms of truth. Of course, with regard to maxims and aphorisms, the concept of truth is relative to the aphorist’s intentions: to say that an aphorism expresses a truth means to say that its purpose is not only to express what the author understands to be true but also to convince his readers of this. But in general a maxim or aphorism is not necessarily intended to appear witty, nor does it aim to offend current opinions: rather it is intended to expand on a point regarding which current opinion appears superficial, and should be examined in greater depth.
Here is a maxim from Chamfort: “The richest of men is he who lives within his budget; the poorest of men is the miser” (Maxims and Thoughts, I, 145). The wit lies in the fact that popular opinion tends to consider the thrifty as those who do not waste their scant resources in order to ensure they can deal with their own needs, and misers as people who amass resources far greater than their needs require. So the maxim would run counter to popular opinion, except that “poor” is also understood in relation to the satisfaction of needs, and not just in the moral sense, while “rich” is understood in relation to resources. The rhetorical game having been revealed, we can see that the maxim does not run contrary to current opinion, but corroborates it.
When, instead, an aphorism goes violently against the conventional view, so that at first sight it appears to be false and unacceptable, and appears to hold some barely acceptable truth only once its hyperbolic form has been judiciously reduced, then we have a paradox.
The history of literature is rich in aphorisms and a little less rich in paradoxes. The art of the aphorism is easy (proverbial expressions are aphorisms, too: your best friend is your mother, its bark is worse than its bite) while the art of the paradox is difficult.
Some time ago I became interested in a master of the aphorism, the Italian writer Pitigrilli, and here are some of his most brilliant maxims. Albeit in a humorous way, some are intended to state a truth that does not run contrary to popular opinion in the slightest:
Gastronome: a cook who went to high school.
Grammar: a complicated instrument that teaches you languages but prevents you from speaking them.
The fragment: a providential resource for writers who can’t put together a whole book.
Dipsomania: a scientific word that’s so beautiful it makes you want to take to drink.
Others, rather than express a presumed truth, state an ethical choice, a rule of conduct: