On the Shoulders of Giants Read online

  This is a fine example of a complete and satisfactory representation of the meaning of a term. But other expressions instead have fuzzy, imprecise meanings—and diminishing degrees of clarity. For example, even the expression the highest even number has a meaning; we immediately know that it would have to have the property of being divisible by two (and so we would be able to distinguish it from the highest odd number) and we even possess a vague instrument for producing it, in the sense that we can imagine counting higher and higher numbers, separating the odd ones from the even ones. It’s just that we realize we will never manage to do that—in the way that in a dream we sometimes have a sense that we can grasp something but are not quite able to do so. An expression such as a circle whose center is everywhere and whose circumference is nowhere instead suggests no rule for the production of a corresponding object; not only does it not support any definition, it also defies all our efforts to imagine it, apart from making our head spin. All things considered, the definition of a term such as absolute is tautological—something that is not contingent is absolute, but something that is not absolute is contingent—but it does not suggest descriptions, definitions, and classifications. We cannot think of instructions for the production of a corresponding thing. We know none of its properties, except to suppose that it has them all—and that it is probably the id cuius nihil maius cogitari possit (something compared to which nothing greater can be thought) that Saint Anselm of Canterbury talked about. (And this, by the way, reminds me of a comment attributed to Arthur Rubinstein: “Do I believe in God? No, I believe in something much greater.”) The best we can manage to imagine in trying to conceive of God is the reduction of the world’s variety into what Hegel ridiculed as a “night in which all cows are black.”

  It is certainly possible not only to name but also to represent visually those things that we cannot conceive. But these images do not represent the inconceivable: they simply invite us to try to imagine something inconceivable, and then frustrate our expectations. What we feel in trying to understand them is precisely the sense of powerlessness expressed by Dante in the last canto of the Paradiso (XXXIII, 82–86) where he would like to tell us what he saw when he was able to look upon the divinity, but all he can manage to say is that he cannot put it into words, and he falls back on the intriguing metaphor of a book with an infinite number of pages:

  O grace abounding, by which I have dared

  To fix my eyes through the eternal Light

  So deeply that my sight was spent in it!

  Within its depths I saw gathered together,

  Bound by love into a single volume,

  Leaves that lie scattered through the universe.

  Substance and accidents and their relations

  I saw as though they fused in such a way

  That what I say is but a gleam of light.

  The universal pattern of this knot

  I believe I saw, because in telling this,

  I feel my gladness growing ever larger.

  One moment made more slip my memory than

  Twenty-five centuries reft from the adventure

  That awed Neptune with the shadow of the Argo.

  Nor is this any different from the feeling of impotence expressed by Giacomo Leopardi when he describes the infinite (“thus my mind sinks into this immensity / and sweet it is to founder in this sea”). This is reminiscent of a Romantic painter such as Caspar David Friedrich when he tried to express the sublime, which was the earthly thing best able to call up the experience of the absolute.

  In times long gone by Pseudo-Dionysius the Areopagite wrote that, since the divine One is so far from us as not to be either understood or reached, we must perforce talk about it through metaphors and allusions, but especially, owing to the poverty of our language, through negative symbols and dissimilar expressions: “The lowest images are also used, such as fragrant ointment, or the cornerstone, and they even give It the forms of wild animals and liken It to the lion and panther, or name It a leopard, or a raging bear bereaved of its young” (Pseudo-Dionysius the Areopagite, The Celestial Hierarchy, book II).

  Some naive philosophers have suggested that poets alone can tell us what being and the absolute may be, but all they are really expressing is the indefinite. This was the poetics of Stéphane Mallarmé, who spent a lifetime trying to provide an “orphic explanation of the world.” “I say a flower, and beyond the oblivion whence my voice relegates all shapes, insofar as it is something other than any known calyx, there arises musically a pleasant idea, the absence of all bouquets and fragrance.” In point of fact this statement is untranslatable; all it tells us is that a word is selected, detached from the white space surrounding it, and from it the totality of the unsaid must spring, but in the form of an absence. “To nominate an object is to suppress three-quarters of the power of poetry, which is all about working things out gradually: to suggest, that is the dream.” Mallarmé spent all his life in the quest for this dream, but it never came true. Dante had taken this problem for granted right from the start, understanding as he did that it would take the pride of Lucifer to claim to express the infinite in finite terms, and he avoided this problem of poetry by making the poetry of the problem, not the poetry of the unsayable but the poetry of the impossibility of saying it.

  We should consider the fact that Dante (like Pseudo-Dionysius and Nicholas of Cusa) was a believer. Is it possible to believe in an absolute and state that it is unthinkable and undefinable? Of course, by accepting the substitution of the impossible thought of the absolute with the feeling of the absolute and hence of faith, since “faith is the substance of things that are hoped for and the evidence of things that are not seen.” During a conference, Elie Wiesel quoted Kafka’s observation that it is possible to talk with God but not about God. While for philosophers the absolute is a night in which all cows are black, for the mystic who, like Saint John of the Cross (sixteenth century), saw it as noche oscura (“Oh night that guided me / oh night more lovely than the dawn”), it is the source of ineffable emotions. Saint John of the Cross expresses his mystical experience through poetry: faced with the indescribable nature of the absolute, we might find comfort in the fact that this unsatisfied tension may resolve itself materially in a finished form. And this allowed Keats in his “Ode on a Grecian Urn” (1819) to see beauty as a substitute for the experience of the absolute: “Beauty is truth, truth beauty: that is all ye know on earth and all ye need to know.”

  This is fine for those who have decided to practice an aesthetic religion. But Saint John of the Cross would have told us that it was only his mystical experience of the absolute that guaranteed him the sole possible truth. This has led many persons of faith to maintain that philosophical systems that reject any possibility of knowing the absolute automatically reject all criteria of truth or, by not accepting an absolute criterion of truth, they reject the possibility of any experience of the absolute. But it is one thing to say that a philosophical system does not accept any possibility of knowing the absolute and another to say that it rejects all criteria of truth—even for matters concerning the contingent world. Are truth and the experience of the absolute so inseparable?

  The belief that some things are true is of fundamental importance for the survival of humankind. If we did not think that the things other people tell us can be either true or false, society would be impossible. We could not even rule out the idea that a box with “aspirin” written on it might contain strychnine instead.

  A specular theory of truth is adaequatio rei et intellectus (the adequation of the intellect and the thing), as if our mind were a mirror that, when working properly and not a distorting one or misted over, must faithfully reflect things as they are. This is the theory put forward by Thomas Aquinas, for example, but also by Lenin in his Materialism and Empirio-Criticism (1909). And since Aquinas could not have been a Leninist, it follows that when it came to philosophy, Lenin was a Neo-Thomist. But, with the exception of ecstatic states, we are obliged
to speak and to say what our intellect reflects. Hence we define as true (or false) not things but the assertions we make about how things are. According to Alfred Tarski’s famous definition, the statement “snow is white” is only true if the snow is white. Now, if we forget the whiteness of snow for a moment, because the way things are going it has become a highly debatable subject, we might consider another example: the statement “it’s raining” (between quote marks) is true only if outside it is actually raining (without quote marks).

  The first part of the definition (the one between quote marks) is a verbal statement and represents nothing other than itself, but the second part ought to express how things actually are. But what ought to be a state of things is once more expressed in words. To avoid this linguistic mediation we should say that “it’s raining” (between quote marks) is true if “that thing there” (while pointing to the falling rain without saying a word). But, while we can make this indexical appeal to the senses with the rain, it would be harder to do the same thing with the statement “the Earth revolves around the sun” (because if anything our senses would tell us the exact opposite).

  To establish whether the statement corresponds to a state of things, we first need to interpret the term to rain and stipulate a definition for it. We need to establish that in order to state that it is raining it is not enough to notice drops of water falling from above, because it may be that someone is watering flowers on a balcony; second, the consistency of the drops must be of a certain size, otherwise we would talk of dew or frost; third, the sensation must be constant (otherwise we would say that it tried to rain but stopped right away), and so on. This having been established, we must move on to an empirical test, which in the case of rain is available to all (you just hold out your hand and trust in your senses).

  But in the case of the statement “the Earth revolves around the sun,” the verification procedure is more complex. What is the meaning of the word true in each of the following statements?

  I have a bellyache.

  Last night I dreamed that Padre Pio appeared to me.

  It will definitely rain tomorrow.

  The world will end in 2536.

  There is life after death.

  Statements 1 and 2 express subjective facts, but a bellyache is an evident feeling that cannot be suppressed whereas, in recalling a dream of the night before, I might not be sure of the accuracy of my recollections. In addition, the two statements cannot be immediately verified by others. Of course, a doctor who wants to know if I really have colitis or if I am a hypochondriac would have the means to check that out. But if I told a psychoanalyst I had dreamed about Padre Pio, she would have more of a problem, because I could easily be lying.

  Statements 3, 4, and 5 are not immediately verifiable. But the chance of rain tomorrow can be verified tomorrow, whereas the idea of the world ending in 2536 would pose us a few problems (and that is why we make a distinction between the credibility of a met office forecaster and that of a prophet). The difference between 4 and 5 is that 4 will become true or false at least in 2536, whereas 5 can never be empirically verified.

    6.  Every right angle necessarily has 90 degrees.

    7.  Water always boils at 100 degrees.

    8.  Apples are angiosperms.

    9.  Napoleon died on May 5, 1821.

  10.  If you follow the path of the sun you will come to the coast.

  11.  Jesus is the son of God.

  12.  The correct interpretation of Holy Writ is determined by the teachings of the Church.

  13.  Embryos are already human beings and have a soul.

  Some of these statements are true or false in relation to rules we have established. A right angle only has 90 degrees within the ambit of a system of Euclidean postulates. That water boils at 100 degrees is true not only if we accept a physical law worked out through inductive generalization but also on the basis of the definition of degrees centigrade. An apple is an angiosperm only on the basis of some rules of botanical classification.

  Some others require us to trust in matters checked out by others before our time: we believe it to be true that Napoleon died on May 5, 1821, because we accept what the history books tell us, but we must always recognize the possibility that some hitherto unknown document might be discovered tomorrow in the archives of the British admiralty that says he died on another date. Sometimes for utilitarian reasons we take as true an idea that we know is false: for example, to find our way in the desert, we behave as if it were true that the sun moves from east to west.

  As for statements concerning religion, I don’t think they admit of no resolution. If we accept the Gospels as historically accurate testimony, the proof of Christ’s divinity ought to convince even a Protestant. But this is not the case with the teachings of the Catholic Church. The statement regarding the soul of the embryo depends solely on establishing the meanings of terms such as life, human, and soul. Thomas Aquinas, for example, held that embryos had only a sensitive soul, like the animals, and therefore as they are not yet human beings with a rational soul they will not take part in the resurrection of the flesh. Today he would be accused of heresy, but in that most civilized age they made him a saint.

  It is therefore a matter of deciding each time which criteria of truth we are using.

  Our sense of tolerance is based on this very recognition of the different degrees of verifiability or acceptability of a truth. I can have the scientific and didactic duty to fail a student who maintains that water boils at 90 degrees like the right angle—this was apparently suggested in an exam—but a Christian would also have to accept that for some people there is no other god than Allah and that Mohammed is his prophet (and Christians expect Muslims to return the compliment).

  Instead in the light of some recent polemics it seems that this distinction between different criteria of truth, typical of modern thought and especially of logical-scientific thinking, gives rise to a relativism understood as the historical malady of contemporary culture, which rejects any idea of truth. But what do anti-relativists mean by relativism?

  Some encyclopedias of philosophy tell us that there is a cognitive relativism, according to which objects can be known solely under conditions determined by human faculties. But in this sense, Kant, too, would have been a relativist as he never denied that it was possible to state laws of universal value—and, moreover, he believed in God, albeit only on moral grounds.

  In another encyclopedia of philosophy I find that relativism means “every concept that does not admit of absolute principles in the field of knowledge and action.” But rejecting absolute principles in the field of knowledge or in the field of action is not the same thing. Some people are prepared to maintain that “pedophilia is a bad thing” is a truth relative only to a particular system of values, since in certain cultures it was or is allowed or tolerated, while claiming nonetheless that Pythagoras’s theorem must be valid for all times and in all cultures.

  No one could seriously label Einstein’s theory of relativity as an example of relativism. To say that any measurement of motion depends on how fast or slow the observer is moving is considered to be a valid principle for every human being in every time and in every place.

  Relativism as a philosophical doctrine of that name arose together with nineteenth-century positivism, which held that the absolute was unknowable and that at best it could be understood as the constantly fluid limit of ongoing scientific research. But no positivist has ever claimed that objectively verifiable scientific truths valid for everyone cannot be attained.

  One philosophical position that, after a hasty reading of the textbooks, could be defined as relativistic is so-called holism, according to which all statements are true or false (and acquire a meaning) only within an organic system of assumptions, a given conceptual scheme or, as others have said, within a given scientific paradigm.

  A holist maintains (rightly) that the notion of space has a different mea
ning in the Aristotelian and Newtonian systems, thus making them incommensurable, and that one scientific system is as good as another to the extent to which it successfully explains a set of phenomena. But holists are the first to tell us that some systems fail to explain a set of phenomena and that in the long term some systems prevail simply because they explain things better than others. So, in their apparent tolerance, holists are faced with something they have to explain and, even when they do not say so, they stick to what I would define as a minimal realism, according to which things must exist or behave in a certain way. Perhaps we will never know how this is, but if we do not believe that it exists, our research would make no sense, nor would it make any sense to keep on trying out new systems for explaining the world.

  Holists are usually said to be pragmatists, but in this case, too, we should not read the philosophy textbooks in haste: the true pragmatist, as Charles Sanders Peirce was, did not say that ideas are true only if they show themselves to be effective, but that they show their effectiveness when they are true. And when he supported fallibilism—namely, the possibility that all our knowledge can always be questioned—at the same time he maintained that through the constant correction of knowledge the human community continues to carry “the torch of truth.”

  What makes people suspect that these theories are relativistic is the fact that the various systems are mutually incommensurable. The Ptolemaic system is certainly incommensurable with the Copernican one, and only in the former do the notions of epicycle and deferent take on a precise meaning. But the fact that the two systems are incommensurable does not mean they are not comparable, and it is precisely by comparing them that we understand the nature of the celestial phenomena that Ptolemy explained with the notions of epicycle and deferent, and we realize that they were the same phenomena that the Copernicans wanted to explain in accordance with a different conceptual scheme.