PROOF AS THE UNIFIER OF SCIENCE
Bacon saw the existence of contending schools as an unmitigated evil - similar to divisions between warring empires. Had any school possessed the truth, he said, there would be neither need nor room for schools.
Truth speaks for itself, truth shines, truth appears naked.This doctrine, which Popper labels the doctrine of manifest truth or of truth as manifest, may sound as if it were a version of naive realism and thus in contradiction with the theory that Nature loves to hide. Far from it: nature does love to hide, but not forever; under some conditions, She even has to reveal Herself; but whereas when She hides She merely drops hints and clues as to Her whereabouts, when She does appear, Truth appears in her stark nakedness and dazzling beauty; and then no one need nor can doubt Her; the Naked Truth does not carry a handbag containing identification, corroboration, or letters of recommendation.
Taking what I have just said somewhat seriously may suggest that there is never any need for proof; truth is just known as truth. To this one might retort, but we must be able to distinguish the feeling of certainty from certainty proper; to use Sir John Herschel’s terminology, we must differentiate psychological certitude from mathematical certitude. Indeed. But if we take seriously the idea that truth is manifest, then this aspect of truth is covered as well. If we could see the truth clearly yet doubt that the clarity is in fact and not in our minds, then there would be at least this lack of clarity in the picture. You may say, perhaps, that if we demand such a high degree of clarity from ourselves before we can claim knowledge of the truth, then we can never claim knowledge. Perhaps; it is harder however, to deny that once we do clearly see the truth, we can claim knowledge. And so, it looks as if it were analytic, or near-analytic to declare that we do not need proof when we see the truth.
This is what we mean when we say, it is so obvious, I do not know how to put it; it is so clear, I do not know how to explain it. To put it more congenially, knowing a truth is knowing a proof inside out - at a glance, as we say - seeing all steps at once. This idea is shared by many thinkers up to, and including, Wittgenstein - of the Tractatus in which truth 'shows itself’ as well as of the Remarks on The Foundations of Mathematics. Once you accept this idea, you see that when we speak of a truth in need of a proof, we either speak of a hypothesis which only may be true, of a truth revealed to me needing proving to you so that you can see it as well. So the role of proof, of proving, is inevitably that of introducing the newcomer to the truth. And the mode of introduction is, in my opinion, what differentiates - at least traditionally - science from mysticism. The mystic too - be he Oriental or European Mediaeval - introduces novices to the truth; but his introduction is only highly preliminary: most of the pilgrimage on the road to truth must be done alone, and he who has travelled it successfully is an initiate. Not so in science. This is a point endorsed even in the twentieth century by those who address themselves to the problem: it is agreed by most writers that it is the public character of science (to use Popper’s expression of a common sentiment), as opposed to the esoteric character of mysticism which makes us prefer science to mysticism. And so, again, we see the universalist ethic behind science.To approach matters differently: Russell says there must be a difference between the views of Einstein and the ravings of a madman. The difference lies precisely in the universality of the one, through rational justification, as against the caprice and idiosyncrasy of the other. What Bartley calls “the justificationist doctrine of rationality” is the view that what distinguishes the rational from the mad is the former’s appeal to universally valid proof. Take as a conspicuous instance Parmenides’ doctrine that the world is full, round, immobile, unalterable, etc.
As a doctrine it may be declared a variant of mysticism, not much different from some Oriental or Occidental doctrines. As a doctrine it may be declared madness - as many if not all mystic doctrines were viewed by rationalists through the ages. But Parmenides presented proofs of his doctrine - indeed one may view him as the father of Western justificationism, as Popper does, and as the father of Western mathematics as Lakatos does.The justificationist approach seems essentially different from that of truth as manifest; rationality is identified with proof rather than selfevidence. But not at all: for, self-evidence and proof are one: proof is what makes one see the objective truth, and acceptance of objective truth is rational as opposed to subjective, idiosyncratic, arbitrary. Rationality is universality, i.e. objectivity, i.e. truth; proof is the universalist method of revealing the truth. Indeed, were proof a matter for the initiate, then our whole edifice would collapse. Or, were proof of falsehood possible, then our whole edifice would collapse.
Consider the discoveries of Lakatos in this light. What has happened to Parmenides’ proofs? They have been refuted, of course, and his view is not a proven theorem, of course. For, were the proof valid, we would be able to prove falsehoods. But how can one claim to have a proof without having it? How is error or deception at all possible if proof is the same as revealing a truth in all its clarity? There is ho answer; such cases are freaks, they are rare, their proper place is therefore in the origins of mathematics or of a mathematical theory. But look at the history of mathematics, says Lakatos. There is almost no acceptable proof in Euclid, almost no acceptable possible proof in the calculus before the mid-19th century; there is, in brief, no proof a century old or more that an ordinary mathetnatician today cannot knock out.
What, then, is the role of proof? For Lakatos it is a challenge, an invitation to refute a proven theorem and a guideline for a possible refutation.
This is exactly the same, I contend, as the role of every kind of proof in science, whether a priori, a gedanken experiment, or empirical support. Just as Lakatos views the world of mathematics as a system of ever increasing possible alternatives, so I view science as a system of ever increasing possible alternatives. And so, I think, every proof indicates something - and is thus quite informative - of the prover’s shortcoming, of the limitations of his (intellectual) imagination.I do not invite the reader to accept such views but to consider the difference between viewing proofs in.this way from viewing proofs as establishing the truth in a manner open to all to follow and be convinced by. Indeed, once justification is rejected, the problem of objectivity arises full force all over again. Popper has stressed this point in connexion with science in his Logic of Scientific Discovery, and he has substituted for the universality of proof the universality of empirical criticism. In his Open Society he raised the problem a little more generally, but there he neither gave examples of criticisms outside the domain of empirical science, with the exception of an all-too-sketchy outline of criticism in ethics, nor did he claim that criticism pertains to all intellectual activity: he explicitly claimed, for instance, that interpretations in history, historical points of view, are immune to criticism.
The broadest presentation of the problem, how can we develop a non- justificationist philosophy of objectivity, equally applicable to science, religion, and morality, was forcefully presented by Bartley, in his Retreat to Commitment and elsewhere. He feels that the tu quoque argument of the esotericists of our century, the claim that rationalism too rests on esoteric foundations, must be answered, not to the satisfaction of the irrationalist - whose judgments may be too arbitrary anyway - but to the satisfaction of that rationalist who, though a non-justificationist, wishes to carry over from justificationist philosophy the vestiges of objectivism and universalism that can be salvaged.
For my part, although I do not agree with Bartley’s solution (comprehensively critical rationalism), I find his presentation of the problem admirable. Indeed, if universalism and objectivism is to be retained, I feel, it can be retained not by a doctrine, be it Kant’s or Bartley’s, but by a perennial struggle towards objectivity and universality. On this point I am in full agreement with the doctrine which Gurwitsch ascribes (rightly or not, I cannot judge) to Husserl (who was, nonetheless, a justificationist). According to Gurwitsch, the most rational thing to do in the absence of a theory of rationality is to search for one (rather than sink into irrationalist despair).14 This point is, doubtlessly, a minimum thesis that all non- justificationists would accept; it is in intention close to the attitude of the Age of Reason, but in points of technicality it is its extreme opposite. For Bacon and his followers, disagreements and splits between and within schools are anathema, the symptom of faulty justification; for Popper and his followers the opposite should obviously hold. That it does not always hold, only shows that non-justificationists can hold nothing as manifest, not even non-justificationism, not even to the arch-non-justificationist. I should therefore state tentatively, that it is always the case that we do not know that we have a satisfactory theory of rationality, so we may always try to either criticize existing doctrines, or create alternatives to them, or both. We may or may not be successful in this, but we may always try.
This point, too, is no novelty. Sextus Empiricus already notes that the consistent skeptic (etymologically, searcher) exercises a skeptical attitude even towards his own skepticism. This, he adds, leads to peace of mind. But, he adds a rider to this rider: this claim for peace of mind is not a dogma but a (psychological) hypothesis which, historically, came to his school as an after-thought.15
IV.