Great Ideas of Philosophy

II. A philosopher is engaged in the search for truth—that which can be known certainly. That there is such truth isverified by the universal truths of mathematics.A. The answer to the question “What is a right-angle triangle?” is: “Whatever figure satisfies the statement a 2+ b 2 = c 2 .” It is the latter that is the true form, whereas the drawn figure is but a transitory, defective, oftenmisleading depiction. The true form suffers no change—ever.B. Nothing drawn in the sand by Socrates is the Pythagorean theorem. The visible right triangle is, after all,soon to be swept away by the wind and the traffic of the road.C. The difference between the drawn figure and the true right triangle is that the latter is, finally, not an objectof sense but a formal relationship.D. What is it about the soul, about rationality, that can make contact with a truth of that kind? We can’t comeup with mathematical truths experientially. Surely, Pythagoras did not arrive at that theorem by laying hismeasuring rod along various right-angle triangles, luckily finding the first one to be a 3–4–5 triangle.E. Obviously, such ideas must exist, in a sense, in an a priori way, which doesn’t necessarily mean temporallyprior to experience, but logically prior to experience, because there is nothing in experience that willconvey such truths. Given that rational beings are clearly in possession of these ideas, they must be inpossession of them independently of experience.F. This is an intuitionist’s theory of knowledge, a theory of knowledge based on the proposition that what isfirmly known, and known to be true, and could not possibly be known as a result of experience must bepart of the very gift of rationality itself. It must be something co-extensive with the life and thought of arational being.G. We might note that Aristotle, commenting on Platonic teaching, insists that it was not Socrates but hisdisciples who conferred ontological standing on the “true forms.” Our concern is with the larger issue:whether or not true forms in the Platonic sense can legitimately be regarded as having some kind ofontological standing, some immaterial but nonetheless real standing in the domain of actual things.III. If the skeptic says, “How can you possibly stand behind the proposition that there is such a thing as unchangingtruth?” one reply will present the truths of mathematics.A. Plato was satisfied that the truths of mathematics were sufficient to put skepticism on notice. Mathematicshas established that some things can be known with certainty. The problem of knowledge then becomes asearch for the kind of truths that will match up with mathematical certainties.B. But if such “true forms” cannot be reached through experience, what is left? The answer is: a rationalenterprise that takes the form of a dialectical or argumentative approach, an elenchis in the Greek.1. This approach is not simply a rhetorical device; it’s an investigative device. Through the philosophicalmode of investigation, we come to consult whatever is contained in the rational resources of the soulitself.2. The truths we are looking for can’t be held up and shown to anybody. We must discover them in theway Pythagoras must have discovered the Pythagorean theorem: by engaging in an internalcontemplative discourse within the soul itself, a kind of introspective, spiritually guided form ofinquiry into what Aristotle will call “first things.”3. Only through the dialectical method and the guidance of the philosopher is one able to get past theephemera of sense to truths possessed by the soul from the outset.C. This approach gives us, if not a solution to the problem of knowledge, a recognition of just what it is thatmakes knowledge problematical. Knowledge is problematical owing to a slavish reliance on experience.1. As we have said, experience can’t get at certain truths. Animals have experiences; wicked and foolishpeople have experiences. Further, if one person’s experiences are insufficient, little is gained byadding those of another. Self-deception is not eliminated by increasing the number of those thusdeceived!2. We begin to see that in the solution to the problem of knowledge, there is already skepticism aboutdemocratic approaches to questions of conduct and governance.Recommended Reading:Plato. Meno, in The Dialogues of Plato, 2 vols., B. Jowett, trans. Random House, 1937.©2004 The Teaching Company Limited Partnership 21