The pretense to reason

The logic books define two words that ought to cause more trouble than they do. The words are "sound" and "valid." They are qualities of argument. An argument begins by assuming premises, a few statements of fact taken for granted—the argument needs to start somewhere. From the premises it draws intermediate statements that proceed in logic, concluding finally with the point it had hoped to justify.

Some arguments are better than others. If an argument's conclusion does in fact "follow" from the premises, if its statements "flow" from them by logical necessity, our books say to call the argument valid. We cannot do without the metaphor of follow and flow here; it is interesting we must take this recourse. Next, in addition to validity, if an argument's premises are actually true our books say to call the argument sound. The two words hang together: Valid arguments furnish logical conclusions from a set of premises. Sound arguments start from true premises, so their conclusions are not only logical but true. Sound arguments count as knowledge.

It might appear a sound argument not only counts as knowledge but creates it. Psychologically this may be the case for the hearer—and the psychological sense is the more important for us, for it is the more therapeutic. As for a logical or epistemic newness, however, no argument can actually boast to offer that sort of innovation. Each step in an argument is assembled from what had already been said. A statement in an argument does nothing but logically combine or rephrase its premises. Each line succeeds its prior line because it came from the prior line, and conclusions flow ultimately from premises the way water in a falls flows from the river upstream. We might do well to say the premises "contain" the conclusions already, the way a lake contains all the water that may one day strike the falls. Therefore, does the conclusion offer anything else than—the premises, exposed and unpacked? Socrates is a man; men are mortal; therefore Socrates is mortal. This is valid, one can accept it if the premises are true. Yet it is nothing but a skillful combination of the premises: Socrates, man, mortal.

And as for the premise that Socrates is man? We crave soundness. Is the premise true, which would make the argument sound? To find out we announce a probe of his manhood: "Is Socrates man?" We need to establish his virility. We need to argue again—an argument, hence a new set of premises and a new series of steps drawn from them. Obediently we gather data from history for the premises, and construct another valid argument by logic, arriving at the proposition Socrates is man. A success in terms of validity, but we still crave soundness: This new argument that Socrates is man, is this new argument sound? This new argument, are its premises also true? We shall need yet another argument. Every sound conclusion flows from its premises, which may themselves derive from the conclusion of some prior argument. One may start with any conclusion and trace it back through a flow of prior conclusions and prior premises hoping to stop somewhere—at an "axiom," a self-evident root of thought, a premise unshakable—at least for the sake of argument.

The history of philosophy is partially a history of increasing precision in logical argument. It has earned dividends. After 2,500 years of philosophical hindsight, years spent practicing the kind of meticulousness that breaks youth and eyesight, we now can very well guess what sorts of conclusions flow from what sorts of premises. More grandly, we can very well guess what sorts of philosophies will spring from what sorts of axioms. Since we know the relation, let us ask: Which axioms shall we choose—for the sake of argument? Do not assume I am commenting on foundationalism here, the position that truth requires a premise of ultimate self-evidence. You do not have to agree with foundationalism to recognize the importance of choosing premises for argument. Every argument has to start somewhere, regardless of whether you agree with foundationalism. Those are the "rules of the game." In the game of soccer we must choose strikers, midfielders, defenders. In philosophy, for the sake of argument, we must eventually choose axioms. But we crave soundness. Which axioms are the right ones? Note I do not write: which axioms are the sound ones? For soundness is a quality of argument.

The axiom is the real question, and here is the real problem: one cannot argue for axioms, for then—they would not be axioms. One may not premise them without robbing them of their self-evidence. One may not question their virility. We have experience in argument, centuries of meticulous practice in argument, we compete with the world's best in exactitude today and before and probably hence, and yet we find that we have exhausted the market's demand for logic. Knowing the sorts of conclusions that the various axioms lead to, precision is no longer something for which we will pay a premium. What we really need to know is: How do we choose the axioms? This is the only question worth asking, but it cannot be answered "rationally," because then we would give an argument and—all is lost. We have premised the axioms in argument, which poses the question: What are the axioms' axioms?

Imagine the following, for it happened and is happening. You tell me the axioms, and we—even I—can give you the set of conclusions you will likely reach. Reach, that is, even after you publish your judicious and even-handed critique of the status quo, followed by an incisive book-treatise throwing open a door to an unrepresented alternative and (necessarily) the publishing of a follow-up for popular audiences founding a tradition, and some papers noting its continuity with favored past sages (now pre-sages)—then a timely heretic appears, a century of internecine squabble passes and hones the essential insight, paring away all assumptions unnecessary to the seed, but the dissension weakens the tradition; it fades for a generation as new fashions in philosophy obscure it. Philosophy, the love of wisdom, whose self-declared sophophiles are actually sophophages. They regard your work as itself a fashion, "considered historically, objectively and according to contemporary criteria"—and are they perhaps right? A depressing anxiety. They unearth your splintered monuments, in a chaste future resigned to scour the past not for answers but to classify. Finding you and your progeny they file the collected works in a library for students to write papers on your grammar and your footnotes. Ironically they shelve your collected works beside others saying the contrary. Is a bookshelf of contrary philosophies not like three wines of separate vintage combined to make a more "palatable" blend? Our future sopho-connoisseurs finish by coding your work in a decimal system that distinguishes philosophical books by—yes—by their "school" which really means—finally, yes—by their axioms. The axioms which chose the conclusions. You could have started with your conclusions and reverse engineered the axioms. How distasteful and yet, did you do that? It's disheartening to worry that one may have begun with conclusions and only then have chosen the axioms. But was it better to begin with axioms, which no less had to chosen, for no argument can be offered for them? Either way, it strikes you, it doesn't really matter, for either way there was: a choice.

At the bottom, choice. Centuries of argument proving—proof, unnecessary! Arriving no closer to a "rational basis for belief" precisely because—we have one. And that basis founded in axiom, the ultimate premise for any line of argument, itself having—no basis in any line of argument. Vanity of vanities. Where is Anaximenes now? He might be interested to learn we have discovered what he always knew, that it is all: air.