The Foundations of Value, Part I

Logical Issues: Justification (quid facti),
First Principles, and Socratic Method

after Plato, Aristotle, Hume, Kant, Fries, & Nelson

If you wish to justify your beliefs, you give reasons for them. You say that you believe proposition Z because of reason Y. Willingness to give reasons all by itself may be calledrationality -- as long as the reasons are relevant. You may also wish, however, to justify proposition(s) Y. So you cite proposition(s) X as the reason for believing proposition(s) Y. Aristotle noticed two things about this procedure. First, we must be able to describe how Y provides a reason for Z and X provides a reason for Y. Logic is just the description of how X implies Y and Z, or that Y and Z are logical consequences of X. Logic can prove Y and Z on the basis of X, but it cannot prove X without further reasons (premises), e.g. propositions U, V, or W. Logic alone can only secure the truth of its conclusions if the premises are true. Thus, it remains an inconvenient but unquestionable truth of logic that one can be perfectly logical and yet, with false premises, never say anything true.

If we continue to give reasons for reasons, from Z to Y, to X, to W, to V, to U, this is called the Regress of Reasons. Aristotle's second point, then, was just that the regress of reasons cannot be an infinite regress. If there is no end to our reasons for reasons, then nothing would ever be proven. We would just get tired of giving reasons, with nothing established any more securely than when we started. If there is to be no infinite regress, Aristotle realized, there must be propositions that do not need, for whatever reason, to be proven. Such propositions he called the first principles (archai, principia) of demonstration. Since principium -- from princeps, which is from primus andcapio, "to take" -- already means "first" (primus), "first principles" is a redundant expression. This has happened because "principle" has come to mean a rule, perhaps a very basic rule, but not necessarily a first principle in the logical sense. Such a drift of meaning already had occurred in Mediaeval Latin, so that we get principia expanded into principia prima.

How we would know first principles to be true, how we can verify or justify them, if they cannot be proven -- the modern terminology is that they must be "non-inferentially" justified -- is the Problem of First Principles. Aristotle decided that first principles are self-evident, which means that we can know intuitively that they are true just by understanding them (by noûs, "mind"). This was widely believed to be the case for many centuries, especially since it seemed to fit perfectly the best example of a deductive system based on first principles: geometry, where all the theorems are ultimately derived from a small set of axioms. In other areas, however, self-evident first principles didn't seem to work very well. Ultimately, Hume and Kant decided that most first principles are not self-evident. Hume thought this meant that we couldn't really even know them to be true, although we had to assume that they were. Kant thought that we could know them to be true, even though they couldn't be proven and were not self-evident.

Kant said that such propositions were "synthetic a priori." "Synthetic" means that they can be denied without contradiction, i.e. they do not contradict themselves or anything else that is true. Now that is called "axiomatic independence." "A priori" means that they are known to be true independent of experience. Although there is not much agreement on whether Kant explained this successfully, Leonard Nelson (1882-1927), following a suggestion in Kant, later thought that there were really two questions involved: 1) the actual justification, what Kant called the quid juris, or matter of right, which we can set aside for the moment; and 2) the question of whether the first principles are simply there, i.e. whether we use them -- something never doubted by Hume and called the quid facti, or matter of fact, by Kant. Nelson understood that this could lead to a theory of knowledge much like Plato's. In recent philosophy, virtual nihilists (perhaps "non-cognitivists" is the polite expression) like Richard Rorty solve the Problem of First Principles by saying that we simply get tired of giving reasons. In a way this is true, or, more like it, we simply run out of ideas (rather quickly), but this does not solve any of the logical or epistemological issues of justification.

Aristotle had hoped that first principles could be discovered through induction. An inductive inference is the generalization that results from counting individual objects or events. The Problem of Induction is the realization that we can never know how many individuals or events we need to count before we arejustified in making the generalization. Francis Bacon believed that empirical science uses induction, and his views influenced everyone's view of science until this century. But Bacon couldn't answer the objection that induction never proves anything. Nor could anybody else, and Hume twisted the knife in the wound.

In The Logic of Scientific Discovery Karl Popper shattered the conundra of induction and the verification of first principles by just dismissing them. Induction never had proven anything. Even Aristotle understood that, but it finally wasn't until Hume that the point was really driven home -- although even modern partisans of Hume don't seem to understand the result. Aristotle's problem of verifying first principles was resolved by Popper with the observation that deductive arguments can go in two directions: ponendo ponens, "affirming by affirming," ormodus ponens, "the affirming mode": if P implies Q, and P is true, then Q is true. This held out the mirage of verification, since all we have to do to secure things is somehow get P. But a deductive argument can also use tollendo tollens, "denying by denying," or modus tollens, "the denying mode": if P implies Q, and Q is not true, then P is not true. This means that premises can be falsified even if they cannot be verified. If we cannot somehow get P, we might simply be able to ascertain that Q is wrong, especially when P is a general statement and Q its application to some individual.

Popper says that this is a form of Kantianism, and in fact it is rather like what Immanuel Kant says in the Critique of Pure Reason at A646-647 under "The Regulative Employment of the Ideas of Pure Reason." Popper also says that it is conformable to the Friesian variety of Kantianism, since Jakob Fries (1773-1843) and Nelson, returning to a consideration of the original problem in Aristotle, stoutly maintained that first principles cannot be logically proven/inferred. This explains many peculiarities in the history of science and is, indeed, the "logic of scientific discovery," although people like Thomas Kuhn have muddied the waters with other issues (some of them legitimate, some not) -- in The Structure of Scientific Revolutions.

In relation to Popper's understanding of the logic of scientific discovery, the point of interest is how Socratic Method uses falsification. The form of Socratic discourse is that the interlocutor cites belief X (e.g. Euthyphro, that the pious is what is loved by gods, or Meletus, one of the accusers of Socrates in the Apology, that Socrates is an atheist). Socrates then asks if the interlocutor also happens to believe Y (e.g. Euthyphro, that the gods fight among themselves). With assent, Socrates then leads the interlocutor through to agreement that Y implies not-X (e.g. the pious is both loved and hated by the gods). The interlocutor then must decide whether he prefers X or Y. That doesn't verify or prove anything, but one or the other is falsified: just as in science a falsifying observation may be itself rejected instead of the theory it discredits. Although Y often has more prima facie credibility, the heat of the argument is liable to lead the interlocutor into rejecting Y for the sake of maintaining their argument for X (though, with Euthyphro, Socrates does not agree with either premise). Socrates then, of course, finds belief Z, which also implies not-X. After enough of that, X starts looking pretty bad; and the bystanders and readers, at least, are in no doubt about the outcome of the examination.

The logical structure evident in Socratic Method was already being used in the form of Indirect Proof or the reductio ad absurdum argument in mathematics and elsewhere. In this, the contradiction of what is to be proven is assumed. It is then shown that this implies a contradiction with other assumptions or definitions in the matter. Logically, according to the Law of Clavius[(-P > P) > P], this establishes the truth of what is to be proven. Classic examples of Indirect Proof are the arguments discovered by the Greeks that there is no largest prime number and the square root of 2 is an irrational number.

Why it was always possible for Socrates to find another belief that would imply not-X is a good question. Plato had thought that true first principles [note] were unavoidable. We use them always, even though we usually don't realize it and even when we may even think that we aren't. Whenever Socrates questioned people, he had always been able to maneuver them into contradictions. Plato decided that this happened because Socrates could always find the way to bring out the conflict between everyone's false beliefs and the true principles that they inevitably employed somewhere. With a contradiction, however, which side is true and which is false, or whether maybe both sides are false, is an open question. Thus, Plato conceived of Socratic Method as the way to discover the truth on the principle that a completely consistent system of belief is possible only for the true first principles. Otherwise false beliefs would create contradictions with the unavoidable true principles. As Hume said, whatever our philosophical doubts, we leave the room by the door and not by the window -- the same Hume who ruled out, not just miracles, but also free will and chance because he thought they all violated the same principle of causality that he so famously doubted. Nelson suspected that consequently, while Socratic Method did not really justify the first principles, it did provide a way to discover them. In a practical sense, that may be just as good as justification, and we can even say that Hume did more or less that very thing. It does always give Socrates, and us, a way to pursue the inquiry when we seem to reach an impasse.

Socratic Method thus shares the logic of falsification with Popper's philosophy of science and thereby avoids the pitfalls that Aristotle encountered after he formulated the theory of deduction and faced the problem of first principles and of induction. Both Socrates and Popper are left in a certain condition of ignorance because the weeding process of falsification never leaves us with a final and absolute truth: we always may discover some inconsistency (or some observation) that will require us to sort things out again. Our ignorance, however, may be of a peculiar kind. We may actually know something that is true, but the limitation will be in our understanding of it. Galileo was in a position toknow that the sun was a star, but his understanding of what a star was still was most rudimentary. Isaac Newton had a theory of gravity that still works just fine for moderate velocities and masses -- the force of gravity still declines as the square of the distance -- but Einstein provided a deeper theory that encompassed and explained more. When it comes to matters of value that scientific method cannot touch, Plato had a theory of Recollection to explain our access to knowledge apart from experience, and his theory was actually true in the sense that we do have access to knowledge apart from experience; but Immanuel Kant ultimately provides a much deeper, more subtle, and less metaphysically speculative theory that does the same thing.

Plato's own (reductio) argument against Protagoras's relativism brings out this point. It is that relativism itself uses the very principle of absolute truth that it explicitly rejects. Relativism cannot even make its own claim without holding thatit is above the relativity that it postulates. But if relativism is not absolute, then it allows its opposite, namely absolutism. Relativism could be true only if it were relatively relative, and that is not a denial of absolutes. Subjectivism has the same problem. If there is no knowledge (objectivity), how can we know that? If there is no objective truth, that would be an objective truth. So if subjectivism were true, clearly we couldn't know it, we would just have our subjective impression that no one would need to pay any attention to.

Be careful whenever a philosopher (like Hegel) begins talking about "reason" -- just as when Mr. Spock used to say in Star Trek, "Logic dictates." Logic doesn't dictate very much, and we must be very careful what someone means by "reason" when they begin invoking it. As you have seen, logic requires premises, and it ultimately cannot prove those premises. If "reason" means logic, it really only means consistency; but in principle, there could be an infinite number of consistent logical systems. Since Hume thinks that all first principles are established by sentiment, he properly asserts that, "Reason is and ought to be the slave of the passions." Other philosophers (Aristotle, Plato, Kant) may mean more by "reason" than consistency, but we must be clear exactly how that differs from logical consistency.

What would make the principles revealed by Socratic Method true is a deeper issue that will be considering in the following essay, "The Foundations of Value, Part II, Epistemological Issues: Justification (quid juris) and Non-Intuitive Immediate Knowledge."

The Reasoning of Sherlock Holmes

Epistemology

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