I think there is a lack of subtlety in the modern debate around meaning and truth. People struggle with ham-fisted dichotomies and adversarial arguments that never go anywhere, because of this low resolution notion of meaning. I want to suggest that we think of meaning in three different ways, and that each of them has a context and a scope that is appropriate to that distinction. VALENCE Valence is the truth value of a proposition.
Dirty little secret about logic: If induction has a justification problem (and it does), then so does deduction. Why? Because deductions rely on inductive conclusions imported into their premises. Here are a few examples. A. Aristotelian Syllogism: All men are mortal Socrates is a man C: Socrates is mortal Look at premise 1. What gives us the right to say that this is a true premise? Well, because we cast our gaze over a range of humans, and we see that they have all grown old and died.
The so-called problem of induction, plainly stated, comes down to this: inductive reasoning appears to have no rational justification. Unlike deductive reasoning, which offers apparent justification in its formal structure, the form of an inductive argument can at best only offer probabilistic confidence, and at worst, no justification at all, if we examine it’s application in the context of, say, a causal explanation. To see why this is the case, let’s examine some formal examples.
It has been asked how, if at all, one might resolve the Sorites paradox. I am not convinced a solution is possible, and in this paper I will explain the responses I have become aware of, and why they fail. In the end, I will conclude that there is no solution to the paradox, but I will offer a few suggestions for a way forward. The first response might simply be to reject the first premise of the argument.
Susan Haack nicely diagrammed the problem of circularity in her 1976 paper, The Justification of Deduction. In that diagram, she drew a direct parallel to the circularity of the inductive justification of induction, as outlined originally by Hume. Haack argues that justification must mean syntactic justification, and offers an illustrative example argument to show why semantic justification fails – namely, that it is an axiomatic dogmatism: deduction is justified by virtue of the fact that we have defined it to be truth preserving.
“What is truth?” ~ Pontius Pilate This is an interesting and surprisingly difficult question. If you look in the OED, what you’ll find there are entirely circular and self-referential explanations: “the quality or state of being true“, ” that which is true or in accordance with fact or reality“, and “a fact or belief that is accepted as true“. So, the poor souls that rely on the dictionary are left with, essentially, “truth is what’s true”, and “what’s true is what we agree are the facts of reality.
The Epistemic Regress (specifically, the Skeptical variety) is a little out of my depth at the moment, but what is plainly obvious by various presentations of the problem, is that at it’s core lies the Problem of Knowledge. The key question that arises in the examination of major premises in any deductive argument, is “how do you know?” This suggests that something essential about the nature of the premises needs to be discovered, before we are going to solve the riddle.