# Logic

## Three Views of Truth

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. You may disagree with this (and we can certainly debate it), but I take the metaphysical realist position that truth is necessarily bivalent. Which is to say, I take Dummett’s argument that realism necessarily entails that propositions are - and can only be - true or false. Whether that truth value can be assigned on the basis of “evidence transcendent” means is also a debate for another time. Suffice to say here, that I am committed to both ‘rational’ (a priori) truth, and ‘sensible’ (a posteriori) truth, and I think we can indeed call our awareness of those valences ‘knowledge’ of the truth. All of this demands a great deal more explication. But the point here, is just to briefly identify and define the first form of meaning.

## Deduction Seems Vulnerable to the Problem of Induction

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:

1. All men are mortal
2. Socrates is a man
3. 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. So, we all must die, yes? That’s an inductive inference. How is it justified?

## Induction - An Introduction to the Problem

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.

## The Sorites Paradox - Some Doubtful Thoughts

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. In other words, simply deny that a man with 10 hairs is in fact bald, or that 100 grains of sand is in fact a heap. In essence, this would render vague predicates useless at best, meaningless at worst, since no predicate that allows for a vague border case would be permitted to apply to anything. There is one way in which we might stretch this into plausibility, but I will address the other responses first, before returning to this in the conclusion.

## Haack, Dummett, and the Justification of Deduction

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.

## Getting a Handle on the Truth

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.” But what if we’re wrong and we still agree? Or worse, what if we disagree, but one of us is right? This can’t be the last word on this topic. What can we say with any confidence about truth, as such? To put it in the words of Bertrand Russell:

## Knowledge Certainty and Logic

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.