Topics Logic

Question Why are the laws of logic considered to be truth preserving? I would have trouble accepting any theory that says these are mere conventions of men since they all seem to have a universal application and do describe realtiy as we know it. Did God make these laws like other grand laws of the universe or did they just appear or create themselves?

Accepted:
August 22, 2009

Comments

A logically valid inference is one that is necessarily truth-preserving. That's pretty much a matter of definition. We just wouldn't count an inference as logically valid if it didn't meet that condition. (In other words, necessarily preserving truth is a necessary condition for an inference to count as valid. Perhaps it is sufficient too; or perhaps rather more is needed for a genuinely valid inference: e.g. some relation of relevance between the premisses and conclusion. But we needn't worry about that. For present purposes it is enough that it is agreed on all sides that to count as valid an inference must at least be truth-preserving.)

Now, the "laws of logic" are general principles specifying which types of inference are indeed logically valid. So again, it is pretty much a matter of definition that instances of the laws of logic have to be truth-preserving. That's what it takes for a law to be a law of logic.

It isn't as if we can first identify a class of principles as laws of logic and then wonder "why are they considered to be truth-preserving?". It is the other way about: it is only the principles of inference that are necessarily truth-preserving which are counted as laws of logic in the first place.

Still, an interesting issue remains (and perhaps this is what the original question was after). Suppose we are given a rule of inference which is in fact necessarily truth-preserving, so a candidate law of logic. We can ask why the rule necessarily preserves truth.

Here's a sketch of one answer. Take the very simplest case. Consider the principle that from A and B we can infer A (where 'A' and 'B' stand in for propositions). This is plainly a necessarily truth-preserving principle and a logical law, for if a proposition of the form A and B is true, then of course A in particular has to be true. But why is that so? Surely, the rule works because of what 'and' means. But equally we might say that what 'and' means is fixed by, among other things, the fact that we take inference from A and B to A is to be absolutely compelling and watertight. The meaning of the logical word "and" and the rule of inference for using it are tied together.

If something starting along those lines is right, then the principle that from A and B we can infer A isn't so much a "grand law of the universe" as an articulation of the structure of the conceptual framework in which we talk and think about the universe. Similarly for other logical laws.