Logical Absolutes

[Angrboda]

With regard to Dillahunty and Slick, theism does provide an explanation for the origin or source of these things that naturalism currently lacks.  Unfortunately, their explanation is not a very good one, as it leaves them open to charges of vacuity.  If the laws of logic and morality are whatever God thinks they are, then they are both arbitrary and subjective.  Theists try to circumvent this problem by suggesting that God possesses a nature that "just is" the correct one, but as I showed Chloroform recently, this doesn't eliminate the charge of arbitrariness and vacuity.  The Euthyphro dilemma is in full force whether it's God's commands or his nature.

As to things like the laws of logic being reflections of empirical facts or merely descriptive, I'd have to disagree.  The idea that 2 + 2 = 4 seems true in a way that is more than just a convention of language.  The problem of abstracts is a tough one, and one that I see no easy answer for.

First, there are several different 'logics'. Aristotle produced the first list of 'laws of logic', but he was rather vague about specifics and it took later thinkers to straighten out some of his mess.

Boole gave a formal that, essentially, encompassed propositional logic, but his system didn't include phrases like 'there exists' and 'for every', which are usually seen as logical connectives.

That leads to quantifier logic. But that doesn't include aspects of equality or mathematics.

Because of the attempts to provide a logical foundation to mathematics that spanned the turn of the last century, a number of different approaches to logic were investigated. For example, intuitionist logic denies the classical 'law of excluded middle', especially as it applies to infinite systems. Other systems explicitly allow certain types of contradiction, but still manage to avoid triviality.

I would claim that the statement 2+2=4 seems obvious cause the number of definitions and assumptions required to prove it are minimal. I would bet that it is far less obvious that 29*31=899 or that a number is divisible by three if and only if the sum of its decimal digits is divisible by three.

In fact, the assumptions required to prove 2+2=4 are few enough that they would NOT be enough to show that 3 and 4 are different numbers. In essence, simply having a notion of 'next' and definitions of 2,4, and + are enough.

It wasn't the triviality of proving 2 + 2 = 4, but rather that as abstracts, the numbers seem to reflect metaphysical truths, that there's something underlying them that's ontic in a way that linguistic conventions aren't.