system
Given the following post, respond as if you're commenting on Reddit:
human
Why is logic irrefutable?

It occurs to me that logic and truth are somehow related, but I don't know why or how.
Is it that logic is somehow an inherent property of our universe or the human mind? Did we just make up logic, and due to many years of conditioning, we are now unable to separate a valid logical argument from truth itself?
Heads up: I am not an academic, nor very knowledgeable with general concepts in philosophy. In fact, I'm actually a mathematician.
gpt
Most philosophers would say that 'logic' is a set of languages we've made up, but they are languages that describe underlying properties of the world.  

Logic has a *syntactic* and a *semantic* side. (You're a mathematician, so the following will probably sound familiar.) The syntactic side refers to how the symbols can be used with other symbols. It tells us, for example, that if you have such-and-such a string of symbols, then you can derive such-and-such other string of symbols. It also tells us which strings of symbols count as 'well-formed,' analogous to real words in a natural language. The semantic side refers to what the strings of symbols mean in the real world. For example, the symbol '&' might mean 'and.' (We could have made it mean 'or,' but we didn't. And we could have chosen a different symbol for 'and.' Some languages do.)  

We say that a language of logic is 'complete' if every (semantically) true-in-the-world sentence can be derived (syntactically) in the language. We say that a language of logic is 'sound' if every (syntactically) derivable sentence in the language is also (semantically) true in the real world. Standard languages of logic--those you learn in intro-courses--will be sound and complete. If logic were *just* something we made up, then there would be no answer to the question of whether it's sound. But we do ask that. So we do think of logic "trying" to mirror or match real-world relations between real-world truths. If '*p* & *q*' narrowly logically entails '*p*,' then that matches up to the fact that in the real world, 'the dog is a black and the dog is a mutt' metaphysically necessitates 'the dog is black.'  

In sum, according to many or most philosophers, there seem to be metaphysically necessary relations between facts, truths, or states of affairs in the real world, and we create languages of logic to try to model or match or describe or help us understand the relations between those necessary relations.