system
Given the following post, respond as if you're commenting on Reddit:
human
Does logic exist independent of minds?
gpt
In one sense, a 'logic' is a language. It's a set of rules for manipulating formulas. If you have a certain formula on one line, then you can write another formula on a new line, etc. In the standard logic you learn in college, for example, something like this will be permitted:  

    1    (1)  p & q   (assumption)
    1    (2)  p       (from 1, &-elimination)  

But of course we could perfectly permissibly create a language in which  

    p & q  

*doesn't* allow you to write  

    p  

on a new line.  

Why didn't we create *that* language instead? Because we think that that inference is special: it actually corresponds to a *real-life property of the world*. That is, metaphysically necessarily, *in real life*, whenever a conjunction is true, each of its conjuncts is true. What we say is that the language we created doesn't just have a *syntax* (rules for manipulating symbols); it has a *semantics*. We define the vocabulary of the language and we say that the symbol '&' corresponds to the real-life phenomenon of conjunction: something *and* something else being true.  

In real life, if you have a conjunction, both of its conjuncts will be true. (This fact seems to be mind-independent: before humans, when Mercury and Venus were closer to the Sun than Earth, it was also true that Mercury was closer to the Sun than Earth.) Our language of logic captures that. That's a good thing; it helps our language be *complete*. In addition, our language of logic doesn't allow us, from 'p or q,' to "infer" (scare-quotes because languages of logic, syntactically, don't really claim anyone infers anything) p. We didn't decide to do that because *in real life*, a disjunction doesn't entail each of its disjuncts. If our language had allowed us to do that, then the language would have been *unsound*.  

**In sum**: Languages of logic are mind-*dependent*, but standard, sound-and-complete languages of logic correspond to *real, metaphysical rules* that (apparently, arguably) *do* exist independently of minds.  

(Edit: Typos.)