"Do you believe the moon isn't there if you're not looking at it?"
The Moon is not logic. Logic is human rationalization, but don't take my word for it look it up.
Ah, so we're just having a semantic breakdown.
Like in mathematics, there is a distinction between the study of something (including the formalisms, paradigms, syntax, symbols, words, etc.) and the thing being studied itself.
Fine, I will clarify then: the laws that we study that we categorically name "logic" are not contingent. Our formalisms for expressing them, however, are contingent.
Make more sense now? I would have thought that my statements about things still being what they are regardless of whether anyone's around to note such state of affairs would be enough to show that I'm talking about the objects we study in logic, not the practice of studying them itself.
This same problem comes up with mathematics a lot: someone will assert that we create mathematics, but what someone might mean by "Mathematics are external to minds" is that the objects of mathematics are external; not the study itself -- same thing here.
Edit: I swear I didn't mean to come off as snippy as this post sounds, lol.