>>580697
I value various systems of logic because they can reliably be used to understand a course of actions without having to actually take place (thought) and can be used to create reliable predictions within my world view which have been useful with such a level of persistence that I place a certain amount of assumption that it will continue to maintain that level of uniform predictability with the result. The same reasons as to why I decide to drive a car at speeds fast enough that would involve, once again from that same net of beliefs in my world view, a probably prediction of death.

Basically, how I derive value from logic is from a practical sense and don't really inherently value anything. I don't really know enough about what other people generally claim to make claims for anyone else. Don't really get out so the people in my general interaction, this "we", may generally hold entirely different public views on the matter. They could be lizard people in semi decent human suits for all I pay attention to them.

What in particular does this have to do with history and humanities?

>>580729
>they can reliably be used to understand a course of actions without having to actually take place (thought) and can be used to create reliable predictions within my world view
then why can nobody prove this statement ?

>>580697
Wittgenstein argued in the Tractatus contra Frege that there can be no rules for logic, or in modern terms that language should be its own meta-language, as is indeed the case with natural languages. "And what can not be said should be passed over in silence", which is probably "Wittgenstein's mysticism" that Russell mentions. However, Russell himself was well aware of Wittgenstein's position, but suggested a hierarchy of languages instead.

>>580697


Many have argued that logic is empirical, or as you describe it, logic's "axioms are dependent on observation".

Quine, in his paper "Two Dogmas of Empiricism" questioned the analytic-synthetic distinction, and suggested that even analytic propositions were dependent on empirical evidence. Since the rules of logic were analytic propositions par excellence, they too, were ultimately dependent on empirical data, and were not absolute laws.

Birkhoff and Von Neuman proposed in the 1930s that the paradoxes of Quantum Mechanics can be explained if we abandoned classical logic and used some form of Quantum logic instead. Such a Quantum logic would change or abandon all together some of the rules of classical logic, and would be a perfect case of logical axioms arrived at by observation.

Hilary Putnam discussed this in depth in his paper "Is Logic Empirical?" Later republished as "The Logic of Quantum Mechanics.". In it he argued that, just as empirical physical results - relativity - forced us to abandon Euclidean geometry, so it is possible that the results of quantum mechanics will force us to abandon classical logic.

Although Quantum logic is still an active field of study up to the present day, it is does not get much attention from most philosophers and had been abandoned completely by physicists. Those who do study view it mainly as a mathematical tool for studying Quantum phenomena, not as some sort of fundamental logic to replace our current classical rules of logic.

>>581044
The main problem that is faced by Quantum logic (or any such radical revision of logic, empirically justified or otherwise), is that we tend to think and communicate in classical logic. It would be very difficult, or in Kantian fashion, outright impossible for us, to perceive and discuss the world in anything other than classical logic - it seems to be hardwired into our brains. Although the logical atomist program failed as a metaphysical theory, it did show us just how ingrained classical logic is into our linguistic and mental structure. As Wittgenstein stated, the limits of language are the limits of the world: No one can place themselves outside of logic, and then pick among different logics to reason and argue with, even if those alternative logics are justified.

Those non-classical logics which have been successful (fuzzy logic, modal logic, intuitionistic logic) are those that extend classical logic, as opposed to replacing it, or at least respect classical truth tables in the limiting case.

As an after thought, one of my favorite Sci-fi short stories discusses the idea that while logic is indeed subjective, we learn classical logic at a very young age and once we grow into adults, we are incapable of unlearning it. If we were to somehow come across non-classical logics at a very young age, we would be capable of all sorts of superhuman feats. The story is of course, just sci-fi, but I do find the idea compelling.

What is modal logic? Does it look like regular abstract mathematics?