In the realm of philosophy, is logic objective or subjective?

Godel's proof is revolutionary in metallographic histology, but their impact on logic "objectivity" is less important.

Godel shows that in a logical system that can axiomize arithmetic operations, certain statements are "undecidable". In other words, we can not prove whether they are true or false (we can not prove Φ or prove - Φ). He extended this to prove that the logical system based on the architecture can not prove its own consistency - ie it can not show that all true statements are not contradictory.

However, the incompleteness theorem actually applies only to a specific subset of logic (a system with recursive axioms such as Peano 's atheism and theoretical foundation of mathematics). So what they are saying is that we can not be sure that our mathematical theorem is not contradictory. But mathematicians do not care about it, do not worry so much. We can not prove that these systems are complete and consistent, but it is impossible or impossible to generate a theorem that is inconsistent with normal pan and butter theory. But since we can not decide, we never know

So what Godel did was to put mathematical consistency uncertain. Probably each theorem is consistent with axioms. It may not be the case. I can not prove that this is the fact

By the way, pure classical propositional logic (there is no logic of quantifiers) is complete and consistent. But without quantifiers you can not base on mathematics, so unquantified logic is not that powerful.

Even if you can prove that the system in question is complete and consistent, it does not mean that few axioms you choose based on agreement. This only shows that we chose some good axioms.

In "Logic philosophy" of Frege, logic consists of logical entities. Logical functions, range of values, and truth - true and false - are considered to be objectively real entities that exist outside the physical and psychological world. (As shown below, Frege is also committed to other logical entities like senses and thoughts.) Logical axioms are real. Therefore, Frege denies the general view that logic has no content or metaphysical commitment. Frege is also a strict criticism of psychology in logic. Logical truth is the truth about psychology. Frege believes that logic may determine how people should think about the law, but logic is not a science of how people think. Even if no one believes them or uses them for inference, the logical truth is still true. Whether true or false, ineffective and effective is not dependent on someone's psychology or someone's beliefs.

Before Hegel, this theme (essential doctrine) was not considered to be part of logic at all. Today, it is often covered by historical and scientific philosophy or research methods. It is called objective logic because it explains the process of unknowingly executing knowledge, as determined by objective laws. In contrast, subjective logic begins with an abstract concept whose central creative concepts are developed and become increasingly more specific theoretical practices such as the history of scientific development; for example, in the Periodic Table of the Elements Chemical science after discovering concept