I know similar questions have been asked and i know my terminology might be wrong but I am trying to come to an answer to whether math can be derived from logic. Wikipedia defines logic as use and study of valid reasoning and I assume something "logical" is defined as something that is consistent with this valid reasoning. There are few things here that trouble me. The term "valid reasoning" can be rather subjective and broad. Since logic is not a thing, but more of a process, I'm not sure how to define it as objective or subjective but regardless of that, the term "valid reasoning" is subjective. Is it even possible for humans to define that term?
Now, taking all this into consideration, I would come to think it is possible to define a mathematical theory or a whole branch of math based on some absurd ( what troubles me again is that even the term "absurd" is subjective) axioms we define. Now if we use this axioms to define a theory, wouldn't that mean by the concept of inference that the whole theory is absurd. Does this mean it can't be derived from logic or does it just mean we don't know how to do it.
I am sorry if i made any major mistakes or used incorrect definitions and terms, but the whole concept of logic puzzles me, especially the fact that it is considered a science.
A valid reasoning in ultimate case is a convention.
The general convention for valid reasoning is that it dont fall on contradiction (however Im not sure that this condition can be proved for all logical systems),i.e, the system must be consistent.
In a more broad sense "dont fall in contradiction" means that the system to measure something give to us information.
The axioms can be as "absurd" as you want... but they need to be consistent to be useful.