Giambattista Vico

Giambattista Vico's primary concern was opposing Renee Descartes. Descartes believed that there were only a few factual, legitimate parts of thinking - math and science. Vico, unlike Descartes, believed that math and science weren't any more factual, legitimate, or whatever verb you want to use. Math and science, like law, history, art, language, and etc., aren't any more factual because they still rely argument and conviction.

I won't spend too much time on why law, history, art, language, and etc. are based on argument and conviction. Essentially, all of these aspects of human knowledge are up for debate. Thinking of art as the primary example, there is a strong rhetorical argument about what is and what is not art. There is not a clear, distinct line. Now, Descartes would argue that math and science are the opposite of this. There is a clear line of what is mathematically correct and incorrect, or what is scientifically correct and scientifically incorrect.

I do have to agree with Vico is a sense here. Yes, law, history, art, language, and etc. are very subjective, but in a way math and science are too. Surely, they are less subjective, but that isn't the point. The point is, there is a level of subjectivity that brings their level of credibility down.

In math specifically, it is based off of axioms in order to make proofs. Axioms are essentially the laws to math. However obvious or right they may be, they still need to be established. In order to establish axioms, it takes an intervening human interaction. Humans still need to establish what is "true" and what is not "true." Therefore, according to Vico, it still requires both argument and conviction to do this.

In science, you see this happening quite a bit. Science is still interpreted, experimented, and "proved" (a thought I will get to in a moment) by humans. To be completely objective is certainly impossible. Humans are not machines or robots that can throw away emotions. In science, everything is based off of theory for a reason. Theory is the repeated testing of the same hypothesis with the same result. It doesn't say anything about "proving" anything, because the field of science is too smart to ignore the fact that you can't actually prove anything. You can merely see trends, not absolutes. It still deals with some level (maybe not to the extent as the other fields) of argument and conviction.