>>12729557Ok, it wasn't a good idea to split the posts. Let's merge them.
I am here for you. I always wanted to study philosophy along with pure math and pure physics, and it is very simple: you just do it. Want to start? Let me highjack this thread to talk about formalism, skipping so much motivation that we could use but that we will find sooner or later.
The first two keywords are sign and logic. How is logic related to signs and how are logical signs related to math. For this we will have to learn first order logic, which is based on very basic linguistic framework. The idea is that of formalization, formal system, formal language, formal calculi, and so on. There is no need to rush, let's talk about the subject just calmly and comfy. Why formalization right away and not informal but exact reasoning first, as it is tradition? Well, i ask myself the same thing too. It is an arbitrary choice, let us try this and let's see how far we can go.
>exact reasoningThis is, to say, math itself. Rigor is another thing, different from exactness. It is not so much about exact reasoning, but about being completely explicit about each defined concept, each assumption, and the underlying logic employed in the deduction process of the reasoning. Rigor plus formalization is the standard that we have in first order logic, where theorems and proofs are not just usefull metaconcepts but fully defined, rigorous ones.
Anyways, there must be a transition from formal to informal proofs. Moreover, some mathematicians like Terry Tao talk about the stages of pre-rigorous, rigorous and post rigorous mathematics (Lakatos, instead of "rigorous", uses the word "formal").
