oblmov

I am focusing on mathematics because I am more familiar with mathematics than philosophy and dislike seeing it misrepresented, particularly to use as a cudgel against a related field that I respect.

The passages that you describe as "worthless philosophical ramblings" are part of Tarski's results. He could not have left them out without obscuring the meaning of his proofs. Possibly model theory would not exist today had he done so. It would certainly have taken longer to develop.

Another instructive example is Per Martin-Lof's lectures On the Meanings of the Logical Constants and the Justifications of the Logical Laws: https://www.ae-info.org/attach/User/Martin-L%c3%b6f_Per/Othe.... Unlike Tarski's paper, this contains no formal proofs whatsoever; if the sentence you quote is worthless, then I imagine "There is no evidence outside our actual or possible experience of it. The notion of evidence is by its very nature subject related, relative to the knowing subject, that is, in Kantian terminology." is worse than worthless. Nevertheless these lectures have been of great importance in logic and computer science. You can see some of their impact in the citations here: https://scholar.google.com/scholar?cites=2483744927635326348

You may be unable to find any useful meaning in this kind of writing, but most mathematicians do not share your difficulty. This is fortunate, since the field would be greatly impoverished if it purged itself of all philosophy and philosophy-adjacent work. I would normally encourage you to read https://terrytao.wordpress.com/career-advice/theres-more-to-... on the role of non-rigorous big picture thinking in mathematics, but it deals entirely with human understanding of mathematics and is therefore only of interest to Terence Tao and other such pseudoscientists.

If by "philosophy" you mean work that not only lacks a rigorous proof, but isn't even a step in the direction of a rigorous proof, you'll be happy to hear that many philosophers - sorry, mathematicians who mistakenly consider themselves philosophers - share your opinion of it. When I said "philosophy" I was referring to the academic field, which includes a lot of work that you consider math. While I think complete non-mathematician philosophers like Deleuze have value in their own way, I certainly wouldn't call them rigorous or useful to modern science.

I'm not clear on whether you think The Concept of Truth in Formalized Languages falls into the "actually just mathematics" category or the "making up random equations" category. If the latter, I assure you that Tarski's proofs are sound. Here's a simple explanation of the most famous result from the paper in case you found the original proof inaccessible: https://qubd.github.io/files/TarskiUndefinability.pdf. A more general discussion of Tarski's work and other axiomatic theories of truth can be found at the Stanford Encyclopedia of Mathematics: https://plato.stanford.edu/entries/truth-axiomatic/

All of the mathematicians I mentioned believed philosophy was relevant to their mathematical work, and that period of work on the foundations of mathematics was accompanied by extensive discussion of the work of Frege, Russell, Wittgenstein, etc. Even if we pretend philosophy never involves rigorous proofs, mathematical theorems do not spring out of thin air, and saying "anything that isn't a formal, rigorous proof is useless to mathematics" is like saying "anything that isn't a finished house is useless to the process of building a house". https://arxiv.org/pdf/math/9404236.pdf discusses this in more detail.

Here's a paper by Tarski, widely cited by both mathematicians and philosophers and containing both formal and informal reasoning: http://www.thatmarcusfamily.org/philosophy/Course_Websites/R... I don't know how one could "remove the philosophy" from this work without making it far less useful to mathematicians. The entire reason the T-schema is used in model theory is because of Tarski's philosophical argument that it provides a meaningful definition of truth.

I'm not sure how one could "remove the mathematics part" without removing the philosophy as well. The two aren't divided by hard boundaries and were particularly close during early 20th century work on the foundations of mathematics. Poincare, Cantor, Gödel, Tarski, Bernays, Hermann Weyl, and Hans Hahn all published philosophical work, just to name a few; even those who weren't themselves philosophers were at least involved with philosophy, e.g. Hilbert with the Berlin Circle. There are plenty of modern examples of crossover as well, such as Kripke, Putnam, Jaakko Hintikka, Saunders Mac Lane, George Boolos...