to be even clearer....

modern mathematics doesn't even tell you what rules of inference to accept. it can't; it's a limitation in the idea of math, itself. it just simply cannot argue that one rule of inferences is more valid in some imaginary objective reality than any other is, it can only tell you what rules of inference are being used in context, so you understand what is being done.

what i just said is summarized using the term hilbertian, as it is a reflection of david hilbert's dominant philosophical influence on modern mathematics. hilbert's famous catchphrase was:

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

that may be a paraphrase in translation (hilbert mostly wrote in german), but i don't think it's apocryphal.

together, hilbert & godel are the dominant influences on modern mathematical logic. godel was a weirdo that was quite plausibly on the autism spectrum along with einstein and cantor, but hilbert wrote widely and is not particularly inaccessible for arts students. i hear he makes more sense in german....