[pjacotg]

I recently read this book review [0] where a mathematical proof was described as a dialogue between two semi-adversarial but collaborative actors, the Prover and the Skeptic, who together aim to aquire mathematical insight.

I thought it was an interesting perspective.

[0] https://jdh.hamkins.org/book-review-catarina-dutilh-novaes-t...

[mikhailfranco]

This is Game Theoretic Semantics. See Hintikka's Principles of Mathematics Revisited and his framing of Independence Friendly Logic:

https://plato.stanford.edu/entries/logic-if/

[hgsgm]

This also what philosophical discussion/debate is.