Wittgenstein on rules
On the rules a lot has been written and will be written in the future.
here what some philosophers have to say about rules in general.
Logic is a great source to start.
Is Mathematics just following rules formalism or is there more to it?
Wittgenstein: “Of that about which we cannot speak we must remain silent” (“Wovon man nicht sprechen kann, darüber muss man schweigen”)
need more to be continued
emeraldemon: I think there is an interesting analogy between mathematical formalism and rules formalism. Early mathematicians focused on intuitive results, without to much concern about which specific axioms were required for their proofs. Only later did they ask questions like "what is a 2?" and "when is a proof sound?" And some of the results from these seemingly obvious questions were quite counterintuitive, like the axiom of choice leading to the Banach–Tarski paradox, or Gödel's theorems.
Something similar happened (or is happening) in go: I think people began playing go without a clear idea of the rules, which is why there were disputes in some early games. There have been many attempts to create a ruleset that matches well with people's intuitive idea of what go should feel like, with limited success. I personally feel the Tromp-Taylor Rules probably do the best job of capturing the flavor and simplicity of Go, but they don't allow for voluntary removal of stones, something most players agree to in practice.
tapir: actually the wittgenstein quote is from the end (Proposition 7) of the tractatus logico-philosophicus. and he refers there to most important things - most of all morals (about which you can't speak in the logical ways he explained in the tractatus). he later recognized that something can and needs to be said about all those non-logic phenomena even if it may be totally lost on some mathematicians and analytical philosophists.
- "But still, it isn't a game, if there is some vagueness in the rules". -- But does this prevent its being a game? -- "Perhaps you'll call it a game, but at any rate it certainly isn't a complete game." This means: it has its impureties, and what I am interested in at the present is the pure article. - But I want to say: we misunderstand the role of the ideal in our language. That is to say: we should indeed call it a game, only we are dazzled by the ideal and therefore fail to see the actual use of the word "game" clearly.