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> Really? What are those rules? This is too fun so I can't help myself. A stark example here is of haikus, which generally have few requirements by way of gram

> Really? What are those rules? This is too fun so I can't help myself. A stark example here is of haikus, which generally have few requirements by way of grammar, and only require syllabic rules. To parallel propositional logic, we can define an English haiku as a logic through the following: The set of symbols are the words of the English language, with punctuation marks and newline symbols. The language is defined as the free language generated by the symbols. Transformation (inference) rules consist of the following: If we have no sentences we may add (infer) an axiom. If the first sentence consists of five syllables, we may infer a new sentence of free words consisting of seven syllables. If the second sentence consists of seven syllables, we may infer a new sentence of free words consisting of five syllables. If the third sentence consists of five syllables, we may infer top. Otherwise if none of these rules are productive, we may infer bottom (we never infer bottom). Our axiom set consists of all five syllable sets of English words. That is the formal system of haikus. Now you can argue that this system doesn't have interesting or useful results, but it's a bit difficult to argue that purely syntactically. You probably need some notion of semantics, and it becomes quite difficult to explain semantics purely using symbols and rules. In particular it can get a bit thorny to describe what a "result" is purely syntactically, i.e. only as the consequence of symbols and manipulation rules.

lisper 5y ago
> haikus I must confess I had to think about this one for a while. Yes, haikus adhere to strict rules (as do sonnets). But here is something that adheres to the rules of haiku: foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo which I think you would agree is not a haiku, or at least not a very good one (unless you're a Dadaist). There is something essential to a haiku, and to a poem in general, that is not captured by the rules. But there are situations where the boundary between math and poetry can be very fuzzy indeed.
- bawolff 5y ago
  I think i would say the same about math. You can manipulate logical statements in an infinite number of ways, but only a subset are interesting. What makes an interesting/good poem is just as subjective as what makes an interesting/good theorem.
  - lisper 5y ago
    That's not quite true. Some math is objectively useful in ways that poems are not because the math corresponds to -- and hence allows you to accurately predict -- the behavior of physical systems.

lisper 5y ago

> haikus I must confess I had to think about this one for a while. Yes, haikus adhere to strict rules (as do sonnets). But here is something that adheres to the rules of haiku: foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo which I think you would agree is not a haiku, or at least not a very good one (unless you're a Dadaist). There is something essential to a haiku, and to a poem in general, that is not captured by the rules. But there are situations where the boundary between math and poetry can be very fuzzy indeed.

bawolff 5y ago
I think i would say the same about math. You can manipulate logical statements in an infinite number of ways, but only a subset are interesting. What makes an interesting/good poem is just as subjective as what makes an interesting/good theorem.
- lisper 5y ago
  That's not quite true. Some math is objectively useful in ways that poems are not because the math corresponds to -- and hence allows you to accurately predict -- the behavior of physical systems.