> be me> mathlet trying to understand language> read Chomsky, think I'm big brain> professor says "meaning is just a functor bro"> what> ok so you have a category of syntax> objects are types, morphisms are terms> "alice loves bob" is just a morphism n⊗(n^r⊗s⊗n^l)⊗n s> sure whatever> so where does MEANING come from> you map it to another category with a functor> words become vectors, sentences become linear maps> compositionality is just the functor law [[f∘g]] = [[f]]∘[[g]]> mfw the entire philosophy of language is a commutativity condition> ok but what if two interpretations disagree> those are just natural transformations between functors> mfw a debate between Frege and Wittgenstein is a 2-morphism> ask professor "but what's the CANONICAL interpretation?"> "it's the counit of the syntax-semantics adjunction"> stare blankly> syntax is the INITIAL ALGEBRA> there's a unique homomorphism from syntax to every model> every possible meaning assignment is just one specific arrow out of syntax> syntax is not one language among many> syntax IS the self-representing model> Yoneda lemma means it's fully determined by the identity morphism> mfw language is its own reflection in the mirror of category theory> mfw there was never any meaning, only structure-preserving maps> mfw I am also just a morphism> go outside> touch grass> grass is an object in the category of physical reality> touching is a morphism> I am not okay
Chomsky's been to the island bro
>>16953147Nobuo Yoneda is clean though
>>16953145What is love, anon?
>>16953145This is exactly why mathematical linguistics is the highest form of humanity.
>>16953145> "I am also just a morphism"correctyou are a badly-typed morphism in the category of sleep deprivationtouching grass won't help btwyou'll just model it as a morphismthere is no escape from functoriality
this is a philosophy of mind problem, not /sci/ related
>>16953147As did Hawking
>>16953148I never understood the Yoneda lemma but this yazuka looking guy invented it? Baded
>>16953145Incorrect. A structure requires basic elements which must exist outside of the structure. Consider a relation f(x) = A -> B, given the recursive motif, the relation reduces to some C->D, so f(x) = C->D(A->B) or perhaps A->B(A->B). There is two or four elements which your perspective rests on which are outside of relation, at minimum. The could be of a relational construction as well, but that would imply your system has no meaning without importing that entire relational construct and its underlying elements.
