#307673* (?/79) ⚐Flag
<cky> "Nothing is better than sex. Masturbation is better than nothing. Therefore, masturbation is better than sex."
<jmkeyes> ohhh logical fallacies
<cky> jmkeyes: Indeed!!
<cky> The fallacy here being that "nothing" is not a single point, but is a massive space.
<cky> And that the two "nothings" above refer to different points in that space.
<KirarinSnow> cky: the fallacy is that 'nothing' is not of the same semantic type as any particular thing
<KirarinSnow> though it appears to be syntactically the same
<KirarinSnow> a particular thing is of type e
<KirarinSnow> 'nothing' is of type <<e, t>, t>
<KirarinSnow> in other words, to evaluate a sentence "the cake is a lie", where "the cake" is an expression of type e denoting an object
<KirarinSnow> and "is a lie" is an expression of type <e, t> (that is, a predicate mapping objects of type e to truth values)
<KirarinSnow> we apply the function denoted by "is a lie", which is λx.[x is a lie]
<KirarinSnow> to the individual denoted by "the cake"
<KirarinSnow> and we get a truth value
<KirarinSnow> with 'nothing', on the other hand, you have the sentence "nothing is a lie"
<KirarinSnow> you can't apply the same function because 'nothing' is not an expression of type e
<KirarinSnow> instead, you apply the function denoted by 'nothing' to the predicate instead
<KirarinSnow> 'nothing' denotes \lambda P. \lambda x.~P(x)
<KirarinSnow> when you apply this lambda to the function denoted by "is a lie"
<KirarinSnow> you get by beta reduction
<KirarinSnow> \forall x.~[(\lambda y.[y is a lie])(x)]
<KirarinSnow> another round of beta reduction gives you
<KirarinSnow> \forall x.~[x is a lie]
<KirarinSnow> this is how quantifiers work in semantics (on the basic level)
<KirarinSnow> linguists love lambdas
<Daeken> wow
<Daeken> it's rare that 30 lines here will go completely over my head. you pulled it off. |