begbert2, i didn’t think formality was so necessary. i figured you would have no trouble figuring out it was modus ponens, and figuring out which lines were used (which you did have no trouble doing).
i also didn’t realize you would try to make such a distinction between:
E(x) s.t. P(x)
and:
Ex(P(x))
even after i said i was using “there exists an x” as a second-order property. is there anything wrong with the following formulation, short of its lack of formality:
Ex,y (T(x) -> H(y)).
Et(T(t))
:. Ei(H(i))
other than its demonstration isn’t as powerful as you’d like it to be? E(x) is not intended as a predicate. my fault for symbolizing it like one.
you do a great job explaining why my existence should be taken as an axiom. i would be at a loss to explain anything if i didn’t.
i’ve already explained that my criticism is that “i think therefore i am” does not demonstrate anything, as a logical argument. if you do not wish to disagree with me on that any more, i have nothing more to add. that “i exist”, i have no qualms with. saying that it can be demonstrated through proof does indeed take the argument into a logical forum, and is a statement i disagree with.
again, i erred originally in phrasing the proposition that way. as i said, it didn’t occur to me that using “exists” as a predicate was a bad idea. so i’ll try to stay away from it from now on. i meant to in my “proof”. instead of saying “~E(x) -> ~H(x)”, i would now say you can’t say H(x) without saying Ex(H(x)).
i think this is more a comment on the way we give properties to things, and the meaning of existence. H(x) -> E(x) seems to make sense, but it doesn’t have a whole lot of place here, as i said i will try to no longer use existence as a predicate. instead of saying “x exists” explicitly in the proof, this restricts how we can say “x thinks”.
not using “exists” as a predicate severely limits the ability to prove that something exists. basically, it requires us to give that existant thing a property. i called it a “thinker”. so instead of saying “x exists”, you would say “for some x, x is a thinker”. i suppose that implies its existence, and doesn’t fall into the holes we wish to avoid by not using “exists” as a predicate.
so then, saying “there is a thought, so there is a thinker” is a sound argument. do you agree?