well, we've come head-to-head with the enemy. an upper-level philosophy course purportedly all about language that has, so far, been all about truth, and i'd like to share and ridicule a "logical" "proof."
this is a real answer from our first problem set. the comments in brackets were not on our homework.
6) Given the definition of truth: For any proposition x, x is true iff [if and only if] (for some p)(x = the proposition that p and p). Does this definition entail the proposition "The proposition that John is bald is true iff John is bald."? Yes!
1. By the definition of truth provided, the proposition that John is bald is true iff (for some p)(the proposition that John is bald = the proposition that p and p).
[The proposition that p is a concept, keep in mind, and 'p' is a statement about the real world. a fact, if you will. from outside language. but i shouldn't have written it in quotes just there, because that makes it a sentence, which is different from either a fact or a proposition.]
2. By Assumption, the proposition that John is bald = the proposition that q and q.
[we all konw what they say about assumption...]
3. By Assumption, the proposition that John is bald is a true proposition of language L.
[oh ho! yeah, this seems like a good place to start.]
4. It follows from the given Equivalence Principle that if the proposition that John is bald = the proposition that q, then John is bald iff q.
[if the propositions are the same, then the facts in the world are the same. ?]
5. By 2, 4, and logic, John is bald iff q.
[don't ask me what logic is.]
6. By 2, 5, and logic, John is bald.
[don't ask me what logic is.[did i just state the same proposition twice?]]
7. By 1 and 6, and the Rule of Existential Instantiation, John is bald.
[honestly, i've forgotten what the REI is already, but it was very handy for situations like this, where we needed to be able to get from the proposition that John is bald to the fact that John is bald via our previous assumptions both implicit and explicit... clearly, if 'john is bald' is true, then john is bald. don't quote that.]
8. By 2 and 7, if the proposition that John is bald is a true sentence of L, then John is bald. (conditional proof).
there's a second argument to this proof, but we don't know if it's necessary or not... just to give you some idea, though, it begins with "1. By assumption, John is bald."
i'm so glad language is actually illogical. all this common sense makes my head hurt.