In the course of Bill's recent discussion on the Univocity of 'Exist(s)', I recalled a much earlier posting where a lack of what we might call 'logical hygiene' leads to much confusion. This is especially evident in the comments. Bill offers the following conundrum:
1. (x)(x = x) (Principle of Identity)Correctly, in my view, Bill identifies the trouble in the move from (1) to (2), though he tables a couple of other panaceas that he says are 'essentially equivalent'. He says that we need a supplementary premise, namely,
2. John McCain = John McCain (From 1 by Universal Instantiation)
3. (Ex)(x = John McCain) (From 2 by Existential Generalization)
4. John McCain exists. (From 3 by translation into ordinary idiom)
1.5 'John McCain' refers to something that exists.I would not put it quite that way myself. The notion of 'reference' is a big topic that we have discussed endlessly at Maverick Philosopher, and the 'something that exists' seems to leave open the possibility that there might be something that doesn't exist, and we will be on the road to Meinongia. So for simplicity I prefer to replace Bill's (1.5) with my own variant,
DB. There is something named 'John McCain'.I call this the mention before use rule for proper names. This is just as effective as Bill's proposal for removing the rabbit out of a hat result that the existence of the contingent John McCain 'is validly deducible from an a priori knowable necessary truth of logic', as Bill puts it. But in this response to my suggestion, Bill seems to reject the idea, saying that I 'seem to be denying the very possibility of coherent fictional discourse' and that he doesn't see the need for my brand of logical hygiene. We await with interest.