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Thursday, January 24, 2019

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One woman's modus ponens etc. This is a good argument against ‘propositions’.

If your argument is sound, then necessarily something exists. But it is absurd and false that necessarily something exists. Therefore (modus tollens) your argument is not sound.

It seems to be valid. Therefore one or more of your premisses is false. The likely culprit is the major premiss (1). You defend this with a second argument. The likely culprit is (5) ‘If p, then the proposition expressed by 'p' is true’. This implies there is always something that ‘the proposition expressed by 'p'’ refers to. As you go on to say ‘The RHS has an ontological commitment that the LHS does not have: the RHS commits us to a proposition.’

I hold, with Aristotle, that a proposition is a special kind of sentence, one which (unlike a prayer or a command or a question) is capable of truth or falsity. Ergo, if nothing exists, nothing is a sentence, and if every a proposition is a sentence, nothing is a proposition. Ergo etc. It could be true that nothing exists, without there having to exist anything that has the ‘property’ of being true. Corollary: the account of truth must be deflationary.

You have proved many excellent things here, Bill.

>>But it is absurd and false that necessarily something exists.<<

'Absurd' in a logical context means self-contradictory. Or are you using 'absurd' in some emotive way?

So if you are not emoting, you are saying that the following is self-contradictory: Necessarily, something exists. You thereby must be affirming that the following is a logical truth: Possibly, nothing exists.

Do you really want to say that? At a minimum, you are begging the question against me. I gave a rigorous argument. The only way to block it is by denying (5), and rejecting Bivalence. But you accept that principle, although I think you confuse it with Excluded Middle.

So you ought to accept my argument and admit that necessarily, something exists.

It is worth noting that from 'Necessarily, something exists' it does not immediately follow that 'Something is such that it necessarily exists.' That would be a further step, one I haven't taken above.

>>The only way to block it is by denying (5), and rejecting Bivalence.

Not at all. I reject the ontological commitment of the RHS that you mention. I already gave the argument above. Shall I repeat it?

OK I will repeat it.

This implies there is always something that ‘the proposition expressed by 'p'’ refers to.

>> But you accept that principle, although I think you confuse it with Excluded Middle.

In no way do I ever confuse bivalence with EM.

Perhaps there is another confusion here. You write

5) If p, then the proposition expressed by 'p' is true.
Therefore

6) If nothing exists, then nothing exists is true.

7) The consequent of (6) commits us to the existence of at least one proposition.


Why does the consequent of (6)commit us to the existence of at least one proposition? If I read (6) as saying

(6*) If nothing exists, then it is true that nothing exists.

then there is no existential implication (on a deflationary interpretation). If on the other hand I read it as

(6**) If nothing exists, then there exists a true proposition *nothing exists*.

Your argument works on the second interpretation, but justify the second interpretation.

Do we read 6) as : If nothing exists, then 'nothing exists' is true?David

Dave,

(6) says that if nothing exists, then the proposition expressed by 'nothing exists' is true.

You can say the same thing in different languages. The same thing is the proposition.

By the way, your comment got sent to the dreaded spam corral for some reason.

BV, I was surprised to see you distinguishing between bivalence and the LEM. As far as I can tell, in the traditional and most common formulations, they are identical. My knowledge of the literature on logic is far from exhaustive, but as far as I can tell, the notion that the excluded middle involves the "not" connective is a modern innovation designed to make the LEM a dual to the Law of Contradiction. Symbolically:

LEM: p or ~p
LC: ~(p and ~p)

This is cute, but doesn't fit the tradition I was taught, where the LEM was stated as "every proposition is true or false" that is, bivalence.

I'm curious whether you have some more profound reason to prefer the modern retreading of the LEM other than this clever duality, especially given that the new formulation does not exclude a middle. That is,

p or ~p

only says that p is true or ~p is true, it does not say that neither p nor ~p can be something other than true or false.

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