[hist-analytic] The "Analytic A Posteriori"

Baynesr at comcast.net Baynesr at comcast.net
Thu Sep 3 09:15:13 EDT 2009



I think the proof sketch I sent from Marcus should suffice to answer most of your questions. 



As for the rest, my point is, simply, this: knowing the truth of 'Nec(x=y)' may entail empirical knowledge of 'x=y'; but empirical knowledge that x=y is not sufficient for knowing 'Nec(x=y). The difference is made up by drawing the inference, logically from one to the other. Keep in mind we are speaking of knowledge not truth. 



Regards 



Steve 




----- Original Message ----- 
From: "Danny Frederick" <danny.frederick at tiscali.co.uk> 
To: "hist-analytic" <hist-analytic at simplelists.co.uk> 
Sent: Wednesday, September 2, 2009 5:03:19 PM GMT -05:00 US/Canada Eastern 
Subject: RE: The "Analytic A Posteriori" 





Hi Steve, 



Excuse me if I have got it wrong, but it seems to me that what you want to say is that ‘a=b’ is empirical and ‘if a=b, then Nec a=b’ is a priori. When you combine the two you get the conclusion ‘Nec a=b,’ which therefore combines empirical and a priori. 



A view of this kind is espoused by Peacocke here: 



http://www.columbia.edu/~cp2161/Online_Papers/TheAPriori.pdf 



If my memory is correct (it might not be), Gareth Evans put forward a similar view (‘Varieties of Reference’ I would guess – but I’ve not read it for more than 20 years). I don’t accept the view myself, of course. 



I also do not accept the principle ‘if a=b, then Nec a=b,’ UNLESS a and b are necessary existents. My assumption here is that ‘a=b’ is false (or, at least, not true) if a or b does not exist. So if a or b is a contingent existent, a=b must be contingent. 



I think Bruce made a valid point. ‘The cat is fat v ~the cat is fat’ is necessarily true, quite independently of the truth or falsity of ‘the cat is fat.’ But ‘Nec a=b’ has no chance of being true if a=b is false (even ignoring the issue about contingent existence). 



I think you are mistaken in affirming that even if the designators are not rigid 'Nec(a=b)' follows from a=b by first order logic by substitution of predicates. Consider a specific example. The inventor of bifocals = the first postmaster general. This says (according to Russell) that there is just one person who both invented bifocals and was the first postmaster general. Even supposing it is true, it does not follow that it is necessarily true that just one person did these two things; in fact it seems plainly possible that two different people might have invented bifocals and been the first postmaster general, even if ion fact one person did both. 



Cheers. 



Danny 
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