[hist-analytic] The "Analytic A Posteriori"

Baynesr at comcast.net Baynesr at comcast.net
Thu Sep 3 08:47:07 EDT 2009



Bruce asks: 

  

"Are you supposing 'Nec(a = b)' is a logical truth?" 

and 

  

"When you say "'Nec(a = b)' follows from first order knowledge by 
substitution of predicates, what do you mean. What predicates are 
substituted?" 



I'm a little surprised. I'm sure you've heard of the proof etc. But here is the proof in one form. 

  

1. x=y --> (P)(Px iff Py)                         Substitutivity of identicals 



2 x=y --> (N(x=x) iff N(x=y))                   U.I. 1 



3. N(x=x)                                              Assumption 



4. x=y                                                  Assumption for C.P 



5. N(x=x) iff N(x=y)                               M.P. 4, 2 



6. N(x=x) --> N(x=y)                             5, df 'iff' 



7. N(x=y)                                             M.P. 3, 6 



8. x=y --> N(x=y)                                  C.P. 4-7 



Although I believe similar proofs had been suggested earlier, the proof procedure is found in "Modalities and Intentional Languages" by Ruth Barcan Marcus (then Ruth Marcus).Synthese xiii, 4, 1961. It is also to be found in her "A Functional Calculus of First Order Based on Strict Implication," theorem XIX. 



Bruce is curious about my "attitude" towards rigid designation. Well, in one form or another it (or something very much like it) has been suggest by Kaplan, Hintikka, Marcus (I am told) and in a weak form without worlds, Russell. When I see a common name, I know it; when I see a definite article I know it; but when I see a word that looks like a common name, and I am told that it is a rigid designator I ask "What is the basis for this." Also, this and the "necessary a posteriori" have become sacred cows. I've never been a believer is sacred cows. 



I would answer the other question Bruce raises, about the "theorem"; but the only theorem I was talking about was the one above, viz. x=y --> N(x=y), which doesn't make ANY assumptions about rigid designators. 



Regards 



Steve 
----- Original Message ----- 
From: "Bruce Aune" <aune at philos.umass.edu> 
To: Baynesr at comcast.net 
Cc: "hist-analytic" <hist-analytic at simplelists.co.uk> 
Sent: Thursday, September 3, 2009 8:05:42 AM GMT -05:00 US/Canada Eastern 
Subject: Re: The "Analytic A Posteriori" 

Steve, 

A posteriori knowledge is not just knowledge by experience in your   
sense; if it were, only observational knowledge and possibly memory   
knowledge would be a posteriori knowledge.  But many things we know   
about the world are known inferentially; and what is thus known has   
always been considered a posteriori knowledge. 

When you say "'Nec(a = b)' follows from first order knowledge by   
substitution of predicates, what do you mean.  What predicates are   
substituted?  Are you supposing 'Nec(a = b)' is a logical truth? 

I have neve understood your attitude towards rigid designators.  The   
whole idea of such designators was introduced to deflect objections   
that commit a fallacy of equivocation.  Some people objected to the   
theorem on the ground that if a = the F, it may yet be false that N(a   
= the F) because it is possible that (there are possible situations in   
which) someone other than a = the F.  But if "the F" is being used to   
single out a particular person, the fact that someone else might   
satisfy the description "the F" would not show that the person singled   
out might possibly be different from the person a.  Could there be a   
situation in which I am different from myself or anyone is different   
from him- or herself?  NO.  There is nothing problematic, I think,   
about using a definite description to refer to a particular thing as   
opposed to anything that might satisfy that description. 

Bruce 
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