[FOM] axioms and implicit definitions

[rgheck]

praatika at mappi.helsinki.fi wrote:
> There is a traditional conventionalist idea, sometimes ascribed to  
> Hilbert, and apparently held e.g. by Schlick, that axioms *implicitly  
> define* the meanings of the primitive expressions of the system, or  
> something like that.
>
> (The notion of "implicit definiability" intended here should not be  
> conflated with the different idea with the same name in model theory;  
> e.g. in Beth's theorem)
>
> Surely many things could be said about this view, but it is not clear  
> to me whether there is some widely accepted, standard criticism of  
> this idea? Some standard references?
>
> I have some patchy ideas about this, but I would be grateful for any  
> informed advice.
>
>   
My sense is that Quine's various writings on conventionalism are often 
taken to be the locus classicus for that sort of criticism. For a more 
recent defense, there's a paper by Crispin Wright and Bob Hale, 
"Implicit Definition and the Apriori", that strives to resuscitate some 
such view. A draft seems still to be online here:
http://www.st-andrews.ac.uk/~arche/old/pages/papers/Implicit%20Definition%20and%20the%20A%20Priori.pdf.

rh

-- 
-----------------------
Richard G Heck Jr
Professor of Philosophy
Brown University