[FOM] Re Second-Order Logic and Logicism.

[Panu Raatikainen]

Alan Weir <Alan.Weir at glasgow.ac.uk>:

> but I do find Panu's  remarks ... [about British philosophers] ...
> and the contrast with 'competent people' like Burgess, Heck and  
> Linnebo, puzzling.


I am very sorry if my message suggested such a contrast. I certainly  
intended no such thing. These were two separate thoughts.

I was simply recording my subjective experience; that there exist such  
philosophers: with somewhat one-sided strong enthusiastic opinions  
about SOL and perhaps neo-logicism, but not aware about many the  
issues I discuss in my paper (which is hardly surprising; I guess some  
of them are not taught even in the advanced mathematical logic  
courses, but you'll have to learn them from various sources). As I  
haven't really spent much time elsewhere than in UK, that happens to  
be my sample. But certainly there are lots of "competent people" (in  
whatever sense) in UK.

Then again, there are some people such as Burgess, Heck and Linnebo  
(and few others) who have worked with these issues intensively for a  
long time; they hardly represent the average philosopher, and what may  
well be clear to them is hardly clear for everyone, and perhaps still  
worth spelling out explicitly.

BTW, I am inclined to agree that whether or not SOL is a "logic" is  
not the key issue (largely verbal). But whether or not SOL (even if  
given only in the form of the Gentzen-style introduction and  
elimination rules; cf. Wright 2007) brings with it, over HP or Q (or  
such), some additional set-theoretical power, is a different and  
substantial question. In my paper, I am trying to argue, and make the  
case as clear as I can, that it really does.


All the Best

Panu


-- 
Panu Raatikainen

Ph.D., Adjunct Professor in Theoretical Philosophy

Theoretical Philosophy
Department of Philosophy, History, Culture and Art Studies
P.O. Box 24  (Unioninkatu 38 A)
FIN-00014 University of Helsinki
Finland

E-mail: panu.raatikainen at helsinki.fi

http://www.mv.helsinki.fi/home/praatika/