Re: Is 1+1=2 analytic or synthetic?

exanews_at_gmail.com
Date: 12/31/04 

Date: 31 Dec 2004 05:40:27 -0800

The vindication of the analytic/synthetic distinction, one of the
central dogmas of logical positivism is due to Quine.

The modern view would try to take a fair amount of non-reductionism
into account. From where do the truth and use of "1+1=2" follow? Would
there be any arithmetic statement if they had no use? My opinion is
that there would not, the meaning of this statement is derived from
world experience. This Platonist concept of something being purely
apriori may be slightly out of date. Frege's idealist leanings should
not confuse us.

The question is not whether there are synthetic instantiations. The
question is what are the material causes of such a statement? My answer
is that they are a product of common sense, e.g. mathematics is
continuous with common sense. In that part, I agree with Quine.

>>From a computationalist POV, we would say that the said arithmetic
statement models a common computational phenomenon. (See Aaron Sloman's
article in Matthias Scheutz's collection "Computationalism: The Next
Generation" for that. )It's everywhere, and in one's mind, too, that's
why one could arrive at it "a priori", but I do not think necessarily.
Even if it is in your mind, for it to attain any meaning at all, one
must indulge in computational observations and modelling which is
subjectively synthetic.

All of these easy observations show that the analytic/synthetic
distinction is not a definite border, it's one of those fuzzy
subjective categories with little use or meaning.

This is of course not something the naive idealists/pythagoreans could
accept. Some people want to reserve a special place for these
supposedly analytic propositions. I disagree, computation comes first.

Although I dislike terminological discussions, note also the Platonist
force of the word "instantiation".

Regards, 

--
Eray Ozkural
Quantcast