Re: Is 1+1=2 analytic or synthetic?
From: Andrew (andrzej-tomaszewski_at_wp.pl)
Date: 12/31/04
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Date: 31 Dec 2004 04:35:40 -0800
Dear Eray,
> The analytic/synthetic distinction is a somewhat artificial
distinction
> which was drawn by logical positivists, a fortunately extinct species
> of positivists who seemed to worship strange things at times.
>
> 1 + 1 = 2 is quite synthetic because it represents physical and
mental
> events in the real world, e.g. I have a pen, if I buy another I have
> two pens, or I have a plan, and if I make another plan I have two
> plans. This isn't merely folk mathematics, a physicist will tell you
> that if an electron enters a region in which there is only a single
> electron, there will be two electrons.
>
> On the other hand, it has an analytic component, too, e.g. as belongs
> to a larger formal system of arithmetic, for instance. In this vein,
> the theorem follows from a collection of basic truths which have
little
> to do with past observations.
>
> There may of course be concepts that are more analytic than
synthetic,
> but I don't know how seriously one should take a concept like god.
>
> I think it's worth considering that the distinction is a matter of
> degree.
I agree with you, of course. But you see, it was Frege who first
suggested the a priori analyticity of the proposition 1+1=2 in his
seminal work Grundlanden der Arithmetic (I found out about it just
yesterday). Still, there may be synthetic instantiations of this
concept, which is perfectly understandable.
I am sorry, you surely are familiar with the assertions I made, and I
may be missing something.
Thank you very much for posting to this thread.
Kindest regards,
Andrew
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