Re: Red and blue (again)

At 19:28 +0100 28/7/05, David J. Pym wrote:
>>Am I missing anything? (It's a bit late but I still didn't drink my beer.)
>
>Oh, missing so many things! :-)   But mainly that 
>mathematical/conceptual/application naturality (and certainly not 
>order)  is what matters. (Though see my second message.) But let's 
>have a more relaxed discussion about all this once you've arrived 
>and settled in Bath next term. Should be fun.

Why waiting? Let's try to have some fun right now, I'm relaxed and I 
also just had my beer.

I certainly agree with you that mathematical/conceptual/application 
naturality is what matters, and I'm not missing anything here because 
I didn't even try to argue about that. However, order matters a lot.

You seem to want to confine the discussion within categorical 
semantics, which is fine with me even if I'm no expert. So, you argue 
that the kind of structures you like (and which I have no reason 
whatsoever to dislike) actually predates the sequent calculus of 
linear logic by 18 years.

I think (but I certainly might be wrong) that you are missing a major 
point here: categorical semantics is predated by the sequent calculus 
by 54 years!! Lambek's semantics has been *made* for the sequent 
calculus. So, again, I see no justification in saying that it's good 
that the sequent calculus behaves correctly for its own semantics! Of 
course!!

Give another deductive formalism to some good category theorist and 
I'm sure he'll be able to find different, beautiful structures in 
less than 54 years. Am I right Francois?

Anything else I'm missing?

-Alessio