On Sep 16, 2008, at 1:37 PM, Pat Hayes wrote:
We have argued about that point before, and logicians and philosophers have taken many different positions on it. Although I do not believe that the real world *is* a model, it is at least conceivable that some people might make that claim.
It might be conceivable, but I don't know how anyone could *plausibly* make that claim. By definition a model is a mathematical entity of a certain sort, usually an ordered n-tuple of some ilk. The real world, whatever it is, isn't an n-tuple.
Well now, lets engage on this question. Because it seems to me that both of you are falling into a trap here, one that treats mathematical language as making a kind of restricted ontological commitment because it speaks about 'mathematical stuff'
No, I'm certainly not falling into that trap, as I think formal models can be full of ordinary (and not to ordinary) objects, properties, and relations.
If someone objects: but such a description will always be incomplete, always omit some aspect of reality; then the reply is: yes, of course: so what? An incomplete description of something can still be of that complete thing. Semantics is not about being exhaustive, it is an analysis of what descriptions are, or can be, about.
Of course, but that's just the point, isn't it, Pat? If the model is incomplete, then it can't be identical to the world.
Now, I am pretty sure that Chris agrees with all the above. But let me ask: why, then, is it implausible to claim that the real world is an n-tuple? After all, what does this mean? It means only that the real world exhibits a structure which can be mathematically described in terms of n-tuples.
Seems to me pretty clear that it does not mean that! Indeed, your last sentence is exactly what I'd say about the relation between a model -- the mathematical "description" -- and the world. But really now. Let's define a model (for a given first-order language L, say) to be a triple <D,R,V>, where D is a set of objects, R a set of extensional relations over D, and V is a mapping from L to appropriate semantic values in D and R. Surely neither *the world*, nor any physical part of it, is literally such a triple.