On Feb 12, 2009, at 3:48 PM, Chris Partridge wrote:
>> CP> I think John was espousing in an earlier set of emails (in
>>> relation to Aristotelian syllogisms), which is that logic is
>>> a formalism for describing the way the world is - or more
>>> grandly, what exists. And that in some way the form of the
>>> logic reflects the structure/nature of the world.
>>
>> I didn't claim that logic reflects the structure of the world,
>> but that logic in combination with an ontology can be used to
>> describe someone's conception of the structure of the world.
>
> Apologies. I may have been a little unclear. My point was intended
> to be the
> well-known one that it is extremely difficult to eradicate ontological
> commitment from a form of representation - and that the form of a
> logic
> being used for description is likely to imply some ontological
> commitment to
> the form of what is being described. And you are right, you did not
> explicitly make this point, though hopefully you do not disagree
> with it.
>
> So, for example, in the case of the syllogism, the form of the
> syllogism
> reflects the transitive nature of the subsumption/subtype relation
> between
> types in the world. (01)
There are 256 syllogistic forms; what do you mean by the form of THE
syllogism? It is, in fact, the case that universal affirmative
statements "All As are Bs" expresses, in effect, that {x | x is an A}
is a subclass of {x | x is a B}, so what you *might* mean is that the
form of a universal affirmative statement represents the subclass
relation. And it is indeed in virtue of the transitivity of subclass
that, e.g., a Barbara syllogism is valid. Is that what you have in
mind? (02)
Be that as it may, I think your general point is well taken. Every
logic worth the name comes with a semantics that will involve some
very high level of ontological commitment. FOL, in particular, is
committed to, at least, "things" (the range of the quantifiers) and
"predicables" (the values of predicates). That's pretty thin,
ontological gruel, however, since things and predicables are the basic
ingredients of *any possible* ontology, and hence don't distinguish
one ontology from another. So logic certainly reflects a little
something about the structure/nature of the world; just not that much. (03)
-chris (04)
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