|
8698
|
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
|
|
Full Idea:
The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
|
|
From:
report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
|
|
A reaction:
Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?
|
|
10263
|
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
|
|
Full Idea:
The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
|
|
From:
comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
|
|
A reaction:
I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?
|
|
15956
|
The peripatetics treated forms and real qualities as independent of matter, and non-material [Alexander,P]
|
|
Full Idea:
The peripatetic philosophers, in spite of their disagreements, all treated forms and real qualities as independent of matter and not to be understood in material terms.
|
|
From:
Peter Alexander (Ideas, Qualities and Corpuscles [1985], 54)
|
|
A reaction:
This is the simple reason why hylomorphism became totally discredited, in the face of the 'mechanical philosophy'. But there must be a physical version of hylomorphism, and I don't think Aristotle himself would reject it.
|
|
15975
|
Can the qualities of a body be split into two groups, where the smaller explains the larger? [Alexander,P]
|
|
Full Idea:
Is there any way of separating the qualities that bodies appear to have into two groups, one as small as possible and the other as large as possible, such that the smaller group can plausibly be used to explain the larger?
|
|
From:
Peter Alexander (Ideas, Qualities and Corpuscles [1985], 5.02)
|
|
A reaction:
Alexander implies that this is a question Locke asked himself. This is pretty close to what I take to be the main question for essentialism, though I am cautious about couching it in terms of groups of qualities. I think this was Aristotle's question.
|
|
15963
|
Science has been partly motivated by the belief that the universe is run by God's laws [Alexander,P]
|
|
Full Idea:
The idea of a designed universe has not been utterly irrelevant to the scientific project; it is one of the beliefs that can give a scientist the faith that there are laws, waiting to be discovered, that govern all phenomena.
|
|
From:
Peter Alexander (Ideas, Qualities and Corpuscles [1985], 03.3)
|
|
A reaction:
Of course if you start out looking for the 'laws of God' that is probably what you will discover. Natural selection strikes me as significant, because it shows no sign of being a procedure appropriate to a benevolent god.
|