|
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?
|
|
18933
|
Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
|
|
Full Idea:
I. Nothing exists. a) Not-Being does not exist. b) Being does not exist as everlasting, as created, as both, as One, or as Many. II. If anything does exist, it is incomprehensible. III. If existence is comprehensible, it is incommunicable.
|
|
From:
report of Gorgias (fragments/reports [c.443 BCE], B03) by Diogenes Laertius - Lives of Eminent Philosophers 09
|
|
A reaction:
[Also Sextus Empiricus, Against Logicians I.65-] For Part I he works through all the possible modes of being he can think of, and explains why none of them are possible. It is worth remembering that Gorgias loved rhetoric, not philosophy!
|
|
9866
|
Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
|
|
Full Idea:
Gorgias insists that the art of persuasion is superior to all others because it enslaves all the rest, with their own consent, not by force, and is therefore by far the best of all the arts.
|
|
From:
report of Gorgias (fragments/reports [c.443 BCE]) by Plato - Philebus 58a
|
|
A reaction:
A nice point, and it is not unreasonable to rank the arts in order of their power. To enchant, without achieving agreement, and to speak truth without persuading, are both very fine, but there is something about success that cannot be gainsaid.
|