8921
|
Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
|
|
Full Idea:
With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do.
|
|
From:
Geoffrey Hellman (Structuralism [2007], §1)
|
|
A reaction:
Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed.
|
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?
|
20752
|
For man, being is not what he is, but what he is going to be [Ortega y Gassett]
|
|
Full Idea:
Being consists not in what it is already, but in what it is not yet, a being that consists in not-yet-being. Everything else in the world is what it is….Man is the entity that makes himself….He has to determine what he is going to be.
|
|
From:
José Ortega y Gassett (Toward a Philosophy of History [1941], p.112,201-2), quoted by Kevin Aho - Existentialism: an introduction 4 'Problem'
|
|
A reaction:
[p.112 and 201-2] This seems to be Ortega y Gasset's spin on Heidegger's concept, by adding a temporal dimension to it.
|
20756
|
Instead of having a nature, man only has a history [Ortega y Gassett]
|
|
Full Idea:
Man lives in view of the past. Man, in a word, has no nature; what he has is history. Expressed differently: what nature is to things, history is to man.
|
|
From:
José Ortega y Gassett (Toward a Philosophy of History [1941], p.217), quoted by Kevin Aho - Existentialism: an introduction 5 'Situated'
|
|
A reaction:
Makes explicit the existentialist denial of human nature. The foundation of ethics can only be total freedom, to choose both yourself and your actions. What is inescapable is the social and culture contexts. What is the role of the 'history'?
|