8 ideas
| 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'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 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? |
| 21925 | For Schelling the Absolute spirit manifests as nature in which self-consciousness evolves [Schelling, by Lewis,PB] |
| Full Idea: (Like Schopenhauer) Schelling understood the Absolute - spirit rather than will - to manifest itself as nature in which man evolves with self-consciousness. | |
| From: report of Friedrich Schelling (Outline of a System of the Philosophy of Nature [1799]) by Peter B. Lewis - Schopenhauer 4 | |
| A reaction: The influence of Spinoza seems strong here. Is his Absolute just Spinoza's 'God'? |
| 22045 | Metaphysics aims at the Absolute, which goes beyond subjective and objective viewpoints [Schelling, by Pinkard] |
| Full Idea: Schelling never lost his youthful conviction that any metaphysics had to be an explication of the 'absolute' as something that went beyond both subjective and objective points of view. | |
| From: report of Friedrich Schelling (Outline of a System of the Philosophy of Nature [1799]) by Terry Pinkard - German Philosophy 1760-1860 12 | |
| A reaction: Even for a scientific and analytic modern philosopher there must be a target of an ideal account that includes human subjectivity within an objective view of the world. Even Mysterians like McGinn would like that. |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red. | |
| From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5 | |
| A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts. |
| 22057 | Schelling sought a union between the productivities of nature and of the mind [Schelling, by Bowie] |
| Full Idea: Schelling's philosophy of nature aims to connect nature's 'unconscious productivity' with the mind's 'conscious productivity'. | |
| From: report of Friedrich Schelling (Outline of a System of the Philosophy of Nature [1799]) by Andrew Bowie - German Philosophy: a very short introduction 3 | |
| A reaction: If you have a fairly active view of nature (as Leibniz did), then this is a promising line. I like the unpopular view that the modern idea of spontaneous 'powers' in nature is applicable to explanations of mind. |
| 22031 | Schelling made organisms central to nature, because mere mechanism could never produce them [Schelling, by Pinkard] |
| Full Idea: Schelling made the image of the 'organism' central to his conception of nature, arguing that merely mechanical processes could never produce 'life' (as a self-producing, self-sustaining, self-directing process). | |
| From: report of Friedrich Schelling (Outline of a System of the Philosophy of Nature [1799]) by Terry Pinkard - German Philosophy 1760-1860 08 | |
| A reaction: At that date this seems a reasonable claim, but subsequent biochemistry has undermined it. |