Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'Mathematics without Numbers' and 'Philosophical Remarks'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

7 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

21757	Philosophy is the conceptual essence of the shape of history [Hegel]
	Full Idea: Philosophy is the supreme blossom - the concept - of the entire shape of history, the consciousness and the spiritual essence of the whole situation, the spirit of the age as the spirit present and aware of itself in thought.
	From: Georg W.F.Hegel (Lectures on the History of Philosophy [1830], p.25), quoted by Stephen Houlgate - An Introduction to Hegel 01
	A reaction: This sees philosophy as intrinsically historical, which is a founding idea for 'continental' philosophy. Analysis is tied to science, in which the history of the subject is seen as irrelevant to its truth. Does this mean we can't go back to Aristotle?

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

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?

9. Objects / A. Existence of Objects / 3. Objects in Thought

22320	An 'object' is just what can be referred to without possible non-existence [Wittgenstein]
	Full Idea: What I once called 'objects', simples, were simply what I could refer to without running the risk of their possible non-existence.
	From: Ludwig Wittgenstein (Philosophical Remarks [1930], p.72), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 52 'Simp'
	A reaction: For most of us, you can refer to something because you take it to be an object. For these Fregean influenced guys (e.g. Hale) something is an object because you can refer to it. Why don't they use 'object*' for their things?

19. Language / A. Nature of Meaning / 2. Meaning as Mental

18283	Language pictures the essence of the world [Wittgenstein]
	Full Idea: The essence of language is a picture of the essence of the world.
	From: Ludwig Wittgenstein (Philosophical Remarks [1930], p.85), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 17
	A reaction: Hence for a long time the study of language seemed to be the way to do metaphysics. Now they study mathematical logic, with the same hope.

19. Language / A. Nature of Meaning / 5. Meaning as Verification

18282	You can't believe it if you can't imagine a verification for it [Wittgenstein]
	Full Idea: It isn't possible to believe something for which you cannot imagine some kind of verification.
	From: Ludwig Wittgenstein (Philosophical Remarks [1930], p.200), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 13 'Constr'
	A reaction: In 1930 LW was calling this his 'old principle'. As it stands here it is too vague to assert very much.