Combining Philosophers

All the ideas for Theodosius, Geoffrey Hellman and George Dickie

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9 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

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.

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?

8922	Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
	Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'.
	From: Geoffrey Hellman (Structuralism [2007], §1)
	A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics.

15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds

1799	If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius]
	Full Idea: We can't say the school of Pyrrho is sceptical, because the motion of the mind in each individual is incomprehensible to others, so we don't know Pyrrho's disposition.
	From: report of Theodosius (Chapters on Scepticism [c.100 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.8

21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude

20443	The aesthetic attitude is nothing more than paying close attention [Dickie, by Giovannelli]
	Full Idea: Once analysed, Dickie claimed, the so-called aesthetic attitude is not special at all, but is rather just a matter of close attention and focus on the subject.
	From: report of George Dickie (The Myth of the Aesthetic Attitude [1964]) by Alessandro Giovannelli - Some contemporary developments (aesthetics) 1
	A reaction: Sounds wrong. If a paint specialist gives close attention to a painting, they do not necessarily have an aesthetic view of it. You need to know the aim of the activity, just as when you watch a game.

21. Aesthetics / B. Nature of Art / 6. Art as Institution

20329	A work of art is an artifact created for the artworld [Dickie]
	Full Idea: A work of art is an artifact of a kind created to be presented to an artworld public.
	From: George Dickie (The New Institutional Theory of Art [1983], p.53)
	A reaction: This is the culminating definition in his paper, deriving originally from Danto, and an improvement of his earlier more complex definition. Since this definition amounts to 'this is art if I say it is art', it doesn't seem to reveal much.

8114	The institutional theory says only a competent expert can decree something to be an art work [Dickie, by Gardner]
	Full Idea: Dickie's institutional theory of art says that something is a work of art if and only if it has had that status conferred on it by a competent member of the artworld.
	From: report of George Dickie (Introduction to Aesthetics [1997], Ch.8) by Sebastian Gardner - Aesthetics 3.1
	A reaction: The idea that a single 'competent' person can do this sounds daft, and probably circular. A consensus in the artworld sounds more plausible, but this still leaves the revolutionary genius, who - in retrospect - produced unrecognised 'art'.