Combining Texts

All the ideas for 'Events and Their Names', 'On the Concept of Number' and 'Structuralism'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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
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.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
     Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence.
     From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist'
     A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!).
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Events are made of other things, and are not fundamental to ontology [Bennett]
     Full Idea: Events are not basic items in the universe; they should not be included in any fundamental ontology...all the truths about them are entailed by and explained and made true by truths that do not involve the event concept.
     From: Jonathan Bennett (Events and Their Names [1988], p.12), quoted by Peter Simons - Events 3.1
     A reaction: Given the variable time spans of events, their ability to coincide, their ability to contain no motion, their blatantly conventional component, and their recalcitrance to individuation, I say Bennett is right.
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Facts are about the world, not in it, so they can't cause anything [Bennett]
     Full Idea: Facts are not the sort of item that can cause anything. A fact is a true proposition (they say); it is not something in the world but is rather something about the world.
     From: Jonathan Bennett (Events and Their Names [1988], p.22), quoted by Jonathan Schaffer - The Metaphysics of Causation 1.1
     A reaction: Compare 10361. Good argument, but maybe 'fact' is ambiguous. See Idea 10365. Events are said to be more concrete, and so can do the job, but their individuation also seems to depend on a description (as Davidson has pointed out).