Combining Texts

All the ideas for 'works', 'Is Mathematics purely Linguistic?' and 'Putnam's Paradox'

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7 ideas

5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction

10121	Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
	Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth.
	From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
	A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong.

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

14212	A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis]
	Full Idea: A consistent theory is, by definition, one satisfied by some model; an isomorphic image of a model satisfies the same theories as the original model; to provide the making of an isomorphic image of any given model, a domain need only be large enough.
	From: David Lewis (Putnam's Paradox [1984], 'Why Model')
	A reaction: This is laying out the ground for Putnam's model theory argument in favour of anti-realism. If you are chasing the one true model of reality, then formal model theory doesn't seem to offer much encouragement.

6. Mathematics / C. Sources of Mathematics / 7. Formalism

21570	Numbers are just verbal conveniences, which can be analysed away [Russell]
	Full Idea: Numbers are nothing but a verbal convenience, and disappear when the propositions that seem to contain them are fully written out.
	From: Bertrand Russell (Is Mathematics purely Linguistic? [1952], p.301)
	A reaction: This is the culmination of the process which began with his 1905 theory of definite descriptions. The intervening step was Wittgenstein's purely formal account of the logical connectives.

7. Existence / D. Theories of Reality / 4. Anti-realism

14213	Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis]
	Full Idea: Anti-realists say the only world is imaginary, or only has the parts or classes or relations we divide it into, or doubt that reference to the world is possible, or doubt that our interpretations can achieve truth.
	From: David Lewis (Putnam's Paradox [1984], 'Why Anti-R')
	A reaction: [compression of a paragraph on anti-realism] Lewis is a thoroughgoing realist. A nice example of the rhetorical device of ridiculing an opponent by suggesting that they don't even know what they themselves believe.

9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts

14210	A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis]
	Full Idea: The mereological sum of the coffee in my cup, the ink in this sentence, a nearby sparrow, and my left shoe is a miscellaneous mess of an object, yet its boundaries are by no means unrelated to the joints of nature.
	From: David Lewis (Putnam's Paradox [1984], 'What Might')
	A reaction: In that case they do, but if there are no atoms at the root of physics then presumably their could also be thoroughly jointless assemblages, involving probability distributions etc. Even random scattered atoms seem rather short of joints.

19. Language / B. Reference / 3. Direct Reference / b. Causal reference

14215	Causal theories of reference make errors in reference easy [Lewis]
	Full Idea: Whatever happens in special cases, causal theories usually make it easy to be wrong about the thing we refer to.
	From: David Lewis (Putnam's Paradox [1984], 'What Is')
	A reaction: I suppose the point of this is that there are no checks and balances to keep reference in focus, but just a requirement to keep connected to an increasingly attenuated causal chain.

19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description

14209	Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis]
	Full Idea: Description theories of reference are supposed to have been well and truly refuted. I think not: ..it is still tenable with my seven points, and part of the truth of reference [7: rigidity, egocentric, tokens, causal, imperfect, indeterminate, families].
	From: David Lewis (Putnam's Paradox [1984], 'Glob Desc')
	A reaction: (The bit at the end refers to his seven points, on p.59). He calls his basic proposal 'causal descriptivism', incorporating his seven slight modifications of traditional descriptivism about reference.