Combining Texts

All the ideas for 'Mathematics without Numbers', 'Meaning and Reference' and 'Aristotle on Substance'

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13 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
9. Objects / C. Structure of Objects / 3. Matter of an Object
Aristotelian matter seriously threatens the intrinsic unity and substantiality of its object [Gill,ML]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
A statement can be metaphysically necessary and epistemologically contingent [Putnam]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Conceivability is no proof of possibility [Putnam]
18. Thought / C. Content / 6. Broad Content
I can't distinguish elm trees, but I mean by 'elm' the same set of trees as everybody else [Putnam]
'Water' has an unnoticed indexical component, referring to stuff around here [Putnam]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
We need to recognise the contribution of society and of the world in determining reference [Putnam]
19. Language / F. Communication / 4. Private Language
Language is more like a cooperative steamship than an individual hammer [Putnam]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
Prime matter has no place in Aristotle's theories, and passages claiming it are misread [Gill,ML]
Prime matter is actually nothing and potentially everything (or potentially an element) [Gill,ML]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
If water is H2O in the actual world, there is no possible world where it isn't H2O [Putnam]