Combining Texts

All the ideas for 'Abstract Objects', 'Meaning and Reference' and 'works'

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17 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
All of mathematics is properties of the whole numbers [Kronecker]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
God made the integers, all the rest is the work of man [Kronecker]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
How we refer to abstractions is much less clear than how we refer to other things [Rosen]
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]
18. Thought / E. Abstraction / 2. Abstracta by Selection
The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen]
18. Thought / E. Abstraction / 5. Abstracta by Negation
Nowadays abstractions are defined as non-spatial, causally inert things [Rosen]
Chess may be abstract, but it has existed in specific space and time [Rosen]
Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen]
18. Thought / E. Abstraction / 6. Abstracta by Conflation
Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Functional terms can pick out abstractions by asserting an equivalence relation [Rosen]
Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen]
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 / 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]