Combining Texts

All the ideas for 'works', 'Continuity and Irrational Numbers' and 'Meaning and Reference'

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13 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
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 / 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]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]