Combining Texts

All the ideas for 'On Certainty', 'Letters to Russell' and 'What Numbers Are'

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8 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17813

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

18253

I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17812

Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

18166

The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

18269

Logical objects are extensions of concepts, or ranges of values of functions [Frege]

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism

3597	Foundations need not precede other beliefs [Wittgenstein]

13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique

3596	Total doubt can't even get started [Wittgenstein, by Williams,M]

19. Language / A. Nature of Meaning / 10. Denial of Meanings

4721	If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein]