Combining Texts

All the ideas for 'Ethical Studies', 'On Platonism in Mathematics' and 'Letters to Queen Charlotte'

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9 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304

Very few things in set theory remain valid in intuitionist mathematics [Bernays]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers

23026

We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10303

Restricted Platonism is just an ideal projection of a domain of thought [Bernays]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

10306

Mathematical abstraction just goes in a different direction from logic [Bernays]

9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities

13189

A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz]

10. Modality / D. Knowledge of Modality / 1. A Priori Necessary

19432

Intelligible truth is independent of any external things or experiences [Leibniz]

12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities

19430

We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz]

12. Knowledge Sources / D. Empiricism / 1. Empiricism

19431

There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz]

22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness

5655	Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton]