Combining Texts

All the ideas for 'Defending the Axioms', 'Logic (Port-Royal Art of Thinking)' and 'Essays on Active Powers 3: Princs of action'

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17 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
10502 We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
12. Knowledge Sources / B. Perception / 3. Representation
18258 We can only know the exterior world via our ideas [Arnauld,A/Nicole,P]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
16784 Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
10499 We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
10501 A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
10500 No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
23674 If an attempted poisoning results in benefits, we still judge the agent a poisoner [Reid]
23. Ethics / B. Contract Ethics / 2. Golden Rule
23675 We shouldn't do to others what would be a wrong to us in similar circumstances [Reid]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
23672 To be virtuous, we must care about duty [Reid]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
23673 Every worthy man has a principle of honour, and knows what is honourable [Reid]