Combining Texts

All the ideas for 'Defending the Axioms', 'Survival and Identity, with postscript' and 'reports'

expand these ideas     |    start again     |     specify just one area for these texts

25 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
1798 He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1800 Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius]
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]
10. Modality / A. Necessity / 4. De re / De dicto modality
16079 De re modal predicates are ambiguous [Lewis, by Rudder Baker]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
6595 If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
6593 The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
6592 Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin]
13. Knowledge Criteria / E. Relativism / 1. Relativism
1805 Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius]
1807 Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius]
1810 Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius]
1802 Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius]
1801 Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius]
1804 Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius]
1808 Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius]
1806 Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius]
1809 Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius]
1803 Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius]
26. Natural Theory / C. Causation / 7. Eliminating causation
3062 There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
3063 Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius]