Combining Texts

All the ideas for 'Defending the Axioms', 'Essays on Intellectual Powers 6: Judgement' and 'What Price Bivalence?'

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20 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
23657 The existence of tensed verbs shows that not all truths are necessary truths [Reid]
2. Reason / F. Fallacies / 7. Ad Hominem
23655 An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid]
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 / D. Assumptions for Logic / 1. Bivalence
19043 Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine]
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 / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
19042 Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
23659 If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
23662 The existence of ideas is no more obvious than the existence of external objects [Reid]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
23661 We are only aware of other beings through our senses; without that, we are alone in the universe [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
23654 In obscure matters the few must lead the many, but the many usually lead in common sense [Reid]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
23660 The theory of ideas, popular with philosophers, means past existence has to be proved [Reid]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
23658 Consciousness is an indefinable and unique operation [Reid]
18. Thought / A. Modes of Thought / 8. Human Thought
23656 The structure of languages reveals a uniformity in basic human opinions [Reid]
18. Thought / E. Abstraction / 2. Abstracta by Selection
23653 If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
23663 There are axioms of taste - such as a general consensus about a beautiful face [Reid]