Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Notebooks' and 'Defending the Axioms'

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26 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
8093 Seek wisdom rather than truth; it is easier [Joubert]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
8095 We must think with our entire body and soul [Joubert]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
8107 The love of certainty holds us back in metaphysics [Joubert]
2. Reason / A. Nature of Reason / 9. Limits of Reason
8099 The truths of reason instruct, but they do not illuminate [Joubert]
2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
3. Truth / A. Truth Problems / 1. Truth
8098 Truth consists of having the same idea about something that God has [Joubert]
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 / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
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 / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
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]
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
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]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
8101 To know is to see inside oneself [Joubert]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
8094 The imagination has made more discoveries than the eye [Joubert]
18. Thought / A. Modes of Thought / 1. Thought
8103 A thought is as real as a cannon ball [Joubert]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
8100 Where does the bird's idea of a nest come from? [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
8096 He gives his body up to pleasure, but not his soul [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
8104 What will you think of pleasures when you no longer enjoy them? [Joubert]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
8097 Virtue is hard if we are scorned; we need support [Joubert]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
8106 In raising a child we must think of his old age [Joubert]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
8105 We can't exactly conceive virtue without the idea of God [Joubert]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
8102 We cannot speak against Christianity without anger, or speak for it without love [Joubert]