Combining Texts

All the ideas for 'Realism in Mathematics', 'Letters to Russell' and 'Rationality'

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13 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling]
2. Reason / A. Nature of Reason / 1. On Reason
You can be rational with undetected or minor inconsistencies [Harman]
2. Reason / A. Nature of Reason / 6. Coherence
A coherent conceptual scheme contains best explanations of most of your beliefs [Harman]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Atomic facts correspond to true elementary propositions [Wittgenstein]
14. Science / C. Induction / 1. Induction
Enumerative induction is inference to the best explanation [Harman]
14. Science / C. Induction / 3. Limits of Induction
Induction is 'defeasible', since additional information can invalidate it [Harman]
14. Science / C. Induction / 4. Reason in Induction
All reasoning is inductive, and deduction only concerns implication [Harman]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Ordinary rationality is conservative, starting from where your beliefs currently are [Harman]
19. Language / D. Propositions / 4. Mental Propositions
A thought is mental constituents that relate to reality as words do [Wittgenstein]