Combining Texts

All the ideas for 'Believing the Axioms I', 'Philosophical Essay on Probability' and 'Intro to Positive Philosophy'

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26 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
12104 All ideas must be understood historically [Comte]
12105 Our knowledge starts in theology, passes through metaphysics, and ends in positivism [Comte]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
12112 Metaphysics is just the oversubtle qualification of abstract names for phenomena [Comte]
1. Philosophy / G. Scientific Philosophy / 2. Positivism
12106 Positivism gives up absolute truth, and seeks phenomenal laws, by reason and observation [Comte]
12111 Positivism is the final state of human intelligence [Comte]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
12114 Science can drown in detail, so we need broad scientists (to keep out the metaphysicians) [Comte]
12116 Only positivist philosophy can terminate modern social crises [Comte]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13013 The Axiom of Extensionality seems to be analytic [Maddy]
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
12108 All real knowledge rests on observed facts [Comte]
13. Knowledge Criteria / C. External Justification / 7. Testimony
7458 The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
14. Science / A. Basis of Science / 1. Observation
12109 We must observe in order to form theories, but connected observations need prior theories [Comte]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
12107 Positivism explains facts by connecting particular phenomena with general facts [Comte]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
12115 Introspection is pure illusion; we can obviously observe everything except ourselves [Comte]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
3441 If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]
26. Natural Theory / C. Causation / 7. Eliminating causation
12113 The search for first or final causes is futile [Comte]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
12110 We can never know origins, purposes or inner natures [Comte]