Combining Texts

All the ideas for 'fragments/reports', 'Believing the Axioms I' and 'Philosophy of Science: Very Short Intro (2nd ed)'

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22 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
23367 Even pointing a finger should only be done for a reason [Epictetus]
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]
7. Existence / C. Structure of Existence / 2. Reduction
22180 Multiple realisability is said to make reduction impossible [Okasha]
14. Science / A. Basis of Science / 3. Experiment
22172 Not all sciences are experimental; astronomy relies on careful observation [Okasha]
22177 Randomised Control Trials have a treatment and a control group, chosen at random [Okasha]
14. Science / A. Basis of Science / 6. Falsification
22174 The discoverers of Neptune didn't change their theory because of an anomaly [Okasha]
22175 Science mostly aims at confirming theories, rather than falsifying them [Okasha]
14. Science / B. Scientific Theories / 1. Scientific Theory
22182 Theories with unobservables are underdetermined by the evidence [Okasha]
14. Science / B. Scientific Theories / 5. Commensurability
22185 Two things can't be incompatible if they are incommensurable [Okasha]
14. Science / C. Induction / 1. Induction
22176 Induction is inferences from examined to unexamined instances of a given kind [Okasha]
14. Science / C. Induction / 6. Bayes's Theorem
22178 If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
22173 Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha]