Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Mathematics without Foundations' and 'Philosophy of Science: Very Short Intro (2nd ed)'

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20 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
9944 We understand some statements about all sets [Putnam]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
9937 I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
9939 It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9940 Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9941 Science requires more than consistency of mathematics [Putnam]
7. Existence / C. Structure of Existence / 2. Reduction
22180 Multiple realisability is said to make reduction impossible [Okasha]
7. Existence / D. Theories of Reality / 4. Anti-realism
9943 You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
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]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
22173 Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha]