Combining Texts

All the ideas for 'fragments/reports', 'Sets and Numbers' and 'The Rationality of Science'

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27 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
We do not wish merely to predict, we also want to explain [Newton-Smith]
The real problem of science is how to choose between possible explanations [Newton-Smith]
For science to be rational, we must explain scientific change rationally [Newton-Smith]
1. Philosophy / G. Scientific Philosophy / 2. Positivism
Critics attack positivist division between theory and observation [Newton-Smith]
Positivists hold that theoretical terms change, but observation terms don't [Newton-Smith]
3. Truth / A. Truth Problems / 6. Verisimilitude
More truthful theories have greater predictive power [Newton-Smith]
Theories generate infinite truths and falsehoods, so they cannot be used to assess probability [Newton-Smith]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
The master science is physical objects divided into sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Sets exist where their elements are, but numbers are more like universals [Maddy]
Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
De re necessity arises from the way the world is [Newton-Smith]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We must assess the truth of beliefs in identifying them [Newton-Smith]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Defeat relativism by emphasising truth and reference, not meaning [Newton-Smith]
14. Science / A. Basis of Science / 1. Observation
A full understanding of 'yellow' involves some theory [Newton-Smith]
14. Science / A. Basis of Science / 5. Anomalies
All theories contain anomalies, and so are falsified! [Newton-Smith]
The anomaly of Uranus didn't destroy Newton's mechanics - it led to Neptune's discovery [Newton-Smith]
Anomalies are judged against rival theories, and support for the current theory [Newton-Smith]
14. Science / B. Scientific Theories / 1. Scientific Theory
Why should it matter whether or not a theory is scientific? [Newton-Smith]
14. Science / B. Scientific Theories / 5. Commensurability
If theories are really incommensurable, we could believe them all [Newton-Smith]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Explaining an action is showing that it is rational [Newton-Smith]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]