Combining Texts

All the ideas for 'fragments/reports', 'Philosophy of Science: Very Short Intro (2nd ed)' and 'On the Introduction of Transfinite Numbers'

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17 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
7. Existence / C. Structure of Existence / 2. Reduction
Multiple realisability is said to make reduction impossible [Okasha]
14. Science / A. Basis of Science / 3. Experiment
Not all sciences are experimental; astronomy relies on careful observation [Okasha]
Randomised Control Trials have a treatment and a control group, chosen at random [Okasha]
14. Science / A. Basis of Science / 6. Falsification
The discoverers of Neptune didn't change their theory because of an anomaly [Okasha]
Science mostly aims at confirming theories, rather than falsifying them [Okasha]
14. Science / B. Scientific Theories / 1. Scientific Theory
Theories with unobservables are underdetermined by the evidence [Okasha]
14. Science / B. Scientific Theories / 5. Commensurability
Two things can't be incompatible if they are incommensurable [Okasha]
14. Science / C. Induction / 1. Induction
Induction is inferences from examined to unexamined instances of a given kind [Okasha]
14. Science / C. Induction / 6. Bayes's Theorem
If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]