Combining Texts

All the ideas for 'fragments/reports', 'Mathematical logic and theory of types' and 'Categories, Classification, Cogn. Anthropology'

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18 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche]
7. Existence / E. Categories / 2. Categorisation
Several words may label a category; one word can name several categories; some categories lack words [Ellen]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander]
The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander]
Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius]
Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius]