Combining Texts

All the ideas for 'fragments/reports', 'Rearrangement of Particles' and 'Logicism Revisited'

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17 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]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism seems to exclude all creative, growing mathematics [Musgrave]
Formalism is a bulwark of logical positivism [Musgrave]
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 / B. Change in Existence / 1. Nature of Change
You can't deny temporary intrinsic properties by saying the properties are relations (to times) [Lewis]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius]
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]
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]