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All the ideas for 'fragments/reports', 'Remarks on the definition and nature of mathematics' and 'fragments/reports'

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17 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
Diogenes of Apollonia was the last natural scientist [Diogenes of Apollonia, by Simplicius]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Saying mathematics is logic is merely replacing one undefined term by another [Curry]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Each thing must be in some way unique [Diogenes of Apollonia]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Start a thesis with something undisputable [Diogenes of Apollonia]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
Perception must be an internal matter, because we can fail to perceive when we are preoccupied [Diogenes of Apollonia, by Theophrastus]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The older Diogenes said the soul is air, made of the smallest particles [Diogenes of Apollonia]
19. Language / F. Communication / 3. Denial
Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
Diogenes of Apollonia offered the first teleological account of cosmology [Diogenes of Apollonia, by Robinson,TM]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Air is divine, because it is in and around everything, and arranges everything [Diogenes of Apollonia]
Everything is ultimately a variation of one underlying thing [Diogenes of Apollonia]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Plants and animals can only come into existence if something fixes their species [Diogenes of Apollonia]
Things must retain their essential nature during change, or mixing would be impossible [Diogenes of Apollonia]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus]
28. God / C. Attitudes to God / 5. Atheism
The gods are just personified human benefits [Prodicus]
He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus]