Combining Texts

All the ideas for 'What Numbers Are', 'fragments/reports' and 'Lives of Eminent Philosophers'

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19 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
1542 Diogenes of Apollonia was the last natural scientist [Diogenes of Apollonia, by Simplicius]
2. Reason / C. Styles of Reason / 1. Dialectic
3035 Dialectic involves conversations with short questions and brief answers [Diog. Laertius]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
489 Each thing must be in some way unique [Diogenes of Apollonia]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
483 Start a thesis with something undisputable [Diogenes of Apollonia]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
1544 Perception must be an internal matter, because we can fail to perceive when we are preoccupied [Diogenes of Apollonia, by Theophrastus]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
1816 Sceptics say demonstration depends on self-demonstrating things, or indemonstrable things [Diog. Laertius]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
1819 Scepticism has two dogmas: that nothing is definable, and every argument has an opposite argument [Diog. Laertius]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3064 When sceptics say that nothing is definable, or all arguments have an opposite, they are being dogmatic [Diog. Laertius]
14. Science / C. Induction / 4. Reason in Induction
3033 Induction moves from some truths to similar ones, by contraries or consequents [Diog. Laertius]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
24042 The older Diogenes said the soul is air, made of the smallest particles [Diogenes of Apollonia]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
1838 Cyrenaic pleasure is a motion, but Epicurean pleasure is a condition [Diog. Laertius]
23. Ethics / A. Egoism / 1. Ethical Egoism
1769 Cynics believe that when a man wishes for nothing he is like the gods [Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
5995 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
488 Air is divine, because it is in and around everything, and arranges everything [Diogenes of Apollonia]
484 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
486 Plants and animals can only come into existence if something fixes their species [Diogenes of Apollonia]
485 Things must retain their essential nature during change, or mixing would be impossible [Diogenes of Apollonia]