Combining Texts

All the ideas for 'works (all lost)', 'Identity' and 'On the Infinite'

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25 ideas

1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
1749 If all laws were abolished, philosophers would still live as they do now [Aristippus elder]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12456 I aim to establish certainty for mathematical methods [Hilbert]
12461 We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
16014 It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
12462 Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
12455 The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457 There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
16024 I could have died at five, but the summation of my adult stages could not [Noonan]
9. Objects / E. Objects over Time / 5. Temporal Parts
16023 Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan]
9. Objects / F. Identity among Objects / 2. Defining Identity
16015 Problems about identity can't even be formulated without the concept of identity [Noonan]
16017 Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]
16016 Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
16020 Identity can only be characterised in a second-order language [Noonan]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
16018 Indiscernibility is basic to our understanding of identity and distinctness [Noonan]
16019 Leibniz's Law must be kept separate from the substitutivity principle [Noonan]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636 My theory aims at the certitude of mathematical methods [Hilbert]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
3558 Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
5835 The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon]
23. Ethics / A. Egoism / 3. Cyrenaic School
3018 People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius]
1751 Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
1755 Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius]