Combining Texts

All the ideas for 'Elements of Geometry', 'Symposium' and 'Enquiry concerning Principles of Morals'

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26 ideas

2. Reason / E. Argument / 6. Conclusive Proof
8623 Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
13907 If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
6297 Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9603 An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
9894 A unit is that according to which each existing thing is said to be one [Euclid]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
8738 Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
22278 Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
8673 Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
10250 Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
14157 Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
1600 Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
22. Metaethics / B. Value / 2. Values / f. Altruism
3926 The human heart has a natural concern for public good [Hume]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
5845 Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
23. Ethics / A. Egoism / 1. Ethical Egoism
3929 No moral theory is of any use if it doesn't serve the interests of the individual concerned [Hume]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
3925 Personal Merit is the possession of useful or agreeable mental qualities [Hume]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
3922 Justice only exists to support society [Hume]
23560 If we all naturally had everything we could ever desire, the virtue of justice would be irrelevant [Hume]
23. Ethics / D. Deontological Ethics / 2. Duty
3918 Moral philosophy aims to show us our duty [Hume]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
3919 Conclusions of reason do not affect our emotions or decisions to act [Hume]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
3928 Virtue just requires careful calculation and a preference for the greater happiness [Hume]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
3923 No one would cause pain to a complete stranger who happened to be passing [Hume]
3924 Nature makes private affections come first, because public concerns are spread too thinly [Hume]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
3921 The safety of the people is the supreme law [Hume]
24. Political Theory / C. Ruling a State / 3. Government / a. Government
3927 Society prefers helpful lies to harmful truth [Hume]
25. Social Practice / B. Equalities / 4. Economic equality
3920 If you equalise possessions, people's talents will make them unequal again [Hume]