Combining Texts

All the ideas for 'fragments/reports', 'Elements of Geometry' and 'Discourse on Metaphysics'

expand these ideas     |    start again     |     specify just one area for these texts

26 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
23367 Even pointing a finger should only be done for a reason [Epictetus]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
19342 Reason avoids multiplying hypotheses or principles [Leibniz]
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]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
12711 The immediate cause of movements is more real [than geometry] [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
19349 The complete notion of a substance implies all of its predicates or attributes [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
7558 Substances mirror God or the universe, each from its own viewpoint [Leibniz]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
16761 Forms are of no value in physics, but are indispensable in metaphysics [Leibniz]
9. Objects / D. Essence of Objects / 1. Essences of Objects
13088 Subjects include predicates, so full understanding of subjects reveals all the predicates [Leibniz]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
13085 Leibniz is some form of haecceitist [Leibniz, by Cover/O'Leary-Hawthorne]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
5024 Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc. [Leibniz]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
5027 If a person's memories became totally those of the King of China, he would be the King of China [Leibniz]
16. Persons / F. Free Will / 1. Nature of Free Will
5023 Future contingent events are certain, because God foresees them, but that doesn't make them necessary [Leibniz]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
2119 People argue for God's free will, but it isn't needed if God acts in perfection following supreme reason [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
5025 Mind and body can't influence one another, but God wouldn't intervene in the daily routine [Leibniz]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics
5026 Animals lack morality because they lack self-reflection [Leibniz]