Combining Texts

All the ideas for 'Elements of Geometry', 'Properties and Predicates' and 'Possible Worlds and Necessary A Posteriori'

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

21 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]
8. Modes of Existence / B. Properties / 2. Need for Properties
8568 A property is merely a constituent of laws of nature; temperature is just part of thermodynamics [Mellor]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
8564 There is obviously a possible predicate for every property [Mellor]
8. Modes of Existence / D. Universals / 2. Need for Universals
8566 We need universals for causation and laws of nature; the latter give them their identity [Mellor]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
8565 If properties were just the meanings of predicates, they couldn't give predicates their meaning [Mellor]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14633 How do we tell a table's being contingently plastic from its being essentially plastic? [Jackson]
14635 An x is essentially F if it is F in every possible world in which it appears [Jackson]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14632 Quine may have conflated de re and de dicto essentialism, but there is a real epistemological problem [Jackson]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
14631 How can you show the necessity of an a posteriori necessity, if it might turn out to be false? [Jackson]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
8567 Singular causation requires causes to raise the physical probability of their effects [Mellor]