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All the ideas for 'Elements of Geometry', 'Dispositions and Powers' and 'Completeness of Axioms of Logic'

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28 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]
4. Formal Logic / C. Predicate Calculus PC / 3. Completeness of PC
17751 Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki]
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 / 1. Nature of Properties
23708 Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG]
23709 Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
23707 Powers are properties which necessitate dispositions [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
23714 Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
23711 A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye]
23712 Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
23698 Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye]
23699 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye]
23700 A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye]
23701 A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye]
23702 A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye]
23703 Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye]
23704 We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
23710 Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
23706 Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye]