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All the ideas for 'fragments/reports', 'Nature Without Essence' and 'Elements of Geometry'

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27 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
20768 Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]
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]
5. Theory of Logic / K. Features of Logics / 6. Compactness
17867 If a concept is not compact, it will not be presentable to finite minds [Almog]
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 / d. Natural numbers
17877 The number series is primitive, not the result of some set theoretic axioms [Almog]
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]
9. Objects / D. Essence of Objects / 4. Essence as Definition
17872 Definitionalists rely on snapshot-concepts, instead of on the real processes [Almog]
17871 Fregean meanings are analogous to conceptual essence, defining a kind [Almog]
17866 Essential definition aims at existence conditions and structural truths [Almog]
17868 Surface accounts aren't exhaustive as they always allow unintended twin cases [Almog]
9. Objects / D. Essence of Objects / 10. Essence as Species
17870 Alien 'tigers' can't be tigers if they are not related to our tigers [Almog]
9. Objects / D. Essence of Objects / 13. Nominal Essence
17869 Kripke and Putnam offer an intermediary between real and nominal essences [Almog]
9. Objects / D. Essence of Objects / 15. Against Essentialism
17876 Individual essences are just cobbled together classificatory predicates [Almog]
18. Thought / C. Content / 5. Twin Earth
17873 Water must be related to water, just as tigers must be related to tigers [Almog]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
3049 The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]
23. Ethics / D. Deontological Ethics / 1. Deontology
3549 Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
17864 Defining an essence comes no where near giving a thing's nature [Almog]
17863 Essences promise to reveal reality, but actually drive us away from it [Almog]