### All the ideas for Michael Burke, Helen Cartwright and Euclid

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20 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]
###### 5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
 10670 A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack]
###### 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
 10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
 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]
 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 / A. Existence of Objects / 5. Individuation / e. Individuation by kind
 16235 Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
 14753 The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
###### 9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
 16072 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
 14751 Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
 16071 Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
 16234 Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
 13278 Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
 14750 Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]