Combining Philosophers

All the ideas for Geoffrey Gorham, Euclid and Ryan Wasserman

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26 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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
16065 Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman]
16067 Constitution is not identity, because it is an asymmetric dependence relation [Wasserman]
16069 There are three main objections to seeing constitution as different from identity [Wasserman]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
16068 The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman]
9. Objects / F. Identity among Objects / 3. Relative Identity
16074 Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman]
14. Science / A. Basis of Science / 6. Falsification
22189 Why abandon a theory if you don't have a better one? [Gorham]
22190 If a theory is more informative it is less probable [Gorham]
14. Science / B. Scientific Theories / 1. Scientific Theory
22192 Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham]
22194 Structural Realism says mathematical structures persist after theory rejection [Gorham]
22195 Structural Realists must show the mathematics is both crucial and separate [Gorham]
14. Science / B. Scientific Theories / 3. Instrumentalism
22197 Theories aren't just for organising present experience if they concern the past or future [Gorham]
22196 For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham]
14. Science / D. Explanation / 2. Types of Explanation / d. Consilience
22193 Consilience makes the component sciences more likely [Gorham]
26. Natural Theory / A. Speculations on Nature / 1. Nature
22198 Aristotelian physics has circular celestial motion and linear earthly motion [Gorham]