Combining Texts

All the ideas for 'fragments/reports', 'Concepts:where cogn.science went wrong' and 'Elements of Geometry'

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26 ideas

2. Reason / D. Definition / 13. Against Definition
We have no successful definitions, because they all use indefinable words [Fodor]
2. Reason / E. Argument / 6. Conclusive Proof
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
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
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
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
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
Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
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
Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
7. Existence / A. Nature of Existence / 2. Types of Existence
If 'exist' is ambiguous in 'chairs and numbers exist', that mirrors the difference between chairs and numbers [Fodor]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
Empiricists use dispositions reductively, as 'possibility of sensation' or 'possibility of experimental result' [Fodor]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Associationism can't explain how truth is preserved [Fodor]
18. Thought / C. Content / 2. Ideas
Mental representations are the old 'Ideas', but without images [Fodor]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
Fodor is now less keen on the innateness of concepts [Fodor, by Lowe]
18. Thought / D. Concepts / 3. Ontology of Concepts / a. Concepts as representations
It is essential to the concept CAT that it be satisfied by cats [Fodor]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
I prefer psychological atomism - that concepts are independent of epistemic capacities [Fodor]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
Definable concepts have constituents, which are necessary, individuate them, and demonstrate possession [Fodor]
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
Many concepts lack prototypes, and complex prototypes aren't built from simple ones [Fodor]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
The theory theory can't actually tell us what concepts are [Fodor]
19. Language / C. Assigning Meanings / 2. Semantics
English has no semantic theory, just associations between sentences and thoughts [Fodor]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]