Combining Texts

All the ideas for 'Elements of Geometry', 'works' and 'Naturalizing the Mind'

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23 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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
5806 Belief is the power of metarepresentation [Dretske]
11. Knowledge Aims / A. Knowledge / 4. Belief / f. Animal beliefs
5801 A mouse hearing a piano played does not believe it, because it lacks concepts and understanding [Dretske]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
5802 Representations are in the head, but their content is not, as stories don't exist in their books [Dretske]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / d. Purpose of consciousness
5809 Some activities are performed better without consciousness of them [Dretske]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
5808 Qualia are just the properties objects are represented as having [Dretske]
16. Persons / C. Self-Awareness / 1. Introspection
5807 Introspection is the same as the experience one is introspecting [Dretske]
5803 In a representational theory of mind, introspection is displaced perception [Dretske]
5805 Introspection does not involve looking inwards [Dretske]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
5804 A representational theory of the mind is an externalist theory of the mind [Dretske]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
5800 All mental facts are representation, which consists of informational functions [Dretske]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
4366 We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse]