Combining Texts

All the ideas for 'Laches', 'Elements of Geometry' and 'Knowledge, Possibility and Consciousness'

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28 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / E. Argument / 6. Conclusive Proof
Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Truth has to be correspondence to facts, and a match between relations of ideas and relations in the world [Perry]
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]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Identity is a very weak relation, which doesn't require interdefinability, or shared properties [Perry]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Possible worlds thinking has clarified the logic of modality, but is problematic in epistemology [Perry]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are indices for a language, or concrete realities, or abstract possibilities [Perry]
15. Nature of Minds / A. Nature of Mind / 3. Mental Causation
We try to cause other things to occur by causing mental events to occur [Perry]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Brain states must be in my head, and yet the pain seems to be in my hand [Perry]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
It seems plausible that many animals have experiences without knowing about them [Perry]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
If epiphenomenalism just says mental events are effects but not causes, it is consistent with physicalism [Perry]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Prior to Kripke, the mind-brain identity theory usually claimed that the identity was contingent [Perry]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
If physicalists stick with identity (not supervenience), Martian pain will not be like ours [Perry]
18. Thought / C. Content / 1. Content
Although we may classify ideas by content, we individuate them differently, as their content can change [Perry]
18. Thought / C. Content / 8. Intension
The intension of an expression is a function from possible worlds to an appropriate extension [Perry]
19. Language / D. Propositions / 2. Abstract Propositions / b. Propositions as possible worlds
A proposition is a set of possible worlds for which its intension delivers truth [Perry]
19. Language / E. Analyticity / 3. Analytic and Synthetic
A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]