Combining Texts

All the ideas for 'Elements of Geometry', 'On the Genealogy of Ethics' and 'The Mind and the Soul'

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19 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
Early Greeks cared about city and companions; later Greeks concentrated on the self [Foucault]
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]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Not only substances have attributes; events, actions, states and qualities can have them [Teichmann]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
Body-spirit interaction ought to result in losses and increases of energy in the material world [Teichmann]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Why couldn't a person's life become a work of art? [Foucault]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
Greeks and early Christians were much more concerned about food than about sex [Foucault]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
The Soul has no particular capacity (in the way thinking belongs to the mind) [Teichmann]
No individuating marks distinguish between Souls [Teichmann]