Combining Texts

All the ideas for 'fragments/reports', 'A Defense of Abortion' and 'Elements of Geometry'

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21 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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
25. Social Practice / F. Life Issues / 3. Abortion
4059 It can't be murder for a mother to perform an abortion on herself to save her own life [Thomson]
4057 A newly fertilized ovum is no more a person than an acorn is an oak tree [Thomson]
4695 Maybe abortion can be justified despite the foetus having full human rights [Thomson, by Foot]
4696 The foetus is safe in the womb, so abortion initiates its death, with the mother as the agent. [Foot on Thomson]
4060 The right to life does not bestow the right to use someone else's body to support that life [Thomson]
4061 The right to life is not a right not to be killed, but not to be killed unjustly [Thomson]
4058 Is someone's right to life diminished if they were conceived by a rape? [Thomson]
4062 No one is morally required to make huge sacrifices to keep someone else alive for nine months [Thomson]