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All the ideas for 'Clitophon', 'Elements of Geometry' and 'Law,Liberty and Morality'

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23 ideas

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]
22. Metaethics / B. Value / 2. Values / f. Altruism
The just man does not harm his enemies, but benefits everyone [Plato]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Conduct is not isolated from its effect on the moral code [Hart,HLA]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
In an organised society all actions have some effect on other people [Hart,HLA]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA]
Some private moral issues are no concern of the law [Hart,HLA]
Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA]
Is the enforcement of morality morally justifiable? [Hart,HLA]
Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA]