Combining Texts

All the ideas for 'works', 'Elements of Geometry' and 'The Symposium'

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33 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
14179 The finest branch of wisdom is justice and moderation in ordering states and families [Plato]
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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
1607 Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
174 True opinion without reason is midway between wisdom and ignorance [Plato]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
181 Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato]
180 We call a person the same throughout life, but all their attributes change [Plato]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
173 Beauty and goodness are the same [Plato]
4026 Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato]
172 Love of ugliness is impossible [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
183 Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato]
184 Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
171 Music is a knowledge of love in the realm of harmony and rhythm [Plato]
22. Metaethics / B. Value / 2. Values / g. Love
176 Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato]
14177 Love assists men in achieving merit and happiness [Plato]
179 Love is desire for perpetual possession of the good [Plato]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
177 If a person is good they will automatically become happy [Plato]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
14178 Happiness is secure enjoyment of what is good and beautiful [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
170 The only slavery which is not dishonourable is slavery to excellence [Plato]
182 The first step on the right path is the contemplation of physical beauty when young [Plato]
28. God / A. Divine Nature / 3. Divine Perfections
175 Gods are not lovers of wisdom, because they are already wise [Plato]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]