Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Human Nature' and 'Elements of Geometry'

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21 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour
Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes]
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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
The actual universe is the richest composite of what is possible [Leibniz]
16. Persons / F. Free Will / 5. Against Free Will
A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Conceptions and apparitions are just motion in some internal substance of the head [Hobbes]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
There is no absolute good, for even the goodness of God is goodness to us [Hobbes]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes]
25. Social Practice / F. Life Issues / 5. Sexual Morality
Lust involves pleasure, and also the sense of power in pleasing others [Hobbes]