Combining Texts

All the ideas for 'Foundations of Geometry', 'Logicism, Some Considerations (PhD)' and 'comedies (frags)'

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15 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
An adequate account of a number must relate it to its series [Benacerraf]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Additional or removal of any part changes a thing, so people are never the same person [Epicharmus]
13. Knowledge Criteria / E. Relativism / 1. Relativism
A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Hands wash hands; give that you may get [Epicharmus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Against a villain, villainy is not a useless weapon [Epicharmus]
28. God / A. Divine Nature / 3. Divine Perfections
God knows everything, and nothing is impossible for him [Epicharmus]
29. Religion / D. Religious Issues / 3. Problem of Evil / c. Human Error
Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus]