Combining Texts

All the ideas for 'fragments/reports', 'Foundations of Geometry' and 'Epistemology'

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13 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
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]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
The phenomenalist says that to be is to be perceivable [Cardinal/Hayward/Jones]
Linguistic phenomenalism says we can eliminate talk of physical objects [Cardinal/Hayward/Jones]
If we lack enough sense-data, are we to say that parts of reality are 'indeterminate'? [Cardinal/Hayward/Jones]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
Primary qualities can be described mathematically, unlike secondary qualities [Cardinal/Hayward/Jones]
An object cannot remain an object without its primary qualities [Cardinal/Hayward/Jones]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
My justifications might be very coherent, but totally unconnected to the world [Cardinal/Hayward/Jones]
19. Language / F. Communication / 1. Rhetoric
Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
Destroy seriousness with laughter, and laughter with seriousness [Gorgias]