Combining Texts

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

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13 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea]
The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea]
5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea]
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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / A. Speculations on Nature / 1. Nature
If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea]
27. Natural Reality / C. Space / 5. Relational Space
If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]