Combining Texts

All the ideas for 'Laches', 'fragments/reports' and 'Remarks on axiomatised set theory'

expand these ideas     |    start again     |     specify just one area for these texts


13 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
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 / B. Foundations for Mathematics / 1. Foundations for Mathematics
Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Mathematician want performable operations, not propositions about objects [Skolem]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]
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]