Combining Texts

All the ideas for 'fragments/reports', 'fragments/reports' and 'Principles of Arithmetic, by a new method'

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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 / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
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]