Combining Texts

All the ideas for 'Attacks (frags)', 'Mathematics without Numbers' and 'Isolation and Non-arbitrary Division'

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15 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 / 4. Using Numbers / a. Units
Objects do not naturally form countable units [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
We can still count squares, even if they overlap [Koslicki]
There is no deep reason why we count carrots but not asparagus [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki]
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]