Combining Texts

All the ideas for 'Concepts and Counting', 'Mathematics and the Metaphysicians' and 'Syntagma'

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10 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
In mathematic we are ignorant of both subject-matter and truth [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A collection is infinite if you can remove some terms without diminishing its number [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
8. Modes of Existence / B. Properties / 8. Properties as Modes
If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Self-evidence is often a mere will-o'-the-wisp [Russell]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]