Combining Texts

All the ideas for 'On Being (lost)', '14: Superstition' and 'Cardinality, Counting and Equinumerosity'

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16 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
Is counting basically mindless, and independent of the cardinality involved? [Heck]
Counting is the assignment of successively larger cardinal numbers to collections [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Equinumerosity is not the same concept as one-one correspondence [Heck]
We can understand cardinality without the idea of one-one correspondence [Heck]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Being is one [Melissus, by Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
There is no real motion, only the appearance of it [Melissus, by Diog. Laertius]
27. Natural Reality / C. Space / 1. Void
The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
Nothing could come out of nothing [Melissus]
28. God / C. Attitudes to God / 5. Atheism
Absurd superstitions make people atheist, not disharmony in nature [Plutarch]