Combining Texts

All the ideas for 'Cardinality, Counting and Equinumerosity', 'De modo distinguendi phaenomena' and 'The Method of Truth in Metaphysics'

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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 / D. Theories of Reality / 2. Realism
If experience is just a dream, it is still real enough if critical reason is never deceived [Leibniz]
The strongest criterion that phenomena show reality is success in prediction [Leibniz]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
Light, heat and colour are apparent qualities, and so are motion, figure and extension [Leibniz]
16. Persons / A. Concept of a Person / 1. Existence of Persons
Metaphysics requires the idea of people (speakers) located in space and time [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Sentences held true determine the meanings of the words they contain [Davidson]