Combining Texts

All the ideas for '67: Platonic Questions', 'Proper Names' and 'Cardinality, Counting and Equinumerosity'

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17 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
We don't normally think of names as having senses (e.g. we don't give definitions of them) [Searle]
How can a proper name be correlated with its object if it hasn't got a sense? [Searle]
'Aristotle' means more than just 'an object that was christened "Aristotle"' [Searle]
Reference for proper names presupposes a set of uniquely referring descriptions [Searle]
Proper names are logically connected with their characteristics, in a loose way [Searle]
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]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch]