Combining Philosophers

All the ideas for Stilpo, Henry of Ghent and Richard G. Heck

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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 / E. Categories / 3. Proposed Categories
Substance, Quantity and Quality are real; other categories depend on those three [Henry of Ghent]
8. Modes of Existence / A. Relations / 1. Nature of Relations
The only reality in the category of Relation is things from another category [Henry of Ghent]
8. Modes of Existence / B. Properties / 8. Properties as Modes
Accidents are diminished beings, because they are dispositions of substance (unqualified being) [Henry of Ghent]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Kant says things-in-themselves cause sensations, but then makes causation transcendental! [Henry of Ghent, by Pinkard]
28. God / C. Attitudes to God / 5. Atheism
Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius]