Combining Texts

All the ideas for 'Letters to Remond de Montmort', 'Cardinality, Counting and Equinumerosity' and 'Against Structural Universals'

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32 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
17453 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
17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17450 Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
17451 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
17459 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
17454 Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17458 Equinumerosity is not the same concept as one-one correspondence [Heck]
17449 We can understand cardinality without the idea of one-one correspondence [Heck]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
15435 If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis]
8. Modes of Existence / B. Properties / 5. Natural Properties
15451 I assume there could be natural properties that are not instantiated in our world [Lewis]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
15433 Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis]
8. Modes of Existence / D. Universals / 2. Need for Universals
15436 Universals are meant to give an account of resemblance [Lewis]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
15438 We can add a primitive natural/unnatural distinction to class nominalism [Lewis]
9. Objects / C. Structure of Objects / 1. Structure of an Object
15448 The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis]
15449 If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis]
15439 The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis]
15441 The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis]
15445 Butane and Isobutane have the same atoms, but different structures [Lewis]
15434 Structural universals have a necessary connection to the universals forming its parts [Lewis]
15437 We can't get rid of structural universals if there are no simple universals [Lewis]
9. Objects / C. Structure of Objects / 5. Composition of an Object
15446 Composition is not just making new things from old; there are too many counterexamples [Lewis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
15440 A whole is distinct from its parts, but is not a further addition in ontology [Lewis]
15444 Different things (a toy house and toy car) can be made of the same parts at different times [Lewis]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
12732 Some necessary truths are brute, and others derive from final causes [Leibniz]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
19438 Our large perceptions and appetites are made up tiny unconscious fragments [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
15450 Maybe abstraction is just mereological subtraction [Lewis]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
19415 Passions reside in confused perceptions [Leibniz]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
15443 Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis]
28. God / A. Divine Nature / 2. Divine Nature
19439 God produces possibilities, and thus ideas [Leibniz]