Combining Texts

All the ideas for 'Substance and Individuation in Leibniz', 'Introduction to 'Absolute Generality'' and 'Nature and Meaning of Numbers'

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41 ideas

2. Reason / D. Definition / 9. Recursive Definition
22289 Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
13451 The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10183 An infinite set maps into its own proper subset [Dedekind, by Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
22288 We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
13452 Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10706 Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
13449 We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
13450 Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13453 Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9823 Numbers are free creations of the human mind, to understand differences [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
10090 Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
7524 Order, not quantity, is central to defining numbers [Dedekind, by Monk]
17452 Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
14131 Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
14437 Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
18094 Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
9824 In counting we see the human ability to relate, correspond and represent [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
9826 A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
13508 Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
18096 Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
18841 Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
14130 Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
8924 Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
9153 Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
8. Modes of Existence / A. Relations / 1. Nature of Relations
13076 Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne]
9. Objects / A. Existence of Objects / 3. Objects in Thought
9825 A thing is completely determined by all that can be thought concerning it [Dedekind]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
13103 Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne]
13102 If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
13104 Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
13100 Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
13068 We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
13069 The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13072 Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne]
17080 Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne]
9. Objects / E. Objects over Time / 12. Origin as Essential
13101 Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13081 Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
13071 We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9189 Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett]
9827 We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9979 Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
13448 The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]