Combining Texts

All the ideas for 'fragments/reports', 'A World of States of Affairs' and 'Nature and Meaning of Numbers'

expand these ideas     |    start again     |     specify just one area for these texts

29 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]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
4742 Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong]
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 / G. Formal Mereology / 1. Mereology
10706 Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
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]
17452 Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
7524 Order, not quantity, is central to defining numbers [Dedekind, by Monk]
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]
7. Existence / D. Theories of Reality / 7. Fictionalism
9497 Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong]
8. Modes of Existence / B. Properties / 1. Nature of Properties
15550 Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis]
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]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
4743 The truth-maker for a truth must necessitate that truth [Armstrong]
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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
4798 In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos]