Combining Texts

All the ideas for 'Arguments (frags)', 'Nature and Meaning of Numbers' and 'Metaphysics: an introduction'

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31 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
18859 Metaphysics is a quest for truthmakers [Tallant]
2. Reason / D. Definition / 9. Recursive Definition
22289 Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
2. Reason / D. Definition / 12. Paraphrase
18861 Maybe number statements can be paraphrased into quantifications plus identities [Tallant]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
18866 Maybe only 'positive' truths need truth-makers [Tallant]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18860 A truthmaker is the minimal portion of reality that will do the job [Tallant]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
18863 What is the truthmaker for a possible new power? [Tallant]
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]
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 / B. Properties / 13. Tropes / a. Nature of tropes
18864 The wisdom of Plato and of Socrates are not the same property [Tallant]
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 / B. Unity of Objects / 2. Substance / d. Substance defined
18865 Substance must have two properties: individuation, and property-bearing [Tallant]
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 / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
18862 Are propositions all the thoughts and sentences that are possible? [Tallant]