Combining Texts

All the ideas for 'works', 'Nature and Meaning of Numbers' and 'Letter to Menoeceus'

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

40 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
14052 Begin philosophy when you are young, and keep going when you are old [Epicurus]
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 / 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]
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]
16. Persons / F. Free Will / 6. Determinism / b. Fate
14062 Sooner follow mythology, than accept the 'fate' of natural philosophers [Epicurus]
16. Persons / F. Free Will / 7. Compatibilism
1837 We should not refer things to irresponsible necessity, but either to fortune or to our own will [Epicurus]
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]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
1836 Prudence is more valuable than philosophy, because it avoids confusions of the soul [Epicurus]
20. Action / C. Motives for Action / 4. Responsibility for Actions
14061 Our own choices are autonomous, and the basis for praise and blame [Epicurus]
22. Metaethics / B. Value / 2. Values / e. Death
14055 The wisdom that produces a good life also produces a good death [Epicurus]
14054 Fearing death is absurd, because we are not present when it occurs [Epicurus]
14053 It is absurd to fear the pain of death when you are not even facing it [Epicurus]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
1833 Pleasure is the first good in life [Epicurus]
14058 Pleasure is the goal, but as lack of pain and calm mind, not as depraved or greedy pleasure [Epicurus]
14057 All pleasures are good, but it is not always right to choose them [Epicurus]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
14063 Sooner a good decision going wrong, than a bad one turning out for the good [Epicurus]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
14059 The best life is not sensuality, but rational choice and healthy opinion [Epicurus]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
1835 True pleasure is not debauchery, but freedom from physical and mental pain [Epicurus]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
14056 We only need pleasure when we have the pain of desire [Epicurus]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
14060 Prudence is the greatest good, and more valuable than philosophy, because it produces virtue [Epicurus]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
20239 Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]