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All the ideas for 'Frege's Concept of Numbers as Objects', 'Vague Identity: Evans misunderstood' and 'fragments/reports'

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64 ideas

1. Philosophy / A. Wisdom / 2. Wise People
A wise man's chief strength is not being tricked; nothing is worse than error, frivolity or rashness [Zeno of Citium, by Cicero]
1. Philosophy / C. History of Philosophy / 1. History of Philosophy
We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
When shown seven versions of the mowing argument, he paid twice the asking price for them [Zeno of Citium, by Diog. Laertius]
1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
Philosophy has three parts, studying nature, character, and rational discourse [Zeno of Citium, by Diog. Laertius]
2. Reason / C. Styles of Reason / 1. Dialectic
The best way to understand a philosophical idea is to defend it [Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Someone who says 'it is day' proposes it is day, and it is true if it is day [Zeno of Citium, by Diog. Laertius]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck]
There are five Peano axioms, which can be expressed informally [Wright,C]
Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C]
What facts underpin the truths of the Peano axioms? [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K]
Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend]
Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck]
It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Number platonism says that natural number is a sortal concept [Wright,C]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Treating numbers adjectivally is treating them as quantifiers [Wright,C]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C]
The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C]
7. Existence / A. Nature of Existence / 2. Types of Existence
The idea that 'exist' has multiple senses is not coherent [Wright,C]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Whatever participates in substance exists [Zeno of Citium, by Stobaeus]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Semantic vagueness involves alternative and equal precisifications of the language [Lewis]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Perception an open hand, a fist is 'grasping', and holding that fist is knowledge [Zeno of Citium, by Long]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
A grasp by the senses is true, because it leaves nothing out, and so nature endorses it [Zeno of Citium, by Cicero]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
If a grasped perception cannot be shaken by argument, it is 'knowledge' [Zeno of Citium, by Cicero]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
A presentation is true if we judge that no false presentation could appear like it [Zeno of Citium, by Cicero]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
When a slave said 'It was fated that I should steal', Zeno replied 'Yes, and that you should be beaten' [Zeno of Citium, by Diog. Laertius]
A dog tied to a cart either chooses to follow and is pulled, or it is just pulled [Zeno of Citium, by Hippolytus]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
Incorporeal substances can't do anything, and can't be acted upon either [Zeno of Citium, by Cicero]
17. Mind and Body / E. Mind as Physical / 5. Causal Argument
A body is required for anything to have causal relations [Zeno of Citium, by Cicero]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
A concept is only a sortal if it gives genuine identity [Wright,C]
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
A milder claim is that understanding requires some evidence of that understanding [Wright,C]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
A sentence always has signification, but a word by itself never does [Zeno of Citium, by Diog. Laertius]
19. Language / B. Reference / 1. Reference theories
If apparent reference can mislead, then so can apparent lack of reference [Wright,C]
19. Language / C. Assigning Meanings / 3. Predicates
We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Zeno said live in agreement with nature, which accords with virtue [Zeno of Citium, by Diog. Laertius]
Since we are essentially rational animals, living according to reason is living according to nature [Zeno of Citium, by Diog. Laertius]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
The goal is to 'live in agreement', according to one rational consistent principle [Zeno of Citium, by Stobaeus]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Zeno saw virtue as a splendid state, not just a source of splendid action [Zeno of Citium, by Cicero]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
One of Zeno's books was 'That Which is Appropriate' [Zeno of Citium, by Long]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Zeno says there are four main virtues, which are inseparable but distinct [Zeno of Citium, by Plutarch]
27. Natural Reality / C. Space / 1. Void
There is no void in the cosmos, but indefinite void outside it [Zeno of Citium, by Ps-Plutarch]
27. Natural Reality / E. Cosmology / 1. Cosmology
Things are more perfect if they have reason; nothing is more perfect than the universe, so it must have reason [Zeno of Citium]
Since the cosmos produces what is alive and rational, it too must be alive and rational [Zeno of Citium]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Rational is better than non-rational; the cosmos is supreme, so it is rational [Zeno of Citium]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
If tuneful flutes grew on olive trees, you would assume the olive had some knowledge of the flute [Zeno of Citium]
28. God / C. Attitudes to God / 2. Pantheism
The cosmos and heavens are the substance of god [Zeno of Citium, by Diog. Laertius]