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All the ideas for 'Frege's Concept of Numbers as Objects', 'Rationale and Maxims in Study of Concepts' and 'Launching Points to the Realm of the Mind'

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58 ideas

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 / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy has its own mode of death, by separating soul from body [Porphyry]
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]
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 / 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 / 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]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
The presence of the incorporeal is only known by certain kinds of disposition [Porphyry]
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]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
Diversity arises from the power of unity [Porphyry]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Memory is not conserved images, but reproduction of previous thought [Porphyry]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
The soul is everywhere and nowhere in the body, and must be its cause [Porphyry]
16. Persons / C. Self-Awareness / 2. Knowing the Self
Successful introspection reveals the substrate along with the object of thought [Porphyry]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
The soul is bound to matter by the force of its own disposition [Porphyry]
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 / 3. Ontology of Concepts / a. Concepts as representations
If concepts just are mental representations, what of concepts we may never acquire? [Peacocke]
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 / 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 / e. Human nature
Justice is each person fulfilling his function [Porphyry]
22. Metaethics / B. Value / 2. Values / g. Love
We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry]
Civil virtues control the passions, and make us conform to our nature [Porphyry]
Purificatory virtues detach the soul completely from the passions [Porphyry]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
There are practical, purificatory, contemplative, and exemplary virtues [Porphyry]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
Time is the circular movement of the soul [Porphyry]
27. Natural Reality / D. Time / 1. Nature of Time / e. Eventless time
Some think time is seen at rest, as well as in movement [Porphyry]
28. God / A. Divine Nature / 2. Divine Nature
God is nowhere, and hence everywhere [Porphyry]
28. God / C. Attitudes to God / 2. Pantheism
Everything existing proceeds from divinity, and is within divinity [Porphyry]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry]
Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry]