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All the ideas for 'Centring', 'Frege's Concept of Numbers as Objects' and 'The Laws'

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89 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 / e. Philosophy as reason
We shouldn't always follow where the argument leads! [Lewis on Plato]
2. Reason / A. Nature of Reason / 1. On Reason
It is foolish to quarrel with the mind's own reasoning processes [Plato]
2. Reason / A. Nature of Reason / 4. Aims of Reason
We ought to follow where the argument leads us [Plato]
2. Reason / A. Nature of Reason / 9. Limits of Reason
Mortals are incapable of being fully rational [Plato]
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 / A. Truth Problems / 3. Value of Truth
Truth has the supreme value, for both gods and men [Plato]
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 / A. Nature of Existence / 3. Being / h. Dasein (being human)
Being is revealed at the point between waking and sleep [Anon (Cent)]
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]
9. Objects / D. Essence of Objects / 4. Essence as Definition
To grasp a thing we need its name, its definition, and what it really is [Plato]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Soul is what is defined by 'self-generating motion' [Plato]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
Neglect your self, and feel the consciousness of each other being [Anon (Cent)]
16. Persons / B. Nature of the Self / 3. Self as Non-physical
My individuality is my soul, which carries my body around [Plato]
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 / 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]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
Just as you have the impulse to do something, stop [Anon (Cent)]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
People who value beauty above virtue insult the soul by placing the body above it [Plato]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
An action is only just if it is performed by someone with a just character and outlook [Plato]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
Attempted murder is like real murder, but we should respect the luck which avoided total ruin [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
It would be strange if the gods rewarded those who experienced the most pleasure in life [Plato]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
The conquest of pleasure is the noblest victory of all [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue is a concord of reason and emotion, with pleasure and pain trained to correct ends [Plato]
A serious desire for moral excellence is very rare indeed [Plato]
Every crime is the result of excessive self-love [Plato]
The only worthwhile life is one devoted to physical and moral perfection [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Virtue is the aim of all laws [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
The Guardians must aim to discover the common element in the four cardinal virtues [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / b. Temperance
Excessive laughter and tears must be avoided [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Injustice is the mastery of the soul by bad feelings, even if they do not lead to harm [Plato]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
The best people are produced where there is no excess of wealth or poverty [Plato]
Virtue and great wealth are incompatible [Plato]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
Totalitarian states destroy friendships and community spirit [Plato]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Education in virtue produces citizens who are active but obedient [Plato]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Bondage and liberation are relative terms, which only frighten those already terrified of the universe [Anon (Cent)]
25. Social Practice / B. Equalities / 1. Grounds of equality
Friendship is impossible between master and slave, even if they are made equal [Plato]
Men and women should qualify equally for honours on merit [Plato]
25. Social Practice / C. Rights / 1. Basis of Rights
Sound laws achieve the happiness of those who observe them [Plato]
25. Social Practice / D. Justice / 1. Basis of justice
Justice is granting the equality which unequals deserve [Plato]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Children's games should channel their pleasures into adult activity [Plato]
Control of education is the key office of state, and should go to the best citizen [Plato]
Mathematics has the widest application of any subject on the curriculum [Plato]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Education is channelling a child's feelings into the right course before it understands why [Plato]
The best way to educate the young is not to rebuke them, but to set a good example [Plato]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
Creation is not for you; you exist for the sake of creation [Plato]
27. Natural Reality / E. Cosmology / 3. The Beginning
Movement is transmitted through everything, and it must have started with self-generated motion [Plato]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
In 'The Laws', to obey the law is to be obey god [Plato, by MacIntyre]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
Self-moving soul has to be the oldest thing there is [Plato]
The only possible beginning for the endless motions of reality is something self-generated [Plato]
Self-generating motion is clearly superior to all other kinds of motion [Plato]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Soul must be the cause of all the opposites, such as good and evil or beauty and ugliness [Plato]
If all the motions of nature reflect calculations of reason, then the best kind of soul must direct it [Plato]
28. God / C. Attitudes to God / 5. Atheism
If astronomical movements are seen as necessary instead of by divine will, this leads to atheism [Plato]
29. Religion / A. Polytheistic Religion / 1. Animism
The heavens must be full of gods, controlling nature either externally or from within [Plato]
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
There must be at least two souls controlling the cosmos, one doing good, the other the opposite [Plato]
29. Religion / C. Spiritual Disciplines / 4. Zen Buddhism
Feel your whole body saturated with cosmic essence [Anon (Cent)]
Abandon attachment to body, and feel the joy of being everywhere [Anon (Cent)]
The serenity in blue sky beyond clouds [Anon (Cent)]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Imagine fire burning up your whole body, but not you [Anon (Cent)]