Combining Texts

All the ideas for 'Frege's Concept of Numbers as Objects', 'Human, All Too Human' and 'Structure and Ontology'

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


92 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
The highest wisdom has the guise of simplicity [Nietzsche]
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 / 7. Despair over Philosophy
Deep thinkers know that they are always wrong [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 8. Humour
Comedy is a transition from fear to exuberance [Nietzsche]
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 finds fewest champions not when it is dangerous, but when it is boring [Nietzsche]
3. Truth / A. Truth Problems / 7. Falsehood
Convictions, more than lies, are the great enemy of truth [Nietzsche]
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]
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 / B. Certain Knowledge / 1. Certainty
Being certain presumes that there are absolute truths, and means of arriving at them [Nietzsche]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuition only recognises what is possible, not what exists or is certain [Nietzsche]
16. Persons / C. Self-Awareness / 2. Knowing the Self
Just as skin hides the horrors of the body, vanity conceals the passions of the soul [Nietzsche]
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 / 3. Abstracta by Ignoring
A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
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 / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
People always do what they think is right, according to the degree of their intellect [Nietzsche]
Our judgment seems to cause our nature, but actually judgment arises from our nature [Nietzsche]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
Why are the strong tastes of other people so contagious? [Nietzsche]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Artists are not especially passionate, but they pretend to be [Nietzsche]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Nietzsche said the will doesn't exist, so it can't ground moral responsibility [Nietzsche, by Foot]
The history of morality rests on an error called 'responsibility', which rests on an error called 'free will' [Nietzsche]
Ceasing to believe in human responsibility is bitter, if you had based the nobility of humanity on it [Nietzsche]
It is absurd to blame nature and necessity; we should no more praise actions than we praise plants or artworks [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Intellect is tied to morality, because it requires good memory and powerful imagination [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
Originally it was the rulers who requited good for good and evil for evil who were called 'good' [Nietzsche]
22. Metaethics / B. Value / 2. Values / f. Altruism
No one has ever done anything that was entirely for other people [Nietzsche]
22. Metaethics / B. Value / 2. Values / g. Love
Simultaneous love and respect are impossible; love has no separation or rank, but respect admits power [Nietzsche]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
We get enormous pleasure from tales of noble actions [Nietzsche]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
We can only achieve happy moments, not happy eras [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
First morality is force, then custom, then acceptance, then instinct, then a pleasure - and finally 'virtue' [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
You are mastered by your own virtues, but you must master them, and turn them into tools [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
The 'good' man does the moral thing as if by nature, easily and gladly, after a long inheritance [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
All societies of good men give a priority to gratitude [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Justice (fairness) originates among roughly equal powers (as the Melian dialogues show) [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
Pity consoles those who suffer, because they see that they still have the power to hurt [Nietzsche]
Apart from philosophers, most people rightly have a low estimate of pity [Nietzsche]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Many people are better at having good friends than being a good friend [Nietzsche]
Women can be friends with men, but only some physical antipathy will maintain it [Nietzsche]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
In Homer it is the contemptible person, not the harmful person, who is bad [Nietzsche]
23. Ethics / F. Existentialism / 1. Existentialism
We could live more naturally, relishing the spectacle, and not thinking we are special [Nietzsche]
23. Ethics / F. Existentialism / 4. Boredom
People do not experience boredom if they have never learned to work properly [Nietzsche]
23. Ethics / F. Existentialism / 5. Existence-Essence
Over huge periods of time human character would change endlessly [Nietzsche]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
If self-defence is moral, then so are most expressions of 'immoral' egoism [Nietzsche]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The state aims to protect individuals from one another [Nietzsche]
24. Political Theory / B. Nature of a State / 5. Culture
Culture cannot do without passions and vices [Nietzsche]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
If we want the good life for the greatest number, we must let them decide on the good life [Nietzsche]
25. Social Practice / A. Freedoms / 1. Slavery
Slavery cannot be judged by our standards, because the sense of justice was then less developed [Nietzsche]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
Laws that are well thought out, or laws that are easy to understand? [Nietzsche]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
Execution is worse than murder, because we are using the victim, and really we are the guilty [Nietzsche]
25. Social Practice / E. Policies / 1. War / a. Just wars
People will enthusiastically pursue an unwanted war, once sacrifices have been made [Nietzsche]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
Don't crush girls with dull Gymnasium education, the way we have crushed boys! [Nietzsche]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Education in large states is mediocre, like cooking in large kitchens [Nietzsche]
Interest in education gains strength when we lose interest in God [Nietzsche]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Teachers only gather knowledge for their pupils, and can't be serious about themselves [Nietzsche]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
In religious thought nature is a complex of arbitrary acts by conscious beings [Nietzsche]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
Modern man wants laws of nature in order to submit to them [Nietzsche]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The Greeks saw the gods not as their masters, but as idealised versions of themselves [Nietzsche]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Science rejecting the teaching of Christianity in favour of Epicurus shows the superiority of the latter [Nietzsche]
The Sermon on the Mount is vanity - praying to one part of oneself, and demonising the rest [Nietzsche]
Christ was the noblest human being [Nietzsche]
Christ seems warm hearted, and suppressed intellect in favour of the intellectually weak [Nietzsche]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion is tempting if your life is boring, but you can't therefore impose it on the busy people [Nietzsche]