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All the ideas for 'Protagoras', 'Frege's Concept of Numbers as Objects' and 'The Gay (Joyful) Science'

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82 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 / F. Analytic Philosophy / 5. Linguistic Analysis
Grammar only reveals popular metaphysics [Nietzsche]
2. Reason / B. Laws of Thought / 4. Contraries
Only one thing can be contrary to something [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
Is the will to truth the desire to avoid deception? [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
Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
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]
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 / c. Becoming
We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche]
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 / D. Universals / 6. Platonic Forms / c. Self-predication
If asked whether justice itself is just or unjust, you would have to say that it is just [Plato]
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]
10. Modality / A. Necessity / 2. Nature of Necessity
Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
The strength of knowledge is not its truth, but its entrenchment in our culture [Nietzsche]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
The most important things in life are wisdom and knowledge [Plato]
The only real evil is loss of knowledge [Plato]
12. Knowledge Sources / B. Perception / 1. Perception
We became increasingly conscious of our sense impressions in order to communicate them [Nietzsche]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
We have no organ for knowledge or truth; we only 'know' what is useful to the human herd [Nietzsche]
13. Knowledge Criteria / E. Relativism / 1. Relativism
We assume causes, geometry, motion, bodies etc to live, but they haven't been proved [Nietzsche]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
Nietzsche's perspectivism says our worldview depends on our personality [Nietzsche, by Fogelin]
It would be absurd to say we are only permitted our own single perspective [Nietzsche]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / d. Purpose of consciousness
All of our normal mental life could be conducted without consciousness [Nietzsche]
Only the need for communication has led to consciousness developing [Nietzsche]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
Only our conscious thought is verbal, and this shows the origin of consciousness [Nietzsche]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
Most of our lives, even the important parts, take place outside of consciousness [Nietzsche]
Whatever moves into consciousness becomes thereby much more superficial [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
Everything resembles everything else up to a point [Plato]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
'Know thyself' is impossible and ridiculous [Nietzsche]
18. Thought / A. Modes of Thought / 1. Thought
Thoughts cannot be fully reproduced in words [Nietzsche]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Most of our intellectual activity is unconscious [Nietzsche]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C]
A concept is only a sortal if it gives genuine identity [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 / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Courage is knowing what should or shouldn't be feared [Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Why do you listen to the voice of your conscience? [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
Higher human beings see and hear far more than others, and do it more thoughtfully [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
A morality ranks human drives and actions, for the sake of the herd, and subordinating individuals [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Nietzsche thought it 'childish' to say morality isn't binding because it varies between cultures [Nietzsche, by Foot]
22. Metaethics / B. Value / 2. Values / j. Evil
No one willingly and knowingly embraces evil [Plato]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
Some things are good even though they are not beneficial to men [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato]
Some pleasures are not good, and some pains are not evil [Plato]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
No two actions are the same [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Many virtues are harmful traps, but that is why other people praise them [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
If we punish wrong-doers, it shows that we believe virtue can be taught [Plato]
Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato]
Socrates did not believe that virtue could be taught [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
You cannot advocate joyful wisdom while rejecting pity, because the two are complementary [Scruton on Nietzsche]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
To see one's own judgement as a universal law is selfish [Nietzsche]
23. Ethics / F. Existentialism / 1. Existentialism
We should give style to our character - by applying an artistic plan to its strengths and weaknesses [Nietzsche]
23. Ethics / F. Existentialism / 2. Nihilism
The ethical teacher exists to give purpose to what happens necessarily and without purpose [Nietzsche]
23. Ethics / F. Existentialism / 4. Boredom
To ward off boredom at any cost is vulgar [Nietzsche]
23. Ethics / F. Existentialism / 7. Existential Action
The best life is the dangerous life [Nietzsche]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
Imagine if before each of your actions you had to accept repeating the action over and over again [Nietzsche]
Nietzsche says facing up to the eternal return of meaninglessness is the response to nihilism [Nietzsche, by Critchley]
28. God / C. Attitudes to God / 5. Atheism
God is dead, and we have killed him [Nietzsche]