Combining Texts

All the ideas for 'works', 'Unpublished Notebooks 1881-82' and 'Principia Mathematica'

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70 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Seeing with other eyes is more egoism, but exploring other perspectives leads to objectivity [Nietzsche]
3. Truth / A. Truth Problems / 3. Value of Truth
I tell the truth, even if it is repulsive [Nietzsche]
The pain in truth is when it destroys a belief [Nietzsche]
3. Truth / A. Truth Problems / 8. Subjective Truth
We don't create logic, time and space! The mind obeys laws because they are true [Nietzsche]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
To think about being we must have an opinion about what it is [Nietzsche]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Essences are fictions needed for beings who represent things [Nietzsche]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
There is no proof that we forget things - only that we can't recall [Nietzsche]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
Our inclinations would not conflict if we were a unity; we imagine unity for our multiplicity [Nietzsche]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
Freud treats the unconscious as intentional and hence mental [Freud, by Searle]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Freud and others have shown that we don't know our own beliefs, feelings, motive and attitudes [Freud, by Shoemaker]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
We contain many minds, which fight for the 'I' of the mind [Nietzsche]
18. Thought / A. Modes of Thought / 1. Thought
Thoughts are signs (just as words are) [Nietzsche]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Freud said passions are pressures of some flowing hydraulic quantity [Freud, by Solomon]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
19. Language / F. Communication / 1. Rhetoric
Great orators lead their arguments, rather than following them [Nietzsche]
19. Language / F. Communication / 5. Pragmatics / b. Implicature
The pragmatics of language is more comprehensible than the meaning [Nietzsche]
20. Action / A. Definition of Action / 1. Action Theory
Actions are just a release of force. They seize on something, which becomes the purpose [Nietzsche]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
Drives make us feel non-feelings; Will is the effect of those feelings [Nietzsche]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
We need lower and higher drives, but they must be under firm control [Nietzsche]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
Our motives don't explain our actions [Nietzsche]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
People who miss beauty seek the sublime, where even the ugly shows its 'beauty' [Nietzsche]
The sublimity of nature which dwarfs us was a human creation [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
We can aspire to greatness by creating new functions for ourselves [Nietzsche]
Greeks might see modern analysis of what is human as impious [Nietzsche]
Once a drive controls the intellect, it rules, and sets the goals [Nietzsche]
Freud is pessimistic about human nature; it is ambivalent motive and fantasy, rather than reason [Freud, by Murdoch]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
For absolute morality a goal for mankind is needed [Nietzsche]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
We always assign values, but we may not value those values [Nietzsche]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Humans are vividly aware of short-term effects, and almost ignorant of the long-term ones [Nietzsche]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Happiness is the active equilibrium of our drives [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Actual morality is more complicated and subtle than theory (which gets paralysed) [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / i. Absolute virtues
Some things we would never do, even for the highest ideals [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
You should not want too many virtues; one is enough [Nietzsche]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Talk of 'utility' presupposes that what is useful to people has been defined [Nietzsche]
23. Ethics / F. Existentialism / 1. Existentialism
The goal is to settle human beings, like other animals, but humans are still changeable [Nietzsche]
23. Ethics / F. Existentialism / 2. Nihilism
My eternal recurrence is opposed to feeling fragmented and imperfect [Nietzsche]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
See our present lives as eternal! Religions see it as fleeting, and aim at some different life [Nietzsche]
The eternal return of wastefulness is a terrible thought [Nietzsche]
25. Social Practice / B. Equalities / 1. Grounds of equality
Justice says people are not equal, and should become increasingly unequal [Nietzsche]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
Reasons that justify punishment can also justify the crime [Nietzsche]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Do away with punishment. Counter-retribution is as bad as the crime [Nietzsche]
25. Social Practice / E. Policies / 1. War / e. Peace
If you don't want war, remove your borders; but you set up borders because you want war [Nietzsche]
25. Social Practice / E. Policies / 5. Education / d. Study of history
Our growth is too subtle to perceive, and long events are too slow for us to grasp [Nietzsche]
27. Natural Reality / C. Space / 2. Space
Unlike time, space is subjective. Empty space was assumed, but it doesn't exist [Nietzsche]
27. Natural Reality / G. Biology / 2. Life
Life is forces conjoined by nutrition, to produce resistance, arrangement and value [Nietzsche]