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All the ideas for 'fragments/reports', 'Fragments from 1885-1886' and 'Principia Mathematica'

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60 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Different abilities are needed for living in an incomplete and undogmatic system [Nietzsche]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Bad writers use shapeless floating splotches of concepts [Nietzsche]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
A text has many interpretations, but no 'correct' one [Nietzsche]
3. Truth / A. Truth Problems / 3. Value of Truth
What is the search for truth if it isn't moral? [Nietzsche]
Like all philosophers, I love truth [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
Logic is a fiction, which invents the view that one thought causes another [Nietzsche]
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 / a. Numbers
Numbers enable us to manage the world - to the limits of counting [Nietzsche]
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 / B. Change in Existence / 4. Events / c. Reduction of events
Events are just interpretations of groups of appearances [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]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
The 'I' does not think; it is a construction of thinking, like other useful abstractions [Nietzsche]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Appearance is the sole reality of things, to which all predicates refer [Nietzsche]
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
Memory is essential, and is only possible by means of abbreviation signs [Nietzsche]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Schematic minds think thoughts are truer if they slot into a scheme [Nietzsche]
13. Knowledge Criteria / E. Relativism / 1. Relativism
Each of our personal drives has its own perspective [Nietzsche]
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
The mind is a simplifying apparatus [Nietzsche]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
Consciousness is our awareness of our own mental life [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Minds have an excluding drive to scare things off, and a selecting one to filter facts [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving
The greatest drive of life is to discharge strength, rather than preservation [Nietzsche]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
That all events are necessary does not mean they are compelled [Nietzsche]
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]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Concepts are rough groups of simultaneous sensations [Nietzsche]
Concepts don’t match one thing, but many things a little bit [Nietzsche]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
Whatever their origin, concepts survive by being useful [Nietzsche]
19. Language / D. Propositions / 1. Propositions
Thought starts as ambiguity, in need of interpretation and narrowing [Nietzsche]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
Aesthetics can be more basic than morality, in our pleasure in certain patterns of experience [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
Caesar and Napoleon point to the future, when they pursue their task regardless of human sacrifice [Nietzsche]
Napoleon was very focused, and rightly ignored compassion [Nietzsche]
23. Ethics / F. Existentialism / 2. Nihilism
For the strongest people, nihilism gives you wings! [Nietzsche]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The great question is approaching, of how to govern the earth as a whole [Nietzsche]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
The controlling morality of aristocracy is the desire to resemble their ancestors [Nietzsche]
24. Political Theory / D. Ideologies / 14. Nationalism
People feel united as a nation by one language, but then want a common ancestry and history [Nietzsche]
25. Social Practice / C. Rights / 4. Property rights
To be someone you need property, and wanting more is healthy [Nietzsche]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
Laws of nature are actually formulas of power relations [Nietzsche]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
27. Natural Reality / F. Chemistry / 1. Chemistry
In chemistry every substance pushes, and thus creates new substances [Nietzsche]