Combining Texts

All the ideas for 'fragments/reports', 'Principia Mathematica' and 'Unpublished Notebooks 1872-74'

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57 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom prevents us from being ruled by the moment [Nietzsche]
1. Philosophy / A. Wisdom / 2. Wise People
Unlike science, true wisdom involves good taste [Nietzsche]
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Suffering is the meaning of existence [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
The first aim of a philosopher is a life, not some works [Nietzsche]
You should only develop a philosophy if you are willing to live by it [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / f. Philosophy as healing
Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Philosophy is more valuable than much of science, because of its beauty [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
It would better if there was no thought [Nietzsche]
Why do people want philosophers? [Nietzsche]
Philosophy is always secondary, because it cannot support a popular culture [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
Kant has undermined our belief in metaphysics [Nietzsche]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
If philosophy controls science, then it has to determine its scope, and its value [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 / A. Overview of Logic / 3. Value of Logic
Logic is just slavery to language [Nietzsche]
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 / C. Structure of Existence / 6. Fundamentals / c. Monads
If some sort of experience is at the root of matter, then human knowledge is close to its essence [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 / A. Knowledge / 4. Belief / a. Beliefs
Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
It always remains possible that the world just is the way it appears [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]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Our knowledge is illogical, because it rests on false identities between things [Nietzsche]
The most extreme scepticism is when you even give up logic [Nietzsche]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 9. Perceiving Causation
We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
It is just madness to think that the mind is supernatural (or even divine!) [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]
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 / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Education is contrary to human nature [Nietzsche]
25. Social Practice / E. Policies / 5. Education / d. Study of history
We should evaluate the past morally [Nietzsche]
25. Social Practice / F. Life Issues / 6. Animal Rights
Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche]
26. Natural Theory / C. Causation / 3. Final causes
We do not know the nature of one single causality [Nietzsche]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Laws of nature are merely complex networks of relations [Nietzsche]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche]