Combining Texts

All the ideas for 'Principia Mathematica', 'The Nature of Thought' and 'The Human Condition'

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55 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Full coherence might involve consistency and mutual entailment of all propositions [Blanshard, by Dancy,J]
3. Truth / D. Coherence Truth / 1. Coherence Truth
Coherence tests for truth without implying correspondence, so truth is not correspondence [Blanshard, by Young,JO]
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]
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]
10. Modality / B. Possibility / 7. Chance
'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes]
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]
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]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
An action may be intended under one description, but not under another [Kekes]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
To control our actions better, make them result from our attitudes, not from circumstances [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
Values are an attempt to achieve well-being by bringing contingencies under control [Kekes]
Values help us to control life, by connecting it to what is stable and manageable [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes]
Practical reason is not universal and impersonal, because it depends on what success is [Kekes]
If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes]
The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes]
We are bound to regret some values we never aspired to [Kekes]
There are far more values than we can pursue, so they are optional possibilities [Kekes]
Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes]
Unconditional commitments are our most basic convictions, saying what must never be done [Kekes]
Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes]
22. Metaethics / B. Value / 2. Values / j. Evil
Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Well-being needs correct attitudes and well-ordered commitments to local values [Kekes]
Control is the key to well-being [Kekes]
23. Ethics / F. Existentialism / 4. Boredom
Boredom destroys our ability to evaluate [Kekes]
Boredom is apathy and restlessness, yearning for something interesting [Kekes]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Society is alienating if it lacks our values, and its values repel us [Kekes]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes]
Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes]
25. Social Practice / B. Equalities / 4. Economic equality
Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes]