Combining Texts

All the ideas for 'Principia Mathematica', 'On 'Generation and Corruption'' and 'Mind, Brain and the Quantum'

expand these ideas     |    start again     |     specify just one area for these texts


47 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
There is nothing so obvious that a philosopher cannot be found to deny it [Lockwood]
1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
There may only be necessary and sufficient conditions (and counterfactuals) because we intervene in the world [Lockwood]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
No one has ever succeeded in producing an acceptable non-trivial analysis of anything [Lockwood]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
If something is described in two different ways, is that two facts, or one fact presented in two ways? [Lockwood]
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 were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
'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 / D. Theories of Reality / 2. Realism
How does a direct realist distinguish a building from Buckingham Palace? [Lockwood]
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 / f. Animal beliefs
Dogs seem to have beliefs, and beliefs require concepts [Lockwood]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Empiricism is a theory of meaning as well as of knowledge [Lockwood]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
Commonsense realism must account for the similarity of genuine perceptions and known illusions [Lockwood]
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]
15. Nature of Minds / A. Nature of Mind / 8. Brain
A 1988 estimate gave the brain 3 x 10-to-the-14 synaptic junctions [Lockwood]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
How come unconscious states also cause behaviour? [Lockwood]
Could there be unconscious beliefs and desires? [Lockwood]
15. Nature of Minds / B. Features of Minds / 7. Blindsight
Fish may operate by blindsight [Lockwood]
16. Persons / C. Self-Awareness / 1. Introspection
We might even learn some fundamental physics from introspection [Lockwood]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Can phenomenal qualities exist unsensed? [Lockwood]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
If mental events occur in time, then relativity says they are in space [Lockwood]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
Only logical positivists ever believed behaviourism [Lockwood]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
Identity theory likes the identity of lightning and electrical discharges [Lockwood]
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 / A. Nature of Meaning / 5. Meaning as Verification
Perhaps logical positivism showed that there is no dividing line between science and metaphysics [Lockwood]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Elements are found last in dismantling bodies, and first in generating them [Albert of Saxony]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Maybe causation is a form of rational explanation, not an observation or a state of mind [Lockwood]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
We have the confused idea that time is a process of change [Lockwood]