Combining Texts

All the ideas for 'Consciousness', 'fragments/reports' and 'Principia Mathematica'

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52 ideas

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]
Physicalism requires the naturalisation or rejection of set theory [Lycan]
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 / C. Structure of Existence / 2. Reduction
Institutions are not reducible as types, but they are as tokens [Lycan]
Types cannot be reduced, but levels of reduction are varied groupings of the same tokens [Lycan]
7. Existence / C. Structure of Existence / 3. Levels of Reality
One location may contain molecules, a metal strip, a key, an opener of doors, and a human tragedy [Lycan]
7. Existence / E. Categories / 3. Proposed Categories
I see the 'role'/'occupant' distinction as fundamental to metaphysics [Lycan]
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 / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
I think greenness is a complex microphysical property of green objects [Lycan]
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 / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
Intentionality comes in degrees [Lycan]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Teleological views allow for false intentional content, unlike causal and nomological theories [Lycan]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
Pain is composed of urges, desires, impulses etc, at different levels of abstraction [Lycan]
The right 'level' for qualia is uncertain, though top (behaviourism) and bottom (particles) are false [Lycan]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
If energy in the brain disappears into thin air, this breaches physical conservation laws [Lycan]
In lower animals, psychology is continuous with chemistry, and humans are continuous with animals [Lycan]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
Two behaviourists meet. The first says,"You're fine; how am I?" [Lycan]
17. Mind and Body / C. Functionalism / 1. Functionalism
Functionalism must not be too abstract to allow inverted spectrum, or so structural that it becomes chauvinistic [Lycan]
If functionalism focuses on folk psychology, it ignores lower levels of function [Lycan]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
The distinction between software and hardware is not clear in computing [Lycan]
17. Mind and Body / C. Functionalism / 5. Teleological Functionalism
Teleological characterisations shade off smoothly into brutely physical ones [Lycan]
Mental types are a subclass of teleological types at a high level of functional abstraction [Lycan]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Identity theory is functionalism, but located at the lowest level of abstraction [Lycan]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
We reduce the mind through homuncular groups, described abstractly by purpose [Lycan]
Teleological functionalism helps us to understand psycho-biological laws [Lycan]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
A Martian may exhibit human-like behaviour while having very different sensations [Lycan]
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]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
We need a notion of teleology that comes in degrees [Lycan]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Physical' means either figuring in physics descriptions, or just located in space-time [Lycan]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero]