Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Kinds of Minds' and 'Principia Mathematica'

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39 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]
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]
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]
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 / 1. Mind / e. Questions about mind
Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
What is it like to notice an uncomfortable position when you are asleep? [Dennett]
16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett]
17. Mind and Body / C. Functionalism / 6. Homuncular Functionalism
We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
Maybe there is a minimum brain speed for supporting a mind [Dennett]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett]
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 / B. Mechanics of Thought / 4. Language of Thought
The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
Concepts are things we (unlike dogs) can think about, because we have language [Dennett]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
25. Social Practice / F. Life Issues / 3. Abortion
Most people see an abortion differently if the foetus lacks a brain [Dennett]
27. Natural Reality / G. Biology / 2. Life
Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett]