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All the ideas for 'Thinking About Mathematics', 'Leibniz' and 'Psychosemantics'

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44 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
'Jocasta' needs to be distinguished from 'Oedipus's mother' because they are connected by different properties [Fodor]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
A particle and a coin heads-or-tails pick out to perfectly well-defined predicates and properties [Fodor]
10. Modality / B. Possibility / 1. Possibility
Early modern possibility is what occurs sometime; for Leibniz, it is what is not contradictory [Arthur,R]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor]
Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor]
Sticklebacks have an innate idea that red things are rivals [Fodor]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / A. Nature of Mind / 1. Mind / e. Questions about mind
In CRTT thought may be represented, content must be [Fodor]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
We can't use propositions to explain intentional attitudes, because they would need explaining [Fodor]
Intentionality doesn't go deep enough to appear on the physicists' ultimate list of things [Fodor]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
Occasionalism contradicts the Eucharist, which needs genuine changes of substance [Arthur,R]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
Behaviourism has no theory of mental causation [Fodor]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
Any piece of software can always be hard-wired [Fodor]
17. Mind and Body / C. Functionalism / 4. Causal Functionalism
Causal powers must be a crucial feature of mental states [Fodor]
17. Mind and Body / C. Functionalism / 6. Homuncular Functionalism
Mind is a set of hierarchical 'homunculi', which are made up in turn from subcomponents [Fodor, by Lycan]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
Supervenience gives good support for mental causation [Fodor]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
Hume's associationism offers no explanation at all of rational thought [Fodor]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
If mind is just physical, how can it follow the rules required for intelligent thought? [Fodor]
18. Thought / A. Modes of Thought / 1. Thought
We may be able to explain rationality mechanically [Fodor]
18. Thought / A. Modes of Thought / 4. Folk Psychology
Folk psychology is the only explanation of behaviour we have [Fodor]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
Belief and desire are structured states, which need mentalese [Fodor]
18. Thought / C. Content / 7. Narrow Content
Obsession with narrow content leads to various sorts of hopeless anti-realism [Fodor]
18. Thought / C. Content / 10. Causal Semantics
Do identical thoughts have identical causal roles? [Fodor]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
Grice thinks meaning is inherited from the propositional attitudes which sentences express [Fodor]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Whatever in the mind delivers falsehood is parasitic on what delivers truth [Fodor]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Many different verification procedures can reach 'star', but it only has one semantic value [Fodor]
19. Language / A. Nature of Meaning / 6. Meaning as Use
The meaning of a sentence derives from its use in expressing an attitude [Fodor]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
Meaning holism is a crazy doctrine [Fodor]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
Very different mental states can share their contents, so content doesn't seem to be constructed from functional role [Fodor]
19. Language / A. Nature of Meaning / 8. Synonymy
Mental states may have the same content but different extensions [Fodor]