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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Intending' and 'Mind and Body'

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35 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / C. Structure of Existence / 2. Reduction
A weaker kind of reductionism than direct translation is the use of 'bridge laws' [Kirk,R]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
Maybe we should see intentionality and consciousness as a single problem, not two [Kirk,R]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
If a bird captures a worm, we could say its behaviour is 'about' the worm [Kirk,R]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Behaviourism says intentionality is an external relation; language of thought says it's internal [Kirk,R]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
Dualism implies some brain events with no physical cause, and others with no physical effect [Kirk,R]
17. Mind and Body / B. Behaviourism / 1. Behaviourism
Behaviourism seems a good theory for intentional states, but bad for phenomenal ones [Kirk,R]
Behaviourism offers a good alternative to simplistic unitary accounts of mental relationships [Kirk,R]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
In 'holistic' behaviourism we say a mental state is a complex of many dispositions [Kirk,R]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
The inverted spectrum idea is often regarded as an objection to behaviourism [Kirk,R]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
All meaningful psychological statements can be translated into physics [Kirk,R]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
Instead of representation by sentences, it can be by a distribution of connectionist strengths [Kirk,R]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
If mental states are multiply realisable, they could not be translated into physical terms [Kirk,R]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
It seems unlikely that most concepts are innate, if a theory must be understood to grasp them [Kirk,R]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
For behaviourists language is just a special kind of behaviour [Kirk,R]
19. Language / B. Reference / 1. Reference theories
Behaviourists doubt whether reference is a single type of relation [Kirk,R]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
An intending is a judgement that the action is desirable [Davidson]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
Davidson gave up reductive accounts of intention, and said it was a primitive [Davidson, by Wilson/Schpall]