Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Letters to Bouvet' and 'The Inessential Indexical'

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38 ideas

2. Reason / E. Argument / 1. Argument
A 'teepee' argument has several mutually supporting planks to it [Cappelen/Dever]
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]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
16. Persons / C. Self-Awareness / 2. Knowing the Self
Prioprioception focuses on your body parts, not on your self, or indexicality [Cappelen/Dever]
We can acquire self-knowledge with mirrors, not just with proprioception and introspection [Cappelen/Dever]
Proprioception is only immune from error if you are certain that it represents the agent [Cappelen/Dever]
17. Mind and Body / C. Functionalism / 1. Functionalism
Folk Functionalism is a Ramsification of our folk psychology [Cappelen/Dever]
18. Thought / A. Modes of Thought / 9. Indexical Thought
It is assumed that indexical content is needed to represent the perspective of perception [Cappelen/Dever]
Indexicality is not significantly connected to agency [Cappelen/Dever]
If some of our thought is tied to its context, it will be hard to communicate it [Cappelen/Dever]
All information is objective, and purely indexical information is not much use [Cappelen/Dever]
You don't remember your house interior just from an experienced viewpoint [Cappelen/Dever]
Our beliefs and desires are not organised around ourselves, but around the world [Cappelen/Dever]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregeans can't agree on what 'senses' are [Cappelen/Dever]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Possible worlds accounts of content are notoriously coarse-grained [Cappelen/Dever]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
Indexicals are just non-constant in meaning, and don't involve any special concepts [Cappelen/Dever]
Fregeans say 'I' differs in reference, so it must also differ in sense [Cappelen/Dever]
All indexicals can be expressed non-indexically [Cappelen/Dever]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
The basic Kaplan view is that there is truth-conditional content, and contextual character [Cappelen/Dever]
It is proposed that a huge range of linguistic items are context-sensitive [Cappelen/Dever]
20. Action / C. Motives for Action / 2. Acting on Beliefs / b. Action cognitivism
We deny that action involves some special class of beliefs [Cappelen/Dever]
23. Ethics / D. Deontological Ethics / 1. Deontology
We want good education and sociability, rather than lots of moral precepts [Leibniz]