Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'The Protestant Ethic and the Spirit of Capitalism' and 'Mental Content'

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36 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]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Some explanations offer to explain a mystery by a greater mystery [Schulte]
18. Thought / C. Content / 1. Content
Naturalist accounts of representation must match the views of cognitive science [Schulte]
On the whole, referential content is seen as broad, and sense content as narrow [Schulte]
Naturalists must explain both representation, and what is represented [Schulte]
Phenomenal and representational character may have links, or even be united [Schulte]
Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte]
Maybe we can explain mental content in terms of phenomenal properties [Schulte]
18. Thought / C. Content / 9. Conceptual Role Semantics
Conceptual role semantics says content is determined by cognitive role [Schulte]
18. Thought / C. Content / 10. Causal Semantics
Cause won't explain content, because one cause can produce several contents [Schulte]
18. Thought / C. Content / 11. Teleological Semantics
Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte]
Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte]
18. Thought / C. Content / 12. Informational Semantics
Information theories say content is information, such as smoke making fire probable [Schulte]
23. Ethics / D. Deontological Ethics / 2. Duty
The idea of duty in one's calling haunts us, like a lost religion [Weber]
24. Political Theory / D. Ideologies / 11. Capitalism
Acquisition and low consumption lead to saving, investment, and increased wealth [Weber]
When asceticism emerged from the monasteries, it helped to drive the modern economy [Weber]
Capitalism is not unlimited greed, and may even be opposed to greed [Weber]
Modern western capitalism has free labour, business separate from household, and book-keeping [Weber]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Punish the heretic, but be indulgent to the sinner [Weber]