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All the ideas for 'Structures and Structuralism in Phil of Maths', 'talk' and 'A Conversation: what is it? What is it for?'

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31 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
The history of philosophy is an agent of power: how can you think if you haven't read the great names? [Deleuze]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Thought should be thrown like a stone from a war-machine [Deleuze]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims to become the official language, supporting orthodoxy and the state [Deleuze]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
When I meet objections I just move on; they never contribute anything [Deleuze]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
We must create new words, and treat them as normal, and as if designating real things. [Deleuze]
2. Reason / C. Styles of Reason / 1. Dialectic
Don't assess ideas for truth or justice; look for another idea, and establish a relationship with it [Deleuze]
Dualisms can be undone from within, by tracing connections, and drawing them to a new path [Deleuze]
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]
5. Theory of Logic / L. Paradox / 2. Aporiai
Before we seek solutions, it is important to invent problems [Deleuze]
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 / A. Nature of Existence / 3. Being / i. Deflating being
Before Being there is politics [Deleuze]
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 / A. Nature of Mind / 1. Mind / d. Location of mind
A meeting of man and animal can be deterritorialization (like a wasp with an orchid) [Deleuze]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
People consist of many undetermined lines, some rigid, some supple, some 'lines of flight' [Deleuze]
25. Social Practice / A. Freedoms / 2. Freedom of belief
Some lines (of flight) are becomings which escape the system [Deleuze]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
God can't have silly perfections, but how do we decide which ones are 'silly'? [Joslin]