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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Persistence, Change and Explanation' and 'Pragmatism - eight lectures'

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46 ideas

3. Truth / A. Truth Problems / 9. Rejecting Truth
Truth is just a name for verification-processes [James]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
In many cases there is no obvious way in which ideas can agree with their object [James]
3. Truth / D. Coherence Truth / 1. Coherence Truth
Ideas are true in so far as they co-ordinate our experiences [James]
New opinions count as 'true' if they are assimilated to an individual's current beliefs [James]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
True ideas are those we can assimilate, validate, corroborate and verify (and false otherwise) [James]
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
By using aporiai as his start, Aristotle can defer to the wise, as well as to the many [Haslanger]
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 / D. Theories of Reality / 1. Ontologies
Ontology disputes rest on more basic explanation disputes [Haslanger]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
A 'thing' is simply carved out of reality for human purposes [James]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
'Substance' is just a word for groupings and structures in experience [James]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
The persistence of objects seems to be needed if the past is to explain the present [Haslanger]
Persistence makes change and its products intelligible [Haslanger]
9. Objects / E. Objects over Time / 5. Temporal Parts
We must explain change amongst 'momentary entities', or else the world is inexplicable [Haslanger]
If the things which exist prior to now are totally distinct, they need not have existed [Haslanger]
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
Truth is a species of good, being whatever proves itself good in the way of belief [James]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism accepts any hypothesis which has useful consequences [James]
14. Science / B. Scientific Theories / 2. Aim of Science
Theories are practical tools for progress, not answers to enigmas [James]
14. Science / B. Scientific Theories / 3. Instrumentalism
Pragmatism says all theories are instrumental - that is, mental modes of adaptation to reality [James]
True thoughts are just valuable instruments of action [James]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Natural explanations give the causal interconnections [Haslanger]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Best explanations, especially natural ones, need grounding, notably by persistent objects [Haslanger]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
We return to experience with concepts, where they show us differences [James]
28. God / A. Divine Nature / 3. Divine Perfections
If there is a 'greatest knower', it doesn't follow that they know absolutely everything [James]
28. God / A. Divine Nature / 4. Divine Contradictions
It is hard to grasp a cosmic mind which produces such a mixture of goods and evils [James]
28. God / B. Proving God / 1. Proof of God
If the God hypothesis works well, then it is true [James]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
The wonderful design of a woodpecker looks diabolical to its victims [James]
Things with parts always have some structure, so they always appear to be designed [James]
28. God / B. Proving God / 3. Proofs of Evidence / d. Religious Experience
Private experience is the main evidence for God [James]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
Nirvana means safety from sense experience, and hindus and buddhists are just afraid of life [James]