Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Jerry A. Fodor on himself' and 'Davidson on himself'

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40 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Truth and objectivity depend on a community of speakers to interpret what they mean [Davidson]
There are no ultimate standards of rationality, since we only assess others by our own standard [Davidson]
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]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Associations are held to connect Ideas together in the way the world is connected together [Fodor]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
There are no such things as minds, but people have mental properties [Davidson]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Intentional science needs objects with semantic and causal properties, and which obey laws [Fodor]
Intentional states and processes may be causal relations among mental symbols [Fodor]
17. Mind and Body / D. Property Dualism / 1. Reductionism critique
If the mind is an anomaly, this makes reduction of the mental to the physical impossible [Davidson]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
Obviously all mental events are causally related to physical events [Davidson]
There are no strict psychophysical laws connecting mental and physical events [Davidson]
Mental entities do not add to the physical furniture of the world [Davidson]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
The correct conclusion is ontological monism combined with conceptual dualism [Davidson]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Most psychological properties seem to be multiply realisable [Fodor]
18. Thought / A. Modes of Thought / 4. Folk Psychology
Folk psychology explains behaviour by reference to intentional states like belief and desire [Fodor]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Absence of all rationality would be absence of thought [Davidson]
18. Thought / C. Content / 6. Broad Content
Our meanings are partly fixed by events of which we may be ignorant [Davidson]
How could the extrinsic properties of thoughts supervene on their intrinsic properties? [Fodor]
19. Language / D. Propositions / 6. Propositions Critique
Propositions explain nothing without an explanation of how sentences manage to name them [Davidson]
19. Language / F. Communication / 4. Private Language
Thought is only fully developed if we communicate with others [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
There is simply no alternative to the 'principle of charity' in interpreting what others do [Davidson]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Without a teacher, the concept of 'getting things right or wrong' is meaningless [Davidson]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Cause and effect relations between events must follow strict laws [Davidson]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
Laws are true generalisations which support counterfactuals and are confirmed by instances [Fodor]