Combining Texts

All the ideas for 'Lewis's Programme', 'The Philosophy of Mathematics' and 'Substitutional Classes and Relations'

expand these ideas     |    start again     |     specify just one area for these texts


13 ideas

2. Reason / D. Definition / 7. Contextual Definition
Any linguistic expression may lack meaning when taken out of context [Russell]
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
8. Modes of Existence / A. Relations / 1. Nature of Relations
There is no complexity without relations, so no propositions, and no truth [Russell]
10. Modality / B. Possibility / 9. Counterfactuals
Problems with Goodman's view of counterfactuals led to a radical approach from Stalnaker and Lewis [Horwich]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Analyse counterfactuals using causation, not the other way around [Horwich]