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All the ideas for '', 'Justified Belief as Responsible Belief' and 'The Philosophy of Mathematics'

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15 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Coherentists seek relations among beliefs that are simple, conservative and explanatory [Foley]
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]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
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]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / c. Disjunctivism
Externalists want to understand knowledge, Internalists want to understand justification [Foley]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
We aren't directly pragmatic about belief, but pragmatic about the deliberation which precedes it [Foley]
Justification comes from acceptable procedures, given practical constraints [Foley]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]