37 ideas
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
20014 | Actions include: the involuntary, the purposeful, the intentional, and the self-consciously autonomous [Wilson/Schpall] |
20019 | Maybe bodily movements are not actions, but only part of an agent's action of moving [Wilson/Schpall] |
20021 | Is the action the arm movement, the whole causal process, or just the trying to do it? [Wilson/Schpall] |
20022 | To be intentional, an action must succeed in the manner in which it was planned [Wilson/Schpall] |
20023 | If someone believes they can control the lottery, and then wins, the relevant skill is missing [Wilson/Schpall] |
20025 | We might intend two ways to acting, knowing only one of them can succeed [Wilson/Schpall] |
20031 | On one model, an intention is belief-desire states, and intentional actions relate to beliefs and desires [Wilson/Schpall] |
20028 | Groups may act for reasons held by none of the members, so maybe groups are agents [Wilson/Schpall] |
20027 | If there are shared obligations and intentions, we may need a primitive notion of 'joint commitment' [Wilson/Schpall] |
20016 | Strong Cognitivism identifies an intention to act with a belief [Wilson/Schpall] |
20017 | Weak Cognitivism says intentions are only partly constituted by a belief [Wilson/Schpall] |
20018 | Strong Cognitivism implies a mode of 'practical' knowledge, not based on observation [Wilson/Schpall] |
20012 | Maybe the explanation of an action is in the reasons that make it intelligible to the agent [Wilson/Schpall] |
20029 | Causalists allow purposive explanations, but then reduce the purpose to the action's cause [Wilson/Schpall] |
20013 | It is generally assumed that reason explanations are causal [Wilson/Schpall] |