42 ideas
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 3756 | Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske] |
| 3757 | Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske] |
| 3759 | You can acquire new knowledge by exploring memories [Bernecker/Dretske] |
| 3752 | Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske] |
| 3753 | Foundationalism aims to avoid an infinite regress [Bernecker/Dretske] |
| 3754 | Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske] |
| 3755 | Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske] |
| 3761 | Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske] |
| 3760 | Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske] |
| 2584 | Lobotomised patients can cease to care about a pain [Block] |
| 2582 | A brain looks no more likely than anything else to cause qualia [Block] |
| 2574 | Behaviour requires knowledge as well as dispositions [Block] |
| 2576 | In functionalism, desires are internal states with causal relations [Block] |
| 2575 | Functionalism is behaviourism, but with mental states as intermediaries [Block] |
| 2583 | You might invert colours, but you can't invert beliefs [Block] |
| 2578 | Could a creature without a brain be in the right functional state for pain? [Block] |
| 2585 | Not just any old functional network will have mental states [Block] |
| 2586 | In functionalism, what are the special inputs and outputs of conscious creatures? [Block] |
| 2579 | Physicalism is prejudiced in favour of our neurology, when other systems might have minds [Block] |
| 2577 | Simple machine-functionalism says mind just is a Turing machine [Block] |
| 2580 | A Turing machine, given a state and input, specifies an output and the next state [Block] |
| 3758 | Semantic externalism ties content to the world, reducing error [Bernecker/Dretske] |
| 2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |