30 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] |
7508 | Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
7510 | Connectionists say the mind is a general purpose learning device [Pinker] |
7513 | Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker] |
7509 | Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker] |
6981 | Determinism clashes with free will, as the past determines action, and is beyond our control [Inwagen, by Jackson] |
7511 | Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker] |
7512 | There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG] |
7505 | Many think that accepting human nature is to accept innumerable evils [Pinker] |
7516 | In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker] |
7515 | All the evidence says evolution is cruel and wasteful, not intelligent [Pinker] |
7514 | Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker] |