30 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
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] |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
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] |
10885 | Computer proofs don't provide explanations [Horsten] |
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] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
22717 | Self-interest can fairly divide a cake; first person cuts, second person chooses [Poundstone] |
22718 | Formal game theory is about maximising or minimising numbers in tables [Poundstone] |
22719 | The minimax theorem says a perfect game of opposed people always has a rational solution [Poundstone] |
22720 | Two prisoners get the best result by being loyal, not by selfish betrayal [Poundstone] |
22721 | The tragedy in prisoner's dilemma is when two 'nice' players misread each other [Poundstone] |
22722 | TIT FOR TAT says cooperate at first, then do what the other player does [Poundstone] |
22723 | Do unto others as you would have them do unto you - or else! [Poundstone] |