45 ideas
| 8952 | We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher] |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| 8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
| 8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| 8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher] |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| 8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher] |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| 8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |
| 8944 | Vagueness can involve components (like baldness), or not (like boredom) [Fisher] |
| 8941 | We can't explain 'possibility' in terms of 'possible' worlds [Fisher] |
| 8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher] |
| 8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |