42 ideas
| 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] |
| 9688 | A 'singleton' is a set with only one member [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] |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| 10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
| 10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
| 10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
| 10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |
| 10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
| 10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
| 10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
| 10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
| 10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
| 10787 | Is being just referent of the verb 'to be'? [Marcus (Barcan)] |
| 10789 | Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)] |
| 10796 | If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)] |
| 579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
| 10797 | Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)] |
| 578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |