1994 | The Structure of Paradoxes of Self-Reference |
§2 | p.27 | 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it |
§2 | p.27 | 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them |
§2 | p.27 | 13365 | Russell's Paradox is a stripped-down version of Cantor's Paradox |
§3 | p.28 | 13368 | The 'least indefinable ordinal' is defined by that very phrase |
§3 | p.29 | 13369 | By diagonalization we can define a real number that isn't in the definable set of reals |
§3 | p.29 | 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction |
§4 | p.30 | 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar |
§4 | p.30 | 13371 | If you know that a sentence is not one of the known sentences, you know its truth |
§5 | p.32 | 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong |
1998 | What is so bad about Contradictions? |
p.73 | 9123 | Someone standing in a doorway seems to be both in and not-in the room |
1998 | works |
p.160 | 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions |
2001 | Intro to Non-Classical Logic (1st ed) |
Pref | p.-9 | 9672 | Free logic is one of the few first-order non-classical logics |
0.1.0 | p.-5 | 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets |
0.1.10 | p.-6 | 9685 | <a,b&62; is a set whose members occur in the order shown |
0.1.10 | p.-6 | 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order |
0.1.10 | p.-5 | 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets |
0.1.2 | p.-7 | 9686 | A 'set' is a collection of objects |
0.1.2 | p.-7 | 9687 | A 'member' of a set is one of the objects in the set |
0.1.2 | p.-7 | 9673 | {a1, a2, ...an} indicates that a set comprising just those objects |
0.1.2 | p.-7 | 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) |
0.1.2 | p.-7 | 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X |
0.1.4 | p.-7 | 9688 | A 'singleton' is a set with only one member |
0.1.4 | p.-7 | 9677 | Φ indicates the empty set, which has no members |
0.1.4 | p.-7 | 9676 | {a} is the 'singleton' set of a (not the object a itself) |
0.1.4 | p.-7 | 9689 | The 'empty set' or 'null set' has no members |
0.1.6 | p.-6 | 9680 | The empty set Φ is a subset of every set (including itself) |
0.1.6 | p.-6 | 9679 | X⊂Y means set X is a 'proper subset' of set Y |
0.1.6 | p.-6 | 9681 | X = Y means the set X equals the set Y |
0.1.6 | p.-6 | 9678 | X⊆Y means set X is a 'subset' of set Y |
0.1.6 | p.-6 | 9691 | A 'proper subset' is smaller than the containing set |
0.1.6 | p.-6 | 9690 | A set is a 'subset' of another set if all of its members are in that set |
0.1.8 | p.-6 | 9694 | The 'relative complement' is things in the second set not in the first |
0.1.8 | p.-6 | 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets |
0.1.8 | p.-6 | 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X |
0.1.8 | p.-6 | 9693 | The 'intersection' of two sets is a set of the things that are in both sets |
0.1.8 | p.-6 | 9682 | X∪Y indicates the 'union' of all the things in sets X and Y |
0.1.8 | p.-6 | 9692 | The 'union' of two sets is a set containing all the things in either of the sets |
0.2 | p.-5 | 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas |