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Ideas of Graham Priest, by Text

[British, fl. 2000, At Queensland University, then Professor at the University of Melbourne, and St Andrew's University.]

1994 The Structure of Paradoxes of Self-Reference
2 p.27 The least ordinal greater than the set of all ordinals is both one of them and not one of them
2 p.27 Russell's Paradox is a stripped-down version of Cantor's Paradox
2 p.27 The next set up in the hierarchy of sets seems to be both a member and not a member of it
3 p.28 The 'least indefinable ordinal' is defined by that very phrase
3 p.29 'x is a natural number definable in less than 19 words' leads to contradiction
3 p.29 By diagonalization we can define a real number that isn't in the definable set of reals
4 p.30 If you know that a sentence is not one of the known sentences, you know its truth
4 p.30 There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar
5 p.32 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 Someone standing in a doorway seems to be both in and not-in the room
1998 works
p.160 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 Free logic is one of the few first-order non-classical logics
0.1.0 p.-5 X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
0.1.10 p.-6 <a,b&62; is a set whose members occur in the order shown
0.1.10 p.-6 An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
0.1.10 p.-5 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 A 'set' is a collection of objects
0.1.2 p.-7 A 'member' of a set is one of the objects in the set
0.1.2 p.-7 a ∈ X says a is an object in set X; a ∉ X says a is not in X
0.1.2 p.-7 {x; A(x)} is a set of objects satisfying the condition A(x)
0.1.2 p.-7 {a1, a2,} indicates that a set comprising just those objects
0.1.4 p.-7 {a} is the 'singleton' set of a (not the object a itself)
0.1.4 p.-7 Φ indicates the empty set, which has no members
0.1.4 p.-7 A 'singleton' is a set with only one member
0.1.4 p.-7 The 'empty set' or 'null set' has no members
0.1.6 p.-6 A set is a 'subset' of another set if all of its members are in that set
0.1.6 p.-6 A 'proper subset' is smaller than the containing set
0.1.6 p.-6 The empty set Φ is a subset of every set (including itself)
0.1.6 p.-6 X = Y means the set X equals the set Y
0.1.6 p.-6 X⊆Y means set X is a 'subset' of set Y
0.1.6 p.-6 X⊂Y means set X is a 'proper subset' of set Y
0.1.8 p.-6 X∪Y indicates the 'union' of all the things in sets X and Y
0.1.8 p.-6 X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
0.1.8 p.-6 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 The 'union' of two sets is a set containing all the things in either of the sets
0.1.8 p.-6 The 'relative complement' is things in the second set not in the first
0.1.8 p.-6 The 'intersection' of two sets is a set of the things that are in both sets
0.2 p.-5 The 'induction clause' says complex formulas retain the properties of their basic formulas