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Ideas of Graham Priest, by Text
[British, b.1948, At Queensland University, then Professor at the University of Melbourne, and St Andrew's University.]
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1994
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The Structure of Paradoxes of Self-Reference
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§2
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p.27
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13366
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The least ordinal greater than the set of all ordinals is both one of them and not one of them
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§2
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p.27
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13367
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The next set up in the hierarchy of sets seems to be both a member and not a member of it
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§3
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p.28
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13368
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The 'least indefinable ordinal' is defined by that very phrase
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§3
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p.29
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13370
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'x is a natural number definable in less than 19 words' leads to contradiction
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§3
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p.29
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13369
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By diagonalization we can define a real number that isn't in the definable set of reals
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§4
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p.30
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13371
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If you know that a sentence is not one of the known sentences, you know its truth
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§4
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p.30
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13372
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There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar
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§5
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p.32
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13373
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Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong
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1998
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What is so bad about Contradictions?
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p.73
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9123
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Someone standing in a doorway seems to be both in and not-in the room [Sorensen]
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p.160
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8720
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A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Friend]
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2001
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Intro to Non-Classical Logic (1st ed)
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Pref
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p.-9
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9672
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Free logic is one of the few first-order non-classical logics
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0.1.0
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p.-5
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9697
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X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
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0.1.10
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p.-6
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9685
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<a,b&62; is a set whose members occur in the order shown
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0.1.10
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p.-6
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9695
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An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
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0.1.10
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p.-5
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9696
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A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets
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0.1.2
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p.-7
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9673
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{a1, a2, ...an} indicates that a set comprising just those objects
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0.1.2
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p.-7
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9675
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a ∈ X says a is an object in set X; a ∉ X says a is not in X
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0.1.2
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p.-7
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9674
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{x; A(x)} is a set of objects satisfying the condition A(x)
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0.1.2
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p.-7
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9686
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A 'set' is a collection of objects
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0.1.2
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p.-7
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9687
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A 'member' of a set is one of the objects in the set
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0.1.4
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p.-7
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9688
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A 'singleton' is a set with only one member
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0.1.4
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p.-7
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9689
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The 'empty set' or 'null set' has no members
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0.1.4
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p.-7
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9676
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{a} is the 'singleton' set of a (not the object a itself)
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0.1.4
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p.-7
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9677
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Φ indicates the empty set, which has no members
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0.1.6
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p.-6
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9679
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X⊂Y means set X is a 'proper subset' of set Y
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0.1.6
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p.-6
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9681
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X = Y means the set X equals the set Y
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0.1.6
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p.-6
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9678
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X⊆Y means set X is a 'subset' of set Y
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0.1.6
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p.-6
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9691
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A 'proper subset' is smaller than the containing set
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0.1.6
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p.-6
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9690
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A set is a 'subset' of another set if all of its members are in that set
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0.1.6
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p.-6
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9680
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The empty set Φ is a subset of every set (including itself)
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0.1.8
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p.-6
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9694
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The 'relative complement' is things in the second set not in the first
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0.1.8
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p.-6
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9692
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The 'union' of two sets is a set containing all the things in either of the sets
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0.1.8
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p.-6
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9693
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The 'intersection' of two sets is a set of the things that are in both sets
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0.1.8
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p.-6
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9683
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X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
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0.1.8
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p.-6
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9682
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X∪Y indicates the 'union' of all the things in sets X and Y
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0.1.8
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p.-6
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9684
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Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X
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0.2
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p.-5
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9698
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The 'induction clause' says complex formulas retain the properties of their basic formulas
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