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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.]
1994

The Structure of Paradoxes of SelfReference

§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

§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

13371

If you know that a sentence is not one of the known sentences, you know its truth

§4

p.30

13372

There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar

§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 notin the room [Sorensen]


p.160

8720

A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Friend]

2001

Intro to NonClassical Logic (1st ed)

Pref

p.9

9672

Free logic is one of the few firstorder nonclassical 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 ntuple) 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 ntuples with one member in each of the sets

0.1.2

p.7

9673

{a1, a2, ...an} indicates that a set comprising just those objects

0.1.2

p.7

9675

a ∈ X says a is an object in set X; a ∉ X says a is not in X

0.1.2

p.7

9674

{x; A(x)} is a set of objects satisfying the condition A(x)

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

0.1.4

p.7

9689

The 'empty set' or 'null set' has no members

0.1.4

p.7

9688

A 'singleton' is a set with only one member

0.1.4

p.7

9676

{a} is the 'singleton' set of a (not the object a itself)

0.1.4

p.7

9677

Φ indicates the empty set, which has no members

0.1.6

p.6

9681

X = Y means the set X equals the set Y

0.1.6

p.6

9679

X⊂Y means set X is a 'proper subset' of set Y

0.1.6

p.6

9678

X⊆Y means set X is a 'subset' of set Y

0.1.6

p.6

9690

A set is a 'subset' of another set if all of its members are in that set

0.1.6

p.6

9691

A 'proper subset' is smaller than the containing set

0.1.6

p.6

9680

The empty set Φ is a subset of every set (including itself)

0.1.8

p.6

9692

The 'union' of two sets is a set containing all the things in either of the sets

0.1.8

p.6

9694

The 'relative complement' is things in the second set not in the first

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

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

9683

X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets

0.2

p.5

9698

The 'induction clause' says complex formulas retain the properties of their basic formulas
