Ideas of Graham Priest, by Theme
[British, b.1948, At Queensland University, then Professor at the University of Melbourne, and St Andrew's University.]
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2. Reason / B. Laws of Thought / 3. NonContradiction
9123

Someone standing in a doorway seems to be both in and notin the room [Sorensen]

4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
8720

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

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
9672

Free logic is one of the few firstorder nonclassical logics

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
9697

X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets

9685

<a,b&62; is a set whose members occur in the order shown

9674

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

9673

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

9675

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

9676

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

9677

Φ indicates the empty set, which has no members

9681

X = Y means the set X equals the set Y

9679

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

9678

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

9683

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

9682

X∪Y indicates the 'union' of all the things in sets X and Y

9684

Y  X is the 'relative complement' of X with respect to Y; the things in Y that are not in X

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
9686

A 'set' is a collection of objects

9687

A 'member' of a set is one of the objects in the set

9689

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

9688

A 'singleton' is a set with only one member

9690

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

9691

A 'proper subset' is smaller than the containing set

9694

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

9693

The 'intersection' of two sets is a set of the things that are in both sets

9692

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

9698

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

9696

A 'cartesian product' of sets is the set of all the ntuples with one member in each of the sets

9695

An 'ordered pair' (or ordered ntuple) is a set with its members in a particular order

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
9680

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

5. Theory of Logic / L. Paradox / 1. Paradox
13373

Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / b. König's paradox
13368

The 'least indefinable ordinal' is defined by that very phrase

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
13370

'x is a natural number definable in less than 19 words' leads to contradiction

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
13369

By diagonalization we can define a real number that isn't in the definable set of reals

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. BuraliForti's paradox
13366

The least ordinal greater than the set of all ordinals is both one of them and not one of them

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
13367

The next set up in the hierarchy of sets seems to be both a member and not a member of it

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
13371

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

13372

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