### Ideas of Graham Priest, by Theme

#### [British, fl. 2000, 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. Non-Contradiction
 9123 Someone standing in a doorway seems to be both in and not-in the room
###### 4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
 8720 A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions
###### 4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
 9672 Free logic is one of the few first-order non-classical logics
###### 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
 9673 {a1, a2, ...an} indicates that a set comprising just those objects
 9674 {x; A(x)} is a set of objects satisfying the condition A(x)
 9677 Φ indicates the empty set, which has no members
 9676 {a} is the 'singleton' set of a (not the object a itself)
 9679 X⊂Y means set X is a 'proper subset' of set Y
 9681 X = Y means the set X equals the set Y
 9678 X⊆Y means set X is a 'subset' of set Y
 9682 X∪Y indicates the 'union' of all the things in sets X and Y
 9697 X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
 9685
 9675 a ∈ X says a is an object in set X; a ∉ X says a is not in X
 9683 X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
 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
 9695 An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
 9690 A set is a 'subset' of another set if all of its members are in that set
 9688 A 'singleton' is a set with only one member
 9691 A 'proper subset' is smaller than the containing set
 9694 The 'relative complement' is things in the second set not in the first
 9696 A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets
 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
 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
 9693 The 'intersection' of two sets is a set of the things that are in both sets
###### 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)
 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. Burali-Forti's paradox
 13366 The least ordinal greater than the set of all ordinals is both one of them and not one of them