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
Someone standing in a doorway seems to be both in and not-in the room
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
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
X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets
Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X
X = Y means the set X equals the set Y
X⊆Y means set X is a 'subset' of set Y
X⊂Y means set X is a 'proper subset' of set Y
X∪Y indicates the 'union' of all the things in sets X and Y
X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets
<a,b&62; is a set whose members occur in the order shown
a ∈ X says a is an object in set X; a ∉ X says a is not in X
{x; A(x)} is a set of objects satisfying the condition A(x)
{a1, a2, ...an} indicates that a set comprising just those objects
{a} is the 'singleton' set of a (not the object a itself)
Φ indicates the empty set, which has no members
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'empty set' or 'null set' has no members
A set is a 'subset' of another set if all of its members are in that set
A 'proper subset' is smaller than the containing set
The 'union' of two sets is a set containing all the things in either of the sets
The 'relative complement' is things in the second set not in the first
The 'intersection' of two sets is a set of the things that are in both sets
The 'induction clause' says complex formulas retain the properties of their basic formulas
An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order
A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets
A 'set' is a collection of objects
A 'member' of a set is one of the objects in the set
A 'singleton' is a set with only one member
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
The empty set Φ is a subset of every set (including itself)
5. Theory of Logic / L. Paradox / 1. Paradox
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
The 'least indefinable ordinal' is defined by that very phrase
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
'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
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
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 / d. Russell's paradox
Russell's Paradox is a stripped-down version of Cantor's Paradox
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
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
If you know that a sentence is not one of the known sentences, you know its truth
There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar