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. Non-Contradiction

9123	Someone standing in a doorway seems to be both in and not-in 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 first-order non-classical 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

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

9674	{x; A(x)} is a set of objects satisfying the condition A(x)

9676	{a} is the 'singleton' set of a (not the object a itself)

9677	Φ indicates the empty set, which has no members

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

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

9695	An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order

9696	A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets

9698	The 'induction clause' says complex formulas retain the properties of their basic formulas

9689	The 'empty set' or 'null set' has no members

9686	A 'set' is a collection of objects

9687	A 'member' of a set is one of the objects in the set

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

9694	The 'relative complement' is things in the second set not in the first

9692	The 'union' of two sets is a set containing all the things in either of the sets

9693	The 'intersection' of two sets is a set of the things that are in both sets

9691	A 'proper subset' is smaller than the containing set

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. 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

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