Ideas from 'Intro to NonClassical Logic (1st ed)' by Graham Priest [2001], by Theme Structure
[found in 'Introduction to NonClassical Logic' by Priest,Graham [CUP 2001,052179434x]].
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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
9672

Free logic is one of the few firstorder nonclassical logics




Full Idea:
Free logic is an unusual example of a nonclassical logic which is firstorder.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], Pref)

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




Full Idea:
X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets, the set of all the ntuples with its first member in X1, its second in X2, and so on.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.0)

9685

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




Full Idea:
<a,b> is a set whose members occur in the order shown; <x1,x2,x3, ..xn> is an 'ntuple' ordered set.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.10)

9675

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




Full Idea:
a ∈ X means that a is a member of the set X, that is, a is one of the objects in X. a ∉ X indicates that a is not in X.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.2)

9674

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




Full Idea:
{x; A(x)} indicates a set of objects which satisfy the condition A(x).




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.2)

9673

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




Full Idea:
{a1, a2, ...an} indicates that the set comprises of just those objects.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.2)

9677

Φ indicates the empty set, which has no members




Full Idea:
Φ indicates the empty set, which has no members




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.4)

9676

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




Full Idea:
{a} is the 'singleton' set of a, not to be confused with the object a itself.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.4)

9679

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




Full Idea:
X⊂Y means set X is a 'proper subset' of set Y (if and only if all of its members are members of Y, but some things in Y are not in X)




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.6)

9678

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




Full Idea:
X⊆Y means set X is a 'subset' of set Y (if and only if all of its members are members of Y).




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.6)

9681

X = Y means the set X equals the set Y




Full Idea:
X = Y means the set X equals the set Y, which means they have the same members (i.e. X⊆Y and Y⊆X).




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.6)

9683

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




Full Idea:
X ∩ Y indicates the 'intersection' of sets X and Y, which is a set containing just those things that are in both X and Y.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.8)

9682

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




Full Idea:
X ∪ Y indicates the 'union' of sets X and Y, which is a set containing just those things that are in X or Y (or both).




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.8)

9684

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




Full Idea:
Y  X indicates the 'relative complement' of X with respect to Y, that is, all the things in Y that are not in X.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.8)

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
9688

A 'singleton' is a set with only one member




Full Idea:
A 'singleton' is a set with only one member.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.4)

9689

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




Full Idea:
The 'empty set' or 'null set' is a set with no members.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.4)

9690

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




Full Idea:
A set is a 'subset' of another set if all of its members are in that set.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.6)

9691

A 'proper subset' is smaller than the containing set




Full Idea:
A set is a 'proper subset' of another set if some things in the large set are not in the smaller set




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.6)

9694

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




Full Idea:
The 'relative complement' of one set with respect to another is the things in the second set that aren't in the first.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.8)

9693

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




Full Idea:
The 'intersection' of two sets is a set containing the things that are in both sets.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.8)

9692

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




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




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.8)

9698

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




Full Idea:
The 'induction clause' says that whenever one constructs more complex formulas out of formulas that have the property P, the resulting formulas will also have that property.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.2)

9695

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




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




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.10)

9696

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




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




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.10)

9686

A 'set' is a collection of objects




Full Idea:
A 'set' is a collection of objects.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.2)

9687

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




Full Idea:
A 'member' of a set is one of the objects in the set.




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.2)

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)




Full Idea:
The empty set Φ is a subset of every set (including itself).




From:
Graham Priest (Intro to NonClassical Logic (1st ed) [2001], 0.1.6)
