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LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
The Langer philosophy text review, continues.
Some key symbols from the textbook:
≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
· = Therefore
< = Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable
Two complementary classes not only divide the universe between them (universe of discourse, my add), but they are mutually exclusive. (145).
Christians and non-Christians would divide a universe of discourse. (My add).
Christians = A
Non-Christians= -A
This philosophically would encompass the entirety of humanity as a universe of discourse.
Christians = A
Non-Christians= -A
One form is a denial of the other. (145). As consequence, no element in the universe can be true of both forms, and no individual can be of both classes. (145).
Taking this concept to biblical studies and theology:
Christians = A
Non-Christians= -A
Example:
A
Mathew 28: 18-20: New Testament, disciples.
-A
Mathew 28: 18-20: New Testament, non-disciples.
Please see comments section for more examples.
Langer writes that this is a negative statement:
(∃x) : ˜ (x ε A) (145).
x Exists does not equal x is A.
or
x does not equal x is A.
This is in a positive form:
(∃x) : x ε -A (145).
x Exists equals x is not A.
or
x equals x is not A.
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