All truth is God's truth: I
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
· = Conjunction meaning And
0= Null class
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To combine various classes, that are not the same, through the use disjunction or conjunction, positive statements are required to connect membership. (145-146). Langer's example:
C = Cats D = Dogs
(x) : x ε C ⊃ (x ε -D) (146).
Variable equals variable is Cats, is the same as variable is not Dogs.
Philosopher Langer then once again discusses null class (147). Null class is the class which has incompatible properties (147). She suggests for example, a class of cats and not-cats.
x ε A . x ε -A (147).
Variable is cats and variable is not cats. Based on Langer's writing, this is an incompatible premise.
0 represents null class.
(x ε 0) ⊃ (x ε A) . (x ε -A)
Null class is the same as the class of cats and the class of not-cats.
0 ⊨ A . -A
or
0 ⊨ C . -C
Null class entails the class of cats and the class of not-cats.
The null class 0 is included in each complementary pair (147). Every class has a complement and therefore every class includes null class 0. (147).
0 < A
Null class is included in each class. (147).
Practical theology? This is technical philosophical material and even somewhat mathematical. It will help one to read academic materials within philosophy that use symbolic logic. But thinking in theological terms, I appreciate how each class has its complement, its opposite. Therefore, for example, a Christian has a non-Christian as opposite. Academically in both philosophy and theology logic and reason demands that opposites are complementary and cannot be intellectually spun to be otherwise based on worldviews that oppose biblical Christianity.
All truth is God's truth and here philosophy lends support.
