Brief on contradiction

Northern Canada

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy)

Langer uses the example of the wife of King Arthur (122) as in there is at least one element under this concept. (122). One element is within this class. Class is also defined as 'sort'. (122). If there is no wife of King Arthur, then there is nothing of the sort. (122). This is null class.

This operation generates the complement (-a). 'Null' class means that means 'all its members' equals none at all. This null class could be 'No wives of King Arthur'. (123).

Langer explains that for every (a) there is at least one (-a). (192). The proposition which defines the nature (-a) is stated to describe the operation (-), upon the element (a). (192).

She further goes on to explain that the element might of course (as it is symbolic logic) have any name we like. The symbols (b) or (c) could be used. Wherever there is (a), there is the operation (b), or wherever there is (a), there is the operation (c). (192). But she explains that this type of symbolism would be correct but not helpful. (193).

From page 199:

'For every a there is at least one element -a such that the sum of a and -a is the universe class, and their product is the null class.' (199). If a is a universe class of Christians and -a is the universe class of no Christians, their product would be a null class. This means there is nothing of the sort that is a class of both Christians and not Christians. This would be contradiction.

a=Christian (s)
-a=No Christian (s)

a+-a = 0

Christian universe class plus no Christian universe class equals null class.

(a) ⊨ (-a) = 0

Christian universe class entails (would entail) no Christian universe class equals null class.

Practically, it can be reasoned that if one is sorted out as the category of Christian, there needs to be theological and philosophical consistency with premises that would define one as Christian in contrast to contradictory premises of one that is not Christian. 'Null' class means that means 'all its members' equals none at all. (123). The null class of Christians not Christians.

Now I will opine that if this was just a class of human beings, then it would not be null class, but if no human beings was introduced as a class then again it would be null class. The product would be null class.

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications,
New York. (Philosophy)

Key symbols

≡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
cls = Class
int = Interpretation