Zero class?

Majorca, Spain: Facebook. This is one of my favourites, colourized.

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).

Two classes are mutually exclusive if their product is a null-class, as in class A and class B, then A x B = 0. (142). Langer uses the example that there are no individuals that are both Lords and Commons; this class of persons is zero. (142). There are no carnivorous cows. (142). 'A' means carnivorous and 'B' means 'cows', then A x B = 0. (142).

Is this example, Langer changed from A + B to A x B. It appears she is writing that the amount of Lords x (times) the amount of Commons produces no one class of persons. A zero class.

A related entry: April 2017 null class

Theological examples:

There are no individuals that are both

A = Liberal theologians
B = Conservative theologians

For the sake of this argument, they are mutually exclusive. Of course there are theologians with varying positions, but this is a philosophical symbolic logic article and not a primarily theological entry.

Therefore:

A x B = 0

or

L x C = 0

L ⊨ ˜ C

Liberal theologians entail that they are not conservative theologians.

L ˜ ⊃ C

Liberal theologians are not the same as a conservative theologians.

∃! L + ∃! C ∴ R

There exists, liberal theologians plus conservative theologians, therefore, there are religious scholars.

Based on Langer's philosophical symbolic logic; liberal theologians and conservative theologians would be mutually exclusive in a similar way that would be Lords and Commons. They would be of null class, zero class.

However:

Both Lords and Commons would be British citizens. They are both is the class of United Kingdom citizens.

Both liberal theologians and conservative theologians would be in the class of religious scholars.

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