A class of dogs is simply a class of dogs

Tonight, walking back from the Boss's place...

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

The review continues...

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

Last time with this review:

Langer 212-213

Philosopher Langer on page 214 further explains that in symbolic logic the uniqueness of 0 and 1 is guaranteed and therefore a more important equation as the system of the Law of Tautology can be shown. (214).

Tautology is repeating the same idea, not identically.

These propositions are called 'tautology' because they show that no matter how many times a term is mentioned in a sum or in a product (within symbolic logic, my add), a product is not changed by being multiplied or by something in it, nor a sum by having one of its summands added to it. (215).

To simplify, she writes:

A class of dogs is simply a class of dogs. (215).

Adding of multiplying dogs in that class, does not change the fact it is only and simply a class of dogs.

Therefore,  my examples:

z= Dogs

z x z = z

z + z = z
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This text is becoming increasingly technical, but practically, philosophically and theologically, the logic here assists with concepts such as...

The infinite class (God) is simply infinite, nothing can be multiplied or added to that class.

The finite class is simply finite, nothing can be multiplied or added to that class.

This logic would counter philosophies and theologies reasoning the finite can become infinite.

i = infinite
f = finite

i ˜ ⊃ f

The infinite is not the same as the finite.

i ˜ ⊨ f

The infinite does not entail the finite.

Tonight