I continue with the Langer, text review.
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
---
At times within symbolic logic, two classes might not be identical, and yet the classes overlap (138). There is at least one individual in class A that is a member of class B. (138).
If class A and class B were identical:
(x ε A) . (x ε B) (138).
X is Class A, therefore X is Class B.
Also:
(A x B < A) . (A x B < B)
Class A x Class B is included in Class A, therefore, Class A x Class B is included in Class B. (139).
A red apple belongs in the class of red things. (139). Below.
(x ε red thing) . (x ε apple) (139). Langer uses apple.
The defining function of two classes is placed into a class. (139).
But I can also observe using symbolic logic:
(x ε red thing) ˜ (x ε green apple)
A green apple does not belong in the class of a red thing.
Not all Englishmen (A) are socialists. (B). (139). Langer uses this example.
A ˜ B
Not all Englishmen are socialists. But there are English socialists that would be a subclass of both Englishmen and socialists. (139). The product of two classes producing English socialists. Note, female philosopher Langer uses the term Englishmen. This textbook was published in 1967, and originally 1953, and the English language has of course evolved in fifty years and previous.
I reason:
(∃! ES)
or
(∃! x ES)
There exists English socialists.
There exists English x socialists.
(A ˜ B) . (∃! A) . (∃! B) ⊨ (∃! ES).
Not all English are socialists, therefore the English exist, therefore socialists exist, this entails English socialists exist.
 |
| Very demotivational.com |
