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LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
A class is a class of so and so's, as in each member of the class has a certain character. (115). Langer uses the following example, bear in mind this was written in the 1950s and 1960s: A man belongs in the class of politicians, only if he is a politician. Being a politician equals being in the class of politician. (115).
Classes have sub-classes (117).
Class: Sheep
Sub-class: White sheep
Sub-class: Black sheep (117).
ε is epsilon from the Greek alphabet meaning is, a. This ε symbol, according to Langer is specifically meant as a symbol for is, a, in contrast with any symbol for is. Admittedly, my research has shown that ε is at times, interpreted in a variety of ways within mathematics, science and philosophy. But, of course this is a review of philosopher, Langer's text.
A=White sheep
B=All sorts of sheep
A is a sub-class of B.
White sheep are a sub-class of all sorts of sheep.
Every white sheep is a sheep. A sub-class of sheep.
(x)=Class
(x) : (x ε A) ⊃ (x ε B) (118).
C=Christians
P=All sorts of people
⊃=Same as
˜ =Not or false
All Christians are people. A sub-class of people.
(x) : (x ε C) ⊃ (x ε P)
There would be several sub-classes of Christians where not everyone would be a member, such as some Christians are Protestants and some are not.
C=Christians
T=Protestants
R=Roman Catholics
(C ⊃ T) & (C ⊃ R) & (T ˜ R)
