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LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
The author's example (125).
Mayflower passengers (Class A).
Founders of Plymouth (Class B).
These are two very different defining concepts. (125). However, every one of the members of Class A was also a member of Class B. (125).
The two classes are mutually inclusive as they have the same membership. (125).
Langer states that Class A and Class B differ in intensions, but they are identical by their extensions. (125). The extension of Class A is the extension of Class B. The two classes, A and B, define the same class. (125).
Intension is the pure meaning. (125).
Extension is the exemplifications of concepts. (125).
Extension allows the reader to observe how classes relate to each other, in common membership. (125-126). If one is left with intension as concept for class alone, it becomes very difficult to systematize such concepts. (126). Without an extension for context, one would see no common connection between Class A and Class B in Langer's example.
Quote
(a) : (a ε B) ⊃ (a ε A) and A includes B and B includes A. (127).
: (Equal (s) )
ε (Epsilon and means is)
⊃ (Is the same as)
⊨ (Entails)
Class A equals Class A is Class B and is the same as Class A is Class A and includes Class B and Class B includes Class A.
a ⊃ b (Class a is the same as Class b)
a ⊨ b (Class a entails Class b).
Simply put by Langer.
A=B (127).
a ⊃ b : a ⊨ b : a = b : a ε b
Class A is the same as Class B equals Class A entails Class B equals Class A equals Class B equals Class A is Class B.
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
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