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| Yesterday |
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
From the previous entry:
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).
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The idea that Class A in included in Class B, allows for the use of a symbol to be employed. (134).
Here I should acknowledge that the Langer text becomes potentially confusing. She admits that the symbol < within mathematics stands for 'is less than'. (134). However, the author provides an exception from this common case (134) and suggests that within symbolic logic the symbol can stand for 'is included in.' (134).
Therefore her example:
A < B
Class A is included in Class B (Symbolic logic) (134-135).
This opposed to
A < B
Class A is less than Class B (Mathematics).
A reminder that in academics identical terms and symbols may vary from discipline to discipline. This was also the case in archived entries on this website in regard to certain terms with philosophy versus statistical mathematics/social research methods.
≡df=Equivalence by definition (135).
: (Equal (s) )
ε (Epsilon and means is)
⊃ (Is the same as)
⊨ (Entails)
Based on Langer's definition from 135.
A < B ≡df (x) : (x ε A) ⊃ (x ε B)
Class A is included in Class B, is defined as the equivalent of x which equals x is A, which is the same as x is B.
It could also be stated
A ⊨ B
Class A entails Class B.
A reminder that the usefulness of learning symbolic logic is in reading some academic philosophical work that contains symbol logic within argumentation.
This learning may also assist one in understanding mathematics. Philosophy of religion does overlap with theology that overlaps with biblical studies. That is a main reason I am reviewing and learning the text.
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