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LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
Briefly, back to the Langer, philosophical text in Symbolic Logic, which I am slowly, due to other projects, reviewing from cover to cover:
A statement of a system in entirely specific terms requires a particular statement and equation for each assertion. In a general account, it requires fewer statements and equations. (101). Therefore, 'K (L, M, N, O, P, Q, R, S) fm2'
K=interpreted as "creatures".
fm=interpreted as "fellowman of" (101). Or as I explain, in fellowship with. Langer explains, that 'of every two creatures it is either true or false that one is the other's fellowman.' (101).
Some key symbols from the text
˜ = not
⊃ = means the same as
∃ = there exists
∃! = there exists
⊨ = entails (new for my review)
Therefore
(a)˜ (a fm a)=A is not the fellowman of a. One is not the fellowman of self. (101).
(a fm b) ⊃ (b fm a) =A is the fellowman of b means the same as b is the fellowman of a. (101).
John is the fellowman of James, means the same as James is the fellowman of John.
(a fm b) ⊨ (b fm a) =A is the fellowman of b, entails b is the fellowman of a.
Langer writes it is not explained in this system anything beyond that these elements have been documented as creatures. Elements may even be one and the same creature. (102). If, within a different system, two of the creatures were the same, even as represented by two different elements; for example (a, b) were the same creature:
˜ (a fm b)=A is not the fellowman of b, as they are one and the same creature. (102).
This is mental gymnastics, but what can be reasoned is the need for an understanding of a philosophical system in context. A review is required that does not reasonably go beyond the information provided.
