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Further review of symbolic logic from American, philosopher, Suzanne K. Langer.
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
From Langer:
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).
'In logic, the symbol stands for a strict concept, namely its definition. and nothing else...' (136). This can restrict, in context, a particular use of a word. Therefore, if one class in included in another, every member of that class is a member of another class. (136). Here the equation A < B is relevant as Class A is included in Class B. And vice-versa, B < A.
A technical use of a word may be broader than its ordinary use. (136). She uses the example:
A < A (136). Class A is included in Class A.
Therefore, every class within a formal context is a subclass of 'I'. (137). Note, in the text, this symbol to me appears to be a rather funny shaped 'I', even upon close inspection. There is a possibility it is another symbol, but by a close look, it appears to be 'I'. This is a case of mutual inclusion and I =I' (137).
She writes
(I' < I) . (I < I') (137).
I' is included in I therefore I is included in I'
I=I'
I reason, therefore:
C=Canadian
N=Canuck
(C < N) ∴ (N < C)
The class of Canadian is included in the class of Canuck, therefore the class of Canuck is included in the class of Canadian.
or
(C < N) . (N < C)
(C ε N) A Canadian is a Canuck.
(N ⊃ C) A Canuck is the same as a Canadian.
(N ⊨ C) A Canuck entails a Canadian.
(C ε N) ∴ (N ⊃ C) . (N ⊨ C)
A Canadian is a Canuck, therefore a Canuck is the same as a Canadian, therefore one being a Canuck entails one being a Canadian.
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
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| Pinterest: I tag myself Reformed as opposed to Calvinist, but an interesting point. |
