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LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
Chapter 2: The Essentials Of Logical Structure
Continued
I noted the following in comments in the last review of this text, but I now see that I need to include this section in the main body of this post for context.
Langer provides further equations continued from the Chapter: pages 53-54
1. I played bridge with my three cousins
2. I played chess with my three cousins (53)
A=Speaker
B, C, D=Three cousins (54)
A br B, C, D (54)
If in chess each player was played separately
A ch B
A ch C
A ch D
A ch (B-C-D)* (54)
*The hyphen which could also be a + expresses an operation when the two terms are united as one. (54)
So this could be A ch (B+C+D)
I take it here the author means uniting B-C-D, as she explains this will be explained more later and must at this point be taken in faith. (54) It is actually three terms, but I take the point and she means two or more.
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'When a relation-symbol stands in a construct, the number of terms grouped with it reveals the degree of the relation. But when it is not actually used, but merely spoken of, it is sometimes convenient to have some way of denoting its degree. This may be done by adding a numerical subscript; for example, "kd2" means that "killing" is dyadic (a pair), "bt3" that "between" is triadic.' (55).
The examples of different degrees are provided:
ch2
br4 (55)
The author states that two beings named 'John' are not likely to be treated as the same in the language of discourse (56). It is made apparent in context that there is this John and that John. (56).
Symbolic logic provides a new medium of such expression. (57).
For example the following
John a
John b
Are a symbolic way of differentiating between two different persons named John using arbitrary symbols as Langer calls them. (58). Although the example is mine.
Langer writes natural language has a tendency to let one word have and embody many meanings and this leads to in philosophical terms fallacious argumentation and reasoning. (55).
In fact, twisted arguments can be created. (55).
A reason for the use of symbolic logic and reasoning as alternative within philosophy.
In a religious context, philosophy of religion crosses over with theology and there are at times theological arguments that are presented both in natural language and with symbolic logic, and so therefore learning both modes of argumentation is beneficial.
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