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LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
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'The elements which may be meant by a variable symbol are called values. Here again we encounter the use of "value" in a mathematical sense, not to be confounded with any sort of "worth". (87).
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'A value for a variable is any element which the variable may denote. The entire class of possible values for a variable, i.e. of individual elements it may signify is called the range of significance of the variable. (87).
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'In the expression "a fm a" (a is the fellowman of a, or a is in fellowship with a, my add) within our formal context, the range of the variable a is the entire universe of discourse. (87).
Universe of discourse explained previously as according to Langer, quoted from a previous entry:
'The total collection of those and only those elements which belong to a formal context is called a Universe of Discourse. (68).
She states further:
'Any element whatever may be substituted for a, and the result will be a proposition which is either true or false. (88).
But she notes that the two terms a fm a, may be in dyadic relation (88) which is describing the interaction between a pair of individuals. Therefore, Langer reasons that the terms a and b are not 'necessarily distinct.' (88). The first and second mentioned elements may be the same element. 'If the same variable appears in both places, then we know the terms denoted are identical.' (88). If different variables occur, it is not known whether or not they are identical.(88).
Specification is when a specific value is assigned a value. (88). It is not the same as interpretation, where a symbol is commissioned with a meaning.
Interpretation fixes the terms with a universe of discourse and an equation. (88).
From Langer, it is explained as a equals, by specification, the element C. Therefore a=C. This does not tell us that a denotes the sort of thing called a house, but which house it denotes: the house named C.
'The range of significance of a variable, then, is the class of all those and only those elements which may be substituted for it by 'specification.'
In other words, specification in symbolic logic is a specific denotation for a symbol.
My examples:
Interpretation would be h=house
Specification would be w=wood cabin house.
As much as symbolic logic is meant to be a more reasonable and clear approach to dialogue than the linguistic syntax approach, I deduce that this parsing between interpretation and specification will lead to confusion in many instances.
Is explaining the difference between h (house) and w (wood cabin house), or a (a house) and C (a specific house), within symbolic logic going to be simpler than writing the concept out in sentence and paragraph form in English? I think this depends on context and audience.
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