Many categorical syllogisms that are not in standard form as written can be translated into standard form syllogism. The goal is to produce an argument consisting of three standard form categorical propositions that contain a total of three different terms, each of which is used twice in distinct propositions. Since this task involves not only the translation of the component statements into standard form but the adjustment of these statements one to another so that their terms occur in matched pairs, a certain amount of practice is usually required before it can be done with any facility. In reducing the terms to three matched pairs it is often helpful to identify some factor common to two or all three propositions and express this common factor through the strategic use of the parameters. Consider the following argument:
Henry must have overslept this morning because he was late for work,
and is never late for work unless he oversleeps.
All three statements are about Henry, but if the parameter “persons identical to Henry” were selected it would have to be used more than twice. The temporal adverbs in the argument “this morning” and “never,” suggest that “times” might be used. Following this suggestion, we have:
All times identical to this morning are times Henry overslept, because all times identical to this morning are times Henry is late for work, and all times Henry is late for work are times Henry overslept.
We now have a standard form categorical syllogism. If we adopt the following convention,
A = times identical to this morning
B = times Henry overslept
C = times Henry is late for work
The syllogism may then be symbolized as follows:
All C are B. All times Henry is late for work are times Henry overslept
All A are C. All times identical to this morning are times Henry is late for work.
All A are B. Therefore, all times identical to this morning are times Henry overslept.
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