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Quasi-syllogism is a categorical syllogism where one of the premises is singular, and thus not a categorical statement.
For example:
In the above argument, while premise 1 is a categorical, premise 2 is a singular statement referring to one individual. While this is a valid logical form, it is not strictly a categorical syllogism.
Of course, it has been suggested that you can translate any singular statement into a categorical.
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