1 7 3V a l i d i t y f o r C a t e g o r i c a l A r g u m e n t s- All M is P.
Some S is not M.
∴ Some S is not P. - All M is P.
Some M is not S.
∴ Some S is not P. - No M is P.
Some S is M.
∴ Some S is not P. - No P is M.
Some S is M.
∴ Some S is not P. - No P is M.
Some S is not M.
∴ Some S is not P. - No M is P.
Some S is not M.
∴ Some S is not P - No P is M.
Some M is not S.
∴ Some S is not P. - No P is M.
No M is S.
∴ No S is P. - No P is M
All M is S.
∴ No S is P. - No P is M.
All S is M.
∴ No S is P. - All P is M.
No S is M.
∴ No S is P. - All M is P.
No S is M.
∴ No S is P. - Some M is P.
Some M is not S.
∴ Some S is not P. - Some P is M.
Some S is not M.
∴ Some S is P.
Explain why it is a good strategy to diagram a universal premise before
diagramming a particular premise in a syllogism with both.Exercise VIIIPro b l e m s i n aP Pl y i n g T h e Th e o r y o f T h e sy l l o g i s m. After mastering
the techniques for evaluating syllogisms, students naturally turn to
arguments that arise in daily life and attempt to use these newly acquired
skills. They are often disappointed with the results. The formal theory of the
syllogism seems to bear little relationship to everyday arguments, and there
does not seem to be any easy way to bridge the gap.
This gap between formal theory and its application occurs for a number
of reasons. First, as we saw in Chapters 2 and 5, our everyday discourse
leaves much unstated. Many things are conversationally implied rather97364_ch07_ptg01_151-176.indd 173 15/11/13 10:29 AM
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