can involve relations between classes of things. In this case it can be
represented in the following way:
Components
Relationships
Major Premise
Class Q includes Class P
Minor Premise
Class P includes Class R
Conclusion
Therefore Class Q includes Class R
Figure 5.3 Syllogism: Predicate Logic A
Alternatively, the express reference to classes can be omitted and substituted
by the verb ‘to be’. This makes the syllogism in the following form:
Components
Relationships
Major Premise
All P are Q
Minor Premise
All R are P
Conclusion
Therefore all R are Q
Figure 5.4 Syllogism: Predicate Logic B
Soundness of a Syllogism
While it probably seems intuitive from discussion so far that a syllogism yields
a conclusion that is true, it is necessary to explain this further. An argument in
a syllogism is sound if two conditions are satisfied. First, both the major
premise and the minor premise are true in fact. Second, the relationship
between the truth of the two premises and the conclusion is logically valid.
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Let us now illustrate this where we assume that Daffy is a Duck. To do this we
will consider a number of syllogisms that are conveniently numbered Syllogism
1, Syllogism 2 and so on. Syllogism 1 says as follows:
Syllogism 1
Major Premise
All ducks are birds
Minor Premise
Daffy is a Duck
Conclusion
Therefore Daffy is a bird
Figure 5.5 Syllogism: Sound Form
Clearly Syllogism 1 is sound. Both premises are true in fact and the reasoning
process is valid.
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This is explained in the following way in Antony Flew (ed), 1979, A
Dictionary of Philosophy, under “Syllogism”: “If the argument is indeed valid, it is
so in virtue of the fact that it would not be possible to assert the premise and to
deny the conclusion without contradicting oneself”.
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