As we explain in the Introduction to Induction and Deduction, an argument is inductive if its major premise is based on observation or experience, and deductive if its major premise is based on a rule, law, principle, or generalization. In general, there are two distinct ways of expressing a deductive argument: as a syllogism, or as a conditional. Any deductive argument can be expressed as either a syllogism or a conditional, though some arguments may seem to lend themselves more naturally to one form or the other. Similarly, tests for the validity of syllogisms and conditionals may appear quite different, but do essentially the same thing.
Syllogisms: The major premise of a syllogism states that something, Y, is or is not true for all or part of some group, X; the minor premise affirms or denies that some group or individual, Z, is part of X; and the argument then concludes whether that thing Y (from the major premise) is true or not true for that group or individual Z (from the minor premise). One form of a syllogism can be expressed by the following paradigm:
Consider the following example:
We can restate the argument as follows:
Second, in order to avoid confusion, it is always best to use a state-of-being verb (for example, forms of the verb "to be") in the restatement of an argument, and convert the original verbs to other parts of speech. In this case, "received" has become a participial phrase, "receiving instructions," that functions as a noun.
Conditionals: The other common form of a deductive argument, a conditional, expresses that same reasoning in a different way. The major premise is, If something is true of P, then something is true of Q. The minor premise either affirms that it is true of P, or denies that it is true of Q. In the former case, the argument concludes that the something is true of Q; in the latter, that something is not true of P. One form of a conditional is expressed by the following paradigm:
The above example could be given in the form of a conditional as follows:
In the form of the paradigm above, this conditional can be restated as follows:
Notice that a conditional seems to use only two terms (P and Q), while a syllogism uses three (X, Y, and Z). But the third term is actually there. In our example, it is Mandia who is "in class," and Mandia who "received instruction."
Summary. Consider this example:
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