By: James Creighton
§ 41. Relation of Categorical and Hypothetical Arguments.
— It is evident that the form of the hypothetical syllogism is very different from that of the categorical. But, although this is the case, it must not be supposed that with the former we have passed to a new and wholly distinct type of reasoning. In hypothetical reasoning, as in categorical, it is the presence of a universal principle which enables us to bring into relation two facts which formerly stood apart. Indeed, in many cases, it is a matter of indifference in which form the argument is stated. Thus, we may argue in hypothetical form: —
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If a man is industrious, he will be successful,
A is an industrious man,
Therefore A will be successful.
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The same argument may, however, be expressed equally well in categorical form: —
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All industrious men will be successful,
A is an industrious man,
Therefore A will be successful.
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It is clear that, in spite of the different forms in which the argument is expressed, the reasoning is essentially the same in both cases. The middle term, or general principle which makes it possible to unite the subject and predicate of the conclusion, in the hypothetical as well as in the categorical syllogism, is ‘ industrious.’ A will be successful, we argue, because he is industrious, and it is a rule that industrious men are successful.
Moreover, if an argument is fallacious in one form, it will also be fallacious when expressed in the other. The defects of an argument cannot be cured simply by a change in its form. When an hypothetical argument, in which the antecedent is denied, is expressed categorically, we have the fallacy of the illicit major term. Thus, to state the example of denying the antecedent given on page 146, we get: —
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The case of his being well is a case of his writing,
The present is not a case of his being well,
Therefore the present is not a case of his writing.
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Similarly, when an argument in which the consequent is affirmed is changed to the categorical form, the defect in the reasoning appears as the fallacy of undistributed middle —
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If this tree is an oak, it will have rough bark and acorns,
This tree has rough bark and acorns,
Therefore it is an oak.
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When this argument is expressed in categorical form, it is at once clear that the middle term is not distributed in either the major or minor premise: —
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All oak trees are trees having rough bark and acorns,
This tree is a tree having rough bark and acorns,
Therefore this tree is an oak.
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The change from the categorical to the hypothetical form of argument, then, does not imply any essential change in the nature of the reasoning process itself. Nevertheless, it is important to note that hypothetical propositions and hypothetical arguments emphasize one aspect of thinking, which is entirely neglected by the theory of the categorical syllogism. When dealing with the extension of terms (§ 16), we pointed out that every term, as actually used in a proposition, has both an extensive and an intensive function. That is, the terms of a proposition are employed both to name certain objects or groups of objects, and to connote or imply certain attributes or qualities. In the proposition, ‘ these are oak trees,’ the main purpose is to identify the trees given in perception with the class of oak trees. When, on the other hand, we say,’ ignorant people are superstitious,’ the proposition does not refer directly to any particular individuals, but states the necessary connection between ignorance and superstition. Although the existence of ignorant persons who are also superstitious is presupposed in the proposition, its most prominent function is to assert a connection of attributes which is wholly impersonal. We may perhaps say that, in spite of the categorical form, the proposition is essentially hypothetical in character. Its meaning might very well be expressed by the statement,’ if a man is ignorant, he is also superstitious.’ What is here emphasized is not the fact that ignorant persons exist, and are included in the class of superstitious persons, but rather the general law of the necessary connection of ignorance and superstition. The existence of individuals to whom the law applies is, of course, presupposed by the proposition. It is not, however, its main purpose to directly affirm their existence.
Creighton, James Edwin, 1861-1924
“An Introductory Logic.”
Oshea Davis 