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which involves the negative of the subject is a false obversion. We may take as our next illustration of false obversion a proposition which in its original form is negative. This proposition is taken as equivalent to a proposition in which the predicate is affirmed of the negative of the subject. The fallacy occurs in the following argument:

"No trifling business will enrich those engaged in it; a mining speculation is no trifling business; therefore a mining speculation will enrich those engaged in it." (Whately.)

While this reasoning is not likely to mislead, because our knowledge of the facts warns us against the conclusion, we may be a little puzzled to account for the seeming coherence of the argument. Analysis shows that this apparent coherence is due to a false obversion, No trifling business will enrich those engaged in it' being taken as equivalent to,' A business that is not trifling will enrich those engaged in it.' If we grant the truth of this false obverse, then it is true that a mining speculation, which is a business that is not trifling, will enrich those engaged in it. The obversion, however, is false, for it assumes that a statement about' trifling business' warrants a statement about something entirely different, viz., about a' business that is not trifling.'

False Conversion.-It was pointed out that in conversion terms which are undistributed in the original proposition must remain undistributed in the proposition derived by conversion. If the second proposition distributes a term which in the first is not distributed, the scope of that term is extended, which is obviously not permissible. False conversion has to do with

errors in distribution. The following argument is a case in point:

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"When we say that the murderer deserves death,' are we quite sure that we are right as to the fact? Perhaps he may be insane; does he deserve death then?

. . To kill oneself is no better than to kill a fellowcreature; and if temporary insanity be the proper verdict in the one case, why should it not also be proper in the other? Both crimes indicate insensibility to consequences; and what is insensibility to consequences but insanity itself? To us the deed of murder seems so intensely unnatural, so horrible, so awful, that we can only suppose it to be the frenzied conception of a mind violently wrenched from its propriety and responsible to no moral tribunal but the Eternal one.

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In this argument it is asserted that Insensibility to consequences is insanity,' and that the murderer is, therefore, to be considered insane. The only reason, however, that is offered for this opinion is that the crime is so intensely unnatural.' This is hardly conclusive evidence. It seems likely that to the writer the assertion appeared plausible, because Insensibility to consequences is insanity' is not clearly distinguished from Insanity is insensibility to consequences.' The latter of these propositions is presumably true, but does not suffice to give the conclusion; the former does suffice for the conclusion, but its truth is not above suspicion. The two propositions are easily taken as identical, because we tend to pass from Insanity is insensibility to consequences' to 'Insensibility to consequences is insanity,' by simple con. * Eclectic Review, July, 1849, p. 117.

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version. The proposition thus converted, however, is proposition A and must be converted by limitation. The true converse, therefore, is, 'Some insensibility to consequences is insanity.' Granted that this proposition is true, it still remains to be determined whether the insensibility to consequences displayed by the murderer is of the kind that is identical with insanity.

The illustration just cited shows, if the interpretation is correct, how easy it is to confuse a meaning which is true, or at least plausible, but which does not give the desired conclusion, with another meaning which does indeed warrant the conclusion, but which is not true, or at least not beyond serious doubt. The fallacy is not likely to occur, as a rule, except when the subject term and the predicate term of the proposition are very nearly co-extensive. "Thus no one would think of converting the proposition, All United States Senators are members of Congress,' into,' All members of Congress are United States Senators,' but many might fall into the fallacy of converting the proposition, All the Democrats in the Senate voted against the bill,' into, All Senators who voted against the bill were Democrats.'"'*

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# Hibben, Logic, p. 113.

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CHAPTER VI

THE CATEGORICAL SYLLOGISM

The Purpose of the Syllogism.-We have found that classification is important for reasoning, because certain qualities or attributes go together or tend to go together. If we have classified correctly, we are enabled to anticipate experience and say in advance, 'All A is B.' We know that all fire burns, without first testing every possible case of fire, past, present, and future. Such classification is, indeed, frequently surrounded by danger, as the facts of ambiguity attest. By what methods we verify the correctness of our classifications is a problem of extreme importance, but one that must be postponed in favor of another problem of smaller magnitude. The latter is the special problem of the syllogism, and it raises this question: Assuming that certain propositions are true, i.e., that they are accepted without dispute, how can they be made to support some new proposition? This question presupposes that certain classifications are already at hand, and assumes that they are trustworthy. It thus leaves aside the whole subject of ambiguity, and it does not concern itself to ascertain how our original propositions are secured. Its special function is to determine how given propositions must be related to each other, in order to demonstrate the truth of some new proposition.

It should be noted at the outset that the syllogism does not attempt to tell us how reasoning actually goes on, but how the conclusion that is drawn may be justified or necessitated. It deals with the principles that underlie the process of reasoning, and not directly with the reasoning process itself.

The Definition of the Syllogism.-The stock example of a syllogistic argument is the following:

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This argument, when inspected, is found to consist of three propositions, the last one being the conclusion, while the other two are called the premises. The premises are merely unsupported assertions and may at times be wrong. The conclusion, on the other hand, does not stand alone, but sustains to the premises a peculiar relation called validity. To say that a conclusion is valid is not to say that it is true, but that it must be true if the premises are true. A syllogism, therefore, is sufficiently defined if we say that it consists of three propositions so related that one of them is involved or implied in the other two.

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The Parts of the Syllogism.-In order to obtain a valid conclusion, the premises must be related to each other in a certain way. We cannot obtain valid conclusions by combining any two propositions at random. If we had said:

All men are mortal;
Socrates was a Greek;

* Minto, Logic, p. 167.

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