The conclusion of an argument may sometimes be left unexpressed. If the antecedents are strong and the conclusion obvious it weakens the argument to state the conclusion in full, besides reflecting on the capacity of the reader or hearer to draw the conclusion for himself. Hence we find at the end of controversial and indignant writings such expressions as—'Comment is superfluous'—'We leave the reader to draw his own conclusions,'—or simply a point of exclamation is appended.
Sophistical insinuations are suggested in this manner. A train of ideas is laid that generates a conclusion which the speaker is afraid or ashamed to put into words.
The second fault of the syllogism as defined may be called the fallacy of No Application. It consists in arranging propositions so as to end in a classification, but no applicate is detached and no rational conclusion is drawn. 'Jones is a Welshman; all Welshmen are Britons; therefore Jones is a Briton.' If in actual thinking it were ever desired to establish by argument that Jones is a Briton, it would be with the object of applying to him some quality connoted by Briton, but the presence of which in Jones is a matter of doubt. This would be a conclusion—but not the mere classification.
Irrelevant Conclusion—the fallacy called by Aristotelians Ignoratio elenchi—is an attempt to substitute a better argument for the one proposed, but which proves something which has not been denied, or stigmatises something that has not been asserted. It frequently arises from honest ignorance of the question at issue, as in the objections usually made to the Berkeleyan Substantialism. It can also be used as a weapon of sophistry, by confusing the matter in dispute or diverting attention to side issues. It is irrelevant to the truth of a conclusion to point out that he who now supports it formerly opposed it, or that his conduct is inconsistent with a belief in it. Appeals to passion—to reverence for authority—to popular belief—are instances of this fallacy.
The best protection against Fallacy—next to a thorough knowledge of the matter—is a clear notion of the properties of a valid argument; it is useful however to be able to distinguish and name the faulty theorems one constantly meets in controversial speeches and writings.
[17:] One fault of observation is noticed by formal logicians; it is that of assigning an improper cause, Non causa pro causâ or Post hoc ergo propter hoc. It is evident that defects in every other category have an equal light to be noticed.
[18:] Whately complains of the disinclination shown by logicians to put their rules into practice. 'Whenever they have to treat of anything that is beyond the mere elements of Logic, they totally lay aside all reference to the principles they have been occupied in establishing and explaining, and have recourse to a loose, vague, and popular kind of language; such as would be best suited indeed to an exoterical discourse but seems strangely incongruous in a professed logical treatise.... Surely it affords but too much plausibility to the cavils of those who scoff at Logic altogether, that the very writers who profess to teach it should never themselves make any application of, or reference to, its principles, when, and when only, such application and reference are to be expected.' Logic, Book III. Introd. The fact here admitted proves that even logicians do not find their method of any practical use. But what is the meaning of the emphatic 'when only'? Why should a logical method be unsuitable for every sort of subject except those matters of logic that are beyond the mere elements?
[19:] Logic, 'Fallacies,' c. 6.