A slightly different phase of the post hoc fallacy consists in attributing the existence of a certain condition to a single preceding event, when at the most this event could have been only a partial cause of what followed, and may not have been a cause at all. A medicine that could not have effected a cure may have been of some slight benefit. A law that could not possibly have been the sole cause of "good times" may have had a beneficial effect. To avoid this fallacy, one must be sure not only that the assigned cause is operative, but that it is also adequate.
In the following passage, Harpers Weekly, for March 5, 1894, points out the error in the reasoning made by several college presidents who, after compiling statistics, stated that a college education increased a man's chance of success from one in ten thousand to one in forty:—
Not many persons doubt any longer that an American college education is an advantage to most youths who can get it, but in these attempts to estimate statistically what college education does for men there is a good deal of confusing of post hoc and propter hoc. Define success as you will, a much larger proportion of American college men win it than of men who don't go to college, but how much college training does for those successful men is still debatable. Remember that they are a picked lot, the likeliest children of parents whose ability or desire to send their children to college is evidence of better fortune, or at least of higher aspirations than the average. And because their parents are, as a rule, more or less prosperous and well educated, they get and would get, whether they went to college or not, a better than average start in life….
If one boy out of a family of four goes to college, it is the clever one. The boys who might go to college and don't are commonly the lazy ones who won't study. The colleges get nowadays a large proportion of the best boys of the strongest families. The best boys of the strongest families would win far more than their proportionate share of success even if there were no colleges.
An exposure of similarly fallacious reasoning is made by Edward M.
Shepard in The Atlantic Monthly for October, 1904.
The Republican argument is that the whole edifice of our prosperity depends upon high protective or prohibitive duties, and that to them is due our industrial progress. Is it not, indeed, a disparagement of the self-depending faculties of the American people thus to affirm that, in spite of their marvelous advantages, they would have failed in industrial life unless by force of law they could have prevented the competition with them of other peoples? It is only by the sophistry to which I have referred that this disparagement is justified. It is that old argument of veritable folly that, because event Z follows event W, as it follows events A and B and many besides A, therefore W is the sole cause of Z. Theory or no theory, the Republican says that we have in fact grown rich by protection, because in our country prosperity and protective duties have existed together. They ignore every inconvenient fact. They would have us forget that each of the industrial depressions of 1873-78 and 1893-96 followed long operation of a high protective tariff. They ignore the contribution of soil and climate to our prosperity, the vast increase which modern inventions and improved carrying facilities have, the world over, brought to the productivity of labor, and here in the United States have brought more than anywhere else. They ignore the superior skill and alertness of the American workman and the wonderful extent to which he has been stimulated by the conditions and ideals of our democracy. They ignore the freedom of trade, which, since 1789, the Federal Constitution has made operative over our entire country,— by far the most important area of free trade ever known,—and which everyone to-day knows to be a prime condition of the prosperity of our forty-five commonwealths.
From what has been said it is obvious that it is never safe to account for an occurrence or a condition by merely referring to something that accompanies it or precedes it. There must be a connection between the alleged cause and the effect, and this connection must be causal; otherwise, both may be the result of the same cause. The cause must also be adequate; and it must, moreover, be evident that the result has not been produced, wholly or partially, by some other cause or causes.
IV. COMPOSITION AND DIVISION.
COMPOSITION. The fallacy of composition consists of attributing to a whole that which has been proved only of a part. To condemn or to approve of a fraternity because of the conduct of only a few of its members, to say that what is advantageous for certain states in the Union would therefore be beneficial for the United States as a whole, to reason from the existence of a few millionaires that the English nation is wealthy, would be to fall into this fallacy. Furthermore, it is fallacious to think that because something is true of each member of a class taken distributively, the same thing holds true of the class taken collectively. It is not logical to argue that because each member of a jury is very likely to judge erroneously, the jury as a whole is also very likely to judge erroneously. Because each witness to an event is liable to give false or incorrect evidence, it is unreasonable to think that no confidence can be placed in the concurrent testimony of a number of witnesses.
DIVISION. The fallacy of division is the converse of the fallacy of composition. It consists of attributing to a part that which has been proved of the whole. For instance, Lancaster county is the most fertile county in Pennsylvania, but that fact by itself does not warrant the statement that any one particular farm is exceptionally fertile. Because the people of a country are suffering from famine, it does not follow that one particular person is thus afflicted. Again, it would be fallacious to say: It is admitted that the judges of the court of appeal cannot misinterpret the law; Richard Rowe is a judge of the court of appeal; therefore he cannot misinterpret the law.