| I. | |
| What is universallybelieved | is true |
| The existence of God is not universally believed | N. C. |
To establish the conclusion aimed at, it would be necessary to lay down as precedent—'What is not universally believed is not true.'
These theorems from contrast are on a par with the following—
| I. | |
| Cows | are four-footed |
| Sheep are not cows | sheep are not four-footed |
This is the fallacy called in the quaint language of the syllogists 'Illicit Process of the Major Term.'
In False Analogy the resemblance is so slight that the application is untrustworthy, or a conclusion is drawn in excess of the resemblance. If from the habit of calling a deep bay or salt-water loch an 'arm' of the sea from its analogy to a human arm, we conclude that the sea has elbows and wrists, we commit this fallacy. The earth is like an orange, but we must not think that it is pulpy inside.
Akin to this is the fallacy of False Generality or Doubtful Precedent. It consists in carelessly or perversely using bad antecedents when better are available. This applies to such current prejudices as that all Frenchmen are frivolous, all Germans mystical, all Jews dishonest, all Carthaginians faithless, all rich people purseproud, all nobles haughty, and so on. Even if all the Carthaginians we personally knew had proved faithless, our general knowledge of mankind should keep us from inferring that a whole nation should be faithless. The most we should conclude is that some Carthaginians are faithless, but we are free to exercise caution in future dealings with members of that race. All these generalities are grounded on this prior argument: 'when a known portion of a class exhibits certain qualities, we are justified in inferring that the whole class possess these qualities'—which is only occasionally true.
The fallacy of Accident occurs when the precedent is so defined as not to exclude exceptions, and the case happens to be one of the exceptions. 'What gives pain should be abstained from; surgical operations give pain; they should therefore be abstained from.' The painful things that should be universally abstained from are those which give needless or useless pain, not the sort that give less pain than they remove. Falstaff committed this fallacy when he supposed that the King would be a boon companion like the Prince. So did the colonists who introduced rabbits and water-cress into Australia, on the supposition that they would there have the same function or value as in Great Britain. In consequence of the Accidental change the rabbits have developed into a pest, and the water-cress obstructs navigation.
If the applicate is a property of the subject only when the latter is taken collectively, it will not yield a true conclusion when the parts or individuals of the subject are taken separately. All the angles of a triangle are equal to two right angles, but it does not follow that one of them—though it resembles the triangle to some extent—is equal to two right angles. In this instance we should render the meaning clear by saying 'collectively equal,' when no argument follows and no mistake is made. This is called the fallacy of Division.