Neither of these arguments is formally good; nor, of course, is either of them materially valid, if it be possible for trade to prosper in spite of protective tariffs.
An important example of this fallacy is the prevalent notion, that if the conclusion of an argument is true the premises must be trustworthy; or, that if the premises are false the conclusion must be erroneous. For, plainly, that—
If the premises are true, the conclusion is true, is a hypothetical proposition; and we argue justly—
The premises are true;
∴ The conclusion is true;
or, The conclusion is false;
∴ The premises are false (or one of them is).
This is valid for every argument that is formally correct; but that we cannot trust the premises on the strength of the conclusion, nor reject the conclusion because the premises are absurd, the following example will show:
All who square the circle are great mathematicians;
Newton squared the circle:
∴ Newton was a great mathematician.
The conclusion is true; but the premises are intolerable.
How the taking of Contraries for Contradictories may vitiate Disjunctive Syllogisms and Dilemmas has been sufficiently explained in the twelfth chapter.
§ 3. Formal Fallacies of Induction consist in supposing or inferring Causation without attempting to prove it, or in pretending to prove it without satisfying the Canons of observation and experiment: as—
(1) To assign the Cause of anything that is not a concrete event: as, e.g., why two circles can touch only in one point. We should give the 'reason'; for this expression includes, besides evidence of causation, the principles of formal deduction, logical and mathematical.