(6) To simply convert an hypothetical proposition, as—­

      If trade is free, it prospers;
    .’.  If trade prospers, it is free.

This is similar to the simple conversion of the categorical A.; since it takes for granted that the antecedent is co-extensive with the consequent, or (in other words) that the freedom of trade is the sole condition of, or (at least) inseparable from, its prosperity.

The same assumption is made if, in an hypothetical syllogism, we try to ground an inference on the affirmation of the consequent or denial of the antecedent, as—­

    If trade is free it prospers: 
      It does prosper;
    .’.  It is free. 
      It is not free;
    .’.  It does not prosper.

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.

Sec. 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.

(2) To argue, as if on inductive grounds, concerning the cause of the Universe as a whole.  This may be called the fallacy of transcendent inference:  since the Canons are only applicable to instances of events that can be compared; they cannot deal with that which is in its nature unique.