a form of the Sorites to which the name of Goclenius its inventor has been attached, which is the same as the common form, except that the premisses are reversed. It would run

D is E,

C is D,

B is C,

A is B,

... A is E.

In the Goclenian Sorites extension is made more prominent, by starting with the premiss which has the two widest terms; in the common form intension predominates, as the narrower terms precede. The former descends in extension from the predicate of the conclusion; the latter ascends in intension, from the subject. The Goclenian form suits deduction best; the common or Aristotelian form, induction. The Goclenian descends from law to fact; the common ascends from fact to law.*

* A "pretty quarrel" long existed amongst logicians, which of the two was to be called progressive and which regressive. Till Kant's time, the Goclenian was called progressive, the common regressive. Kant reversed it, followed by Kiesewetter and others. Jacob reversed it again, followed by Krug and others. Troxler ii. 100. It was a mere strife about words. If we are discovering truth by the inductive method, the Aristotelian form is progressive; if we are teaching truth, or trying our laws upon new facts, we use deduction, and the Goclenian form is progressive. In an apt but familiar figure-if I am on the ground

This will be clearer from a pair of examples.

The premisses of the Sorites may be, all or some of them, hypothetical; indeed as this argument is but an aggregation of simple syllogisms, the rules for the construction of simple syllogisms apply to its several parts; with this one caution, that in the Sorites each foregoing syllogism furnishes a premiss, not expressed,

floor, and wish to fetch something that is above, my going upstairs is my progress towards my object, and my coming down is a regression; if the positions of myself and the thing are reversed, going down would be progress, and returning up, regress. The inductive truth-seeker is on the ground-floor of facts, and goes up to seek a law; the deductive teacher is on a higher story, and carries his law down with him to the facts.

S

to the next succeeding one, and therefore we must see not only that each is good in itself, but that it will furnish an available premiss to its successor. This may be tried by altering one of the higher premisses in any of the examples into a negative; at the next step, an error will be apparent.

The Dilemma is a complex argument, partaking both of the conditional and disjunctive. It is a syllogism with a conditional premiss, in which either the antecedent or consequent is disjunctive. It may prove a negative or an affirmative conclusion ; in the former case it is said to be in the mode of removal (modus tollens), because it removes or refutes some conclusion that has been proposed for proof: in the latter it is in the mode of position (modus ponens), because the proposed question is laid down as proved. The following forms of it, with the manner in which they are presented as syllogisms, may be sufficient.

I.

If A is B or E is F, then C is D,

But either A is B or E is F;

... C is D.

II.

If A is B, then C is D or E is F,

But neither C is D nor E is F; ... A is not B.

III.

If some A is B, either the m that are A or the n that are B, But neither the m that are A nor the n that are A are B; ... A is not B.

The same regarded as simple syllogisms.

I.

[The cases of A being B and E being F] are [cases of C being D],

This is [a case of A being B or E being F];

... This is [a case of C being D].

II.

[The case of A being B] is [a case of C being D or E being F].

This is not [a case of C being D or E being F];

... This is not [a case of A being B].

III.

Neither m of A nor n of A are B,

All A is either m or n;

... No A is B.

The word Dilemma means "double proposition," so that the whole argument takes its name from the one mixed judgment in it. When this is more than double, as in "If a prisoner is legally discharged, either the magistrate must refuse to commit, or the grand jury ignore the bill, or the common jury acquit, or the crown exercise the prerogative of pardon," the argument has been called a Trilemma, Tetralemma, or Polylemma, according to the number of members the judgment may have.

The following are concrete examples of the for

mulæ.

1. If the king is moved or if he is covered, I am checkmated the next move; One or the other must be; Therefore I shall be checkmated.

II. If a man cannot make progress towards perfection, he must either be a brute or a divinity; But no man is either; Therefore every man is capable of such progress.

III. If some science can furnish a criterion of truth, either a formal or a real science must do so; But (for different reasons) neither the formal sciences nor the real do so; Therefore science affords no criterion of truth.

TRILEMMA. If the system of the universe is not the best possible, we must suppose either that the Creator willed not a better one, or that he knew no better one, or that he could not create a better. The first cannot be true (it is against His goodness). The second cannot be true (it assails His wisdom). The third cannot be true (it limits His power). Therefore the system of the universe is the best.

The popular notion of a Dilemma, that it is a choice of alternatives, each of them fatal to the cause or the character of an adversary, is countenanced by many logicians, but can have no place in pure Logic, into which the object to be gained by arguments, or the personal consequences which follow from admitting them, ought not to enter, and the properties of the arguments themselves are the sole object of consideration.

If the criminal knew the consequences of his act, he was wicked; if he did not know the consequences, he was

insane.