to discriminate these two forms by their essential LECT. differences.

In regard to the Disjunctive Syllogism the case is different; for as the disjunctive judgment is in one point of view only a categorical judgment, whose predicate consists of logically opposing members, it is certainly true that we can draw a disjunctive syllogism in all the four figures.

I shall use the letters P, M, and S; but as the disjunction requires at least one additional letter, I shall, where that is necessary, take the one immediately following.

XXII.

LECT.
XXII.

Second case

P is either M or N;

Neither M nor N is S;
Therefore, S is not P.a

Figure of Of Composite Syllogisms,-I need say nothing conSyllogisms. cerning the Epicheirema, which, it is manifest, may

Composite

be in one figure equally as another. But it is less evident that the Sorites may be of any figure; and logicians seem, in fact, from their definitions, to have only contemplated its possibility in the first figure. It is, however, capable of all the four schematic accidents by a little contortion; but as this at best constitutes only a logical curiosity, it is needless to spend any time in its demonstration.ẞ

So much for the Form of reasoning, both Essential and Accidental, and the Divisions of Syllogisms which are founded thereon.

a See Chr. J. Braniss, Grundriss der Logik, § 394, p. 146. Compare Krug, Logik, p. 387 et seq.

tes in different figures, see Herbart, Lehrbuch zur Einleitung in die Philo sophie, § 70. Drobisch, Neue Darstel

B For a complicated theory of Sori- lung der Logik, §§ 80-84.-ED.

XXIII.

ALL the varieties of Syllogism, whose necessary laws and LECT contingent modifications we have hitherto considered, are, taken together, divided into classes by reference to their Validity; and I shall comprise the heads of what I shall afterwards illustrate, in the following paragraph.

Syllogisms,

rect.

¶ LXXVI. Syllogisms, by another distribution, Par. LXXVI. are distinguished, by respect to their Validity, Correct into Correct or True and Incorrect or False. The and IncorIncorrect or False are again, (though not in a logical point of view), divided, by reference to the intention of the reasoner, into Paralogisms, or Faulty, and into Sophisms, or Deceptive, Reasonings. The Paralogism (paralogismus) is properly a syllogism of whose falsehood the employer is not himself conscious; the Sophism (sophisma, captio, cavillatio), is properly a false syllogism,

VOL. I.

2 F

LECT. XXIII.

Explica

tion.

absolute

criminated.

fabricated and employed for the purpose of deceiving others. The term Fallacy may be applied indifferently in either sense. These distinctions are, however, frequently confounded; nor in a logical relation are they of account. False Syllogisms are, again, vicious, either in respect of their form or of their matter, or in respect of both form and matter."

In regard to the first distinction contained in this paragraph,—of Syllogisms into Correct or True and InLogical and correct or False, it is requisite to say a few words. truth dis- It is necessary to distinguish logical truth, that is, the truth which Logic guarantees in a reasoning, from the absolute truth of the several judgments of which a reasoning is composed. I have frequently inculcated on you that Logic does not warrant the truth of its premises, except in so far as these may be the formal conclusions of anterior reasonings,-it only warrants, (on the hypothesis that the premises are truly assumed), the truth of the inference. In this view the conclusion may, as a separate proposition, be true, but if this truth be not a necessary consequence from the premises, it is a false conclusion, that is, in fact no conclusion at all. Now on this point there is a doctrine prevalent among logicians, which is not only erroneous, but, if admitted, is subversive of the distinction of Logic as a purely formal science. The doctrine in question is in its result this, that if the conclusion of a syllogism be true, the premises may be either true or false, but that if the conclusion be false, one or both of the premises must be false; in other words, that it is possible to infer true from false, but not

a Krug, Logik, § 115.-ED.

false from true. As an example of this I have seen given the following syllogism:

Aristotle is a Roman;

A Roman is a European;

Therefore, Aristotle is a European.

The inference, in so far as expressed, is true; but I would remark that the whole inference which the premises necessitate, and which the conclusion, therefore, virtually contains, is not true, is false. For the premises of the preceding syllogism gave not only the conclusion, Aristotle is a European, but also the conclusion, Aristotle is not a Greek; for it not merely follows from the premises, that Aristotle is conceived under the universal notion of which the concept Roman forms a particular sphere, but likewise that he is conceived as excluded from all the other particular spheres which are contained under that universal notion. The consideration of the truth of the premise, Aristotle is a Roman, is, however, more properly to be regarded as extralogical; but if so, then the consideration of the conclusion, Aristotle is a European, on any other view than a mere formal inference from certain given antecedents, is, likewise, extralogical. Logic is only concerned with the formal truth, the technical validity, of its syllogisms, and anything beyond the legitimacy of the consequence it draws from certain hypothetical antecedents, it does not profess to vindicate. Logical truth and falsehood are thus contained. in the correctness and incorrectness of logical inference; and it was, therefore, with no impropriety that we made a true or correct, and a false or incorrect syllogism convertible expressions."

a Cf. Esser, Logik, § 109.-ED.

LECT. XXIII.