widely different in apparent nature from the strict logic of science; not that it is really different in the end, when thoroughly analysed. But we constantly deal with illogical, inaccurate, or even untrustworthy persons, so that we can seldom be sure that an assertion will be construed and repeated in the form which we originally gave to it. There is too much truth in the saying of Talleyrand, that words were given to us to disguise our thoughts.

8. If Brown says to Jones, 'Because Robinson is foolish you have no need to be foolish,' does Brown assert categorically that Robinson is foolish?

There can be no doubt that, in the logic of common life, Brown would be understood to make an imputation upon the wisdom of Robinson, especially if the remark was not explained by the previous course of the conversation. But in strict logic it seems very doubtful whether the conjunction 'because' should be interpreted differently from 'if,' as in the last question. The fact of Robinson being foolish is no reason, &c.' 'Foolishness on the part of Robinson is no reason for you being foolish.' A logical copula must not be understood to assert the physical existence and occurrence of its subject or predicate; it only asserts a relation between them.

6

9. If P is Q, and Q is R, it follows that P is R: but suppose it to be discovered that no such thing as exists, how is the truth of the conclusion, P is R, affected by this discovery?

I do not see how there is in deductive logic any question about existence. The inference is to the effect that if the

propositions P is Q and Q is R are true, then the conclusion P is R is true. The non-existence of Q may possibly render one or both premises materially false, in which case the reasoning vanishes, but is not logically defective. If I argue, for instance, that satyrs are creatures half man and half goat; and creatures half man and half goat are very hideous, therefore satyrs are very hideous; the reasoning is equally good whether satyrs exist or not. We cannot, of course, say that the conclusion is materially true, if there be no objects to which the material truth can apply. But if I argue that satyrs are creatures half man and half goat, and such creatures exist in Thessaly, therefore, satyrs exist in Thessaly; in this case the non-existence of the middle term would affect the material truth of the second premise, and, if this be held false, we cannot affirm the material truth of the conclusion.

I ought to add that De Morgan in more then one place assumes that the middle term must have existence, or even objective existence; thus he says (Syllabus, p. 67): “In all syllogisms the existence of the middle term is a datum," &c. This is one of the few points in which it is possible to suspect him of unsoundness.

The student may refer to Hamilton's Lectures, Vol. III. pp. 454-5, and p. 459, on 'Sophisms of Unreal Middle;' see also Whately's Analytical Outline, § 3.

10. Lias lies above red sandstone; red sandstone lies above coal; therefore lias lies above coal.

[w.]

This is one of many examples to be found in the logic books of arguments which simulate the syllogistic form. It is often said that they can be solved syllogistically;

but certainly this cannot be done by the ordinary rules and processes of the syllogism. The most that we could get, even by substitution, is that 'Lias lies above what lies above coal.' The fact is that the argument is really a mathematical one, involving simple equations. It is precisely similar to one which has been thus treated by Professor F. W. Newman (Miscellanies, 1869, p. 28), and Mr. J. J. Murphy. The former of these logicians, as quoted by the latter, remarks— "The argument Lead is heavier than silver; Gold is heavier than Lead: therefore Gold is heavier than Silver,' brings to the mind conviction as direct as the simplest of syllogisms. To say that its validity depends on its being reducible to syllogism, is wholly unplausible: for to effect the reduction, you have to make changes of form at least as hard to accept as the direct argument: and when you have got your syllogisms, they are more complicated and cumbrous than the argument as it stands."

Mr. Murphy (The Relation of Logic to Language: Belfast Natural History and Philosophical Society, 17th February, 1875) treats the argument simply as a question of quantity,

thus

"Call the weights of gold, lead, and silver respectively x, y, and z: then x = y + p

y = z + q

x = % + q + p.

In the old logic, the foregoing conclusion could be drawn only by means of the following syllogism:

That which is greater than the greater is greater than the

less:

The weight of gold is greater than that of lead, and the weight of lead greater than that of silver:

1 Newman has inadvertently written Lead is heavier than Gold, which is wrong as to fact.

Therefore the weight of gold is greater than that of silver.

Considered as fact all this of course is true, but considered as. logic it is wrongly stated. That which is here stated as the major premise is really the syllogistic canon. It is not merely a general truth, like the truth that all matter gravitates, but a logical principle, lying as near to the first principles of the science as the axiom that a part of a part is a part of the whole."

We have only to assume x to be the height of lias, y the height of red sandstone, and z of coal above any one fixed datum, and the same equations represent the argument at the head of this section.

It may be added that Reid was doubtless right in denying that we argue syllogistically when we infer that because A and C are both equal to B they are equal to each other. We may throw it into the form, 'Things equal to the same are equal to each other; A and C are things equal to the same, therefore they are equal to each other.' But this is a delusive syllogism. The inference is really accomplished in obtaining the major premise. The inferences of equality are prior to and simpler than the inferences of logic, and the attempt of Herlinus and Dasypodius to throw Euclid into the syllogistic form has been rightly ridiculed, because it is an attempt to prove the more simple and self-evident by means of the more complex.

Some remarks on this point will be found in De Morgan's Second Memoir on the Syllogism, 1850, pp. 50, 51; his Fourth Memoir, 1860, p. 8, &c.; in Mr. Murphy's paper quoted above; and in Hallam's remarkable note to Section 129 of Vol. III., Chapter III., of his Introduction to the Literature of Europe (1st Ed. p. 288; 5th Ed. p. 111).

CHAPTER XVII.

EXERCISES IN HYPOTHETICAL ARGUMENTS.

1. (1) If he is well, he will come he is not well: therefore he will not come.

(2) If he is well, he will come: he will come: therefore he is well. [H.]

(3) I am sure he will not come, for he is not well; and if well he would come.

(4) He will write if he is well; but as he is not well, therefore he will not write.

Analyse the above arguments and point out which are fallacious, and why.

2. Into how many forms of expression can you throw the matter of this proposition? "Sulphuric acid combined with calcium produces gypsum."

3. Throw into the form of hypothetical propositions the following disjunctives

(1) Either the Claimant is Orton, or many witnesses are mistaken.

(2) The tooth of a mammalian is either an incisor, canine, bicuspid, or molar tooth.

L