place to open up the endless problem of Perception here, but it may not be out of place to point out how the knot of the problem is evaded by certain theories. For instance, any theory which makes no distinction between the definite perception of an object and the indefinite belief in a cause leaves out the essence of the phenomena. According to such theories, I perceive an object which I see and feel only in the same sense in which I perceive the author of the book I am reading, or in the same sense in which, when I have a tooth-ache, I perceive the draught that caused it. If this is proved, well and good; what I object to is the assumption of it as a starting-point.

Again, the knot of the problem is missed by a theory which confounds the perception of a present object with the belief in the existence of an object formerly perceived. These two things are carefully distinguished, e.g., by Locke, Hume, and Stewart. Locke admits that we have a sensitive knowledge of things actually present to the senses; whereas he allows no knowledge of the existence of things not so present, 'it being no more necessary that water should exist to-day because it existed yesterday, than that the colours or bubbles [which I once saw on the water] exist to-day because they existed yesterday; though it be exceedingly much more probable, because water hath been observed to continue long in existence, but bubbles and the colours on them quickly cease to be,' although, as he says, it is equally true that I saw the bubbles and that I saw the water. Hume again expressly lays down the distinction- We ought to examine apart those two questions, which are commonly confounded together, viz., why we attribute a continued existence to objects even when they are not present to the senses, and why we suppose them to have an existence distinct from the mind and perception?'-(Treatise on Human Nature, Bk. I. pt. 4, sect. 2).

Stewart also, after commending Reid's treatment of the problem of perception, adds that there is still one omission in it, viz., that he has not accounted for our belief in the independent and continued existence of objects, even when we are not perceiving them (Philosophy, pt. i. ch. 3). Notwithstanding this, Mr. Mill commences his discussion of the problem by asserting that this latter belief is the whole of the phenomenon to be accounted for; and not only this, but he actually affirms that Stewart agrees with him.'

It is scarcely necessary to mention that Kant has steered perfectly clear of such misconceptions as these.

1 Locke's example of the bubbles would not be easily brought under his theory.

T. K. ABBOTT.

LOGICAL NOTES.

I. ON A FLAW IN A RECEIVED LOGICAL PROCESS.

IT

T may seem a bold thing to affirm that a process which has been unquestionably admitted by all logicians, ancient and modern, is invalid. Yet I cannot see how the process known as Reductio ad impossibile can be defended. Of course I do not mean that the reasoning involved in it is fallacious, but that as an attempt at Reduction it is a complete failure. The function of reduction is to show that the Dictum is the universal formal principle of mediate reasoning. The problem, therefore, in any particular case is this: From the given premisses to deduce the conclusion by means of a syllogism or syllogisms in the first figure, combined with immediate inferences. Now, take a syllogism in Baroko. Every P is M; some S is not M; therefore some S is not P. We are told to substitute for this the syllogism, Every P is M ; every S is P ; therefore every S is M. But how is the conclusion-Some S is not P-deduced from this? True premisses, it is said, can only lead to a true conclusion. Therefore, when the conclusion is false, one of the premisses is false; but here the major is assumed true. Therefore the minor is false. Now, here is an additional chain of reasoning which we are bound to state syllogistically. Put in the briefest form it stands. thus (the truth of the major being assumed): If every S is P, every S is M. But some S is not M, therefore some S is not P. This hypothetical syllogism must be reduced to a categorical. But this process will give us back the ori

ginal syllogism. All that we have gained then is, that for the original simple syllogism we have substituted a syllogism in the first figure plus another piece of reasoning not in the first figure.

It is obvious that it would not be admissible to take as a major premiss the formal maxim, 'If the premisses are true the conclusion is true.' To do so would be to make the dictum itself a premiss. But even if we did so, we should be driven back precisely as above upon the original reasoning. The only means of escape would be to take for one premiss the converse of this, viz.: If the conclusion is false (the major being given true), the minor is false, &c. This syllogism might be brought into a categorical form in the first figure. A syllogism with a false conclusion is a syllogism with a false premiss,' &c.; but the hypothetical major is only a converse by negation of the maxim, 'If the premisses are true the conclusion is true.' Applied to the particular case in question it would be: If some S is not M, some S is not P, or 'the case of some S not being M is the case of some S not being P,' &c. This is no reduction. It is clear, however, that logical writers did not contemplate such an evasion of the difficulty; they simply overlooked the difficulty altogether. Satisfied with the production of a syllogism in the first figure, they forgot that it did not complete the reasoning.

Professor Monck, to whom I had mentioned this difficulty, suggests a method of evading the objection, and having stated one syllogism of his process, he says he 'believes' the proof could be completed 'without requiring any other figure than the first' (Introd. to Logic, p. 180, note). This is an admission that the reduction as hitherto exhibited is imperfect (and therefore illusory), and that the possibility of reduction by this method has yet to be proved. His omission to supply the defect is the

more remarkable as he devotes several pages to the received process. I may add that the proof he proposes, even if completed, would not solve the problem. For what he proposes to attempt is a proof of the abstract proposition that 'Baroko is a legitimate mode'; but this, if proved, would still leave the problem of its reduction to the form assumed in the Dictum unsolved.

Logic is nothing if not exact: this is sufficient reason for asking attention to the two following notes:

II. ON THE GEOMETRICAL SYLLOGISM.

WRITERS who undertake to bring Euclid's reasoning into syllogistic form present us with syllogisms of this kind:

Things equal to the same are equal to one another; A and B are equal to the same. Therefore A and B are equal to one another.

In

Now, this syllogism is not formally correct, as will be obvious at once if we attempt to prefix the sign of distribution to the subject of the major: Everything equal to the same is equal to one another, which is nonsense. the first place, as to the subject; 'things' is not taken distributively, but in groups determined by the same.' It is this term 'the same' which really indicates the distribution of the subject. Secondly, as to the predicate, 'equal to one another' does not express any property common to the parts in extension of the subject, nor is it the name of a class in which they are included. Hence it could not be replaced by a symbol. We can say, 'If A and B are x and C and D are x, then A and B and C and D are x;' but we cannot substitute 'equal to one another' for this The fact is, that the expression 'equal to the same,' 'equal to one another,' are abbreviations. A and B and

x.