9. Recollect that, in many cases, although you can show an argument to be fallacious, the conclusion may still be true, and all that you have done is simply to have placed it in the position of being unproved. 10. In order to guard against the obscurity, vagueness, confusion, and ambiguity incident to language, endeavour to conceive when practicable the actual things represented by words; and when the terms are complex, decompose their meaning into its constituent parts.

11. When the definition of an important word on which any of the reasoning turns has been given, make it a practice, in all obscure or dubious passages of the composition where it is employed, to substitute the definition for the term. If the writer under examination has furnished no definition of such a term, form one for yourself and use it in the same manner. 12. When abstract general terms are used in any proposition, translate the proposition into concrete language, and try how the argument in which the proposition is employed will be affected by the change.

ARTICLE III.

THE PRECEDING SUGGESTIONS IN PART EXEMPLIFIED BY AN EXAMINATION OF BERKELEY'S CELEBRATED ARGUMENT TO PROVE THE IMPOSSIBILITY OF SEEING DISTANCE.

FOR the purpose of exemplifying the principal rules here given, I will take Berkeley's celebrated argument to prove the impossibility of seeing distance. It is in his own words as follows:

"It is, I think, agreed by all that distance of itself and immediately cannot be seen. For distance being a line

directed endwise to the eye, it projects only one point in the fund of the eye. Which point remains invariably the same whether the distance be longer or shorter.”

According to our first rule, we have to begin the examination of this argument by finding the conclusion which it seeks to establish. Berkeley has placed it on the very threshold of his treatise:

"Distance of itself and immediately cannot be seen." This conclusion or thesis appears to be clearly and unambiguously expressed. I shall have in the sequel to object to the use here made of an abstract term; but for the present let us take the proposition as it is given.

We next proceed to comply with the third rule.

The reason assigned for the conclusion is, that "distance projects only one point in the fund of the eye;" and in proof of this latter proposition, a reason is also assigned, viz. that "distance is a line presented endwise to the eye.'

There are obviously here two separate arguments which are ostensibly of a demonstrative character, and which, in compliance with our fourth rule, we may spread out into two syllogisms, reversing the order in which the propositions are presented by Berkeley.

First Syllogism.

Lines directed endwise to the eye project only one point in the fund of the eye;

Distance is such a line;

Therefore distance projects only one point in the fund of the eye.

Second Syllogism.

Whatever projects only one point in the fund of the

eye cannot be seen;

Distance projects only one point there;

Therefore distance cannot be seen.

Looking at these syllogisms agreeably to the latter part of our fourth rule, I find that they are perfectly correct. A scholastic logician cannot find in them any non-distribution of middle terms or illicit processes; the language is not ambiguous; and every one of common discernment must see that they are conclusive.

Nothing remains, then, but, in compliance with the sixth rule, to examine the truth of the premises.

It will be obvious to all that the major premise of the first syllogism, if it has any meaning at all, must signify material or physical lines. If it meant any thing else it would be palpably inadmissible, since imaginary or hypothetical lines can project no points on the retina. The projection of points, or more accurately the images of points, on the retina, is a physical operation; and even in this signification the predicate can be affirmed only of material lines stopping short of the eye. Of a material line directed endwise to the eye, the end would undoubtedly project a point on the retina, if it did not approach too near that organ; but if it entered the eye it would project no point at all.

The major premise, then, is true only if material lines are understood, and only if such lines stop short of the eye.

Hence the minor premise, which asserts that distance is such a line as is spoken of in the major, cannot be admitted. If distance can be correctly termed a line at all, it can in no sense be termed a material line, and it would be absurd to speak of it as a line not reaching the organ of vision but distance cannot, in fact, be termed a line at all with any correctness or even definite meaning, although it may be measured by a line.

:

The minor premise being thus shown to be in every way inadmissible, the conclusion of the first syllogism is not established: distance is not proved to project even one point in the fund of the eye.

The minor premise of the second syllogism, being the

same proposition as the unproved conclusion of the first, falls equally to the ground, and carries the whole syllogism along with it.

But if this minor premise were admitted, the second syllogism must share the fate of its predecessor. The major premise is not only untrue, but the very opposite of the truth; for whatever projects a point, or, more accurately, the image of a point, upon the retina, must be seen; and if distance projects such a point (which it cannot be said to do, as the assertion has no real meaning), distance must be

seen.

It has been supposed by some, that by lines directed endwise to the eye, Berkeley meant rays of light; but, if we try this supposition, we shall only be landed in fresh difficulties. What can be made of such a proposition as "distance is a ray of light directed endwise to the eye"?

Discarding, however, any rigid exaction of consistent language, let us, in the spirit of our seventh rule, endeavour to put the argument in its best imaginable form:

Bodies, at various distances, all send rays of light to the eye; which rays must, of course, vary in length with the distances now, as these rays are all right lines, presenting their ends to the retina, it is plain that the eye cannot see the different lengths of the rays, nor, consequently, the distances of the objects whence the rays proceed, any more than if a bundle of rods of various lengths were presented to it endwise, it could perceive that one rod was longer than another.

Here we have two consecutive arguments. 1. Rays of light coming from objects present their ends to the eye; therefore the lengths of the rays cannot be seen. 2. Inasmuch as the lengths of the rays cannot be seen, the distances of the objects whence they proceed cannot be seen.

In reply to the first argument, it may be remarked, that it is a superfluous undertaking to prove that the lengths of the rays of light proceeding from objects to the eye cannot

be seen, since no part of such rays can be seen, neither the ends nor the lengths. They are so far from being seen, that it is only a small number of mankind who are aware that such things as rays of light, proceeding from the objects in view, are concerned in the act of vision. That the lengths of such rays are not perceptible, is, therefore, a notorious fact. But the second argument goes on to allege that as the eye cannot see the various lengths of the rays, it cannot see that the objects from which the rays come are at various distances. Why not? What incompatibility is there between rays being invisible and objects being seen to be at various distances from the spectator? Here is, in fact, an assumption of the very thing to be proved.

The bundle of rods furnishes no analogous case. Rods are visible objects, rays are invisible: rods, when presented endwise to the eye, stop short of that organ; rays enter it and fall on an internal membrane: the ends of rods are external objects which are seen by means of rays of light proceeding from them, while to say that the ends of rays are external objects seen by means of other proceeding from them would be self-evidently absurd.

rays

It is highly probable (to touch upon the inquiry suggested by Rule 8.) that this false analogy between bundles of rods or other material straight lines and rays of light, originally misled Berkeley, as it has undoubtedly misled some of his followers. We see clearly how it may have been the source of his ingenious but unsubstantial paradox, and how it may have betrayed philosophers who ought to have known

* "How can vision of itself give us any notion of the distance of bodies, when we know that the light reflected from them falls in straight lines on the eye, and can present only the ends of these lines to the organ? You can have no notion of the length of a line by being touched merely with one of its ends. We could as well know the length of a staff, by having our eyes confined merely to the breadth of its head." - Young's Lectures on Intellectual Philosophy, p. 113. So loosely is philosophy sometimes written.