liar activity in dealing with this objective existence. That our senses are not absolutely trustworthy may be inferred from the phenomenon of "color-blindness"; from a blow on the head which causes us "to see stars"; from the erroneous report of the senses when we roll a marble under the crossed fingers, or thrust a stick, on a bright day, into a running stream. (See Thomson, § 10; Masson, Recent British Philosophy, p. 56 sq.; Everett, Science of Thought, pp. 13–22; Tent Life in Siberia, pp. 254-5.) This question must, of course, be remanded to Psychology and Metaphysics-Logic being a formal science, and altogether indifferent as to the reality or unreality of the material with which it works. It may be said, however, that the presumption is in favor of the credibility of the senses; and that the burden of proof rests upon those who question the validity of this source of knowledge.

The second question is: Has the mind structural functions which limit and condition it in dealing with the materials of thought? Does it, as Bacon affirms, "like an uneven mirror, blend its own nature with things as they are, distort and discolor them"? or does the mind simply reflect and register presentations, just as they are, without subjective modification? The first view is that of the Transcendentalists, i. e., those who believe that there is something in the mind which transcends experience; the second, that of the Empiricists, who believe that all our knowledge is but transformed experience.

The views of our modern Empiricists are adequately stated and ably combated in the Thæetetus of Plato (Trübner ed., vol. I., p. 251): “For the man who knows anything seems to me to apprehend through the senses what he knows; and, indeed, as it now appears, knowledge is nothing else than sense-perception.

For our present purpose, we assume the correctness of the first view. See Thomson, §§ 32, 33, and Masson, p. 36 sq., p. 48 sq.

8: b. What do you understand by the structural functions of the mind; necessary truths; supersensuous truths; a priori truths?

When we speak of the "structural functions of the human mind," we mean that the mind is not a plane mirror,

or a sensitized plate, reflecting and registering, without modification, impressions received from some determining agency; but is so constituted that it must work in certain directions and develop certain ideas which mere sense-perception could never confer upon it. Such ideas are those of time, space, cause and effect, the axioms of mathematics-and, in general, those ideas the contrary of which is unthinkable. These truths are called necessary truths, because, so soon as the mind begins to think, it can not fail to apprehend them-because it accepts and holds them instinctively, without regard to any process of demonstration by which they are established. Necessary truths require to be comprehended, but they do not require to be proved. That two straight lines can not inclose a space would not, probably, strike us as a self-evident truth if it were stated in Choctaw. These truths are also called supersensuous truths, because no amount of mere generalization from the data afforded by the senses can account, not for the mere existence of the truths, but for that imperative necessity with which the mind invests them, and which is their most distinguishing characteristic. Mansel, pp. 92 (especially note) and 97. They are also called a priori truths, because, to borrow the language of Hamilton, "they are potentially in the mind, anterior to the act of experience by which they are first elicited in consciousness"; but it is not claimed by Hamilton, or any modern philosopher, that they actually exist in the mind prior to experience. Bain, Deductive Logic, p. 10, incorrectly represents the Transcendentalists just here.

See

9. What are the three general divisions of Pure Logic? (1) Conception, which treats of the method of forming general notions.

(2) Judgment, which treats of the comparison of no

tions to test their agreement or disagreement with each other.

(3) Reasoning, which treats of the method of deducing one judgment from another judgment, or other judgments.

9: a. Is the order in which they are discussed in Logical text-books the natural order?

In pursuing the study of Logic, two methods are open to us, the analytic and the synthetic. Adopting the analytic method, we should break up the finished argument of an orator 1, into reasonings; 2, into judgments; 3, into concepts or general notions. This would, of necessity, be our method if we were attempting to create a science of Logic; and then we should naturally discuss the general divisions of our subject in the following order: 1. Reasoning; 2, Judgment; 3, Conception. The process of analysis has, however, been gone through with again and again, and all its results are before us. We can, therefore, if we prefer, adopt, as more convenient for purposes of instruction, the synthetic method, and, approaching the divisions of our subject according to the relative simplicity of the processes which they involve, discuss 1, Conception; 2, Judgment; 3, Reasoning. This course we shall adopt. See Thomson, § 41.

9 b. Are Conception, Judgment, and Reasoning independent processes, or mutually related?

It should be borne in mind that Conception, Judgment, and Reasoning are not strictly independent processes; but, "in reality, only various applications of the same simple faculty, that of comparison" (Hamilton, p. 194); and that "concepts, judgments, and reasonings fall into different classes, as the act and consequently the result of the act-is of a greater or less simplicity.' (Hamilton, p. 83. Cf. Atwater, p. 83 sq.)

10. State the four Fundamental Principles which underlie the Laws of Thought.

These principles serve merely to test the formal cordirectness of our thinking-its self-consistency. Our thinktbeing may be correct in form, yet not true in matter; but it can not be materially true unless it is formally correct. Valid See Thomson, p. 250; Bowen, p. 42.

it must

The principles referred to are :

I. "The Principle of Identity, which expresses the relation of total sameness in which a concept stands to all, and the relation of partial sameness in which it stands to each, of its constituent parts. Its formula is A = A.” (Hamilton, p. 57.)

The formula may also be stated: A =

=

A

· (44); 4 = 4

To illustrate the importance of this principle: Leibnitz says, "The geometrician proceeds from hypothesis to hypothesis; and, while the thought assumes a thousand different forms, it is still but by an incessant repetition of the principle the same is the same' that he performs all his wonders." Condillac says, "Equations, propositions, judgments, are, at bottom, the same; and, consequently, the reasoning process is the same in every science." Cf. Everett, Science of Thought, p. 102.

Scholia. (a) Unless a thing be equal to itself—that is, maintain its essential identity-there can be no such thing as thought. (b) Things that are equal to the same thing are equal to each other. E. g. : AB, B = C, therefore A = C. (c) What is affirmed or denied of a whole, may be affirmed or denied of its parts. E. g. : Man is a rational animal; John is a man; therefore John is a rational animal.

II. The Principle of Non-Contradiction. Aristotle's statement is : "The same attribute can not be at the same time affirmed and denied of the same object."

That is a thing can not be, at the same time, A and not-A; a diagram can not be, at the same time, square and not-square. Kant's statement is: "The attribute can not be contradictory of the object." E. g. : A triangle can not be round. The formula for this law is A -A=0. E. g. Let A represent "two straight lines in the same plane which, however protracted, will never meet." You are required to think of those lines as meeting. The result is A-A = 0, the negation of thought.

III. The Principle of Excluded Middle; that is: Of two contradictories, one or the other must be true; there is no middle course. Examples of contradictories are :

No X is any Y;

Some X is some Y.

The table is square;

The table is not-square.

The table must, of course, be either square or not-square.

Besides contradictory opposition, Logic recognizes contrary opposition; in which both judgments can not be true, but they may both be false. For instance:

No X is any Y;

All X is all Y.

The table is square;

The table is round.

In these cases of opposition the judgments can not both be true, but they may both be false. The truth may be : All X is some Y.

The table is oblong.

IV. The Principle of Sufficient Reason; that is: "Whatever exists must have a sufficient reason why it is as it is, and not otherwise." (Leibnitz.) So far as this principle demands recognition in Logic, it simply insists