truths based upon the primary intuitions of morals and religion.

In regard to the last peculiarity of mathematics I have only to say that when the principles of morals are as definitely settled as those of the mathematics (and no reason but a false philosophy can be assigned why they have not been thus settled long ago), we may expect the same precision in morals as in any other science.

Method of Proof.

Having shown that all reasoning resolves itself into two classes, demonstrative and probable, another topic demanding attention is the method of proof, or the general mode to be adopted in proving a proposition, the truth of which has been already ascertained. In the last Chapter I endeavored to develop those laws of belief which should guide the mind in its inquiries after truth. Now when truth has been discovered and adopted in conformity with those rules, and we wish to present arguments for the purpose of conveying to other minds the same convictions which exist in our own, one rule of fundamental importance presents itself. Present those considerations by which our own mind has been convinced. This rule might, at first thought, seem to be so obviously proper, and so manifestly of universal application, as to render its statement entirely unnecessary. But there is no rule which is more frequently transgressed, and for the obvious reason, that few persons practise self-reflection sufficiently to render themselves distinctly conscious of the real ground of their assent to a vast majority of the truths which they believe. Hence it very commonly happens, that when individuals are called upon to assign reasons for propositions which they most firmly believe to be true, they for the first time, perhaps, begin to doubt the reality of the objects of their faith. This most frequently happens, perhaps, in reference to truths the most obvious, and with which the mind is most familiar. The reason of this most singular fact is obvious. We seldom recur to the grounds of our belief in truths so obvious and familiar, that they have been universally admitted. -The evidence of such truths has come into the mind unsought. The reverse is the fact with respect to truths less obvious and familiar.

Real Proof found in no other Method.

On reflection, it will appear evident, that in no other me

thod of argumentation is real proof to be met with. We may show an individual that the truth of a given proposition necessarily results from principles which he admits. But this (the argumentum ad hominem), is mere hypothetical, and not real proof. For if the principles of the individual are false, the argument is good for nothing, as far as the real establishment of truth is concerned. The same may be said of every other kind of proof, but that of which we are speaking.

Sources of Fallacies in Reasoning.

Assuming the proposition which I have endeavored to establish, as true, to wit: That every conclusion in a process of reasoning is based upon two propositions, called premises, the place where fallacies in reasoning are to be found, if they exist, may be readily pointed out. They must be found in one or both of the premises, or in the conclusion. Hence, in examining any particular process of reasoning, such questions as these are of fundamental importance.-What is the proposition which the author is aiming to establish? What principles has he assumed as previously established or as selfevident? Are these principles legitimately assumed? What statements does he propose as matters of fact? Are they authentic? Do they belong to the principle to which they are applied? Do his conclusions legitimately result from the premises laid down? By such questions as these, fallacies, if they exist, may commonly be detected. Four great questions, I repeat, should be asked, if we would determine correctly whether a proposition has been proved, by a given process of argumentation, to wit: What is the precise nature of the proposition which is the subject of the argument? What are the premises or arguments by which the proposition has been sustained? Are these premises sound? does the conclusion legitimately result from the premises? If fallacies have been introduced into the process, we shall thus discover their particular hiding-places, and know how to bring them into the light.

And

CONCEPTION OF LOGIC.

The object of the present and preceding Chapter has been to lay down certain great principles, in respect to the discovery of truth, and its establishment by a process of argumentation. In this department of our investigations, it remains to speak of but one additional topic, the Conception of Logic.

All Things occur according to Rules.

"Everything in nature," says Kant, and this is one of his most important thoughts, as well in the inanimate as in the animated world, happens or is done according to rules, though we do not always know them. Water falls according to the laws of gravitation, and the motion of walking is performed by animals according to rules. The fish in the water, the bird in the air, moves according to rules."

When we

Again: "There is nowhere any want of rule. think we find that want, we can only say that, in this case, the rules are unknown to us."

The exercise of our Intelligence is not an exception to the above remark. When we speak, our language is thrown into harmony with rules, to which we conform without, in most instances, a reflective consciousness of their existence. Grammar is nothing but a systematic development of these rules. So also when we judge a proposition to be true or false, or to be proved or disproved by a particular process of argumentation; or when we attempt to present to ourselves, for self-satisfaction, or to others for the purpose of convincing them, the grounds of our own convictions--that is, when we reason, our Intelligence proceeds according to fixed rules. When we have judged or reasoned correctly, we find ourselves able, on reflection, to develop the rules in conformity to which we judged and reasoned, without a distinct consciousness of the fact. In the light of these rules, we are then able to detect the reason and grounds of fallacious judgments and reasonings.

Logic defined.

The above remarks have prepared the way for a distinct statement of the true conception of Logic. It is a systematic development of those rules in conformity to which the universal Intelligence acts, in judging and reasoning. Logic, according to this conception, would naturally divide itself into two parts-a development of those rules to which the Intelligence conforms in all acts of correct judgment and reasoning, and a development of those principles by which false judgments and reasonings may be distinguished from the A Treatise on Logic, in which the laws of judging and reasoning are evolved in strict conformity to the above conception, would realize the idea of science as far as this

true.

subject is concerned. Logic, to judging and reasoning, is what Grammar is to speaking and writing. Logic pertains not at all to the particular objects about which the Intelligence is, from time to time, employed, but to rules or laws in conformity to which it does act, whatever the objects may be.

Relations of Logic to other Sciences.

In the chronological order of intellectual procedure, Logic is preceded by judging and reasoning, just as speaking and writing precede Grammar. In the logical order, however, it is the antecedent of all other sciences. In all sciences the Intelligence, from given data, judges in respect to truths resulting from such data. We also reason from such data for the establishment of such truths. Logic develops the laws of thought which govern the action of the Intelligence in all such procedures. As a science, it is distinct from all other sciences, yet it permeates them all, giving laws to the Intelligence, in all its judgments and reasonings, whatever the objects may be about which it is employed.

CHAPTER XVII 1.
XVIII.

MISCELLANEOUS TOPICS.

THERE are a few topics of a miscellaneous character connected with our previous investigation, which I have reserved for a distinct and separate Chapter. The first to which I would direct attention is,

The Bearing of the Philosophy of Locke upon Science, properly so called.

In the philosophy of Locke, axioms have no place, except as objects of ridicule and contempt. He directly denies that any science whatever is founded upon them. Equally removed from his philosophy are all ideas of pure Reason. All the objects of knowledge are qualities external and internal. Now in what sense and in what form is science pertaining to any subject possible, according to the fundamental principles of this philosophy? The answer which I give to this question is this: In no form whatever is science of any kind possible, according to the fundamental principles of this philosophy. We will take in illustration the science of external and material substances. All that we know of these substances, according to this philosophy, is by sensation-that is, qualities, and nothing else. Now the first step in a scientific process pertaining to these qualities, is that of making abstraction of them, in thought, separating those which differ, and uniting those which agree. On what condition can this process take place? On one condition only, to wit: that we have in our minds the ideas of resemblance and difference. But these ideas are pure conceptions of Reason, and are not given by sensation at all. Sensation may give the colors red and yellow, for example; but it can never give the fact, that the one color differs from the other. This