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man," though placed by others in this class of truths, may still more readily be traced to the law of past experience.

The

There are also a set of truths, which are called mathematical axioms, that have ordinarily been classed as intuitive truths. But it is conceived that belief in these also, can all be resolved into the same as belief in our perceptions and memory. Mathematical axioms relate to the qualities and relations of matter, all which qualities and relations are learned through the medium of the senses. For example, take the axiom, "The whole is greater than a part." Here the term whole recalls the conception of a relation which is learned by the senses. The word part recalls another relation which is gained by the senses. The word greater is the name of another relation gained in the same way. mind has the power of conceiving of the whole of a thing, and the part of a thing, as two separate existences, in such a way as to notice a relation between them. When it does thus conceive of a whole and a part, in relation to each other, it perceives that the relation exists to which the term greater in past experience, has always been applied. This it can be seen is a mere act of memory, the same as any application of any name. This axiom is no more an intuitive truth, than the assertion that black is not white, or that the top is not the bottom, or any other truth gained by perception and memory. Mathematical axioms are assertions of truths gained by the senses, in regard to the properties and relations of matter, or they are identical propositions. As an example of an identical proposition of this kind, may be mentioned the axiom; "Magnitudes that fill the same space are equals." The term equals," and the term "magnitudes that fill the same space,” are only different names for the same thing; and this proposition amounts to no more than the assertion, that equals are equals, which is an identical proposition.

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It is a curious fact in the history of mental science, that some of the most profound and investigating minds, led on

either by a desire to support some favourite theory, or by an excessive love of originality, have been led to deny some of these principles of common sense, which unlearned minds never mistake in maintaining.

The denial of these truths has caused many long and abstruse controversies and speculations. The difficulties which arise in disputes on such subjects are insuperable, because the principles of reason being themselves the foundation of all reasoning, cannot be established or defended by reason. If they are denied, it is in vain to attempt to prove them. All that can be done is to show, that whatever men affirm or deny on these points, the conduct of all mankind demonstrate that they are actually believed.

The actions of men are the best evidence of their belief; and we never find mankind by their actions manifesting any disbelief of these fundamental truths. In all the intercourse of life men prove that they believe their senses, their memory, their consciousness, and their personal identity; they prove their belief that "every effect has a cause," in the sense here explained, that the "mind is an independent agent," that " contrivance does not exist without an intelligent designer, and that the nature of a contrivance indicates the design of the contriver," that "things will be in agreement with past experience, unless there is some reason to the contrary," and that "men are obligated not needlessly to destroy happiness or cause pain."

The long discussions occasioned by attempts to destroy and to defend belief in these principles of common sense, have given too much occasion for the pointed definition of Mental Philosophy as "a science, consisting of absurdities, which none but a philosopher ever believed, and of truisms, which none but a philosopher ever doubted."

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CHAPTER XIII.

RATIONAL BELIEF.

An impossibility, is an assertion which the mind cannot conceive of as truth, nor can it conceive of any evidence, which could lead to such a belief. An example of an impossibility is in the assertion that "a thing exists, and does not exist at the same moment of time." This is what the mind not only cannot believe as things now are, but it cannot conceive it to be true in any possible case. All contradictory assertions are impossibilities.

An absurdity, is an assertion which is contradictory to one of the laws of reason, so that if it is believed, one of these laws must be denied. An absurdity is not always an impossibility, for the assertion, that memory is not to be trusted, though contradictory to a law of reason, and thus an absurdity, is not a contradiction; for the mind can conceive of it as true, though it cannot believe it to be so. But if it is asserted that " memory is to be trusted, and is not to be trusted in regard to the same thing, and at the same moment of time," this is a contradiction which the mind cannot even conceive of as truth.

Reasoning is a process for establishing the truth of one assertion, by exhibiting evidence that it is included in a truth already believed; or else a process for showing that an assertion is false, by exhibiting evidence that it is contradictory to a truth already believed. Thus if we wish to establish the assertion, that " an ostrich is a bird," we take a truth already believed, which is, that "a thing having animal life, wings, and feathers, is a bird." We then exhibit the evidence of the senses, or of testimony, that an ostrich has animal life, wings,

and feathers.

If the evidence is such as ensures the belief that an ostrich has these qualities, it is impossible to disbelieve the conclusion that "an ostrich is a bird." For if the first truth is believed, and the second one also, the denying the conclusion, would be maintaining that a thing having wings and feathers is a bird, and is not a bird, which is a contradiction and cannot be believed. This mode of proof is called direct, but when a thing is proved to be true by showing that the denial of it is contradictory to some truth already acknowledged ; this method is called indirect, or "reductio ad absurdum," that is reducing to an absurdity.

A syllogism consists of a regular arrangement of the three propositions, which every act of reasoning involves. The first is the truth already believed, and is called the major proposition. The second is an assertion, which is to be established by evidence, and is called the minor proposition. The third is the conclusion; or the truth which it is the object of the act of reasoning to establish. In the preceding example, the major proposition is, "a thing having animal life, wings, and feathers, is a bird." The minor proposition is, "an ostrich has animal life, wings, and feathers.". This assertion is to be established, either by the evidence of sense, or by testimony, in order to accomplish the object of the act of reasoning. When evidence has been offered to enforce belief of the minor proposition, then the conclusion is drawn, which is, that "an ostrich is a bird." Many seem to suppose, that the mere repetition of the propositions which constitute a syllogism is an act of reasoning. But this is not correct. The act of reasoning consists in offering evidence to establish the assertion of the minor proposition, and when this is done, the object of the process is accomplished, and the conclusion is obtained.

In pursuing any course af reasoning, the mental process seems to be this: The establishment of some proposition by evidence, becomes an object of desire. Immediately all conceptions, which, by the faculty of judgment, are discerned as

having a relation fitted to accomplish this object, through the influence of desire, become interesting to the mind, and by the principles of association, gather around them other connected conceptions. From these new combinations the mind again selects those objects which seem fitted to accomplish the general object of the mind. During this process the truth which is to be the major proposition is discovered, and also the evidence, which will establish the minor.

The chief labour in regard to reasoning, consists in finding evidence to establish the minor proposition. Thus if the object is to prove, that " men are obligated to speak the truth," the process would be this: The major proposition would be, that "men are obligated not to cause needless evil to others;" for it is this principle of reason, which is at the foundation of all moral obligations. The minor proposition would be, that “ "lying is causing needless evil to others." This proposition is to be established by proof, in which the evils caused by this vice are to be exhibited. If sufficient evidence is adduced to establish belief in the minor proposition, then the conclusion is gained, that "men are obligated to speak the truth." If the major proposition is a law of reason, and the minor proposition is proved by sufficient evidence, then belief is inevitable. But often some assertions are taken for the major proposition, to which belief is not accorded. In such cases, the major proposition must be first proved, by seeking some other truth already believed, and showing that it is included in that truth. If this second major proposition is denied, then this must be proved by referring it to another truth, as before. By following this process, we shall at length always reach some law of reason as a major proposition, and then if the assertion is found to be in agreement with this, it can no longer be disputed. This is a sure way to end controversies, if it can be shown that denying the assertion in question, does in fact involve a denial of one of the laws of reason. Whenever this can be done, every sane mind will accord its belief,

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