proach to the things defined, the more nearly does the practical result correspond to the ideal conclusion. Therefore, mathematical truths are not mere ingenious theorems, but pregnant with useful application.

k

Before me, the author of the Philosophy of Rhetoric, as well as Dr. Thomas Brown, objected to the syllogism, as necessarily involving a petitio principii. Dr. Whately does not attempt to prove the contrary, but he answers that the same objection lies against all arguments whatever. All arguments involve a petitio principii! Am I wrong, then, in saying that all reasoning is depreciated in order to suit an artificial and futile system? After this, I need not add another word upon the syllogism.

V. Thus, we have been able to distinguish three kinds of probable reasoning; the inductive, the deductive, and the plain, of which the two former have more affinity to each other than to the third. We are aware that, according to some, all reasoning is of two kinds, the inductive and the deductive; that one author maintains all probable reasoning to be deductive, or, as he calls it, analytic; and another, that all is inductive.'

The words in italics are so printed in the original.

1 Dr. T. Brown maintains that all reasoning, except the Mathematical, or Proportional, as he calls it, is analytic; while Mr. Mill seems to think that all reasoning is in reality inductive.

But it certainly does not appear from an examination of particular instances, that all probable reasonings can be classed under these two heads, much less all reasonings whatsoever.

Premature generalization is the bane of science; and principia media are more applicable and more fruitful than principia generalissima. By generalizing prematurely we have always to begin afresh, nothing is gained; whereas, by advancing more cautiously, we establish one position at least, whence we may hope in time to take a higher flight. Bacon has observed, that the grand error of philosophers before his time consisted in this, that from particulars they rose at once to extreme generalities, whence they endeavoured to deduce every thing; whereas, the true method of progress is to advance by degrees from one step of generalization to another, even unto the highest.

Meanwhile, let us examine what relations are the proper subject of each of these sorts of reasoning; for we have seen that all reasoning consists in the tracing of relations.

The subject of demonstrative reasoning is the relations of Quantity and those alone. The first subject of inductive reasoning is the relation of Resemblance, one of amazing extent, by means of which we arrive, also by induction, at the know

ledge of other relations, those of Cause and Effect.

The relations traced by deductive reasoning are those of Comprehension, of a whole to a part, as when we show that a particular proposition is comprehended under a general one; the policy of a free trade in corn, for instance, un der the policy of free trade in general. Sequences of cause and effect are traced by plain reasoning, as in the examples above given. A is the cause of B, and B of C, therefore, A is the remote cause of C. Relations of Position also are traced by this sort of reasoning, as in the following instance:

York is further from London than Stamford; and Edinburgh is further from London than York; much more then is Edinburgh further from London than Stamford.

From the first proposition, a person totally unacquainted with the position of Edinburgh could infer nothing; and from the second proposition, one unacquainted with the position of Stamford could infer nothing; both, therefore, are necessary to the conclusion, which is not comprehended under either."

m Such relations of Position are, in reality, relations of Quantity, and so, admit of demonstrative reasoning.

VI. It will be observed that we have not attempted, (as some have) to establish an universal principle of reasoning, because we very much doubt whether any such principle exist. We have seen that all reasoning consists in tracing relations, and since these are various, it is natural to presume that the principles of reasoning may be so too. Even in mathematical reasoning, the most simple of any, for it embraces but one kind of relation, clearly distinguished from all other relations, and having its own differences accurately marked out, there is more than one fundamental principle or axiom. Surely then it is unlikely that there can be but one principle for all probable reasoning, which embraces various and complicated relations. The case of mathematics proves, at least, that all reasoning is not based upon one principle. "Things which are equal to the same are equal to one another;" and "if equals be added to equals the wholes are equal;" are not one axiom but two.

Do we clearly understand what is meant by a principle of reasoning? It is a general truth, of which each inference is a particular instance, a truth either self-evident, as in mathematics, or, at least, to be taken for certain, since it is incapable of proof, and at the same time indispensable to the proof of other propositions. In

L L

this, the validity of an inference consists, and upon it, conviction depends. Considered in respect to the reasoning itself, it is an invariable constituent or element; in respect to the influence on the mind, a cause; for, as we have seen," a principle may be either constituent or elemental, or else causal.

Although we do not pretend to lay down one universal principle of reasoning, yet we may arrive at some general truths on this subject. Since all reasoning consists in tracing relations, and since these are either of coexistence or of succession, it follows that the object of reasoning is to prove either that two or more things coexist or do not coexist; or that two or more things succeed or do not succeed each other; generally, if not invariably. The object of science, in particular, is to determine the permanent or invariable coexistence, and succession of things, partly by direct observation, and where that fails, by reasoning or inference. Where one thing is known certainly to exist, there to expect another along with it; or where one thing is ascertained, to look for another after it; such are the anticipations of human science.

Coexistence and succession being two such different relations, it does seem improbable that

n See Article PRINCIPLE.