In examining the nature of syllogistic reasoning, it is now evident that you have,

In the first place, something laid down, granted as true, or assumed as necessary, for the subsequent proceeding of the mind. It does not affect the truth of this position to determine whether you must always have two propositions, as in a regular syllogism, before a conclusion can be drawn; or whether the mind, having admitted one judgement or proposition, be led on from that one to another inevitably following from it. Suffice it, that in every argument you must begin with something laid down, granted, or assumed; in other words, you must have some datum or data, as points from which to start, or ground on which to rest.

Secondly. Having something laid down or granted, it is the characteristic of all cor

proves that Hobbes is about right, though he meets with Mr. Stewart's particular reprobation, in saying that "when a man reasoneth, he does nothing else but conceive a sum total from addition of parcels, or conceive a remainder from subtraction of one sum from another," &c.

rect or logical reasoning, that the conclusion necessarily follows from the premises. It is involved in the premises; it is a consequence inevitably connected with them. An absolute necessity is the quality of all sound reasoning.

How then does logical or common reasoning differ from what we call mathematical or demonstrative reasoning? In both we have data from which to start, and conclusions inevitably resulting, involved in the meaning of the terms, i. e. in our conception of the things signified.

Will any man assert that logical reasoning is not demonstrative in the mathematical sense of the term? that is, does not convey a feeling of certainty to the mind in the justness and necessity of the conclusion. For my own part, I feel no difference in respect of absolute certainty. Having admitted that "whatever exhibits marks of design must have an intelligent author," and that "the universe exhibits marks of design," it appears to me as inevitable to admit that "therefore the universe must have an intelligent author," as to admit that the three angles of

a triangle are equal to two right angles, having admitted that the sum of the angles on the same side of a straight line, at the same point, is equal to two right angles. The conclusion is involved in the meaning of the terms in the latter case it rests upon the notion of equality; in the former, the notion of design. It must be confessed, however, that the notion of design is not so immediately an idea of sensation, to use Locke's phraseology, as that of equality. It is an idea drawn rather from reflection, or what we are conscious of when the mind turns inward upon itself. In common language, two things are said to be equal when there are no sensible marks of difference between them. But an object of nature or of art will indicate design to an observer very much in proportion to the observer's power of appreciating the end aimed at, and the means employed; and surely it is impossible to separate the idea of design from the perception of means and ends.

It is not, then, in the circumstance of starting from certain data or given principles; it

is not in the necessity of the conclusion, as resulting inevitably from the data, that logical or common reasoning, and mathematical reasoning, differ from one another. We must seek for that difference elsewhere. When, therefore, the Edinburgh reviewer, after Kant, talks of necessary and contingent matter, as distinguishing two sorts of logic, one of which he equals to mathematical reasoning, the other to general reasoning, it is a talk without meaning, or at least without clear and sufficient meaning. For in all logic, as in all mathematics, the conclusion is equally necessary, equally contingent; equally necessary in the sense of inevitably following from, or being involved in, the data; equally contingent upon the comprehension or force of the terms; that is, the degree of clearness and exactness in the things signified.

But, again, if in all reasonings you start from some data, and in all reasonings you have necessary conclusions, where lies the difference between what we call mathematical and common reasoning? Obviously

we must seek it in the nature or difference of

the data and here, perhaps, we shall come to see in what sense it is true, if in any sense it be true, that in mathematics you have necessary, in logic contingent, matter. In mathematics we have, as I have shown, definitions, i. e. exact terms, significant of certain clear ideas of figure and quantity; and we are employed in tracing the relations of these ideas one with another. In all other reasoning we have also terms, and these terms are, or ought to be, signs of ideas. But while, in mathematical reasoning, we are concerned with ideas of figure and quantity, (to say nothing of forces and motion, with whatever else can be viewed and treated mathematically,) in logic we have every variety of term and of idea. There is no proposition of any kind, no number of words which can be put together so as to form a proposition, to whatever subject it may relate, which may not form part of a syllogism. It is owing to this comprehensiveness or vastness of logic, in its practical application, that its true nature is so little understood. In all reasoning, in all thought, as communicated from one mind to