complete and necessary connexion between the conclu sion and the premises, than the certainty or the necessity of the truths which the premises assume.

To this observation it may be added, (in order to prevent any misapprehensions from the ambiguity of language,) that Aristotle's idea of the nature of demonstration, is essentially different from that which I have already endeavoured to explain. "In all demonstration," (says Dr. Gillies, who, in this instance, has very accurately and clearly stated his author's doctrine,) "the first principles must be necessary, immutable, and therefore eternal truths, because those qualities could not belong to the conclusion, unless they belonged to the premises, which are its causes."* According to the account of de

96.

* Aristotle's Ethics and Politics, &c. By Dr. Gillies. Vol. I. p. I am much at a loss how to reconcile this account of demonstrative evidence with the view which is given by Dr. Gillies of the nature of syllogism, and of the principles on which the syllogistic theory is founded. In one passage (p. 81.) he tells us, that "Aristotle invented the syllogism, to prevent imposition arising from the abuse of words;" in a second, (p. 83.) that “the simple truth on which Aristotle has reared a lofty and various structure of abstract science, clearly expressed and fully demonstrated-is itself founded in the natural and universal texture of language:" in a third, (p. 86.) that "the doctrines of Aristotle's Organon have been strangely perplexed by confounding the grammatical principles on which that work is built with mathematical axioms." Is it possible to suppose, that Aristotle could have ever thought of applying to mere grammatical principles,—to truths founded in the natural and universal texture of language the epithets of necessary, immutable, and eternal?

I am unwilling to lengthen this note, otherwise it might be easily shown, how utterly irreconcileable, in the present instance, are the glosses of this ingenious commentator with the text of his author. Into some of these glosses it is probable that he has been unconsciously betrayed, by his anxiety to establish the claim of his favourite philosopher to the important specula

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monstrative or mathematical evidence formerly given, the first principles on which it rests are not eternal and immutable truths, but definitions or hypotheses; and therefore, if the epithet demonstrative be understood, in our present argument, as descriptive of that peculiar kind of evidence which belongs to mathematics, the distinction between demonstrative and dialectical syllogisms is reduced to this; that in the former, where all that is asserted is the necessary connexion between the conclusion and the premises, neither the one nor the other of these can with propriety be said to be either true or false, because both of them are entirely hypothetical: in the latter, where the premises are meant to express truths or facts, (supported, on the most favourable supposition, by a very high degree of probability,) the conclusion must necessarily partake of that uncertainty in which the premises are involved,

But what I am chiefly anxious at present to impress on the minds of my readers, is the substance of the two following propositions: First, That dialectical syllogisms (provided they be not sophistical) are not less demonstratively conclusive, so far as the process of reasoning is concerned, than those to which this latter epithet is restricted by Aristotle; and, secondly, That it is to the process of reasoning alone, and not to the premises on which it proceeds, that Aristotle's demonstrations exclusively refer. The sole object, therefore, of these demonstrations, is (as I already remarked) not to strengthen, by new proofs, principles which were doubtful, or to supply

tions of Locke on the abuse of words, and to those of some later writers on language considered as an instrument of thought.

new links to a chain of reasoning which was imperfect, but to confirm one set of demonstrations by means of another. The mistakes into which some of my readers might have been led by the contrast which Aristotle's language implies between dialectical syllogisms, and those which he honours with the title of demonstrative, will, I trust, furnish a sufficient apology for the length of this expla

nation.

Having enlarged so fully on the professed aim of Aris- · totle's demonstrations, I shall despatch, in a very few pages, what I have to offer on the manner in which he has carried his design into effect. If the design be as unphilosophical as I have endeavoured to show that it is, the apparatus contrived for its execution can be considered in no other light than as an object of literary curiosity. A process of reasoning which pretends to demonstrate the legitimacy of a conclusion which, of itself, by its own intrinsic evidence, irresistibly commands the assent, must, we may be perfectly assured, be at bottom unsubstantial and illusory, how specious soever it may at first sight appear. Supposing all its inferences to be strictly just, it can only bring us round again to the point from whence we set out.

The very acute strictures of Dr. Reid, in his Analysis of Aristotle's Logic, on this part of the Syllogistic Theory, render it superfluous for me, on the present occasion, to enter into any details upon the subject. To this small, but valuable tract, therefore, I beg leave to refer my readers; contenting myself with a short extract, which contains a general and compendious view of the conclusion

drawn, and of the argument used, to prove it, in each of the three figures of syllogisms.

"In the first figure, the conclusion affirms or denies something of a certain species or individual; and the argument to prove this conclusion is, That the same thing may be affirmed or denied of the whole genus to which that species or individual belongs.

"In the second figure, the conclusion is, That some species or individual does not belong to such a genus; and the argument is, That some attribute common to the whole genus does not belong to that species or individual.

"In the third figure, the conclusion is, That such an attribute belongs to part of a genus; and the argument is, That the attribute in question belongs to a species or individual which is part of that genus.

"I apprehend that, in this short view, every conclusion that falls within the compass of the three figures, as well as the mean of proof, is comprehended. The rules of all the figures might be easily deduced from it; and it ap pears that there is only one principle of reasoning in all the three; so that it is not strange, that a syllogism of one figure should be reduced to one of another figure.

"The general principle in which the whole terminates, and of which every categorical syllogism is only a particular application, is this, That what is affirmed or denied of the whole genus may be affirmed or denied of every species and individual belonging to it. This is a principle of

undoubted certainty indeed, but of no great depth. Aristotle and all the logicians assume it as an axiom, or first principle, from which the syllogistic system, as it were, takes its departure; and after a tedious voyage, and great expense of demonstration, it lands at last in this principle, as its ultimate conclusion. O curas hominum! O quantum est in rebus inane !"*

When we compare this mockery of science with the unrivalled powers of the inventor, it is scarcely possible to avoid suspecting, that he was anxious to conceal its real poverty and nakedness, under the veil of the abstract language in which it was exhibited. It is observed by the author last quoted, that Aristotle hardly ever gives examples of real syllogisms to illustrate his rules; and that his commentators, by endeavouring to supply this defect, have only brought into contempt the theory of their master. "We acknowledge, (says he) that this was charitably done, in order to assist the conception in matters so very abstract: but whether it was prudently done for the honour of the art, may be doubted." One thing is certain, that when we translate any of Aristotle's demonstrations from the general and enigmatical language in which he states it, into more familiar and intelligible terms, by applying it to a particular example, the mystery at once disappears, and resolves into some self-evident or identical puerility. It is surely a strange mode of proof, which would establish the truth of what is obvious, and what was never doubted of, by means of an argument which appears quite unintelligible, till explained and illustrated by an instance perfectly similar to the very thing to be proved.

This axiom is called, in scholastic language, the dictum de omni et de nullo.