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takes A, B, C, for the terms of the syllogism. Thus, the first mode of the first figure is demonstrated by him in this manner. "For," says he, "if A is attributed to every B, and B to every C, "it follows necessarily, that A may be attributed "to every C." For disproving the illegitimate modes, he uses the same manner; with this difference, that he commonly for an example gives three real terms, such as, bonum, habitus, prudentia; of which three terms you are to make up a syllogism of the figure and mode in question, which will appear to be inconclusive.
The commentators and systematical writers in logic, have supplied this defect, and given us real examples of every legitimate mode in all the figures. We acknowledge this to be 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. I am afraid this was to uncover the nakedness of the theory; it has undoubtedly contributed to bring it into contempt; for when one considers the silly and uninstructive reasonings that have been brought forth by this grand organ of science, he can hardly forbear crying out, Parturiunt montes, et nascitur ridiculus mus. Many of the writers of logic are acute and ingenious, and much practised in the syllogistical art; and there must be some reason why the examples they have given of syllogism are so lean.
We shall speak of the reason afterwards; and shall now give a syllogism in each figure as an example.
No work of God is bad;
The natural passions and appetites of men are the work of God.
Therefore none of them is bad.
In this syllogism, the middle term, work of God, is the subject of the major and the predicate of the minor; so that the syllogism is of the first figure. The mode is that called Celarent; the major and conclusion being both universal negatives, and the minor an universal affirmative. It agrees to the rules of the figure, as the major is universal, and the minor affirmative; it is also agreeable to all the general rules; so that it maintains its character in every trial. And to show of what ductile materials syllogisms are made, we may, by converting simply the major proposition, reduce it to a good syllogism of the second figure, and of the mode Cesare, thus:
Whatever is bad is not the work of God;
All the natural passions and appetites of men are the work of God;
Therefore they are not bad.
Every thing virtuous is praise-worthy;
Some pleasures are not praise-worthy.
Here the middle term praise-worthy being the predicate of both premises, the syllogism is of the second figure; and seeing it is made up of the propositions, A, O, O, the inode is Baroco. It will be found to agree both with the general and special rules and it may be reduced into a good syllogism of the first figure upon converting the major by contraposition, thus:
What is not praise-worthy is not virtuous; Some pleasures are not praise worthy; Therefore some pleasures are not virtuous. That this syllogism is conclusive, common sense pronounces, and all logicians must allow; but it is somewhat unpliable to rules, and requires a little straining to make it tally with them.
That it is of the first figure is beyond dispute; but to what mode of that figure shall we refer it? This is a question of some difficulty. For, in the first place, the premises seem to be both negative, which contradicts the third general rule; and moreover, it is contrary to a special rule of the first figure, That the minor should be negative. These are the difficulties to be removed. 46
Some logicians think, that the two negative particles in the major are equivalent to an affirmative; and that therefore the major proposition, What is not praise-worthy is not virtuous, is to be accounted an affirmative proposition. This, if granted, solves one difficulty; but the other remains. The most ingenious solution, therefore, is
this: Let the middle term be not praise worthy. Thus, making the negative particle a part of the middle term, the syllogism stands thus:
Whatever is not praise-worthy is not virtuous ; Some pleasures are not praise-worthy; Therefore some pleasures are not virtuous. By this analysis, the major becomes an universal negative, the minor a particular affirmative, and the conclusion a particular negative, and so we have a just syllogism in Ferio. en bag s
We see, by this example, that the quality of propositions is not so invariable, but that, when occasion requires, an affirmative may be degraded into a negative, or a negative exalted to an affirmative, Another example:
2 sale at
All Africans are black;
Therefore some men are black. This is of the third figure, and of the mode Darapti; and it may be reduced to Darii in the first figure, by converting the minor.
All Africans are black;
Some men are Africans;
Therefore some men are black. 20.3
By this time I apprehend the reader has got as many examples of syllogisms as will tite for that kind of entertainment.
SECT. 4. On the Demonstration of the Theory.
Aristotle and all his followers have thought it necessary, in order to bring this theory of categorical syllogisms to a science, to demonstrate, both that the fourteen authorised modes conclude justly, and that none of the rest do. Let us now see how this has been executed.
As to the legitimate modes, Aristotle and those who follow him the most closely, demonstrate the four modes of the first figure directly from an axiom called the Dictum de omni et nullo. The amount of the axiom is, That what is affirmed of a whole genus, may be affirmed of all the species and individuals belonging to that genus; and that what is denied of the whole genus, may be denied of its species and individuals. The four modes of the first figure are evidently included in this axiom. And as to the legitimate modes of the other figure, they are proved by reducing them to some mode of the first. Nor is there any other principle assumed in these reductions but the axioms concerning the conversion of propositions, and in some cases the axioms concerning the opposition of propositions.
As to the illegitimate modes, Aristotle has taken the labour to try and condemn them one by one in all the three figures: but this is done in such a manner that it is very painful to follow him. To give a specimen. In order to prove, that those modes