Posterior Analytics (Bouchier)/Book I/Chapter XX

Chapter XX: Middle terms are not infinite

 * Middle terms cannot be limitless; otherwise the subject and attribute could never be brought into the relation demanded by the syllogism. Attribution also is limited both in the direction of the general and of the particular.

That the intervening terms of a predication cannot be infinite if predications terminate both in an upward and a downward direction is obvious. [I mean by ‘upward’ that which is more in the direction of universal, by ‘downward’ that which is nearer to the particular]. For if, when A is predicated of F, the intervening terms (here designated as B) could be infinite, it is clear that if one proceeded from A in the direction of the particular one could continue to predicate one term of another to infinity, [the terms intervening between A and F are here regarded as infinite]; and similarly, if one proceeded from F in the direction of the more general, one would traverse an infinite number of terms before arriving at A. If, however, there can be no such infinite progress or regress, the terms intervening between A and F cannot be infinite.

It is of no avail to maintain that some of the intervening terms, say A, B, C, follow one another so closely as to admit of no further intervening term, while others of the series are not so closely connected. For whichever of the B’s I care to select must have a certain relation to A or to F, and the intervening terms must be finite or infinite. To enquire from what starting point one begins the process to infinity, and whether this process is mediate or immediate is not to the purpose, for everything which follows any given point must be looked on as limitless.