The arte of logick Plainely taught in the English tongue, according to the best approued authors. Very necessary for all students in any profession, how to defend any argument against all subtill sophisters, and cauelling schismatikes, and how to confute their false syllogismes, and captious arguments. By M. Blundevile.

Of Diuision.

WHat is Diuision?

What Diuision is, and how many kindes there be, and what is to be obserued in euery kinde hath been declared before, lib. 2. cap. 4. when we shewed the order of defining and diuiding.

How may we reason from diuision?

Two manner of wayes: first, from the denying of one part or more of the diuision, to affirme another part therof, as thus: Euery sensible body is whole or sicke, but Peter is a sensible body and not sicke: Ergo, hee is whole: or thus. Of sensible bodies there be some whole, some sicke. Peter is a sensible bo∣die and not sicke: Ergo, he is whole. In these two kindes of examples the diuision consisteth onely of two parts, wherein it sufficeth to denie the one for affirming the other. But if the di∣uision consist of many parts, then you must denie all the parts sauing that which you would affirme, as in this example fol∣lowing:

Plato disputeth, is a proposition, but it is neither vni∣uersall, particular, nor indefinite: Ergo, it is a singular proposi∣tion: in which kind of reasoning if you leaue out or omit any part that is to be denied, then the conclusion is naught, for it is no good consequent to say thus: this proposition Plato dis∣puteth, is neither vniuersal nor particular: Ergo, it is indefinite. Notwithstanding, if you ioyne the part omitted in your Ante∣cedent with a coniunction disiunctiue, the argument may be made good; as to say thus: this proposition Plato disputeth, is neither vniuersall nor particular: Ergo, it is either indefinite or singular.

What is the Maxim of this first way of reasoning?

The Maxim is thus: whatsouer agreeth with the thing di∣uided, must needs agree with some one of the parts thereof.

What is the second way of reasoning from Diuision?

The second way is to proceede from the affirming of one of the parts to the denying of the other, if it consist but of two, or to the denying of all the rest, if it consist of many. Of two parts let this bee your example: Of sensible bodies some bee whole, some sicke, but this sensible body is whole: Ergo, he is not sicke. Of many parts thus: of propositions one is vniuer∣sall, another particular; one indefinite, another singular: but this proposition Plato disputeth▪ is singular: Ergo, it is neither vniuersall, particular, nor indefinite.

What is the Maxim of this way of reasoning?

Whatsoeuer agreeth with one of the parts, must needs dis∣agree with all the rest, for euery good diuision would be made of parts meere repugnant, or at the least diuers in kinde one from another: for it is a principall condition requisite to diui∣sion, whereupon the second way of reasoning is grounded euen as the first way is grounded vpon another good conditi∣on belonging also to diuision, which is that the thing diuided may not containe more or lesse then his proper parts.