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 Reduction, and of the kindes thereof, and also of the signi∣fication of certaine consonants in the words of Art seruing to Reduction.

WHat is Reduction?

Reduction here is none other thing, but a declaration, prouing or shewing the goodnes of an vnperfect Syllogisme, by a Syllogisme of a perfect moode.

How manfold is such Reduction?

Two-fold; for it is either offensiue, or else by impossibility.

What is Reduction offensiue?

Reduction offensiue is, when a Syllogisme is reduced to his perfection, either by conuersion, or by transposing the premis∣ses, or else by both at once.

What meane yee by transposing of the premisses, for as touching conuersion ye haue spoken thereof before, lib. 3. cap. 6.

The premisses are said to be transposed, when the Maior is put in the Minors place; or contrariwise the Minor into the Maiors place.

What is Reduction by impossibilitie?

Reduction by impossibility is, when the goodnesse of the Syllogisme is so proued, as the aduersary denying the same, must needs be brought to some absurditie, as to confesse two Contradictories to be both true at once, or some proposition to be false, which he hath confessed before to be true, or is ma∣nifestly true of it selfe. But first we wil speake of Reduction of∣fensiue, and then of Reduction by impossibility; and because that Reduction offensiue is done sometime by conuersion, and sometime by transposition, and sometime by both at once: and againe, that sometime one of the premisses, somtime both, and sometime no more but the Conclusion onely is conuerted, and that sometime by simple conuersion, and sometime by conuer∣sion per accidens: the Schoolemen for •…•…asement of the memo∣rie, haue made eight of the Consonants, besides the Vowels in the words of Art before mentioned, to be significatiue, and to

declare how euery proposition ought to be reduced.

For first, these foure Consonants, b. c. d. f. (with one of the which euery vnperfect moode doth begin) doe shew that such vnperfect moodes ought to bee reduced into those perfect moodes, which doe begin with the like letter, as,

• Baralipton, Baroco, Bocardo, into Barbara,
• C•…•…lantes, Caesare, Camestres, into Celarent,
• Dabitis, Darapti, Disamis, Datisi, into Darij,
• Fapesmo, Frisesomorum, Felapton, Ferison, Festino, into Darij

Which be the other foure Consonants, and what doe they signifie?

The other foure Consonants put betwixt the Vowels, bee these, s. p. m. c. where of s. signifieth simple conuersion, (that is to say) that the Vowell, which next before this Consonant, is to be simply conuerted, p. signifieth conuersion per accidens, m. betokeneth transposition of the premisses, c. in the latter end or midst of the moode, betokeneth Reduction by impossibilitie as in Baroco, and Bocardo.

Giue examples, and shew how such Reduction is to be made.

First, as touching reduction by conuersion, Cesare is redu∣ced into Celarent by simple conuersion of the Maior: as this Syllogisme in Cesare.

• Ce- No tree is a sensible body, which is reduced in∣to Celarent, thus:
• sa- But euery man is a sensible body: which is reduced in∣to Celarent, thus:
• re. Ergo, no man is a tree. which is reduced in∣to Celarent, thus:

• Ce- No sensible body is a tree,
• la- But euery man is a sensible bodie:
• rent. Ergo, no man is a tree.

And Camestres is reduced into Celarent by simple conuer∣ting the Conclusion, and also by transposing the premisses, as this Syllogisme in Camestres.

• Ca- Euery man is a sensible body, which is reduced in∣to Celarent, thus:
• mes- But no tree is a sensible body: which is reduced in∣to Celarent, thus:
• tres. Ergo, no tree is a man. which is reduced in∣to Celarent, thus:

• Ce- No sensible body is a tree,
• la- But euery man is a sensible bodie:
• rent. Ergo, No man is a tree.

Festino is reduced into Ferio, by simply conuerting the Maior, as in this Syllogisme in Festino.

• Fes- No stone is a sensible body, which is reduced in∣to Ferio thus.
• ti- But some man is a sensible body: which is reduced in∣to Ferio thus.
• no. Ergo, Some man is not a stone. which is reduced in∣to Ferio thus.

• Fe- No sensible body is a stone,
• ri- But some man is a sensible body:
• o. Ergo, Some man is not a stone.

Darapti is reduced from Darij by conuerting the minor per accidens, as this Syllogisme in Darapti.

• Da- Euery man is a substance, which is reduced into Darij thus.
• rap- But euery man is a sensible body: which is reduced into Darij thus.
• ti. Ergo, some sensible body is a substance. which is reduced into Darij thus.

• Da- Euery man is a substance,
• ri- But some sensible body is a man:
• j. Ergo, Some sensible body is a substance.

Ferison is reduced into Ferio, by simple conuersion of the mi∣nor, as this Syllogisme in Ferison.

• Fe- No man is a stone. which is reduced into Ferio thus.
• ri- But some man is a sensible body: which is reduced into Ferio thus.
• son. Ergo, some sensible body is not a stone which is reduced into Ferio thus.

• Fe- No man is a stone,
• ri- But some sensible body is a man:
• son. Ergo, some sensible body is not a stone.

And so forth in all the rest, according as the significatiue Consonants doe direct you.