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.

THE ART OF LOGICKE. THE THIRD BOOKE.

CHAP. I.

Of a Proposition.

WHat is a Proposition?

It is a perfect speech whereby some∣thing is manifestly declared to be true or false.

Whereof is such speech specially com∣pounded?

Of Noune and Verbe, which Noune would be of the Nominatiue case, and the Verbe of the Indicatiue Mood, as when I say, Man is a sensible body; for the Logicians do seldome allow any such speeches as are either of the Optatiue, Imperatiue, Interrogatiue, or Vocatiue Mood, as, I would to God I had a good horse: this speech is not accounted to be so true or certaine, as to say, I haue a good horse.

Of how many parts doth a Proposition consist?

Of three, that is to say, the Subiect, Predicat, and Copulat.

What is the Copulat?

It is the Verbe Substantiue, called in Latine, Sum, es, fui, that is, to be, which doth couple or ioine the Predicat with his Sub∣iect,

as when we say, Man is a sensible body: here in this propo∣sition, the word man is the subiect, and the word sensible body is the predicat, and the Verbe is is the copulat: which copulat is not alwaies incident to euery proposition, and specially when the predicat is some other Verbe, and not the Verbe substantiue; as, Plato disputeth, Socrates walketh; which is as much to say, as Plato is disputing, Socrates is walking.

How many waies is a proposition diuided?

Three manner of waies, that is, according to substance, quali∣tie, and quantitie. According to substance thus: Of propositions, some are said to be categoricall, that is, simple, and some hypo∣theticall, that is, compound, of which compound propositions we minde not to speake, before we haue treated of all things be∣longing to a categoricall and simple proposition, which is two∣fold that is to say, absolute and modall.

What is an absolute categoricall proposition?

It is a speech which affirmeth or denieth something absolute∣ly, without any respect; as when we say, God is true, or, Euery man is a lier: and this is otherwise called of the Logicians, Propo∣sitio categorica de inesse.

How is a simple proposition diuided according to qualitie?

Into an affirmatiue and negatiue proposition.

When is it said to be affirmatiue, and when negatiue?

It is said to be affirmatiue, when the predicat is affirmed of the subiect; as when I say, that Iohn is learned: and that is negatiue, when the predicat is denied of the subiect; as, Iohn is not learned. And note, that in such kinde of speech, the negatiue is alwaies ioined to the Verbo.

How many waies is a simple proposition diuided according to quan∣titie?

Foure manner of waies, that is to say, into an vniuersall, parti∣cular, indefinite, and singular proposition.

When is it said to be vniuersall?

When some vniuersall signe is added to the subiect.

Which words are said to be vniuersall signes?

These: all, euery, whatsoeuer, whosoeuer, none, no body, not one, none at all, euery where, no where, and such like; as, Euery man is a lier, No man is true.

When is it said to be a particular proposition?

When some particular signe is added to the subiect▪

Which call you particular signes?

These: some, any, many, few, and such like; as, Some man is wise, Few are wise.

When is it said to be indefinite?

When the subiect is a common word, hauing neither vniuer∣sall nor particular signe added vnto it; as when wee say, Men in these daies be giuen to great sollies.

When is it said to be singular?

When the subiect is some Indiuiduum, as when wee say, that Cicero is eloquent.

What, and how many questions doe rise of these three diuisions?

These three: that is, of what kinde? of what qualitie? of what quantitie? in Latine thus, quae? qualis? & quanta? for if it bee asked what kinde of proposition it is, then you must answere, that it is either categoricall, or hypotheticall, that is, simple or compound: and if it be demanded of what qualitie it be, then you must answere, that it is either affirmatiue, or negatiue: if it be asked of what quantitie, then you must answere, that it is ei∣ther vniuersall, particular, indefinite, or singular.

CHAP. II.

Of the three properties belonging to a simple proposition.

WHich are those?

These: Opposition, Equiualencie, and Con∣uersion.

What is Opposition?

It is the repugnancie of two simple propositi∣ons, hauing one selfe subiect, and one selfe predicat.

How many kindes of opposite propositions be there?

Foure: Contrarie, Subcontrarie, Contradictorie, and Subal∣ternat.

Which are said to be Contrarie?

An vniuersall affirmatiue, and an vniuersall negatiue; as, Euery man is iust, No man is iust.

Which are said to be Subcontrarie?

A particular affirmatiue, and a particular negatiue; as, Some man is iust, Some man is not iust.

Which are said to be Contradictorie?

Either an vniuersall affirmatiue, and a particular negatiue, or else an vniuersall negatiue, and a particular affirmatiue; as, Euery man is iust, and, Some man is not iust: or, No man is iust, Some man is iust.

Which are said to be Subalternat?

Either an vniuersall affirmatiue, and a particular affirmatiue, or else an vniuersall negatiue, and a particular negatiue: as, Euery man is iust, and, Some man is iust: No man is iust, and, Some man is not iust.

All which kinde of opposites you may the better remember, by considering with what order they are placed in this Figure fol∣lowing.

[illustration]

CHAP. III.

Of the Lawes and conditions belonging to these foure kindes of oppo∣sites before recited: and of the diuers matter of a Proposition.

FOr the better vnderstanding of the lawes belon∣ging to the opposites, it shall bee necessarie to speake somewhat of the matter of a proposition, whereupon the said lawes doe partly depend.

How manifold is that matter?

Threefold, that is to say, naturall, casuall, and remote or vnnaturall.

When is a proposition said to consist of matter naturall?

When the predicat agreeth with his subiect essentially, or at the least necessarily: as when the generall kinde is spoken of his speciall kinde, and the speciall kinde of his Indiuiduums, or the difference of his speciall kinde, or the propertie of his subiect: as, Euery man is a sensible body, Iohn is a man, Euery man is rea∣sonable, Euery man is apt to speake.

When is a proposition said to consist of matter contingent?

When the predicat agreeth with his subiect accidentally, so as it may either be, or not be; as, Iohn is learned.

When is a proposition said to consist of matter remote or vnnaturall?

When the predicat agreeth no manner of way with the sub∣iect; as, A man is a horse, A man is a stone, &c.

What are the lawes of contrarie propositions?

Contrarie propositions can be true no way both together; as, Euery man is a sensible body, No man is a sensible body: but they may be both false, and specially consisting of matter contin∣gent; as when I say, Euery man is iust, No man is iust, which are both false.

What are the lawes of subcontrarie propositions?

Subcontrarie propositions, consisting of matter naturall, can∣not be both false at once; as, Some man is a sensible body, Some man is not a sensible body: but consisting of matter contingent▪ both may be sometime true; as, Some man is iust, Some man is not iust.

What be the lawes of contradictorie propositions?

Those can neither be true nor false b•…•…th at once: for if one bee true, the other must needs be false, whether the matter be natu∣rall, or contingent; as, Euery man is iust; Some m•…•…n is not iust: No man is iust; Some man is iust.

What be the lawes of sub alternat propositions?

If the vniuersall be true, the particular must needs be true; as, Euery man is iust, Ergo some man is iust; but not contrarily. Againe, if the particular be false, the vniuersall also must needs be false; as, Some man is a stone, Euery man is a stone.

What good is to be reaped by the knowledge of these opposites?

It teacheth to know what speeches be repugnant one to ano∣ther, and thereby to discerne truth from falshood.

CHAP. IIII.

Of the equiualencie of simple propositions.

WHat is equiualencie?

It is the reconciling or agreeing of two pro∣positions, hauing one selfe subiect, and one selfe predicate, in such sort, that though they be di∣uers in words, yet they are made to bee all one in signification.

How is such reconciliation made?

By the helpe of signes, either vniuersall or particular, that are of like value, and equall one to another, and thereby make the speeches equall.

Giue example.

As thus: Who knoweth not this to be true? Euery man know∣eth this to be true: There is none but that knoweth this to bee true. All these are of like value, and doe signifie one selfe thing. Againe, Some men are wise, Few men are wise, All men are not wise, Not many are wise, are also equiualent speeches. The Schoolemen doe giue diuers rules touching the equiualencie of speeches; but such as, in mine opinion, are neither necessarie, no•…•… profitable, for that they cause many times barbarous, vnusu∣all, and intricate speeches. And therefore I thinke good hereto passe them ouer with silence, wishing all men to iudge the equi∣ualencie of speeches, rather by the eare, and by custome of spea∣king,

and by vsuall manner of taking the same in euery seuerall tongue or language, then by any rules, which perhaps will serue in one tongue, but not in another.

CHAP. V.

Of conuersion of simple propositions.

WHat is conuersion?

It is the changing or turning of the subiect and predicate, the one into the others place.

How manifold is such conuersion?

It is threefold, that is, simple, by accident, and by contraposition.

What is simple conuersion?

It is that whereby the termes are onely changed the one into the others place, the selfe same quantitie and qualitie being still reserued.

What propositions are conuerted by this manner of conuersion?

An vniuersall negatiue, and particular affirmatiue.

Giue examples of both.

Of the first thus: No vertue is discommendable, Ergo no dis∣commendable thing is vertue. Of the second thus: Some man is a Philosopher, and some Philosopher is a man. And by this way sometime vniuersall affirmatiues may be also conuerted, as those whose termes are conuertible, as the speciall kinde and his diffe∣rence or propertie; as, Euery man is reasonable, and euery reaso∣nable thing is man: or, Euery man is apt to speake, and euery thing that is apt to speake, is man.

What is conuersion by accident?

It is that whereby the termes are changed, and also the quan∣titie of the propositions, but not the qualitie.

What propositions are conuerted this way?

An vniuersall affirmatiue into a particular affirmatiue, and an vniuersall negatiue into a particular negatiue.

Giue examples.

Euery patience is fortitude: Ergo some fortitude is patience. Againe: No vertue is vice: Ergo some vice is not vertue.

What is conuersion by contraposition?

It is that whereby neither quantitie nor qualitie is changed,

but only termes finite into termes infinite, that is to say, termes limited into termes vnlimited.

Which call you termes infinite?

All Nounes hauing a negatiue set before them, as, not man, not beast.

What propositions are conuerted this manner of way?

An vniuersall affirmatiue into an vniuersall affirmatiue, and a particular negatiue into a particular negatiue.

Giue examples.

Of the first thus: Euery man is a sensible body, and euery thing that is not a sensible body, is not man. Of the second thus: Some vertue is not Iustice: Ergo, some thing that is not Iustice, is not vertue. These speeches in English haue some sauour; but to be spoken in Latine, after the Schoole manner, are very barbarous, or rather monstrous, as Ualerius termeth them, as to say, Quae∣dam non Iustitia non est non virtus.

CHAP. VI.

Of a Modall Proposition.

WHat is a modall proposition?

It is that which affirmeth or denieth some∣thing, not absolutely, but in a certaine respect, sort, or mood, which mood is commonly the predicat in this kinde of proposition, and all the rest of the subiect called of the Logicians, Dictum.

What is a mood?

Mood is a word determining and limiting the signification of some other word whereunto it is ioined, as a wise man, a white horse: for here this word wise being added to man, doth limit and restraine the generall signification of the word man, which otherwise of it selfe comprehendeth both wise and foolish. And the like is to be said of any other generall word, whereunto any such addition is put: but of moods making modall propositions, there are but these foure, that is, Possible, Contingent, Impossi∣ble, and Necessarie.

How manifold is a modall proposition?

Twofold, that is, Coniunct and Disiunct.

When is it said to be Coniunct?

When the mood is placed either in the beginning or ending of a proposition; as, It is impossible that Iohn is sicke: or thus; That Iohn is sicke it is possible.

When is it said to be Disiunct?

When the mood is placed so, as it diuideth the one part of the subiect from the other; as, for Iohn it is possible to be sicke: and the Disiunct is said many times to be true, when the Coniunct is false, being both made of selfe termes: as for example, the Logi∣cians affirme this to be true, A white man it is possible to bee blacke: but this other, A white man to be blacke it is possible, they affirme to be false.

What maketh them so to doe, sith by construction these two speeches in sense doe seeme to be all one?

Because the mood is the Disiunct, which by parting and seue∣ring the Subiect, maketh the Proposition to seeme spoken in di∣uers respects, as man to be white in one respect, and blacke in another, and so the speech to be true.

CHAP. VII.

Of the proposition, equiualencie, and conuersion of modall propositions.

WE told you before, that of modall propositions, some were called coniunct, and some disiunct: and as for the modals disiunct, they differ but lit∣tle from absolute propositions before declared. And therefore we haue here chiefly to deale with opposition, equiualencie, and conuersion belonging to modall coniunct, the matter whereof being not altogether so necessarie as some men affirme, I minde to make no long speech thereof. But for the better vnderstanding of opposition, equiualencie▪ and conuersion thereof, it is needfull first to declare the quantitie and qualitie of a modall proposition: of both which things, though Aristotle maketh no mention, but only a little of qualitie; yet the latter Writers doe necessarily suppose modall propositions to bee indued with quantitie and qualitie: for they say that the mood necessarie is much like to a signe vniuersall affirmatiue; the mood impossible, to a signe vniuersall negatiue; the moods possible and contingent, which are both of one value, are like to signes particu∣lar

affirmatiue. Now as touching the qualitie, which is to be ei∣ther affirmatiue or negatiue, like as the negatiue in absolute pro∣positions is wont to bee added to the verbe, euen so in modall propositions it is added to the mood, as by the examples set down in the figure of opposition hereafter following ye may easily per∣ceiue.

CHAP. VIII.

Of the opposition of Modals.

HOw many waies are modall propositions said to be op∣posite?

They are said to be opposite foure manner of waies, euen as absolute propositions are, tha is to say, contrarily, subcontrarily, contradictoriy, and subalternately, as you see in this figure fol∣lowing, wherin the mood is set before in the place of the subiect, the better to shew the quantitie & qualitie of euery proposition.

[illustration]

CHAP. IX.

Of the equiualencie and conuersion of modall propositions.

THe Schoolemen doe affirme, that modall propo∣sitions are easily made equiualent, by reason that they may be vttered foure manner of waies, that is to say, two manner of waies affirmatiuely, and two manner of waies negatiuely. The first way af∣firmatiuely, is, when no negatiue is added either to the subiect, or to the mood; as, for a man to be iust, it is pos∣sible, contingent, impossible, or necessarie. The second way af∣firmatiuely, is, when the negatiue is added to the verbe of the subiect, the mood remaining still affirmatiue; as, for a man not to be iust, it is possible, contingent, &c. The first way negatiuely, is, when the negatiue is only added to the mood; as, a man to be iust, it is not possible, contingent, &c. The second way negatiuely, is, when the negatiue is both added to the verbe of the subiect, and also to the mood; as, a man not to be iust, it is not possible, contingent, &c. which is all one and equiualent to this affirma∣tiue proposition, saying, that for a man to be iust, it is possible, contingent, &c. for two negatiues, as well in the Latine tongue, as in ours, do alwaies make an affirmatiue. Again, as touching the cōuersion of modal propositions, they say, that the disiunct being like to an absolute or simple proposition, may be conuerted both simply and per accidens; but the coniunct suffereth no conuersion: & though the Schoolemen do set down diuers & manifold rules, and haue inuented these 4. words of Art, that is, PURPUREA, ILIACE, AM ABIMUS, EDENTULI, attributing as wel to the vowels, as to the consonants thereof, certaine significations, for the better vnderstanding & bearing in memorie the equiua∣lencies & conuersions of the said modal propositions: yet because in mine opinion they are more meet to breed preposterous, intri∣cate & barbarous speeches, then to serue to any other good pur∣pose, I thinke it better to passe them ouer with silence, then to trouble your memorie therwith: wherfore leauing them as things superfluous, I minde now to treat of an hypotheticall or cōpound proposition, & of al the necessarie accidents therunto belonging.

CHAP. X.

Of a compound or hypotheticall proposition.

WHat is a compound proposition?

It is that which consisteth of two or more sim∣ple propositions, coupled together with some coniunction.

How manifold is it?

Threefold, Conditionall, Copulatiue, and Disiunctiue.

When is it said to be conditionall?

When the coniunction If is set before any simple proposition, as thus: If it be a man, it is a sensible body.

When is it said to be copulatiue?

When two simple propositions are ioined together with a con∣iunction copulatiue, as, God is true, and man is a lier.

When is it said to be disiunctiue?

When two simple propositions are ioined together with a coniunction disiunctiue, as thus; Either it is day, or night.

Of how many parts doth a compound proposition consist?

Of two, that is, of the antecedent, and of the consequent?

Which call you the antecedent?

That which followeth next after the coniunction, as thus: If it be iustice, it is a vertue: here this speech, If it be iustice, is the an∣tecedent, and the rest of the speech, that is to say, it is a vertue, is the consequent: and so it should be, though the words were con∣trarily placed, as thus: It is a vertue, if it be iustice.

What things are to be considered in hypotheticall propositions?

These: First, whether they haue any quantitie, or qualitie: then, whether any opposition, equiualence, or conuersion doe belong to them, or not: thirdly, how to know the truth or fals∣hood of euery such proposition, be it conditionall, copulatiue, or disiunctiue. And first, as touching quantitie, they haue none at all: for quantitie is to be measured by signes vniuersall, or parti∣cular, which are only incident to the subiects of categoricall pro∣positions: but qualitie they haue, in that they affirme or denie some thing, by reason whereof there may be contradiction in

hypotheticall propositions, but it cannot bee properly said, that they be either contrarie, subcontrarie, or subalternat, for that they are without quantitie; for want whereof they nei∣ther doe aptly admit opposition, equiualence, or conuersion, but onely contradiction.

How is that Contradiction to be vnderstood?

By reason of affirmation, or negation; which, as in simple propositions is to be taken on the behalfe of the verbe copula∣tiue, and not of the subiect or predicate: so in compound propositions, it is to be taken on the behalfe of the coniuncti∣on, hauing a negatiue set before it; and yet not of euery con∣iunction, but onely of that coniunction conditionall, If: whereof I cannot aptly giue you any example in our natiue tongue, because it is contrarie to our naturall and vsuall speech, to put a negatiue before the coniunction, If; and therefore I leaue to speake thereof any further: and to say the truth, it ma∣keth but a strange kinde of speech in the Latine tongue, and I beleeue is seldome vsed in any disputation: as to say thus, Non si animal est, homo est: or, Non si lux est, dies est: both which are said to be negatiue speeches, according to the rule before giuen, because the negatiue is set before the coniuncti∣on si, and by vertue thereof (as the Schoolemen say) maketh the whole proposition to be negatiue.

CHAP. XI.

Of the truth and falshood of Hypotheticall propositions, and first, of the Conditionall.

WHat is to be considered, to know the truth or falshood of Conditionall Propositions?

First, whether they be affirmatiue or nega∣tiue: for in the affirmatiues it sufficeth, that the one part doth necessarily follow of the o∣ther, as thus: If it be a man, it is a sensible body: and it ma∣keth no matter, though the parts seuerally taken, be both false, so as the Cousequent be good: as, If a tree be a man, a tree is a sensible bodie: for though both these parts be false, yet the

Consequent conditionally is true: for a conditionall Proposi∣tion hath no regard to the truth of the parts, but onely that the Consequent may necessarily follow of the Antecedent.

How is the truth of the negatiue Proposition to be knowne?

By the Consequent: for if the Consequent bee not rightly inferred of the antecedent, then the negatiue is true, as thus: it followeth not that because a Lyon is a sensible body, that therefore a Lyon is a man.

Of the truth and falshood of propositions copulatiue.

WHen is a copulatiue Proposition said to be true or false?

It is said to be true, when both the parts bee true, as when I say, God is true, and man is a lyar: againe it is said to be false, when either one part or both parts be false: as when I say, man is a sensible bodie, and God is not a Spirit. Here be∣cause the first part is true, and the second part false, the whole Proposition is said to be false. It is said also to be false, when both parts are false, as thus; Man is true, and God is a lyar. Heere both parts be false.

What kinde of propositions are wont to bee referred to this co∣pulatiue?

Those which they call Temporall, Locall, by similitude and causall: as of time thus, When a penitent sinner pray∣eth, then God heareth him. Of place thus, Where two or three are gathered together in the Name of the Lord, he is in the midst of them. By similitude thus, As a man dealeth with his neighbour, so will God deale with him. Of the cause thus, Because the Sunne shineth, it is day. And therefore certaine Aduerbes as these, When, Where, Vntill, so long as, as, so as, for, therefore, because and such like, haue the signification sometime of the Coniunction (And) and sometime of the Con∣iunction (If).

Of the truth and falshoode of disiunctiues.

WHat belongeth properly to disiunctiue Propositions?

To consist of repugnant parts, according to the

signification of Coniunctions disiunctiue, such as these bee, vel or eyther, or else, and such like: as eyther it is day, or it is night, whereof the one destroyeth the other: for if the one be, the other can not be: and therefore they can not bee both true: but they may be both false, if there be any mean betwixt the two contraries: as when wee say, This woman is eyther white or blacke, both these are false, if she be browne, which is a meane colour betwixt white and blacke. But the later writers affirme the disiunctiue to bee true, if any one or both of the parts bee true, as thus, Eyther a man is a sensible body, or else a tree is a Substance: and to bee false when both parts bee false, as Eyther a man is true, or God is a lyar.

The end of the third Booke of Logicke.