The Elements of Logic, Book 4
The fourth Booke. Of a SYLLOGISME, and the forme and kindes thereof.
The firſt Chapter. What a Syllogiſme is. Alſo, what a Concluſion is, and a Queſtion, or Probleme, and the parts thereof.
A Syllogiſme is a reaſon or argument in the which from two Enuntiatiōs or propoſitions coupled together by certaine lawes, wee draw and deduce a neceſſary Concluſion. For example, if wee joyne theſe two Propoſitions together,
All that liveth hath a ſoule.
All plants liue.
This concluſion will follow, Therefore all plants hauehave a ſoule.
As Propoſitions are called Enuntiations before they belong to a Syllogiſme; So the Concluſion before it be proved by a Syllogiſme, is not called a Concluſion, but a Queſtion or Proble…e.
Now every queſtion or concluſion hath two parts, namely, the Subject, and the A…tribute. As in the example aboue mentioned Plant is the Subject, and, to hauehave a ſoule, is the Attribute. The Philoſophers call them the two Termes, whereof the ſubject is called the leſſer Terme, and the attribute the greater Terme: becauſe the attribute commonly is more generall then the ſubject. And that which in the Mathematicks is ſaid, to containe, in Logick is ſaid, to be attributed.
The ſecond Chapter. How to make a Syllogiſme, and of the parts of it.
A Syllogiſme is thus made. A queſtion or probleme is propounded: For example, let the queſtion be, Whether Philip be a living creature or no? Now he that will proue by a Syllogiſme that Philip is a living creature, muſt diſmember the ſaid queſtion into two parts; the one whereof is the ſubject, namely, Philip; and the other the attribute, namely, living creature. Then hee muſt looke out ſome third thing, which may be joyned and fitted to each of theſe two parts. For example, the word Man; which he muſt firſt joyne with living creature, and ſay, Every man is a l…ving creature; and then he muſt joyne it with Philip, and ſay, Philip is a man; thence will follow this Concluſion, Therefore Philip is a living creature.
If the Ring A be joyned with the Ring B and the Ring B with the Ring C, it followeth that the Ring A is joyned with the Ring C.
This may alſo be illuſtrated by an example drawne from Numbers, reaſoning thus. Twelue containeth ſix, and ſix containeth three, therefore twelue containeth three. For we ſaid before, that that which is ſaid to containe in Mathematicks, the ſame is ſaid to be attributed in Logick.
Therefore every Syllogiſme is compounded of three parts or Termes, namely, the Subject of the concluſion, the Attribute of the concluſion, and the Meane or middle Terme, which knitteth theſe two parts of the concluſion together.
It is no hard matter ſo ſoone as a Syllogiſme is propounded, preſently to perceiue which is the Middle terme. For it is all that which is not in the concluſion.
The Meane or middle terme joyned with the attribute of the concluſion, maketh that propoſition which is called the Major or Greater: becauſe the attribute of the concluſion which is called the greater terme is there. The ſame Meane being joyned with the ſubject, maketh the other propoſition, which is called the Minor or Leſſer; ſo called becauſe the ſubject of the concluſion which is called the leſſer terme is there. This Minor propoſition is alſo called the Aſſumption. Now for more eaſe in this point, we will call the firſt propoſition ſimply the propoſition, and the ſecond the aſſumption.
The third Chapter. The naturall reaſon vponupon which a Syllogiſme is grounded.
THis ſtructure of a Syllogiſme is grounded vponupon two naturall Maximes, acknowledged to be true by thoſe of the Meaneſt capacitie. Whereof the firſt is. Whatſoever containeth any thing, containeth alſo that which is contained in that thing.
Which Maxime conceived in Logicall termes, is thus to be expreſſed. Whatſoever is generally attributed to any thing, muſt alſo be attributed to ſuch things, as the ſaid thing is attributed vntounto. As, ſeeing that to be a living creature is attributed to all men, it muſt alſo be attributed to Philip, becauſe Philip is a man. This firſt Maxime is the foundatiō of all Syllogiſmes that conclude affirmatiuely.
The ſecond Maxime is, That which agreeth not to a thing and cannot be attributed vntounto it, agreeth not likewiſe to thoſe things which are contained vnderunder that ſaid thing. As, to be Almightie belongeth not to any creature; therefore it belongeth not to Angels, becauſe they are creatures. This Maxime is the ground of all Negatiue Syllogiſmes, that is to ſay, ſuch as conclude negatiuely.
The fourth Chapter. Of the Figures of a Syllogiſme.
BEcauſe the Meane is diverſly joyned with the two termes of the concluſion: hence it comes to paſſe that according to the divers placing of the ſaid Meane, ſundry Figures and Formes of Syllogiſmes doe ariſe. Now theſe Figures are three.
The firſt figure is that wherein the meane is the ſubject in the propoſition, and the attribute in the aſſumption. As, in the examples before named; and alſo in this,
All MEN are ſinners.
Paul is a MAN.
Therefore Paul is a ſinner.
The ſecond figure is when the Meane is the attribute both in the propoſition and in the aſſumption. As,
All birds hauehave FEATHERS.
No Batt hath FEATHERS.
Therefore no Batt is a bird.
The third figure is when the Meane is the ſubject as well in the propoſition, as in the aſſumption. As,
The SOVLE is immortall.
The SOVLE is a creature.
Therefore ſome creature is immortall.
The fifth Chapter. Generall Rules, common to all Figures.
ALL Syllogiſmes that are faultie in any of the Rules following conclude nothing.
The firſt Rule.
A Syllogiſme muſt hauehave three Termes, namely, the Subject, and Attribute of the concluſion, and the Meane; for where there be two Meanes the Syllogiſme is ſtarke naught. The reaſon drawne from nature is this: If two rings be linked with two other ſeverall rings, it followeth not that therefore theſe two former rings be linked together. And likewiſe if you would know whether two peeces of ground agree in quantitie, you muſt not take two ſundry meaſures; but onelyonly one and the ſame. Now the two Termes are like vntounto theſe two pecces of ground, and the Meane is like vntounto the ſaid meaſure.
We vſe to ſay there be foure termes, not onelyonly when wee finde in a Syllogiſme foure differing termes in words; but alſo when one and the ſame word is taken in a double ſenſe, and is equivocall; as,
KING is but one ſyllable.
Alexander is a KING.
Therefore Alexander is but one ſyllab…e.
King in the propoſition is taken for th… word; in the aſſumption for the perſon. Likewiſe if I ſhould ſay,
Every NVMBER is an Accident.
Ten men are a NVMBER.
Therefore ten men are an Accident. I ſhould make foure termes, for in the propoſitiō the word Number is taken for the number numbring, and in the Aſſumption for the number numbred. Thus,
The END is good.
Death is the END.
Therefore death is good.
In the propoſition the word End is taken for the ſcope, & in the aſſumption for the extremitie of a thing.
The ſecond Rule.
Out of two negatiue propoſitions nothing can be concluded. As,
No man is a beaſt.
No horſe is a man.
Hence nothing is concluded. This may be known by the ſecond fundamentall reaſon or Maxime, ſet downe in the third Chapter. And the reaſon is manifeſt: For concluſions are then Negatiue, when the Meane agreeth with one of the termes of the concluſion, and not with the other: whence it is inferred, that the termes of the concluſion agree not together. And therfore the Meane muſt needs agree with one of the two termes; and this is expreſſed by affirmation.
Yet here is an exception, namely, when the propoſition hath two negations equivalent to an affirmation. For example,
Whatſoever is not a living creature is not a man.
A Statua is not a liuing creature.
Therefore a Statua is not a man.
This Syllogiſme is good, for the propoſition having two negations, importeth as much as this affirmatiue: Every man is a living creature.
The third Rule.
If both the propoſitions be particulars, the Syllogiſme is not good, and the forme of it is naught, and can conclude nothing.
This is likewiſe evident by the two fundamentall Maximes ſet downe in the third chapter, where theſe words, Whatſoever containeth any thing, preſuppoſe an vniverſall propoſition.
Nevertheleſſe, from two ſingular propoſitions a particular concluſion may be well drawne in the third figure. As,
NERO was a Minſtrell.
NERO was an Emperour.
Therefore ſome Emperour was a Minſtrell.
Againe.
IVDAS is damned.
IVDAS was an Apoſtle.
Therefore ſome Apoſtle is damned.
Or in the ſecond figure.
Therſites was DEFORMED.
This man is not DEFORMED.
Therefore this man is not Therſites.
Whence it is eaſie to ſee, that ſingular propoſitions are of more force in reaſoning then particulars.
The fourth rule.
The concluſion ever followeth the worſer and the weaker of the two propoſitions: That is to ſay, if one of the propoſitions be Negatiue, the concluſion alſo muſt be negatiue, and if one of the propoſitions be particular, the concluſion alſo muſt be particular.
Whence it followeth, that if the propoſitiō be an vniverſall negatiue, and the aſſumption a particular affirmatiue, the concluſion muſt be a particular negatiue. For affirmation is better then negation, & an vniverſall propoſition is better then a particular, becauſe it teacheth more things. The reaſon of this Maxime is evident. For a thing of leſſe worth cannot bring forth a thing more excellent, then it ſelfe.
The fift Rule.
There muſt not be more in the concluſion then there is in the propoſitions, As,
All that is ordained of God is good.
Marriage is ordained of God.
Therefore marriage is good for an old man; or, with an Infidell.
The ſixt Rule.
True propoſitions well coupled, cannot bring forth a falſe concluſion; but falſe propoſitions may by chance yeeld a true concluſion. Which is done, when wee intend to proue a truth by a falſe reaſon; and a true concluſiō by a Meane which agreeth with neither of the two termes, or onelyonly with the one. As, who would proue Philip to be a living creature, becauſe he is a horſe. Or that a diamond is a ſtone, becauſe it is a man. As,
All men are ſtones.
All diamonds are men.
Therefore all diamods are ſtones.
This concluſion is true, howſoever the two propoſitions be falſe.
The ſixth Chapter. Speciall Rules for every Figure, and firſt for the firſt.
IN the firſt figure the propoſition muſt be vniverſall, and the aſſumption affirmatiue: or els the Syllogiſme is naught. For example,
Some bodie is a living creature.
Every ſtone is a bodie.
Therefore ſome ſtone is a living creature.
This concluſion is falſe, and followeth not from the propoſitiōs: becauſe the firſt propoſition is particular. And if I argue thus,
All men are living creatures,
No horſe is a man.
Therefore no horſe is a living creature.
This concluſion is falſe, and followeth not from the propoſitions; becauſe the aſſumption is negatiue. This rule is grounded vponupon the ſecond Maxime ſet downe in the third Chapter which ſaith, that in Syllogiſmes concluding negatiuely, one of the propoſitions muſt be affirmatiue. Except when the negation doe make a part of the Meane. As if I ſay,
All that is not right is crooked.
This line is not right.
Therefore this line is crooked.
The evidence of this will appeare, if you frame the aſſumption thus, This line is a line which is not right.
For then the aſſumption is turned into an affirmatiue.
The preeminences & prerogatiues of the firſt figure are great aboue the two others. For the ſecond figure cannot conclude affirmatiuely, and the third figure cannot conclude vniverſally, but in the firſt figure we may conclude all manner of wayes, and proue all manner of queſtions: whether vniverſall affirmatiues, or vniverſall negatiues, or particular affirmatiues, or particular negatiues.
Vniverſall affirmatiues. As we may proue that all covetous perſons are theeues, becauſe they withhold other mens goods.
Againe vniverſall negatiues. As we may proue that no covetous perſon is free, becauſe he is a ſlaue to his money.
Wee may alſo proue in the firſt figure a particular affirmatiue concluſion. As we may proue that ſome fiſhes hauehave lungs, becauſe they breath.
Laſtly, we may proue in the firſt figure a queſtion that is particular negatiue. As, that Iudas and Saul are not ſaved, becauſe they were impenitent.
Moreover, the excellencie of the firſt figure appeares in this, that the others are reduced vntounto it. For by changing ſomething in them, they are reduced to the firſt figure; as wee ſhall ſee hereafter.
Rules for the ſecond Figure.
In the ſecond Figure the Meane is the attribute in both the propoſitions.
The firſt propoſition in this figure muſt be vniverſall, or els nothing can be concluded. As,
Some living creatures hauehave two feet.
No horſe hath two feet.
Therefore ſome horſe is not a living creature.
The concluſion is falſe, and followeth not; becauſe the propoſition is particular.
Againe, in the ſecond Figure one of the propoſitions muſt be negatiue, and conſequently the concluſion. For this reaſon were not good to ſay,
All henns hauehave two feet.
You hauehave two feet.
Therefore you are a henne.
The naturall reaſon hereof is apparant. For it followeth not, that if one thing be attributed to two other things, that theſe two things ſhould be the ſame thing. As, if to be yellow belongs both to hony and to gall, it followeth not therefore that hony is gall: but it followeth well in the negatiue. As,
Hony is ſweet.
Gall is not ſweet.
Therefore gall is not hony.
The naturall reaſon heereof is, becauſe if one thing belongeth to one of the two termes of the queſtion, and not to the other, it followeth that the two termes agree not together.
How to reduce t…e Syllogiſmes of this ſecond figure …o the firſt.In this figure when the propoſition is negatiue, it is eaſie to convert and reduce the Syllogiſme vntounto the firſt figure. For then we muſt onelyonly convert the propoſition ſimply. As.
No terreſtriall body mooues vpward.
Smoake mooues vpward.
Therefore ſmoake is no terreſtriall body.
You may convert this propoſition, ſaying thus, Nothing that mooues vpward is a terreſtriall body.
And ſo you ſhall hauehave it in the firſt figure.
But if the aſſumption be negatiue, you muſt put it in the place of the propoſition, and then convert ſimply the concluſion, as alſo the aſſumption, which is become the propoſition. As in this Syllogiſme,
All men are living creatures.
No ſtatua is a living creature.
Therefore no ſtatua is a man.
You muſt change the aſſumption, and ſay, No living creature is a ſtatua.
And ſet it in the place of the propoſition, thus,
No living creature is a ſtatua.
All men are living creatures.
Whence the concluſion followeth well, Therefore no man is a ſtatua.
Which is the ſame concluſion, but onelyonly converted ſimply.
Rules for the third Figure.
In the third figure the Meane is the ſubject in both propoſitions.
The aſſumption muſt be affirmatiue, as in the firſt figure.
The concluſion is alwayes particular, and cannot be vniverſall.
The naturall reaſon hereof is, becauſe if two things are attributed to the ſame thing, it followeth not that theſe two things agree alwaies together: but onelyonly it followeth that they agree ſometimes and in certaine ſubjects. As, if to be bright and round belongs to the Sunne, it followeth not that whatſoever is round muſt bee bright. So to be reaſonable and to hauehave two feet belongs to man; whence it followeth not, that whatſoever hath two feet muſt be reaſonable: but onelyonly that ſomething which hath two feet is reaſonable.
The Syllogiſmes of this figure are reduced to the firſt by converting the aſſumption. As,
All horſes neigh.
All horſes hauehave foure feet.
Therefore ſomething that hath foure feet neigheth.
If you convert the aſſumption,How to reduce the Syllogiſmes of the third figure to the firſt. ſaying, Something that hath foure feet is a horſe,
This Syllogiſme will be in the firſt figure.
But if the propoſition be particular, ac in this Syllogiſme,
Some Apoſtle is damned.
All Apoſtles are ſent of God.
Therefore ſome one that is ſent of God is damned.
Now to reduce this Syllogiſme to the firſt figure, you muſt convert the propoſition, and ſay, Some damned perſons is an Apoſtle.
And then put it in the place of the aſſumption in this manner,
All Apoſtles are ſent of God.
Some damned perſon is an Apoſtle.
Therefore ſome damned perſon is ſent of God.
Which is the very ſame concluſion, but ſimply converted.
The ſeventh Chapter. Certaine artificiall words which ſerue to ſhew how many wayes wee may argue in each figure, and how the ſecond and third figure may be converted into the first.
TO helpe the memory Logicians hauehave found out certaine artificiall words, which ſerue to ſhew how many waies a man may argue in each figure. The words are theſe;
1. BARBARA, CELARENT, DARII, FERIO.
2. CESARE, CAMESTRES, FESTINO, BAROCO.
3. DARAPTI, FELAPTON, DISAMIS, DATISI, BOCARDO, FERISON.
To vnderſtand the vſe of theſe words, you muſt note that every one of theſe words hath but three Syllables: the firſt wherof ſignifies the propoſition, the ſecond the aſſumption, and the third the concluſion.
Againe, note that in all theſe words there are but foure Vowels, namely theſe,
A. E. I. O.
A ſignifieth an vniverſall affirmatiue propoſition.
E ſignifieth an vniverſall negatiue propoſition.
I ſignifieth a particular affirmatiue propoſition.
O ſignifieth a particular negatiue propoſition.
The Syllogiſmes which are made in the firſt figure are noted by theſe words, Barbara, Celarent, Darij, Ferio.
The word BARBARA, intimates, that whenſoever the two propoſitions in the firſt figure ſhall be A, that is, vniverſall affirmatiue, the concluſion ſhall likewiſe be A, that is, an vniverſall affirmatiue.
So the word CELARENT ſignifieth that whenſoever the propoſition in the firſt figure ſhall be E, that is, an vniverſall negatiue, and the aſſumption A, that is, an vniverſall affirmatiue; the concluſion ſhall be E, that is, an vniverſall negatiue. So likewiſe of all the other words.
The Syllogiſmes of the ſecond figure are noted by theſe words, Ceſare, Cameſtres, Feſtino, Baroco,
The word FESTINO intimates, that whenſoever the propoſition in the ſecond figure ſhall be E, that is, an vniverſall negatiue, & the aſſumption I, that is, a particular affirmatiue; the concluſiō ſhall be O, that is, a particular negatiue. As,
FES—No compounded thing is eternall.
TI—Some thing in man is eternall.
NO—Therfore ſomething in man is not compounded.
Note that in theſe foure words, the laſt ſyllables are alwayes either E or O, to ſhew that the concluſion muſt alwayes be negatiue.
The Syllogiſmes of the third figure are noted by theſe words, Darapti, Felapton, Diſamis, Datiſi, Bocardo, Feriſon, and hauehave the ſame vſe.
For example, the word FELAPTON ſignifieth that if the propoſition in the third figure be E, that is, an vniverſall negatiue, and the aſſumption A, that is, an vniverſall affirmatiue; the concluſion muſt be O, that is, a particular negatiue. As,
FE—No Batt hath feathers.
LAP—All Batts flie.
TON—Therefore ſomething that flies hath no feathers.
Note that in all theſe ſix words, the laſt ſyllables hauehave either I or O, to ſhew that the concluſion in the third figure muſt alwayes be particular.
The Conſonants of theſe ſame words are not without their ſpeciall vſe. For they ſerue to know how the Syllogiſmes of the ſecond and third figure may be reduced to the firſt. To this end ſerveth the firſt capitall letter. For Ceſare and Cameſtres are reduced to Celarent: Darapti, Diſamis, Datiſi are reduced to Darij: Feſtino, Felapton, Feriſon are reduced to Ferio.
Baroco and Bocardo cannot be reduced, becauſe one of the propoſitions is a particular negatiue, which cannot enter into the firſt figure.
S ſignifieth that the propoſition which is noted with an S, muſt be ſimply converted. As in Ceſare and Datiſi.
P ſignifieth that the propoſition muſt be converted by Accident, that is to ſay, that the vniverſall affirmatiue muſt be converted into a particular affirmatiue. As in Darapti and Felapton.
M ſignifieth that the propoſitions muſt be tranſpoſed, and muſt change their place. As in Cameſtres and Diſamis, whereof we hauehave given examples.
The eight Chapter. Of an Enthymeme.
AN Enthymeme is nothing els but a Syllogiſme, whereof one of the propoſitions is ſuppreſſed, either for brevities ſake, or for ſome deceipt. For brevitie, as
God ſinneth not.
Therefore God is no lyar.
Or
Nothing that corrupteth man can be the chiefe good.
Therfore Voluptuouſneſſe is not the chiefe good.
For deceipt, as,
This Common-wealth is the greateſt.
Therefore it is the beſt.
Or
Whatſoever troubleth a Common-wealth muſt be baniſhed.
Therefore the Goſpell muſt be baniſhed.
In theſe imperfect Syllogiſmes, that propoſition is ſuppreſſed which is moſt odious, and wherein the falſehood lieth, namely, Every Common-wealth, that is, the greateſt is the best. As alſo this, The Goſpell troubleth a Common-wealth.
Somtimes to make the ſpeech more ſmooth and currant, we put the concluſion in the firſt place. As,
The eſtate of Oligarchy is the worſt of all.
Becauſe it is moſt ſubiect to civill warre.
Rhetoricians call Enthymemes proofes grounded vponupon probable ſignes. As,
Milo killed Claudius:
For he hated him before.
Or
This man is learned:
For he is pale and hath many books.
Theſe proofes are of no force, except they be in great number. For ſignes and conjectures which hauehave no force being alone, become forcible when there are many of them together.
The ninth Chapter. Of Induction, and of Example.
INduction is a Syllogiſme wherein divers ſingulars or particulars are as a Meane to proue an vniverſall concluſion. As when I will proue that all living creatures hauehave feeling; becauſe birds, fiſhes, ſerpents, terreſtriall beaſts, and Amphibia hauehave feeling.
Or thus, the Stag, the Doe, the Hare, the Coney, the Mouſe hauehave a great heart in proportion to their bodie: Now the fearfull creatures are the Stag, the Doe, &c. Therefore all fearfull creatures hauehave a great heart in proportion to their bodies.
By this kinde of diſcourſe all Sciences hauehave beene invented. For example, Phyſicians having by the tryall of many plants of Mercurie or of Parietarie obſerved, that they are laxatiue, hauehave thence gathered a generall rule, that all plants of Mercurie or Parietarie are laxatiue. Thus hauehave men attained to the knowledge of the cauſes of Eclipſes, of Apoplexies, and of Flouds greater then ordinarie about the Aequinoxes by ſundry particular obſervations.
An Example is an imperfect Induction.Of Example. For in ſtead of many particulars we vſe but one.
In naturall cauſes Examples are more forcible then in civill and voluntary actions: becauſe naturall events are much more alike then civill and voluntary actions, which are ſubiect to many changes and chaunces. As if I ſhould ſay, Yeſterday in the evening the skie being red, the day following proved faire: this example hath ſome likelihood to proue, that ſeeing the skie is red this evening, to morrow it will proue a faire day. But if I ſay, Philip digging his garden found a pot of gold, it followeth not that Alexander digging ſhall hauehave the ſame hap.
Orators notwithſtanding do much enlarge themſelues vponupon ſuch examples. And by reaſon of the miſchiefs which hauehave hapned to any one through drunkenneſſe, or lying, or anger, they vſe to exhort others to ſhunne the ſame vices.
The tenth Chapter. Of the Enumeration of parts.
THe Enumeration of parts is alſo a kinde of Syllogiſme, ſerving to conclude both affirmatiuely and negatiuely.
When we will conclude affirmatiuely, we make a rehearſall of all the parts: that ſo having remooved all the parts but one, that one which remaineth may be concluded or affirmed. As,
What goods ſoever a man hath, he hath them either by inheritance, or by purchaſe, or by exchange, or by gift, or by labour, or by play, or becauſe he hath found them, or ſtollen them. But the goods which you hauehave, you hauehave them neither by inheritance, nor by purchaſe, nor by exchange, nor by gift, nor by labour, nor by play, nor becauſe you hauehave found them. Therefore you hauehave ſtole them.
But when we will conclude negatiuely, we remoue all the parts. As, All Frenchmen are either Normans, or Picards, or Champenois, &c. But the Lorrains are neither Normans, nor Picards, nor Champenois, &c. Therefore they are no Frenchmen.
You muſt ever take heed that the Enumeration be not imperfect; as, when we ſay that all mankinde is either male or female: Or that every action is either good or bad. For there are Hermaphrodites; and there be ſome actions that are indifferent. So if I ſhould ſay that every qualitie is either a naturall facultie, or a habit, or an actiue qualitie in the obiects of the ſenſes, this enumeration would proue imperfect. For beſides theſe there are formes and figures.
The eleventh Chapter. Of a Dilemma.
A Dilemma is a forked or horned argument, wherein we giuegive our adverſary his choiſe of two things, to ſhew him that whether of the two ſoever he chooſeth, he is ſtill overcome in both. As, to proue that a man ſhould never marry, wee may argue thus, If thou marrieſt, thy wife will be either faire or deformed; If faire thou wilt proue iealous; If deformed thou wilt not like her. Therefore it is better not to marry. Or, be not a lawyer, for if thou pleadeſt for iniuſtice, thou ſhalt diſpleaſe God; If thou pleadeſt for iuſtice, thou ſhalt diſpleaſe men. Our Saviour Chriſt made a Dilemma when he was buffeted, ſaying, If I hauehave ill ſpoken ſhew wherein; but if well, why ſmiteſt thou me? Thus a man may reaſon againſt one that hath dreamed that we muſt not beleeue dreames: Or that hath ſworne that he will forſweare himſelfe. If thou forſweare thy ſelfe, thou art a periur'd perſon; If thou doeſt not forſweare thy ſelfe, yet art thou ſtill a periur'd perſon; becauſe thou haſt ſworne that thou wilt forſweare thy ſelfe.
Carneades gaue twentie crownes to his Maſter Diogenes to teach him Logick. One day diſputing with his Maſter according to the rules that he had taught him, his Maſter told him that he diſputed not well; Wherevpon his Scholar made him this Dilemma. I diſpute either well or ill: If I diſpute well, why blameſt thou me? If I diſpute ill, giuegive mee backe my twentie crownes? Such was the diſputation betweene Protagoras and his Scholar Evathlus, Gellius. l. 5. c. 10.which example is well knowne, and the recitall would be too too long. You may ſee it in A. Gellius. lib. 5. cap. 10.
The twelfth Chapter. Of a Sorites, or heaping Syllogiſme.
A Sorites is a kinde of argume… which knitteth many propoſitions together, to ſhew that the ſubject of the firſt agreeth with the attribute of the laſt. As,
Whatſoever acteth, mooveth.
Whatſoever mooveth, is mutable.
Whatſoever is mutable, is corruptible.
Whatſoever is corruptible, is not God.
Therefore it is inferred, if God acteth, he is not God.
So many propoſitions, ſo many Syllogiſmes which hauehave God for the ſubiect of the concluſion.
The thirteenth Chapter. Of Conditionall or Hypotheticall Syllogiſmes.
VVE hauehave ſaid that Enuntiations are either ſimple or compound; and that of compounded Enuntiations, ſome are Conditionall or Hypotheticall, and ſome Disjunctiue.
Hitherto we hauehave treated of Syllogiſmes conſiſting of ſimple propoſitions, now we are to ſpeake of Conditionall and Disjunctiue Syllogiſmes, whoſe propoſitions are conditionall or disjunctiue.
A Conditionall Syllogiſme is, whoſe propoſition hath an If. As,
If there be a God, he muſt be ſerved.
But there is a God.
Therefore he muſt be ſerved.
The propoſition hath two parts, the firſt whereof is called the Antecedent, If there be a God: the ſecond is called the Conſequent, He muſt be ſerved.
There are two Rules for theſe Syllogiſmes.
I. Maxime.The firſt is, that if the Antecedent be granted, the Conſequent is alſo granted. As,
If Paul be a man, he is a living creature.
But he is a man.
Therefore he is a living creature.
But you cannot by over-throwing the Antecedent, overthrow the Conſequent. As,
If a flie be a bird, it is a living creature.
But a flie is no bird.
Therefore it is no living creature.
II. MaximeThe ſecond Maxime is, that if the conſequent be overthrowne, the antecedent is overthrowne alſo. As,
If a ſtatua be a man, it is a living creature.
But a ſtatua is no living creature.
Therefore it is no man.
If the antecedent be the ſpecies, and the conſequent be the difference or propertie, then you may overthrow the antecedent to overthrow the conſequent. As,
If a ſtatua be a horſe, it neigheth.
But it is no horſe.
Therefore it neigheth not.
But ſuch concluſions follow by chance, and not by the force of the Syllogiſme.
In theſe Syllogiſmes the aſſumption is part of the propoſition, which propoſition maketh an entire Syllogiſme. And it is probable that this word Aſſumption is borrowed from theſe Syllogiſmes, becauſe that in them the ſecond propoſition is taken and aſſumed out of the firſt.
The foureteenth Chapter. Of Disiunctiue Syllogiſmes.
DIsjunctiue Syllogiſmes are ſuch, whoſe propoſition is compounded of two disjunctiue parts or peeces, or which are ſeparated by this particle OR. As, It is day or night. This number is even or odd. As thus,
This man is dead or aliue.
But he is dead.
Therefore he is not aliue.
Or els thus,
But he is aliue.
Therefore he is not dead.
Or thus,
But he is not aliue.
Therefore he is dead.
For thoſe propoſitiōs are compounded of ſuch parts, the one whereof cannot be granted, without overthrowing the other; Nor can you overthrow the one without eſtabliſhing or graunting the other. And for this cauſe, theſe two parts muſt be immediately oppoſit, ſo as there may be no third. For example, this argument is not good.
There is peace or warre.
But there is no warre.
Therefore there is peace.
For there may be a truce.
In theſe Syllogiſmes to the end that the truth may be evident and without exception, the two parts of the propoſition muſt not be contradictorie, but muſt be either contraries, or privatiues, or relatiues. For example, if I argue thus,
This line is ſtraight, or crooked.
But it is ſtraight.
Therefore it is not crooked.
This argument is cleere and certaine.
But if I argue thus,
Philip is wiſe or vnwiſe.
But he is vnwiſe.
From thence wee can draw no concluſion that may hauehave any likelihood of reaſon.