Abstract of Logic, Book 2 · Chapter 19 – Chapter 21
CHAP. XIX. Of Canons Compared.
Ax. 1. NOW Canons Compared are either of certain, or elſe uncertain Place.
Ax. 2. And the firſt of theſe are either General or Special: Of which theſe contain a Compariſon in every, thoſe only in one certain Genus.
COMMENTARY.
1. §. For Example; This Canon, that whoſe Effect is more ſuch, that it ſelf is more ſuch is of certain Place; becauſe it expreſſes the Place, of the Effect, from whence this Argument is taken; and General, becauſe Adaptible to all things which admit of any kind of Compariſon. But now that that which agrees to the better ſubject, that it ſelf is better, is, indeed of certain Place, becauſe indicating the Argument, was fetch'd from the Place of the Subject: But not General; becauſe only to be adapted to thoſe things which are compared in Goodneſs: But this, that which is more laſting, is beſt, is of uncertain Place, and Special; becauſe it neither expreſſes Where the Place of the Argument is: Neither can it be Adapted to all things which are compared amongſt themſelves, &c.
1. §. Now compared Canons from the Conjugates are theſe; and firſt, that to which one of the Conjugates more agrees, to that alſo the other; As, Caeſar conſulted the Republick more than Bibulus; and therefore in this reſpect was more a Conſul than he.
Secondly, If one of the Conjugates be better than one, then the other of the Conjugates will be better than the other; as, if Piety be before Learning, then a Pious Man will be before a Learned Man, &c.
Thirdly, From the Definition, theſe; and firſt, that to which the Definition moſt agrees, to that alſo the Defined; as, if the Definition of Whiteneſs be a Colour diſperſing the Sight, it will follow, that that which is whiteſt diſperſes the Sight moſt, &c. Secondly, That which agrees to the Definition, that alſo to the Defined; as, if a Habit recalling the Affectious of the Mind and Actions to Mediocrity, confers more to Felicity than Riches, then Virtue confers more to Felicity than Riches, &c.
So from Genus and Species Fourthly, we have theſe; as, firſt, that which agrees moſt to the Genus, that alſo to the Species's; and that which moſt to the Species's, that alſo to the Individuals; as, if a Subſtance Immaterial be more perſpicacious than a Corporeal, then the Soul of Man ſeparate will be more perſpicacious than it is now, when it is in the Body, &c. Secondly, that which is contain'd under the better Genus or Species, that alſo its ſelf is better; and ſo becauſe a living thing is better than a not; a Fly will be better than the Heavent, &c.
Fifthly, From the Whole and Part we have theſe; as, firſt, if the whole Homogenous, or whole conſiſting of Parts of the ſame Name and Nature be more ſo than ſuch a Whole, then its Part will be more ſo than ſuch a Part; and, conrariwiſe; as, If Gold be heavier than Braſs, then it will follow, that every Part of Gold, obſerving the ſame Proportion of Magnitude will be heavier than the like Quantity of Braſs, &c. Secondly, that which is abſolutely ſuch, or effects any thing as ſuch, its Whole will be more ſuch, and Effect, that any thing elſe be more ſuch than its Part; and ſo, if Rhubarb have a Power of Purging Choler, then a Drachm will have a greater Power than has a Scruple; becauſe it is but the third Part of a Drachm, &c. Under which general Maxim are contain'd ſeveral ſpecial; as, firſt, many Goods are to be preferr'd before fewer; and ſo Virtue with Nobility, is to be preferr'd before Virtue alone. Secondly, that which is Honeſt, Pleaſant and Profitable, will be beyond that which is only Honeſt, Pleaſant, or Profitable. Thirdly, that which encreaſes or diminiſhes Good by its Abceſs or Acceſs, is better than that which neither encreaſes nor diminiſhes Good by its Abceſs or Acceſs. Fourthly, by how much more it encreaſes or diminiſhes Good by its Abſence or Acceſs, by ſo much is it better than any other thing, than the which it is better in this Reſpect, &c.
Fifthly, from Matter and Form in the next Place, we have theſe; and firſt, that, whoſe Matter is more ſo, that alſo it ſelf is more ſo. So becauſe Gold is better and more durable than Stone, it follows, that a Golden Statue is better and more durable than a Stone, one, &c. Secondly, that which has a Nobler Form, that it ſelf is alſo Nobler. So becauſe the Form of Man is better than that of Beaſts; becauſe this is Immaterial and Immortal, and that Material and Mortal, it follows, that Man is better than Beaſts, &c.
Sixthly, From the Cauſe Efficient theſe; and firſt that which by it ſelf, ſimply, and by its Nature is ſuch, is more ſo than that which by Accident is ſuch, or in ſome reſpect, or by Participation: And ſo Meat as Meat is wholeſomer than Phyſick; becauſe that of it ſelf is ſo, and this only by Accident; and Light is more Profitable than Darkneſs; becauſe that is uſeful to all, this only to Thieves, and ſuch as will abſcond. Laſtly, the Sun is more ſplendid than the Moon; becauſe that ſhines of its own Nature, this only by Participation, &c. Secondly, that which of it ſelf and by its own Nature is more ſuch, that effects more; and ſo on the Contrary. So Fire heats more than Water, when it is warm'd, becauſe hotter. So, you know Iron to be heavier than Wood, becauſe it more ſwiftly deſcends, &c. This Canon can be uſed only in Cauſes of them ſelves: For in Cauſes by Accident it fails often. For Iron red-hot, altho' not hotter than Flame, burns yet more vehemently, the Denſity of its Matter aſſiſting it, and impreſſing the Heat more ſtrongly upon the Patient; and ſo in other Inſtances of the like Nature. Thirdly, that to which the Cauſe agrees moſt, to that alſo the Effect; and ſo on the Contrary. So you may prove Old Men to be more Prudent than Young; becauſe they have more Experience in Things. Fourthly, that by which any thing is ſuch, that it ſelf alſo muſt be more ſuch. And ſo, becauſe Water grows Warm by Fire, it may be collected, that the Fire is more Hot than it. But this Canon in ſome Caſes will fail us. And firſt in Cauſes by Accident and Aequivocal: For it does not follow, that becauſe ſome one is drunk by Wine, that therefore Wine ſhould be more drunk; or becauſe the Knife is ſharpen'd by the Stone, that therefore the Stone ſhould be ſharper than the Knife. Secondly, in Effects, which receive not more or leſs: As, if you ſhould prove the Father to be more a Man than his Son; becauſe the Son is ſo by his Means. Thirdly, thoſe which depend not upon one Cauſe: For although the Scholar derive his Learning from his Maſter, yet it does not follow that the Maſter muſt be always Learneder than the Scholar: For it may be, that the Scholar may have more Ingeny and Induſtry than his Maſter, &c. Fifthly, thoſe whoſe Operation, Work or Effect, or Uſe is the beſt, thoſe things themſelves are the beſt; and by how much they are the better, by ſo much are they the better; And ſo the Mind than the Senſe, becauſe the Operation of this is the better; and the Architectonical Art than the Shooemaking, becauſe a Houſe is better than a Shooe, and Virtue than Riches; becauſe the Uſe of this belongs to the Soul, and of thoſe to the Body, &c.
Ninthly, From the End and Means theſe: And firſt that to which more agrees the End, to that more agrees the Means; and ſo on the Contrary. So you may prove any one has more Ingeny, Books, Leiſure, Induſtry, becauſe he is more Learned; or more Learned, becauſe more Ingeny, Leiſure, Induſtry, &c. Secondly, the End is better than its Means; as Health than Phyſick. Add to this another; and that is, That which for its own ſake is deſirable, is better than that which for another's; or alſo that whick for the Sake of Opinion or Oſtentation. So you prove that Learning is …tter than a Library; Friends than Riches; Health than Beauty, &c. Thirdly that which approaches nearer to the End is better than that which is farther off. So the Art of Commanding is better than that of Horſemanſhip; becauſe approaching nearer to the Victory. Fourthly, that which is referred to the better End, that it ſelf is the better. So Ariſtotle makes good, That Wiſdom is better than Virtue Moral; becauſe leading to the ſpeculative Felilicity, which, he ſays, is ſo much better than the Practical, by how much Eternal are to be preferred before Periſhing Things. Book 10. Ethick. Cap. 5.
Tenthly, From the Subject and Adjunct; and firſt, That which is in the Nobler Subject; that, if good, is better; and if bad, worſer than that which is in an Ignobler. So Virtue is better than Health, and Vices worſe than Diſeaſes; becauſe the Mind is Nobler than the Body. Secondly, that from which the Subject is Denominated Good, is better than that from which not. So a Good that's Honeſt, is better than that which is Profitable; becauſe from that we are named Good, and from this not, &c. Thirdly, of thoſe, both which make the Subject good, that is the beſt, which affects it with the moſt Goodneſs. So Virtues Theological, viz. Faith, Hope and Charity, are to be preferred before Civil. Fourthly, that which is converſant about the beſt Object, that it ſelf alſo is the beſt. So Philoſophy is better than Medicine; becauſe that's about the Mind, this only the Body. Fifthly, that is beſt from which follows the greateſt Good or leaſt Evil; and upon this Account it is Cicero prefers Book 1. of his Offices, the Counſel of Solon, by which the Areopagites were ſet up, before the Victory of Themiſtocles, at Salamis; becauſe that but once profited, this would be always profitable to the Common-Wealth, &c.
11. From the Diſparates, this, viz. When of Two we deny the One to be in us, that ſo we may aſſume to our ſelves the Other, that we eſteem to be beſt which we would have ſeem to be in us. So becauſe for the moſt Part People deny themſelves to be Laborious that they might ſeem Ingenious, it ſhews that to be Ingenious they eſteem better than to be Laborious, &c.
12. From the Contraries, theſe, viz. Firſt, that which recedes the farther from its Contrary, that is, more ſo. So that is whiter which has the leaſt Mixture of Blackneſs. Secondly, that whoſe Contrary is worſt, that it ſelf is beſt; and ſo on the Contrary. As if Improbity be worſe than Diſeaſes then Probity muſt be better than Health. Thirdly, that whoſe Abſence, Deceaſe, or Loſs is worſe, that it ſelf is beſt; and ſo on the Contrary. As, if the Loſs of a good Eſtimation be worſe than that of Money, then a good Eſtimation is a greater Good than that of Money, &c.
13. From Major, Minor, and Equal, theſe, viz. Firſt, that which is more ſo than the greater, that is more ſo than the leſs. And Secondly, likewiſe if the leſs be more ſo, then ſo will the greater. So if Health is a greater Good than Riches, and Virtue be better than Health, then will it alſo be better than Riches. Thirdly, if one of the Equals be more ſo, then alſo will the other be more ſo. Fourthly, and alſo that that which is more ſo than one of the Equals, that alſo will be more ſo than the other. For Example; If of two Weights equal, one be heavier or lighter than a Third, then alſo the other will be ſo, or if that third be heavier or lighter than one of them, it will be alſo heavier or lighter than the other, &c. Fifthly, if one Genus be more ſo than another, that which is in the moſt excellent will be more ſo than that which is in the leſs. As, if Science be better than Art, then the moſt Noble Science will be better than the moſt Noble Art. Sixthly, if an abſolute Predicate agree with an abſolute Subject of its own Nature, the Increaſe or Increment of the Predicate will agree with the Increaſe or Increment of the Subject. As, if what is honeſt be good, that which is more ſo will be better, and moſt, beſt. I ſaid of its own Nature; becauſe if the Predicate agree not to the Subject in this manner, the Canon will deceive us: For it does not follow; becauſe the Exercitation of the Body is good, that therefore the more the better, and moſt, beſt; becauſe Exercitation is not of it ſelf, and in its own Nature good, but ſo far as it is moderate, &c.
14. From like and unlike, this, viz. that which is moſt like to that which is ſuch; or more ſuch, that, alſo, it ſelf is more ſuch, and ſo on the Contrary. So Ajax is eſteemed to be more valiant than Ulyſſes; becauſe more like to Achilles, the moſt valiant of the Grecians. But here obſerve that the Similitude be inſtituted in its proper Genus: For it does not follow if any one be more like to Achilles in Auger, that therefore he ſhould be more valiant; but only more wrathful, &c.
15. By Teſtimonies Problemes Comparate are to be confirmed after the ſame manner as are the Abſolute. For as by Ariſtotle's Teſtimony it may be proved, that Covetouſneſs is an Evil, ſo may it alſo that it is worſe than Prodigality, &c. So that for Canons Comparate here in this Place there is no need, unleſs perchance for the Diſcernment of Authority of Teſtimonies this Canon ſhould be obſerved, viz. That what God ſays, is more credible than what Man; the Wiſe, than the Vulgar; more, than few; Skilful, than Unskilful; and what any one teſtifies againſt himſelf, than what for himſelf, &c.
16. And theſe are the Comparate Canons, which contain the Deſignation of a certain Place, either Apertly or Hiddenly. In all which the ſame Limitations are to be underſtood, which are added to the Abſolute Canons to which they anſwer. For Example; The firſt Canon Comparate from the Conjugates, anſwers to the firſt Abſolute Canon of the ſame Place, which is this. That to which one of the Conjugates agrees, to that alſo agrees the other. To this Canon is added this Caution, viz. that there ſhould not be adhibited Conjugates joyned only in Affinity of Word, net Nature. This ſame Caution is to be added to the Comparate, which was thus declared. That to which agrees one of the Conjugates more, to that alſo agrees the other: And therefore as it does not follow, that this Man is Drunk; and therefore a Drunkard; ſo neither this, that this Man is more Drunk, and therefore more a Drunkard, &c.
17. There remain of Comparate Canons, which contain no Deſignation of any certain Place; of which many are extant Book 3. Top. Of which we have here ſelected the Principal: As, firſt, the more laſting and conſtant Goods are, the more to be choſen; As, the Goods of the Mind than thoſe of the Body. Secondly, any thing's then the more to be wiſh'd for, when more opportune and uſeful; As, fear in Youth, Prudence in older Age. Thirdly, that which always or often's of uſe, is better than that which ſeldom; As, Temperance than Fortitude. Fourthly, thoſe things which content one in themſelves, are more to be choſen than thoſe which need other things; As, Abundance of things than Money: For he that abounds in the laſt, viz. Money may want other things; But he that abounds in things, cannot want Money, &c. Fifthly, that which is the more ſplendid, is the more to be wiſh'd for: So Glory, than Riches. Sixthly, difficult things are better than thoſe that are more facile. And Seventhly, Proper than Common. By Common here is not to be underſtood Publick, but only thoſe things which many have; by Proper, which we have alone, or in Common with but very few; For theſe are the things which we moſt love. Eightly, thoſe things which cannot be communicated to others, are more precious than thoſe which can; As, Knowledge than Riches. Ninthly, things not neceſſary are to be preferr'd before thoſe that are. So we chuſe rather to live Commodiouſly than to live. Which Canon is is not everted by Cicero, when in his Topicks he ſays, Things neceſſary are to be preferr'd before Unneceſſary: For by Unneceſſary he underſtands Superfluous. But to Ariſtotle Unneceſſaries ſignifie no more than thoſe which belong to the bene eſſe; Neceſſaries, the eſſe. Tenthly, thoſe things which cannot be given by others, are better than thoſe which may; As, Virtue and Learning than Riches, &c. Eleventhly, that which one would have others leave one; As, Friends than Wealth: For Friends we would get to our ſelves; but Riches we had rather that others ſhould leave us, &c.
18. And theſe are the Principal Canons by which Problemes compared are to be confirmed; which were to be drawn either from the Abſolute Canons or Ariſtotle's three Books of Topicks. In all of which, eſpecially thoſe which contain a Compariſon of things in Goodneſs, this Caution is to be uſed, viz. That thoſe things which are compared, be in other things equal. For Example; The more laſting Goods are then to be preferr'd before the leſs, when in other things they are equal, &c. And thus much of the Dialectical Syllogiſm.
CHAP. XX. Of Demonſtration.
Ax. 1. NOW follows Demonſtration, defined foreign; that is, a Syllogiſm begetting Knowledge.
COMMENTARY.
1. §. Demonſtration, in the Greek foreign, is amongſt the Geometricians a Delineation of a Diagram, in which they exhibit the Truth of their Propoſitions to be ſeen by the Eye. To that is oppoſed foreign; that is, a Deſcription or falſe Delineation. Now theſe Words, as many others, which are uſed in the Doctrine of Syllogiſm, are tranſlated from Geometry into Logick; and there Demonſtration is taken ſometimes for any certain and perſpicuous Proof; but here in this Place ſtrictly for Syllogiſm Scientific, and foreign, or falſe Syllogiſm; for Syllogiſm begetting Error, or the contrary to Science, &c.
2. §. Demonſtration's Genus is Syllogiſm: And herein it agrees with the Dialectical. Its Difference is fetch'd from the End, which is Science. Now the Word Science is either taken largely to ſignifie any Cognition or true Aſſent; or ſtrictly, a firm and infallible one; or laſtly, an Aſſent of Propoſitions made known by the Cauſe or Effect. And that only comes under the Notion of Science, here, which is gotten by the Cauſe or the Effect; and is proper to this Place, &c.
Ax. 2. Of Demonſtration, one is, Why a thing is, and the other, That a thing is.
Ax. 3. That of Why is that which not only proves the thing is or is not; but alſo renders a Reaſon, why the thing is or is not.
Ax. 4. The Demonſtration That, only proves that the thing either is or is not.
1. §. Now this Diviſion is fetch'd from the End: For, whereas Demonſtration is a Syllogiſm Scientific, it altogether follows, that how many-fold Science is, ſo many muſt Demonſtration be; But Science, one is Why, and the other That; and therefore ſo muſt Demonſtration be. See Cap. 13. Book 1. of the Poſt.
Science and Demonſtration, in ſhort, Why, differ from that of that a thing is, in the Ratio and Quality of the Medium, which in that of Why a thing is, is the next Cauſe; that is, ſuch a Cauſe as that being put, the Propriety muſt be put alſo; and that taken away, the Propriety alſo muſt be taken away, when that of the other is not the Cauſe, but Effect; at leaſt, not the next, but remote, as will hereafter be made appear, &c.
In the Interim, take we a View of what is neceſſary to be known before we enter upon this Head.
CHAP. XXI. Of Precognitions, or Things requiſite to be known, before we enter upon Demonſtration.
Ax. 1. IN every Demonſtration, foreign, or Why, or Demonſtrative Science, three Things are to be conſidered, viz. Subject, Affection and Cauſe by which demonſtrated, that the Affection is in the Subject, &c.
Ax. 2. Of Subject and Affection is compoſed the Queſtion: Of Cauſe with the Affection, Firſt then, Subject Combined, the Premiſſes or Principles, by which ſuch Queſtion is to be demonſtrated.
Ax. 3. And in theſe, two things are to be conſidered; firſt Precognitions, and then Conditions, which in ſuch a Demonſtration are to be obſerved.
Ax. 4. Of Precognitions, the one is, whether it be? the other, what that is which is ſaid? or what ſignifies the Name?
Ax. 5. Of the three Terms, it is to be foreknown what ſignifies the Name; that is, what the Meaning or Importance of them is. Subject, Cauſe, alſo Premiſſes or Principles, whether they be? And this of the Affection and Concluſion, is to be demonſtrated.
1. §. Of the three Terms, what is the Name; becauſe otherwiſe we ſhould diſpute concerning things unknown.
2. §. Of Subject and Cauſe, whether they be? For when it is uncertain, whether there is any ſuch thing as the Cauſe, the Argumentation is infirm, and begetteth not Science. When Subject, frivolous and inept: For in vain ſhould we prove, for Inſtance, that the Pigmies are Chol…rick; becauſe of their ſhort Stature, unleſs it appears, that there are Pigmies, &c. Of Premiſſes or Principles, alſo that they are true: For otherwiſe we lay a Foundation of Things that are not known: It remains therefore that of the Affection it ſhould be demonſtrated, that it is; and of the whole Concluſion, conſiſting of Subject and Affection, that it be true, or that the Affection is in the Subject, &c.
Ax. 6. Of which Precognitions thoſe that are ſelfevident, that is, ſo, that no body can be ignorant of them, are only made in the mind; thoſe not ſo, but that they may be unknown, are always expreſs'd in the firſt Entrances of Sciences.
Ax. 7. And if ſo ſoon as produc'd, they are believ'd by the Diſciple, they may be properly term'd Suppoſitions; but if not, and the Diſciple be doubtful of them; or even encline to a contrary Opinion, Poſtulata, or things to be required or demanded.
1. §. There are ſome things, ſays Ariſtotle, in Sciences, of which no one can be ignorant, and theſe they call Suppoſitions, as we ſaid before, or Axioms; that is, ſuch as carry ſuch a Native Clarity with 'em, as they are worthy of every body to be credited; ſome of which one may: But yet, ſo ſoon as propoſed by a Maſter, are believed without Proof; And ſuch as theſe, are termed Definitions: And ſome not ſo immediately; but delivered Precariouſly, and by way as it were of Agreement; becauſe the Probation of them, if any, belongs to the Metaphyſicks. And ſuch as theſe they call Poſtulata, or things required, or to be demanded, &c.
And ſo we come to the Conditions which in every Demonſtration Why, are to be obſerved; and Firſt to thoſe of the Queſtion to be demonſtrated, and Medium, which is to be uſed in Demonſtration.