Abstract of Logic, Book 2 · Chapter 23
CHAP. XXIII. Of the Conditions of the Principles of Demonſtration.
Ax. 1. THE Conditions of the Principles, or Propoſitions, of Demonſtrations Why, are either Abſolute or Related.
Ax. 2. Abſolute are thoſe which agree to the Propoſitions in themſelves conſider'd; and Related as Compared with the Concluſion.
Ax. 3. The Abſolute are theſe; and firſt that the Propoſitions be neceſſarily true, and reciprocal. Secondly, Immediate and Firſt,
COMMENTARY.
True; becauſe a Falſe cannot be known; and alſo neceſſarily; becauſe from Propoſitions not neceſſary a neceſſary Concluſion cannot be drawn, unleſs by Chance or Accident.
2. §. Immediate; becauſe if not, there would be a Progreſs to Infinite, which is inconſiſtent with the Nature of Rnowledge.
Ax. 4. Theſe Two in the Major are required Neceſſarily; but that the Minor ſuppoſing it be true, ſhould be alſo Neceſſary and Immediate, is not abſolutely Neceſſary.
1. §. For the Major is to conſiſt of the Affection, and its next Cauſe, which are not only Reciprocated amongſt themſelves; but alſo neceſſarily and immediately cohering: But the Minor of the Affections, Cauſe and Subject, which it is not neceſſary ſhould ſo cloſely cohere, as that they ſhould conſtitute a Neceſſary, Immediate and Reciprocal Propoſition; ſince of the Affection, not Subject, the Knowledge is required, &c.
2. §. Now the Minor is not neceſſary, much leſs Reciprocal, and Univerſally firſt, when the Medium of the Demonſtration is the Cauſe Efficient External of the Predicate. For Example; That which with the Rays of the Sun, the Earth being objected, cannot be illuſtrated, that ſuffers a Defect of Light receiv'd from the Sun; The Moon with the Rays of the Sun, the Earth being objected, cannot be illuſtrated: And therefore, &c. In this Demonſtration the Minor has no Degree of Neceſſity; becauſe it is not perpetual. In Demonſtrations from Cauſe Efficient Internal, or Final, indeed, the Minor is always Neceſſary, but not Reciprocal; becauſe often, the next and Reciprocal Subject wants a Name. For Example; Every Plant, whoſe Humour is apt to congeal at the Foot; or Stalk of its Leaf is apt to ſhed its Leaves: But the Humour of the Vine is apt to congeal at the Foot or Stalk of its Leaf: And therefore the Vine is apt to ſhed its Leaves, &c. In which the Minor is not Reciprocal; becauſe it happens not only to the Vine, to have its Humour congealed, but to all other Plants to whom it happens to ſhed their Leaves. But this happens, becauſe there is not a proper Name by which ſhould be ſignify'd All, and only thoſe Plants to which the Congelation of the Humours and Fall of the Leaf evenes. For the ſame Reaſon is it alſo, that the Concluſion is not Reciprocal. See Book 1. Poſt. Cap. 5. and Book 2. Cap. 66.
3. §. The Minor is not Immediate alſo when the next Cauſe of the Predicate, has any former Cauſe by which it may be demonſtrated For in all Cauſes which enter Demonſtration, there is a certain Series and Subordination; ſo that every Poſterior is the Effect of the Precedent. As often therefore as any Effect is demonſtrated by ſuch a Cauſe as is the Effect of a former Cauſe, that Minor muſt neceſſarily be Mediate; and then that Minor is to be reſolv'd into that former Cauſe; and ſo on till you come to the Firſt of that Series, which conſtitutes a Demonſtration of both Propoſitions Immediate: And this Demonſtration is the Foundation of all the reſt which are of the ſame Series. And therefore, in ſearching of Science, we are to proceed from the firſt Demonſtration to the following in Synthetic Order; and then the Minor Mediate is eſteem'd as it were, Immediate; becauſe now before demonſtrated. For a Demonſtrated Propoſition is no leſs apt to beget Knowledge than a Propoſition Immediate and Indemonſtrable. But yet if any one ſhall happen upon a Demonſtration, whoſe Minor is Mediate, he muſt proceed in Analytic Order towards the firſt and Fundamental Demonſtration. Nor will he firſt have attained Science, before he ſhall have arriv'd at the firſt Cauſe: For in this the Mind acquieſces. But let us add Examples, that the Thing may be ſo much the better underſtood: That which is endu'd with a Three-fold Dimenſion, admits not another Body to be with it at the ſame time, in the ſame Place: All Bodies are endu'd with a Three-fold Dimenſion: And therefore, &c. The Minor of this Syllogiſm may be demonſtrated in this manner: That which conſiſts of Matter and Form is endued with a Three-fold Dimenſion; Every Body conſiſts of Matter and Form: And therefore every body, &c. Now the Minor of this Syllogiſm is Immediate as well as the Major; becauſe to conſiſt of Matter and Form, is the Definition of Body, &c.
4. §. The ſame Series there is in Demonſtration from Cauſe Final, in which the Subordinate is demonſtrated by the farther End until you ſhall come to the laſt in every Genus, in which the Mind acquieſces. For Example: An Animal has Lungs that it may breath, breathes that it may refreſh the Heart; the Heart is to be refreſh'd to preſerve a Temperature of Heat; a Temperature of Heat is to be kept, that the Life of the Animal may be preſerv'd, &c. If theſe Demonſtrations be propos'd in Form, all, excepting the Laſt, will have a Mediate Minor; and the Laſt is the Foundation of all the reſt.
5. §. It ſometimes happens that Demonſtrations from Cauſe Efficient cannot be reſolv'd into Propoſitions Mediate, unleſs the Demonſtration from Cauſe Final be commixt with the Demonſtrations from Cauſe Efficient. For Example; A Man is of a moſt Acute Touch; becauſe he is of a very thin Skin; a thin Skin, becauſe having abundance of Elaborated Animal Spirits; abundance of thoſe Elaborated Animal Spirits, becauſe having a very large Brain, the Shop or Office of thoſe Elaborated Animal Spirits. Hitherto are they all Cauſes Efficient. That a Man has a very large Brain, is to be demonſtrated from the End, to wit, becauſe he ſhould reaſon; that Man ſhould reaſon again, from Cauſe Efficient to wit, becauſe he is a Rational Animal. Here now we acquieſce; becauſe the Minor is the Definition of Man; and therefore Immediate and Indemonſtrable.
Ax, 5. The Conditions of Principles relating to the Concluſion, are Three: And firſt, that they be the Cauſes; Secondly, Prior to, and Thirdly, more known than the Concluſion.
Ax. 6. And theſe Conditions are required in both Propoſitions.
1. §. For, as is the Medium of Demonſtration foreign, with reſpect to the Queſtion to be demonſtrated, ſo are the Principles or Premiſſes to the Concluſion. Wherefore as the Medium is the Cauſe of the Affection, ſo the Principles are the Cauſe, not only why the Concluſion is known: For in this Senſe the Principles are the Cauſe even in all Syllogiſms; but alſo why they are true. And as the Medium is before the Affection, not in time, but Nature; So alſo the Principles obtain a Verity, not in Time, but Nature, prior to that of the Concluſion. Laſtly, as the Medium is more known than the Affection, not as to us, and in way of confus'd Knowledge, but of Nature and diſtinct Cognition. So, alſo, the Principles are more known than the Concluſion. For, becauſe we embrace the Concluſion with a full Aſſent of the Mind, for the ſake of the Principles; we muſt aſſent more to the Principles themſelves of Neceſſity; becauſe that for the ſake of which any thing is ſuch; that it ſelf is more ſuch; as Ariſtotle teaches Book 1. Poſt. Cap. 2. &c.
Ax. 7. Now when the Principles have all theſe Conditions, they are proper to the Thing to be demonſtrated.
Ax. 8. Principles are ſaid to be proper to the thing to be demonſtrated, when they are neither Heterogeneous or Foreign, nor yet Common.
1. §. Now Principles are ſaid to be Heterogeneous then when they are fetch'd from ſome other Science: As if one for the proving of Phyſical Queſtions ſhould make uſe of Mathematical Principles; or Geometrical, Arithmetical. But it is not lawful for a Demonſtrater to paſs from one Science to another; to wit, becauſe the Medium with the Third, that is, the Subject; and the Firſt, that is the Predicate with the Medium ought to agree by it ſelf; as is taught Cap. 6. of the ſame Book; which cannot be if the the Concluſion and Principles are not of the ſame Genus or Subject; that is, of the ſame Science. For that is ſaid to be of the ſame Science, which is of the ſame Genus or Subject, as appears from Cap. 28. of the ſame Book.
2. §. If yet one Science be Subalternate to another; as, Muſick to Arithmetick, or Optick to Geometry: The Queſtions of the Inferiour are to be demonſtrated by the Principles of the Superiour Science: Nor is this a paſſing to another Genus; becauſe the Subalternated Science has, in ſome manner the ſame Subject with the Superiour; and ſo they are not to be eſteemed divers Sciences. I ſaid in ſome manner; becauſe the Subalternated Science conſiders the Subject of the Superiour with ſome ſenſible Quality which yet appertains not to the formal Ratio of the Subject: From whence it is that the Affections of both are diverſe, tho' in the reſt they conſent. So Arithmetick conſiders Number abſolutely; Muſick, which is Subalternated to it, only in …ound. So Geometry conſiders Magnitude abſolutely: The Optick, or Science diſcuſſing the Reaſons of Sight, which is ſubalternate or inferiour to it only in Colour, Light and Shadow. See Cap. 7. of the fore-cited Book.
3. §. The Principles Common are thoſe which may be accommodated to many Sciences. Such Principles as theſe generate not Science; becauſe they contain a Medium which coheres not with the Part of the Queſtion by it ſelf, but Accident. But it is then that we know a Thing truly, when we know it ſo far as it is in the Subject, and that from Principles which are ſuch; as, it is that which it is; as Ariſtotle ſpeaks Cap, 9. of the ſame Book. But that which we know from common Reaſons we know only by Accident, &c. It is not yet to be thought that the Principles of Sciences are Common; which, when of the Superiour are adhibited to the Inferiour Science; becauſe the Science Subalternate, as has been ſaid before, is not eſteem'd diverſe from the Subalternating, &c.
Ax. 9. Now Principles are divided into Axioms and Theſis's.
Ax. 10. And an Axiom is that, the Truth of which knowing only the Signification of the Words, no Perſon can be ignorant of.
Ax. 11. A Theſis, whoſe Truth is not known by the meer Signification of the Words only; but by the Judgment of the Senſes, or ſome other way of Declaration.
Ax. 12. And this is either Definition, or Hypotheſis.
Ax. 13. A Definition is an Oration, as we have obſerved before, in which we declare what a Thing is. An Hypotheſis, whether it be in Being, or no, &c.
This Diviſion of the Principles is fetch'd from Book 1. Poſt. Cap. 2. and 10. Whence Axiom is ſo call'd, is declar'd Book 1 of the Inſtitutions, Cap. 27. The Word Theſis is ſometimes taken for any Propoſition, which is propoſed Pro and Con to be diſputed of, as, Book 8. Top. Cap. 4. and 5. and ſometimes for a Sentence Paradoxal of ſome eminent Philoſopher; as, Book 1. Top. Cap. 1. In Rhetorick it is taken for an infinite Queſtion; but here, for a kind of Propoſition Immediate. Now,
2. §. Ariſtotle Cap. 10. of the fore-cited Book defines an Axiom in this manner, viz. to be that which of neceſſity is true of it ſelf and of the like Neceſſity muſt ſeem ſo. Of Neceſſity true, that is, worthy of it ſelf of our Belief, or that that has no Cauſe of its Truth, by which to be demonſtrated. And this is Common to all, as well Theſis's as Axioms.
Adds, of Neceſſity muſt ſeem ſo; that is, by a Perſon of compleat Reaſon; It cannot ſeriouſly and with the Conſent of his Mind be deny'd: For a Perſon perchance may deny an Axiom rather than confeſs himſelf to be overcome; but no one can be found, who ſuppoſing him of a compleat Reaſon, can deny it in his Soul and Mind. For Example; ſuch Enunciations as theſe; Nothing can, at the ſame time, be and alſo not be: The whole is greater than its Part Thoſe things that are equal to the ſame; thoſe alſo will be equal amongſt themſelves: If from equal things you take away equal, thoſe things which remain will be equal too, &c. The Evidence of which is ſo great, that knowing only the Signification of the Words by which they are expreſs'd, the Truth of them cannot but be apparent. For he who knows what ſignifies a Whole, and what a Part, and what to be greater, cannot be ignorant that a Whole is greater than a Part, &c.
3. §. And in this reſpect differ Axioms from Theſis's: For to the Knowledge of Theſis's, beſides the Knowledge of the Signification of Words, is requir'd the Judgment of the Senſes, and ſometimes the Declaration of a Maſter. Of Definitions Examples may be taken out of every Diſcipline: As for Inſtance; Phyſick: As, a Body Natural is that which conſiſts of Matter and Form: Principles are thoſe which are neither made out of themſelves nor others, and out of which are made all things: Nature's the Principle and Cauſe of Motion and Quiet in that in which it is, firſt, by its ſelf, and not by Accident, &c. Geometry; As, that a Point is that which does not conſiſt of Parts: A Line is a Longitude, void of Latitude: A Right Line that which lies equally betwixt its Points, &c. Hypotheſes in the firſt, that there is a Natural Body, a Heaven, a Soul, &c. Arithmetick; that there is a Unity; ſeu non dari maximum Numerum; that is, that there's no ſuch thing as the higheſt Number: Geometry; that there's a Line, that from one Point to any other Point a right Line may be drawn, &c. All which are ſuch, as, tho' they want not Demonſtration, yet are they ſuch as that out of the Signification of the Words meerly known without the Acceſſion of any thing elſe, they cannot be known to be true: For altho' any one ſhould know what's ſignify'd by the Name Body, yet can he not know by this that every Body conſiſts of Matter and Form: Nay, that there is ſuch a Thing as Natural Body, if not aſſiſted by the Help of his Senſes, &c.
4. §. Hence is it that Axioms ought to be held by him that would learn any Science before he comes to his Maſter. Theſes's, not, becauſe theſe are to be explained in the very Entrances of Sciences. Definitions eſpecially always; but if known by the Judgment of the Senſes, Hypotheſes, indeed, need not, &c.
Ax. 14. Now when a Demonſtration is Conform to theſe Laws, it not only proves, that the Affection's in the Subject, but alſo explains what that is; and contains the perfect Definition of it.
1. §. That is, contains all thoſe things that are neceſſary to it, only in Inverted Order: For a Demonſtration is thus propoſed, viz. The Earth is interpoſed between the Sun and the Moon; and therefore the Moon ſuffers an Eclipſe, or a Defect of Light, viz. receiv'd from the Sun. And a Definition thus, viz. An Eclipſe is a Defect of Light in the Moon, receiv'd from the Sun, by Reaſon of the Earth's Interpoſition, &c. And this of Demonſtration Why. Now come we to that which we call Demonſtratin That, of which the next Chapter; as alſo of that which the Logicians call a Regreſs.