Abstract of Logic, Book 2 · Chapter 22
CHAP. XXII. Of the Queſtion to be demonſtrated, and Medium which is to be uſed in Demonſtration.
Ax. 1. THE Conditions which are to be obſerv'd in Demonſtration Why, are partly belonging to the Queſtion, partly to the Cauſe or Medium of Demonſtration, and partly to the Premiſſes or Principles; of which in the Chapter following.
Ax. 2. Every Queſtion does not admit of a Demonſtration Why; but only that which is true, and has a certain and immutable Cauſe of its Truth.
Ax. 3. And therefore neither Propoſitions immediate, nor fortuitous can be demonſtrated; but only proper Accidents.
1. §. Now Propoſitions immediate cannot; becauſe they have no Medium, or Cauſe of their Truth.
1. §. Chance, likewiſe, cannot; becauſe they have not any Dependance upon any certain Cauſe, or Rule; Accidents therefore, and thoſe proper only can be demonſtrated. For Subſtances have no Cauſe why they're in the Subject; becauſe they are predicated, always as Genus's or Differences. And Accidents improper have no certain and definite Cauſe. Now whether theſe Accidents proper flow from the Eſſence of the Subject, or ſome External Cauſe, or whether they be perpetual, or only frequent, it matters not: But this, that they cohere with their Cauſes ſo as that they being put, theſe alſo be put, and that being taken away, theſe alſo may be taken away, is neceſſary and required. For Inſtance; Altho' the Moon be not always deficient, yet, that ſhe is ſo, when ſo, may be demonſtrated; becauſe ſhe is always ſo, when the Earth is Diametrically interpos'd between the Sun and the Moon; and never ſo when otherwiſe, &c. And ſo much of the Queſtion to be demonſtrated.
Ax. 4. Now the Medium of Demonſtration muſt be the next Cauſe of the Predicate, and that either Efficient or Final; and if Efficient, either Internal or External.
1. §. Now whereas Cauſe is ſaid to be two Ways next, that is, either abſolutely or in its own Genus: In this Place is to be underſtood the Abſolutely next; that is, ſuch as that being put, the Effect alſo muſt be put; and that taken away, the Effect alſo muſt be taken away. And farther, it is required, that it be alſo the Cauſe of the Predicate: For, that it be alſo of the Subject, is not ſo neceſſary; becauſe it is not enquir'd, whether the Subject be; for that is pre-ſuppoſed; but whether the Predicate, or in plainer Terms, whether the Predicate be in the Subject or not, &c.
2. §. This next Cauſe muſt be either Efficient or Final; becauſe the Predicate being an Accident, has not Matter or Form, properly ſo call'd. The Cauſe Final is adhibited in thoſe things which are done for the ſake of another: As, Means, Natural Inſtruments, &c. Alſo Actions and Habits, if ſuch are to be demonſtrated, and in other Caſes the Efficient. It happens ſometimes indeed, that the Cauſe Proximate, viz. the Efficient, is alſo the Form or Matter of the Subject; and when it is ſo, the better: But however they differ not in Specie from the reſt. But theſe things will appear more by Examples, as here,
1. Every Rational Creature is capable of Science;
Every Man is a Rational Creatur….
Every Man therefore is capable of Science, &c.
In this is the Medium Rational the Cauſe Efficient Internal of the Predicate, and Form of the Subject. Here,
2. Every Earthly thing is overwhelm'd, wi…n thrown into the Water:
An Ebony-Tree is an Earthly thing:
And therefore every Ebony-Tree is overwhelm'd when thrown into the Water.
The Cauſe Efficient Internal and Matter of the Subject. Here,
3. Whatever conſiſts of Matter and Form has a Three-fold Dimenſion;
Every body conſiſts of Matter and Form:
And therefore every body has a Three-fold Dimenſion, &c.
Cauſe Efficient Internal of the Predicate, and both Form and Matter of the Subject. Here,
4. That which is endued with a Three-fold Dimenſion, admits not of another Body's being with it in the ſame Place.
But every body is endued with a Three-fold Dimenſion:
&c.
The Cauſe Efficient Internal of the Predicate, and the Propriety of the Subject, &c. Here, viz.
5. That which, the Earth being objected, cannot be illuſtrated by the Rays of the Sun, that ſuffers an Ecclipſe of the Light receiv'd from the Sun;
But the Moon, the Earth being objected, cannot be illuſtrated with the Rays of the Sun: &c.
The Cauſe Efficient External of the Predicate. Here,
6. He who was made for the Contemplation of Celeſtial Things, ought to be of an upright Countenance;
Man was made for the Contemplation of Celeſti-Things:
And therefore Man ought to be of an upright Countenance.
The Cauſe Final, and alſo that of the Predicate, &c.
3. §. Now ſometimes it happens that the ſame Queſtion may be demonſtrated by the Cauſe Efficient, together with the Final; and ſo you may demonſtrate that an Animal ſleeps, viz. either becauſe the common Senſe is ſopited or drown'd by Vapours, and the Paſſage of the External Senſes obſtructed. And this is from the Efficient; or elſe that the Spirits may be refreſh'd, and Strength repair'd. And this is from the Final, &c.
4. §. Demonſtrations Why, are not only affirmed but alſo denied. For, as we may demonſtrate that a Man is capable of Science, becauſe endu'd with Reaſon: So alſo that a Beaſt is not; becauſe not, &c. For as an Affirmation is the Cauſe of an Affirmation, ſo muſt a Negation be the Cauſe of a Negation, &c. See Book 1. Poſt. Cap. 13.
And ſo we proceed to the Chapter of the Conditions of the Principles of Demonſtration in which we are taught what they ought to to be.