An introduction to the art of logick composed for the use of English schools, and all such who having no opportunity of being instructed in the Latine tongue ... / by John Newton ...

CHAP. VI. Of the first Definition and Praecognita of Demonstra∣tion.

I Come now to speak of a special or Mate∣rial Syllogism, as it is restrained to certain conditions of matter.

2. A Special or Material Syllogism, is of three sorts; Apodictical, Dialectical, and So∣phistical.

3. An Apodictical Syllogism otherwise call∣ed a Demonstration, may be defined two ways, either from the end, or from the matter of de∣monstration.

4. From the end of Demonstration an apo∣dictical Syllogism may be defined. Demon∣stration is a Syllogism begetting knowledge, or making to know.

5. Demonstration among Geometricians, is a Delineation by Diagrams, in which, the truth of their propositions is exhibited unto the eye: but amongst Logicians it is sometimes taken for every certain and clear proof; and here it is strictly taken for a scientifical Syllo∣gism.

6. The Genus in this definition is Syllogism, in which it agreeth with Dialectical Syllo∣gism. The difference is taken from the end, which is Science.

7. This word Science may be taken three ways, largly, strictly, and most strictly.

• 1. Largly, for every cognition or true assent.
• 2. Strictly, for firm and infallible assent.
• 3. Most strictly, for the assent to such propositi∣ons, as are known by causes and effects: for firm and infallible cognition is either by sense, and so we know that the sun doth shine at noon; or by understanding, as when the que∣stion is concerning universal propositions, con∣cerning the truth of which sense is not able to judge; but, the cognition of universal propo∣sitions is attained by, or without a Syllogism.

8. Cognition is begotten without a Syllo∣gism, when full assent is given to a propo∣sition for the clearness of it in its self with∣out any proof. Thus we know that the whole is greater than any part thereof; that God must be worshipped, and such like. This kind of Cognition, Aristotle calls Intelligence, and saith it is distinguished from Science by this, that Science doth proceed from ratioci∣nation: but for as much as reason may be brought from several heads, that cognition is here called by the name of Science, which

is begot either by the cause or by the effect. And this is the most strict acception of Sci∣ence, and proper to this place.

9. Or thus, Science is a certain knowledge of conclusions, to which we assent, for our preceding knowledg of the premisses: and the praecognita in every science are these three, the subject, the affection, and the cause, by which it is demonstrated that the affection is in the subject.

10. The Question to be demonstrated is composed of the subject and the affection. The premisses by which the Question is de∣monstrated, are made, first, by joyning the cause with the effect, and then by joyning the cause with the subject. In all these two things are to be considered, the precognitions, which precede the demonstration, and the conditions, which are to be observed in the demonstrati∣on it self.

11. The Precognitions are two. 1. That the thing is. 2. what it is?

12. In these precognitions, the things which are evident and obvious unto all, are so in the understanding only; but the things which are not so evident, but that they may be un∣known, are expressed in the very beginning of sciences.

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presently believe them, they are properly called fuppositions; but if the learner either doubt of them, or be of another opinion, they are cal∣led postulata, or things to which an assent is requested.

14. The first of these precognitions, viz. the Quod sit, That the thing is, includeth two things. 1. That the thing sougt hath a being, or a true existence, and this answereth to the Question, Is there such a thing? 2. That the thing sought is the true predicate in a subject.

15. The other of these precognitions, name∣ly, the Quid sit, What it is? doth also in∣clude two things. 1. The name, or what the signification of the name is. 2. The nature of the thing, that is called by that name, so that from these two precognitions four questi∣ons do arise; of which two are simple and two compounded.

16. The simple questions are those which do equally agree, to accidents and to sub∣stances. The first is made concerning the essence or existence by asking An sit? whether it be or not? The second maketh inquiry con∣cerning the nature of it and asketh, Quid sit, What it is?

17. The compounded questions cheifly agree with accidents: the first asketh, whether the predicate be in the subject? as, whether man be

risible? The other asketh, why the predicate is in the subject? as, why is man risible?

18. Of these four questions the third hath such reference to the fourth, as the first hath to the second; for then in simple terms when we know they have being, we ask what the things are? and in propositions, when we know they have a being, we inquire, why they are?

19. After these precognitions and questions the three praecognita are next to be conside∣red; namely the subject, affection, and cause.

20. The subject is a simple term, or less ex∣tream in the demonstration, concerning which, some accident is demonstrated by its next cause; as, a man; concerning whom we must both know, that he is, and what he is? First that he is, or otherwise we seek the knowledg of him in vain, for there is no knowledge of a thing, that is not; and then we must also know, what he is, not only in respect of his name but also of his nature, for that must be the medium of the demonstrati∣on; and we must know the medium, at least confusedly, before we can infer the conclusi∣on. The precognition of the things existence is called the Hypothesis; of its nature, the Definition.

21. Passion is a proper Accident which is de∣monstrated

of the subject by the proper cause, it is always the greater extream which is pre∣dicated in the conclusion; as, Risibility; the which is necessary to be foreknown in respect of the name, what it is? though not in respect of its nature; and that it be considered how it is inherent; for seeing it supplies the place of the subject, it is in some sort called a sub∣stance. Arist. lib. 1. post. cap. 27. but it is not foreknown, That it is, for that is the thing inquired after, and which we are to find by demonstration.

22. A Cause is that, by which the passion or affection is demonstrated of its subject, and is always the Major proposition of the de∣monstration; as, Every rational animal is risi∣ble; that being known, the conclusion is ver∣tually known also, as being vertually contein∣ed in it; but yet it is not actually known, till the Minor be assumed; which being known, the Conclusion, though after in nature, yet is known at the same time also. What the cause is, cannot be foreknown, because it is a com∣pounded proposition; and what a thing is, is only of uncompounded; but it ought to be known, That it is, or hath a true existence, or else the Conclusion cannot be inferred from it.