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. VII. Of the Conditions to be observed in a perfect Demonstration.

A Demonstration is to be considered, ei∣ther in the respect of the matter, or in respect of the form.

2. In respect of the matter, one kind of Demonstration sheweth, why the predicate is inherent in the subject; and that,

• 1. By an immediate intrinsecal cause, and this is either the before demonstrated mat∣ter, or form, or affection of the subject.
• 2. By an immediate extrinsecal cause, and this is either final or efficient by some transient action.

3. Another kind of Demonstration in re∣spect of the matter, sheweth that the predi∣cate is inherent in the subject, and that ei∣ther by the effect, or by some remote cause.

4. A Demonstration, in respect of the form, is to be considered,

• 1. In quantity, and so it is universal or particular.
• 2. In quality, and so it is affirmative or negative.
• ...

• 3. In the manner of the proof, and so it is either an ostensive demonstration, or a de∣monstration reducing to some impossible thing.

5. In the first of these kinds of demon∣stration called the demonstration Cur sit, why a thing is, the conditions to be observed do partly belong to the question, partly to the cause or medium of the demonstration, and partly to the premisses.

6. Every question doth not admit of the first and most perfect kind of demonstra∣tion, called why a thing is? but such a questi∣on only as is true, and hath a certain and immutable cause of its own truth.

7. The conditions to be observed in the premisses of a demonstration, are absolute or relative.

8. Those are said to be absolute conditions, which are suitable to the premisses consider∣ed absolutely and in themselves; and those are said to be relative conditions, which are suitable to the premisses in reference to the conclusion.

9. The absolute conditions are two, the first is, that the propositions be necessarily true and reciprocal: The second is, that they be immediate or first.

10. Demonstrative propositions must be

true (for that which is false cannot be known) ••nd they must be necessarily so, for from ••ropositions not necessarily true, no necessary ••nclusion can be inferred, unless by chance or ••ccident, and they must be necessarily true in the ••ighest degree, that is, they must be recipro∣••l. For they contein the next cause of the ••••edicate, which is such as that it is reciproca∣••d with its effect.

11. A proposition is said to be immediate, ••o waies. 1. In respect of the subject, ••hen there is no more immediate subject be∣••ween the predicate and the subject; as, a ••an is rational, a man is risible. 2. In re∣••ect of the cause, when no more immediate ••••use doth intervene between the predicate, ••nd the subject; as, that which is rational is ••••sible; a man is rational.

12. In a most perfect demonstration, where ••••e middle term is the material or formal in∣••rnal cause of the subject, and efficient of the ••••fect by emanation, the major proposition 〈◊〉〈◊〉 immediate in respect of the cause, but not ••f the subject, as that which is rational, is ••sible: The conclusion is immediate in respect 〈◊〉〈◊〉 the subject, but not of the cause; as, a ••an is risible: The minor is immediate in re∣••••ect of the cause and the subject both; as, a ••an is risible.

13. In a most perfect demonstration, wher•• the middle term is not the internal cause of th•• subject, though both the major and conclusio•• be immediate, yet the minor is not imme∣diate in respect of the cause. This happen in every chief demonstration from the ex∣ternal cause; as also where we proceed from one affection predemonstrated, to the demon∣stration of another; such as are all mathe∣matical demonstrations for the most part; a•• Zab. de medio demonst. c. 7.

14. The relative conditions to be obser¦ved in reference to the conclusion are three first, that the premisses be the cause of the con¦clusion; secondly, that they be before; thirdly▪ that they be more known than the conclusion

15. The premisses may be said to be th•• cause of the conclusion, as the medium is th•• cause, why an affection is not only the cau•••• why the conclusion is known, but the cau•••• why it is true: and as the medium is before a•• affection, not in time but nature, so the tru•••• of the premisses is first in nature, before th•• truth of the conclusion. Lastly, as the medi¦um is more known than an affection, not b•• a confused knowledge and in respect of us but by a distinct knowledge, and accordin•• to nature: so are the premisses more know•• than the conclusion; because we by reason 〈◊〉〈◊〉

the premisses receive the conclusion with full assent of mind, we must needs assent to that more than to the premisses; for according to Aristotle, That for which another is such as it is, must needs it self be more such. Lib. 1. post. cap. 2.

16. Premiss••s are of two sorts, Axiomes and Theses.

17. An Axiome is a proposition of whose ••ruth no body can be ignorant, the signification of the words being known.

18. A Thesis is a proposition, whose truth doth not sufficiently appear by knowing only the signification of the words, but by the judgment of the senses, or any other declaration; and it ••s either a Definition or an Hypothesis.

1. A Definition is that, by which we shew what a thing is. An Hypothesis is that, by which we shew whether the thing be or not.

20. The medium of a demonstration ought to be the next cause of the predicate; and that either efficient or final; and the efficient either internal or external.

21. A cause may be said to be the next either absolutely, or in his own kind; here it is understood to be the next absolutely, that it is such a cause as doth produce the effect, and without which that effect cannot be:

For as much as there are four kinds of causes, and in every kind some one the next, of the four next causes, there is but one, that is the next absolutely.

22. Moreover it is required that this next cause should be the cause of the predicate, but it is necessary that it should be the cause of the subject also; for the question is not, whe∣ther there be a subject? for this is supposed; but whether there be a predicate, or whether it be inherent in the subject?

23. This next cause must be either the efficient or the final; for when the predicate is an accident it hath neither matter not form properly so called. The final cause is used in those things, which are made for o∣ther; such as are mediums and natural in∣struments; actions also and habits, if any such can be demonstrated. The efficient cause is used in all the rest. Sometimes it falls out that the next efficient cause is also the form o•• matter of the subject, and these kind of de∣monstrations are indeed the most excellent but do not make a different species of them∣selves, but these things will be more clearly understood by the examples following.

1.

• Every rational creature is capable 〈◊〉〈◊〉 knowledge,
• ...

• Every man is a rational creature,
• Therefore every man is capable of knowledge.

In this demonstration the medium, rational, is the internal efficient cause of the predicate, and form of the subject.

2.

• Every terrestial thing doth sink in water,
• Ebene is terrestial,
• Therefore Ebene doth sink in water.

Here the medium is the internal efficient cause, and matter of the subject.

3.

• Whatsoever doth consist of matter and form hath three dimensions.
• Every body doth consist of matter and form,
• Therefore every body hath three dimensions.

Here the medium is the internal efficient cause of the predicate, and both the form and matter of the subject.

4.

• That which hath three dimensions, will not admit of another body in the same place, with it self,
• But every body hath three dimensions,
• Therefore &c.

Here the medium is the internal efficient cause of the predicate, and propriety of the subject.

5.

• That which by the interposition of the earth cannot be enlightened by the Sun-beams, doth suffer an Eclipse of the Sun∣light,
• But the Moon, the earth being interposed can∣not be enlightened by the Sun-beams,
• Therefore the Moon &c.

Here the medium is the external efficient cause of the predicate.

6.

• Whoso is made for the contemplation of Heavenly things, ought to have his counte∣nance lift up,
• Man is made for the contemplation of Hea∣venly things,
• Therefore &c.

Here the medium is the final cause of the predicate.

24. Sometimes it so comes tO pass, that one and the same question may be demon∣strated both by the efficient and final cause so you may demonstrate that a living crea∣ture

doth sleep, either because the common ••ense is overcome by vapours, and that the ••assage of the external senses are obstruct∣••d, and this is a demonstration from the ••ficient cause; or that the animal spirits may be ••efreshed and strengthened, and this is a de∣monstration from the final cause.