The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

CHAP. IV. Of Argumentation.

ARgumentation is an Oration by which some Problem is proved by inference.

1. A Problem, is the proposition or Que∣stion to be proved; the which Problem, when it is so proved is the Conclusion, and follows the Illative note, or note of infe∣rence: All that which precedes is the Ante∣cedent, that which follows is the Consequent or Conclusion; the Illative is commonly this word (therefore,) and in this doth the tye or force of the Argument consist.

2. Argumentation, may be considered ei∣ther in reference to the form and manner of Arguing, which is the more general con∣sideration; or as it is restrained to certain matter, as shall be shewed in his place.

3. The kinds of Argumentation are usual∣ly reckoned to be four; Syllogism, Induction,

Enthymeme, and Example, but may be redu∣ced to two; for an Enthymeme is nothing but an imperfect Syllogism; an Example, an imperfect Induction; Other less principal kinds of Argumentation there are, which either are of no use, or may be reduced to a Syllogism; as, Sorites and Dilemma, which are indeed redundant Syllogisms; Sorites Ca∣tegorical, and Dilemma Hypothetical.

4. A Syllogism, is an Oration, in which something being taken for granted, some∣thing else not granted before, is proved or inferred from them.

5. A Syllogism is two-fold, Categorical, in which all the propositions are Categori∣cal: or Hypothetical, in which one or more of the propositions are Hypothetical; in both which we are to consider the Matter and the Form.

6. The Matter of a Syllogism, is either Remote or Next.

7. The Remote matter, is that of which it is remotely made, as the Simple Terms which in the propositions of the Syllogism are made Subject and predicate.

8. The Simple Terms of a Syllogism are three, of which one is called the Middle Term, the other two are the M••jor and the Minor Extreams, The Major and Minor Extreams are the Predicate, and the other the Subject of the question, and the Middle Term or Argument, is the Term not ex∣pressed

in the question, but is united once to the Major Extream, and once to the Minor.

9. The next or immediate matter of a Syllogism, is that of which the Syllogism is immediately made, as the three propositi∣ons, which are made of the simple terms, of which the first is called the Major, the second the Minor, & the third is call'd the Conclusion.

10. The form of a Syllogism is the right disposing of the two-fold Matter, Next and Remote, and this comprehendeth two things, Figure, and Mood; the one, to wit Figure, hath respect to the Remote Matter or Simple Terms, and Moods respects the next Matter or the propositions.

11. A Figure, is the fit disposing of the middle Terms with the Extreams, in refe∣rence to subjection and Predication; this is three-fold.

12. The first Figure maketh that which is the middle simple term to be the subject in the major proposition and the Predicate in the minor.

13. The second Figure, maketh the middle simple term to be the Predicate, both in the major and the minor propositions.

14. The third Figure maketh the middle simple term to be the subject both in the major and the minor propositions; according to these Distichs.

Both sub and prae, doth the first Figure use. Twice prae the next, the third twice sub I muse.

15. A Mood is the disposing of the pro∣positions according to quantity and quality.

16. There are 19 Moods, of which there are nine in the first Figure; four in the se∣cond; and six in the third, according to these Verses.

• 1. Barbara, Celarent, Darii, Ferio, Baralipton.
• ...Celamtes, Dabitis, Fapesmo, Fricesomorum.
• 2. Cesare, Camestres, Festino, Baroco.
• 3. Darapti:
• ...Felapton, Disamis, Datisi, Bocardo, Ferison.

17. These moods are so many words of Art, which serve only to denote the quali∣ty and quantity of every proposition, by help of the Vowels, A, E, I, O, as hath been shewed already; and are some of them per∣fect, as the four first Moods in the first Fi∣gure, and all the moods in the second and third Figures; the rest are imperfect.

18. And the question propounded is pro∣ved by or inferred from the premises, by help of these moods two ways, viz. Directly, and Indirectly.

1. Directly, when the Minor Extream is the subject in the Conclusion, and the Major in the Predicate.

2. Indirectly, when the Major Extream is the subject in the Conclusion, and the Minor the Predicate, and this is in the five last moods of the first Figure only, according to these Distichs.

All the Nineteen directly do conclude, Except of Figure first, the last 5 Mood.

19. These things premised, a Syllogism, may be made in any Mood and Figure in this manner.

The question propounded is always the conclusion of the Syllogism, and by the quan∣tity thereof doth plainly shew in what mood or moods it may be framed, and by conse∣quence, in what Figure also.

20. If the Syllogism be to be made in such a mood as doth directly infer the Conclusion from the Premises; then the subject in the Proposition is the Minor Extream, and the Predicate the Major; as in the four first moods of the first Figure, and in all the Moods of the second and third Figures; but in the five last Moods of the first Figure, the subject in the Proposition is the Major Extream and the Predicate the Minor; and the mid∣dle term is the Cause or Argument by which the truth or falsitie of the proposition is to be proved.

21. The Middle Term or Argument be∣ing joyned to the Major Extream, doth make the Major proposition, and being joyned to the Minor Extream, it maketh the minor propositi∣on.

Example.

Let this be the Proposition, No Man is a stone: This Proposition being an Universal Negative, the Syllogism may be framed in Celarent, Celantes, Cesare or Camestres; if in Celarent, man is the Minor Extream, and Stone the Major; and to find out the middle Term, I consider of some Reason or Argu∣ment by which to prove the Question; as, A Man is not a Stone, because he is a Living Creature; so then Living Creature is the Middle Term, and these three Terms being thus placed;

[illustration]

Middle Term.

Living Creature.

Minor Extream.

Man.

Major Extream.

Stone.

Because Celarent belongs to the first Fi∣gure, the middle Term Living Creature must be the Subject in the Major Proposition, and the Predicate in the Minor; thus,

	Subj.	Praed.
Major.	Living Creature.	—
Minor.	—	Living Creature.
Conclu.	No man is a Stone.

And joyning this middle Term to the Major Extream, and also to the Minor; the several Propositions will be these;

• ...Major. A living Creature is not a stone.
• ...Minor. A man is a living Creature.
• ...Conclu. A man is not a stone.

Lastly adding the Quantity to every Pro∣position according to the Vowels in this Mood, the Compleat Syllogism is,

• ...Major * 1.1 No living Creature is a Stone.
• ...Minor * 1.2 Every man is a living Creature.
• ...Conclu. * 1.3 No man is a stone.

The like may be done in the other moods.

22. An Enthymem, is an Imperfect Syllo∣gism, inferring the Conclusion from some one Proposition only; as, A man is a living Creature, therefore he hath a soul.

23. An Induction, is an Imperfect syllo∣gism, in which from many singulars, some Universal Conclusion is inferred; as, This man is a living Creature, and that man is a li∣ving Creature, &c. therefore every man is a li∣ving Creature.

24. Example, is an imperfect syllogism, in which from one or more singulars, we infer another particular; as, Catiline was punished

for making of Sedition, therefore this Seditious Fellow should be punished.

25. Sorites, is an imperfect syllogism, in which, from four or more Premises, we in∣fer a Conclusion, in which the first subject is joyned with the last Predicate; as, Socrates is a man, a man is a living Creature, a living Creature is a Body, a Body is a substance, therefore Socrates is a substance.

26. A Dilemma, is an Argumentation which by disjoyning of the Members, doth so enforce the Adversary, that which part soever he chooseth, he will be catched, as, Tribute must be given to Caesar, or to God; If to God, then not to Caesar, and this is Treason; If to Caesar, then not to God, and this is Sacri∣ledge.

And thus much concerning a syllogism in the General, with the several kinds and forms thereof.

Notes

• * 1.1

  Ce-
• * 1.2

  la-
• * 1.3

  rent.