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.

THE ENGLISH ACADEMY: The SEVENTH PART. Of the ART of LOGICK. (Book 7)

CHAP. I Of Simple Themes.

LOgick, is an Art which conducteth the Mind in the knowledge of Things.

2. The Parts of Logick are two, Thematical and Organical.

3. The Thematical part is that, which Treateth of Themes, with their various af∣fections, and second Notions, as of the mat∣ter of which Logical Instruments are com∣posed.

4. The Organical part, is that which trea∣teth of these Instruments, and their Com∣position.

5. A Theme, is any thing propounded to

the understanding, that it may be known.

6. A Theme, is either simple or compound.

7. A Simple Theme, is one Voice, signifi∣ing one thing as, a Man, a Horse.

8. A Compound Theme, is a Theme made of several simple themes rightly Joyned to∣gether; signifying many or several things; such are all Orations.

9. A Simple Theme or Voice, is,

• 1. Concrete, which expresseth a thing Concretely or Joyntly; as, Learned.
• 2. Abstract, which noteth something Ab∣stracted from all others; as, Learning.

10. An Abstract Voice, or simple theme, is Singular or Universal.

11. A singular theme, is that which in its own nature can be spoken of no more than one, and is called an Individual.

12. Individuals are of two sorts.

• 1. Such as are Certain and Determinate; as, this man, Paul, Alexander, the Apostle of the Gentiles, &c.
• 2. Such as are uncertain and indetermi∣nate, as some man.

13. An Vniversal simple Theme, otherwise called a Predicable, is that which may be spoken of many; as, a Body; and this is either of the first or second Intention.

14. A simple Theme of the first intention, is that which expresseth the thing it self; as, Gold, Stone, &c. so called, because they are the names by which the things themselves are first made known.

15. A simple Theme of the second Intention, is that which doth not express the things it self, but certain affections agreeing to the thing, and such are all Words of Art; as, a Noun, a Metaphor, &c.

16. An Vniversal simple Theme, may be spoken of many, two ways.

1. In Quid? or by declaring what a thing is; and thus it is spoken of such as do dif∣fer in the species, and is called Genus; as, a li∣ving Creature, colour, &c. or else of such as do differ in number only, and is called spe∣cies; as, a Man.

2. In Quale, or by declaring what a kind of thing it is, of which it is spoken; & that Essentially or Accidentally, Essentially, and then it is called Difference, the which is,

1. Divisive, by which a Genus is divided in∣to its several species, as by rational and irra∣tional a Living Creature is divided into a Man or a Beast.

2. Constitution, which doth Essentially constitute some species, and this is,

1. Generical, which doth constitute some remote species, but not the next, for the next is the Genus, thus sensibility in respect of Man, is a generical difference, constituting first a living Creature, and then a man. And this is always spoken of many differing in species, or number.

2. Specifical, which doth constitute the nearest species; as, rationalibility doth constitute man.

2. Accidentally, and that either of neces∣sity,

and then it is called a proper Accident, which is convertable with its Species, per∣petually inherent in every of them, and in no other, as the visible faculty in a Man.

Or not of necessity, and then it is called a common or simple Accident, not converti∣ble with its Species; as white.

17. All simple Themes, may be reduced to ten ranks or orders, called Predicaments, of which some are more principal, some less.

18. The more principal Predicaments are the first six, the less principal, are the other four.

19. The Predicamental Ranks or Orders, are of two sorts, the one of Substance, and the other of Accidents.

20. Of Substance, there is only one, and it is called by that name Substance, which is a thing subsisting of it self, and it is ei∣ther first or second.

21. The first substance, is a Singular sub∣stance, or a substance that cannot be predi∣cated of its subject; as, Alexander.

22. The second Substance is an Universal substance, or a substance which may be pre∣dicated of its subject; as, a Man, a Horse. The first substance is chiefly and properly a substance, and among the second substan∣ces, every one is by so much more a substance, by how much it is nearer to the first.

23. The Predicamental Ranks or Orders of Accidents, are of two sorts.

1. Absolute, as the Predicaments of quan∣tity,

Quality, Action, and Passion.

2. Relative, as the Predicament of Relation.

24. Quantity, is an absolute accident, by which a thing is said to be great in bulk or number.

25. Quality, is an absolute Accident, by which it is simply and determinately decla∣red what kind of thing, that subject is, of which it is the Quality.

26. Action, is an Accident, by which a subject is said to be doing.

27. Passion, is an Accident, by which the subject is called Patient; or it is the recep∣tion of Action.

28. Relation, is a respective accident, by which one thing is predicated of another, or may by some way be referred unto another.

29. The less principal Predicaments are these four, When, Where, Scituation, and Habit.

30. The Predicament When, is an acci∣dent, by which finite things are said to be in time, past, present, or to come.

31. The Predicament Where, is an acci∣dent, by which things finite, are said to be in some place.

32. The Predicament of Scituation, is a certain Ordination, or placing of parts in Generation.

33. The Predicament of Habit, is an ac∣cident, by which some garment or something like a Garment, is put about, hanged upon, or some way or other joyned to a Body.

CHAP. II. Of Compounded Themes.

HItherto of Simple Themes: Compounded Themes, or such as are made of several Simple Themes are next to be considered; otherwise called Enunciations, or Propositions.

2. An Enunciation, or Proposition, is an Indi∣cative, Congruent and perfect Oration, signi∣fying true or false without any Ambiguity.

3. The parts of a Proposition are two, the parts Signing or Signed.

4. The parts Signing are simple terms, whose parts can signifie nothing, being se∣parated from the whole, or no such thing as they did signifie being joyned all together.

5. These simple terms are of two sorts, Categorematical, or Syncategorematical.

6. Categorematical, or Significative terms, or such simple terms, as do by themselves signifie something perfectly; and these are either Nouns or Verbs.

7. A Noun, is a simple term or word, which doth signifie some certain thing with∣out destinction of time; as, a man, a horse.

8. A Verb, is a simple term, which doth sig∣nifie something, with some destinction of time past, present, or to come; as, he runneth.

9. Syncategorematical, or Consignificative terms, are simple terms, which of them∣selves do not signifie any certain thing, or

constitute a Proposition, but being joyned with other Words, are significative, to ex∣press the manner of such a thing; and such are all Words which serve to express the quantity of a proposition; as, all, none, some, &c. with all Adverbs, Conjunctions, Pre∣positions, and Interjections.

10. The parts signed are three; the Sub∣ject, the predicate, and the Copula.

11. The subject is all that which precedes the Copula in the Proposition.

12. The Predicate, is all that which is spoken of the subject.

13. The Copula, is the principal Verb, joyning the Predicate to the subject, and in e∣very Proposition is some person of this Verb Substantive, as in this Proposition, A Man is a living Creature; a Man is the sub∣ject; a living Creature is the Predicate; and the Verb is the Copula; sometimes the Co∣pula is some Person of a Verb Adjective; as in this Proposition, Socrates lived at Athens.

Here note, that the subject doth not always precede, and the predicate follow the Copula, in order of the parts or terms, but in sense and construction; and also, that in some Pro∣positions, the three terms are not always ex∣prest, but implyed; as, I walk, for I am walking.

14. Propositions are distinguish'd three ways, according to Substance, Quantity, and Quality.

15. A Proposition, in respect of the substance or parts of which it doth consist, is either Categorical or Hypothetical.

16. A Categorical Proposition, is that which doth consist of one subject, one Predicate, and one Copula; as, a man is a Living Creature, and this is either Pure or Modal.

17. A Pure Categorical Proposition, is when the Predicate is purely affirmed or de∣nyed of the subject, without expressing the manner of affirming or denying.

18. A Modal Categorical Proposition, is when besides the subject, predicate, and Copu∣la, we add some modification, to shew how the Predicate is in the Subject, as, it is neces∣sary; it is contingent, it is possible; it is impos∣sible that a man should be without reason.

19. An Hypothetial Proposition, is that which doth consist of two Categorical Propositions, joyned together by some Conjunction, as, if a man be a living Creature, then a man is a Body.

20. A Proposition, in respect of Quality, is distinguished two ways; first, according to the Quality of the sign, and so it is Affirmative or Negative; secondly, according to the quantity of the thing; & so it is either True or False.

21. A Proposition, in respect of Quantity, is universal, particular, indefinite, or singular.

22. An Vniversal proposition, is that which hath a note of Universality added to a com∣mon or universal Subject; as, every man is a Living Creature.

23. A particular proposition, is that in which a note of particularity is added to an universal

Subject; as, some man is a Living Creature.

24. An Indefinite proposition, is that, in which no note, whether Universal or Par∣ticular is put before the universal Subject; as, a man is a Living Creature.

25. A Singular proposition, is that in which the subject is singular, whether it be a proper Name; as, Secrates is a Philosopher; or whether it be a common name, with a note of singulari∣ty set before it; as, this man is Learned.

26. Pure Categorical propositions, as they have reference to one another, have three affections; Opposition, Aequipollency, and Conversion.

27. Opposition, is the repugnancy of two ca∣tegorical propositions, either in quantity alone, or in quality alone, or else in quantity and qua∣lity both, in which there is the same subject, the same predicate, and the same Copula, as, every man is just, no man is just.

28. The categorical propositions, may be said to be opposite four ways; Contrarily, Subcon∣trarily, Subalternately, and Contradictorily.

29. Two propositions, that are contrarily, and subcontrarily opposite, are opposite only in quality; and such as are subalternately oppo∣site, are opposite only in quantity; and such as are contradictorily opposite, are opposite both in quantity and quality.

30. Opposition, by way of contrariety is the repugnancy of two Universal Propositions in quality; as, every man doth run, no man doth run;

and these in a contingent matter, may be both False, but cannot be both together true.

31. Subcontrary Opposition, is the repugnan∣cy of two particular Propositions in quality; as, some man doth run, some man doth not run; and these in a contingent matter may be both true, but cannot be both together False.

32. Sabalternate Opposition, is the repug∣nancy of two Affirmative, or two Negative Propositions in their quantity; as, every man doth run, some man doth run.

33. Contradictory Opposition, is the repug∣nancy of two Propositions, both in quality and in quantity, so that if one of them be Affirmative, the other shall be Negative; if one be Universal, the other shall be particu∣lar; as, Every man is Learned, some man is not learned: All which may be easily appre∣hended by the following Scheme.

[illustration]

34. Aequipollency, is the equivalency of two Propositions, in sense and signification, though they differ in Words, by virtue of this Word of Negation (not) being set be∣fore the Sign and Subject, after the Sign and Subject, or both before and after, in which there is the same Subject, and the same Pre∣dicate; as, some man is Learned; not every man is Learned: The several varieties where∣of are fully expressed in these Distichs.

If after sign and subject, this (not) be, Contraries then, make Aequipollencie. Only before make contradictories, But 'fore and aft' are subalternate guise.

35. Conversion, is an apt mutation of the whole subject, into the place of the whole Predicate, and of the whole Predicate, into the place of the whole subject, keeping the same Quality, but sometimes changing the Quantity; as, Every man is a Living Crea∣ture; some Living Creature is a man.

36. This Conversion is three-fold;

1. Simple, in which the predicate is chan∣ged into the place of the whole Subject, and the Contrary, keeping the same both qua∣lity and quantity; as, No man is a Stone, therefore no stone is a man.

2. By Accident, in which the whole pre∣dicate is changed into the place of the whole Subject, and the Contrary, keeping the same

Quality, but changing of the Quantity; as, Every man is a living Creature, therefore some Living Creature is a man.

3. By Contraposition, in which the whole Subject is changed into the place of the whole predicate; and the contrary, keep∣ing both the same Quality and Quantity, but changing the terms from Finite to Infi∣nite; as, Every-Man is a Living Creature, therefore every thing that is a Living Creature, is not a man: What Propositions may be con∣verted this or that way, these Verses do express.

E E, I I, Conversion Simple make. A I, E O, of Accident partake. A A, O O, for Contraposits sake.

And what these Letters A, E, I, O, do signifie there Distichs do declare:

A, affirmes, E, denies both universal are, I, affirms, O, denies, but both particular.

CHAP. III. Of Difinition and Division.

HAving done with the first part of Logick, namely, that which treateth of Themes.

I come now unto the second, called the Organical, or that which treateth of Logical Instruments, and their Composition.

2. Logical Instruments are four; Definiti∣on, Division, Argumentation, and Method.

3. Definition, is the explication of the thing which is defined; and this is either Nominal, or Real.

4. A Nominal Difinition, is that which sheweth the Signification of the Name; whe∣ther it be by giving the Etymology thereof, or by expressing it by some other Synony∣mous word more generally known.

5. A Real Definition, is that which shew∣eth what the thing is; and this is either perfect or imperfect.

6. A Real and a Perfect Difinition, is that which doth explain the thing by Essential Attributes.

7. A Real, but Imperfect Definition, other∣wise called a Description, is that which ex∣plains the Nature of a thing, by certain Ac∣cidental Attributes.

8. Division, is the Deduction of some¦thing

that is large, into a straighter and narrower comprehension; and this is either of some ambiguous word, into its several significations, and then it is called Distincti∣on, or of the whole into its parts.

9. The whole is either Simple, or Aggre∣gate; Division of the whole, simply and pro∣perly so called is three-fold.

1. Vniversal into its subjective parts, or of the General into the Specials; as, to di∣vide Animal into Man and Beast.

2. Essential, which resolves the whole in∣to essential parts, and this either of a Species into its Genus and Difference, or of some spe∣cial nature into its matter and form; as, A Man into Soul and Body.

3. Integral, which resolveth the whole in∣to Integral parts, and this is the Division of some individual, either into its sensible or material parts.

4. Division of the aggregated whole into its parts, and by Accident is five-fold.

1. When the Subject may be divided by its Accidents; as, Men are Learned or Vn∣learned.

2. When an Accident may be divided by its Subjects; as, Feavers are in the Spirits or in the Humours, or in the solid parts.

3. When an Accident may be divided by Accidents; as, Good is either profitable, ho∣nest, or pleasant.

4. When things may be divided by their

Objects; as, Sight by Colours, Hearing by Sound.

5. When Causes may be divided by their Effects; and the Contrary; as, Heavenly heat is from the Sun, and Elementary from Fire.

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.

CHAP. V. Of A Material Syllogism.

I Come now to speak of a Special or Mate∣rial syllogism, as it is constrained to cer∣tain Conditions of Matter.

2. A special or material syllogism, is of

three sorts; Apodictical, Dialectical and So∣phistical.

3. An Apodictical syllogism, otherwise cal∣led a Demonstration, may be defined two ways; either from the end, or from the mat∣ter of Demonstration.

4. From the end of Demonstration, an Apo∣dictical syllogism, is a syllogism begetting knowledge, or making to know. And we are then said to know a thing, when we know the cause for which it is so, and can∣not be otherwise.

5. All Knowledge is of such Conclusions, to which we assent, for our preceding know∣ledge of the Premises; and the Praecognita in every Science are these three: The Sub∣ject, the Affection, and the Cause. And the means by which these are foreknown, are called Praecognitions, and they are two; That a thing is, and what a thing is.

6. The subject, is the less Extream, in a Demonstration, concerning which some acci∣dent is Demonstrated by its next Cause; as, a man, concerning whom we must know both that he is, and what he is.

7. Affection or Passion, is a proper acci∣dent, which is Demonstrated of the subject, by a proper Cause, it is always the greater Extream, which is Predicated in the Conclu∣sion; as, Risibility, the which is necessary to be foreknown, in respect of its name, What it is, but not, that it is; for that is the thing

to be enquired after, the thing we are to find by Denomination.

8. A Cause, is that by which the Affection is Demonstrated of its subject, and is always the Major Proposition in the Demonstrati∣on; as, Every rational Animal is risible; what the Cause is cannot be foreknown, be∣cause it is a compounded Proposition, but it ought to be known, That it is, or else the Conclusion cannot be inferr'd from it.

9. An Apodictical syllogism, being defined from the matter of Demonstration, is a syl∣logism, which proveth its Conclusion from such Premises, as are of themselves suffici∣ently known.

10. A Demonstration, is to be considered, either in respect of the Matter or in respect of the Form.

11. In respect of the Matter, one kind of Demonstration, sheweth why the Predicate is inherent in the subject, and another sheweth that it is inherent in the subject.

12. In the first of these kinds of Demon∣stration, called the Demonstration causal, 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 Premises.

13. Every Question doth not admit of the first and most perfect kind of Demon∣stration, called, Why a thing is? but such a Question only as is true, and hath a certain

and immutable Cause of its own Truth.

14. The Medium of a Demonstration, ought to be the next Cause of the Predicate; and that either Efficient or Final, and the Ef∣ficient either Internal or External.

15. The Conditions to be observed in the Premises of a Demonstration, are Absolute or Relative.

16. 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, in respect of the subject; as, A man is Rational, and in re∣spect of the Causes; as, That which is ratio∣nal, is visible, a man is rational, Ergo.

17. The Relative Conditions to be obser∣ved in reference to the Conclusion, are three. 1. That the Premises be the Cause of the Conclusion. 2. That they be before it: and 3. That they be more known than the Con∣clusion.

18. The other less principal kind of De∣monstration in respect of the Matter, or the Demonstration what, is two-fold, the one is from some sensible Effect, and the o∣ther from a remote Cause.

19. The form of these Demonstrations, is descerned partly from the Quantity, and so it is Vniversal or Particular; Partly from the Quality, and so it is Affirmative or Ne∣gative; partly from the manner of the proof, and so it is Ostensive, or by Reduction to Im∣possibility.

CHAP. VI. Of a Topical Syllogism.

HItherto we have spoken of a Demon∣strative syllogism, whose matter is ne∣cessary, and the end a perfect Knowledge; come we now to a Dialectical or Topical syl∣logism, whose matter is Probable and Con∣tingent, and the end Opinion.

2. In a Dialectical, or Topical Syllogism, we are to consider of Problems, Propositions, and Invention of Arguments.

3. A Problem or Question, is the thing of which it is probably discoursed, and the Conclusion of a syllogism already made.

4. Dialectical Propositions, ought to be certain, at least probable, and not Paradox∣es; now that is said to be Probable, which not being absolutely true, doth seem to be true rather than false: And that is said to be a Paradox, which is true, though contra∣ry to the vulgar opinion.

5. For the Invention of Arguments, we are to consider Common places and Rules.

6. A Place, is common Note, by whose help an Argument is found.

7. A Rule or Canon is a Proposition, con∣taining

the Reason of the Consequence, in a Dialectical syllogism.

8. Arguments are of two sorts, Artificial and Inartificial.

9. Artificial Arguments, are such as from the consideration of the parts of a Problem, are not found but by Rules of Art.

10. Inartificial Arguments, are such as are found without any help of Art, and these are nothing but Testimonies.

11. Artificial Arguments, may be raised from these seven Topicks or Heads. 1. From the Cause and the Effect. 2. From the sub∣ject and the Accident. 3. From Dissentany and Comparison. 4. From Conjugates and Notation. 5. From the Whole and its Parts. 6. From Genus and Species. 7. From Defi∣nition and Division.

12. A Cause in General, may be defined to be that, by whose power a thing is.

An Argument therefore from the Cause, is when in a probable syllogism, the middle term is the cause of the Major Extream.

13. There are two kinds of Causes; In∣ternal as the material, or matter, of which a thing is made; and the Formal, by which a thing is; as, The shape and form of a statue.

External, as the Efficient, which doth bring the thing to pass; and the Final or End, for which a thing is done.

14. An Argument from the Efficient Cause, is when in a probable syllogism, the

middle Term is the Efficient of the Major Ex∣tream: as, The Earth is Diametricaly inter∣posed between the Sun and the Moon, therefore the Moon shall be eclipsed.

15. An Argument from the Final Cause, is when in a probable syllogism, the middle Term is the Final Cause of the major Ex∣tream.

16. An Argument from the material cause, is when in a probable syllogism, the middle Term is the material cause of the Major Ex∣tream, or the Genus or Species thereof.

17. An Argument from the Formal Cause, is when in a Probable syllogism, the middle Term is the Form, Definition, Description, or Difference of the major Extream.

18. In the Topicks of the subject and the Accident, we do not take the subject for the substance, in which the Accident is inherent, or the Accident for that which doth precise∣ly and adiquately adhere to the substance; but subject is here taken for all that, to which any thing not belonging to its essence is at∣tributed: And Accident is here taken for a∣ny such attribute, as, Number is the subject of Equality, that is, it is an Accident of an Accident.

19. An Argument from the subject, is as oft as the middle Term in a Probable syllo∣gism, is the subject of the major Extream.

21. The third General Topick for the In∣vention of Arguments, is from Dessentainies and Comparison.

22. Dessentanes, are either Opposites or Disparates; as, a Horse, and a Bull: There are four kinds of Opposites; Relative, Contra∣ry, Privative, and Contradictory. Compari∣sons are either in respect of quality; as, like and unlike, or in respect of quantity, or also of degrees; as, equal and unequal; and what ever may be said to be more or less or equal.

23. An Argument from Dissentanies, is when in a Probable Syllogism, the middle Term is opposed to the Major Extream, whether it be by way of a Disparate, or a Contrary, or otherwise.

24. An Argument from Comparison, is as oft as in a probable syllogism, one part of the Major Proposition is compared with the other, in reference to their agreement or their disagreement.

25. The fourth general Topick, for the Invention of Arguments, is from Conjugates and Notation. And they are properly cal∣led Conjugates, which for the affinity of signification, have also an affinity in the Voice or Sound; as, Just, Justice, and Just∣ly; some Conjugates are only Nominal, and some Real, and some both, and do compre∣hend Denominatives under them, and are either substantives where one is a Noun sub∣stantive abstracted from the Subject; as, Justice, Just; or Adjectives, where they be both Denominatives, or Concretes, which

shew the form in the Abstract; as, Just, Justly. Notation or Etymology, is the Ex∣plication of a Word by the Original there∣of; as, a Consul, from Counselling the Com∣mon-Wealth.

26. An Argument from Conjugates, is as oft as in a probable syllogism; the one the Conjugates in the major proposition, is the subject of the major Term; as, He that doth Justly is Just.

27. The first General Topick for the In∣venting of Arguments, is from the whole and its parts. And an Argument from the thing divided to the divided members, is as oft as the thing divided is the middle Term, and the dividing Members the Major Ex∣tream, in a Probable Syllogism. And an Argument from the dividing Members, to the thing divided, is as oft as the di∣viding Members are the middle Term, and the thing divided the Major Extream.

28. The sixth General Topick, is from Genus and Species; And an Argument from Genus and Species, is when we prove that a thing doth not agree with the Genus, be∣cause it doth not agree with the species; o•• that it doth not agree with the species, be∣cause it doth not agree with the genus.

29. The seventh General Topick for the Inventing of Arguments, is from Definition, and Division. We raise an Argument from the Topick or Definition, when we seek for

the Definition of either Extream, that is, of the Subject or the Predicate in the question, which being found, is put into the place of the Mean, that it may be known whether the Extreams should be conjoyned or sepa∣rated; thus we prove that Peter is a man, because he is a Rational living Creature. We argue from the Topick of Division, when we shew something to agree with the dividing Members, because it agrees with the thing divided, or not to agree with the thing di∣vided, because it doth not agree with any of the Dividing Members.

30. Inartificial Arguments, are only such as are raised from Divine or Humane Te∣stimony. And an Argument is raised from Testimony, as oft as the Authority of him that beareth witness, is the middle Term, a∣greeing or not agreeing with the Major Ex∣tream.

CHAP. VII. Of a Sophistical Syllogism.

A Sophistical Syllogysm, is a Captious Ar∣gumentation, which is seemingly, or apparently true, but is indeed deceitful.

2. Sophistical, or Fallacious Arguing, is either in respect of the Words or of the Things.

3. Fallacies in Words, are five; Ambigui∣tie, Amphibolie, Composition, Division, and Figure of a Word.

4. Fallacies in things are seven, Accident, Of a thing spoken after a sort, to a thing spoken Simply; Ignorance of the Argu∣ment; a false or wrong Cause, Consequent, Beginning of the Question, and an asking of many Questions.

CHAP. VIII. Of Method.

MEthod is the disposing of things belong∣ing to the same Matter or Subject, so, as that they may be best understood, and ea∣siest remembred.

2. Method is two-fold, Natural or Arbitrary.

3. A Natural Method is that, in which the order of Nature and our distinct Know∣ledge is observed.

4. In a Natural Method, we must speak first of Generals, and then of Particulars, and as we proceed from one thing to ano∣ther, every part must have a dependence on that, which was last spoken of by some apt transition.

5. A Natural Method is either Total, or Partial.

6. A Total Method is that, in which a whole Science is Methodically ordered or dispersed. And this is either, Synthetical, or Analytical.

7. A Synthetical or Compositive Method is that, which begins with the first and most simple Principles, and so proceeds to those which do arise from, or are Composed of the first Principles.

8. An Analytical or Resolutive Method, is

that, which begins with the end, and so pro∣ceeds still lower and lower, till we come to the first and most Simple beginnings.

9. A Partial Method is that, by which a∣ny part of any Art or Science is Methodi∣cally ordered or disposed: or by which any particular Theme or Subject is handled by it self.

10. An Arbitrary Method is that, which not regarding the Natural order, is fitted for such a confused Knowledge, as may be most taking with the People, or sure best with their Capacities.

And thus much concerning Method, which is the fourth and last-Logical Instrument; and with this I shall conclude these my Lo∣gical Precepts, and last Part of my English A∣cademy: He that desires to be more fully ac∣quainted with these Arts and Sciences, may for all, but Musick, Read my other particu∣lar Tracts of these Subjects, till some body that hath more knowledge in them, shall fur∣nish us with more ample and perfect Instru∣ctions; and as for Musick, I am much of Opinion, that Mr. Playford's Introduction may very well serve, to Instruct our Youth in the first Principles of that excellent Science; For which, and all other helps of Learning, To the only Wise God, be all Honour and Glory, now and for ever. Amen.

FINIS.

Notes

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