gifms, and their parts, we fhall now enter more particularly into the fubject, examine their va rious forms, and lay open the rules of argumentation proper to each. In the fyllogifms above men tioned, the middle term is the fubject of the major propofition, and the predicate of the minor. This difpofition, though the most natural and obvious, is not however neceffary; as it often happens, that the middle term is the subject in both the premiles, or the predicate in both; and fome times, directly contrary to its difpofition in the preceding fections, the predicate in the major, and the fubject in the minor. Hence the diftinc tion of fyllogifms into various kinds, called figures by logicians. For figure, according to their ufe of the word, is nothing elfe but the order and difpofition of the middle term in any fyllogifm. And as this difpofition is fourfold, fo the figures of fyllogins thence arifing are 4 in number. When the middle term is the fubject of the major propofition, and the predicate of the minor, we have what is called the firft figure: As, " No work of God is bad :—The natural paffions and appetites of men are the work of God-Therefore none of them is bad." If, on the other hand, it is the predicate of both the premises, the fyllogifm is faid to be the fecond figure: As," Whatever is bad is not the work of God:-All the natural paffions and appetites of men are the work of God:-Therefore the natural paffions and appetites of men are not bad." Again, in the third figure, the middle term is the fubject of the two premifes: As, "All Africans are black:-All Africans are men :-Therefore fome men are black." And laftly, by making it the predicate of the major, and fubject of the minor, we obtain fyllogifms in the fourth figure: As, "The only being who ought to be worthipped is the Creator and Governor of the world: The Creator and Governor of the world is God: Therefore God is the only being who ought to be worshipped."

II. But, befides this fourfold diftinction of fylfogifms, there is a farther fubdivifion of them in every figure, arifing from the quantity and quality, as they are called, of the propofitions. By quantity we mean the confideration of propofitions, as univerfal or particular; by quality, as affirmative or negative.

Now as, in all the feveral difpofitions of the middle term, the propofitions of which a fyllogifm confifts may be either univerfal or particular affirmative or negative; the due determination of thele, and fo putting them together as the laws of argumentation require, conftitute what logi cians call the MOODS of fyllogifms. Of thefe moods there is a determinate number to every figure, including all the poffible ways in which propofitions differing in quantity or quality can be combined, according to any difpofition of the middle term, in order to arrive at a juft conclu Lion.

The first figure has only four legitimate moods. The major propofition in this figure must be univerfal, and the minor affirmative; and it has this property, that it yields conclufions of all kinds, affirmative and negative, universal and particular. The 2d figure has alfo 4 legitimate moods. Its major propofition must be univerfal, and one of

the premises must be negative. It yields conclufions both univerfal and particular, but all negative.

The 3d figure has fix legitimate moods. Its minor muft always be affirmative; and it yields conclutions both affirmative and negative, but all particular. These are all the figures which were admitted by the inventor of fyllogifms; and of which, fo far as we know, the number of legitimate moods has been ascertained, and severally demonftrated. In every figure it will be found upon trial, that there are fixty-four different moods of fyllogifm; and he who thinks it worth while to conftruct fo many in the fourth figure, always remembering that the middle term in each must be the predicate of the major and the subject of the minor propofition, will eatly difcern what number of these moods are legitimate, and give true conclufions.

Betides the rules that are proper to each figure, ARISTOTLE has given some that are common to all, by which the legitimacy of fyllogifms may be tried. Thefe may be reduced to five:-1. There muft be only three terms in a fyllogifm: As each term occurs in two of the propofitions, it must be precifely the fame in both; if it be not, the fyllogifm is faid to have four terms, which makes a vicious fyllogifm. 2. The middle term must be taken univerfally in one of the premises. 3. Both premiles must not be particular propofitions, nor both negative. 4. The conclufion must be particu lar, if either of the premises be particular; and negative, if either of the premises be negative. 5. No term can be taken univerfally in the conclusion, if it be not taken univerfally in the premises.

For understanding the 2d and 5th of these rules, it is neceffary to obferve, that a term is faid to be taken univerfally, not only when it is the subjec of a universal propofition, but also when it is the predicate of a negative propofition. On the other hand, a term is faid to be taken particularly, when it is either the subject of a particular or the predi cate of an affirmative propofition.

III. The divifion of fyllogifms according to mood and figure refpects those especially which are known by the name of plain fimple fyllogifms; that is, which are bound to three propolitions, all fimple, and where the extremes and middle term are connected, according to the above rules. But as the mind is not tied down to any one precise form of reafoning, but fometimes makes ufe of more, fometimes of fewer premises, and often takes in compound and conditional propofitions, it may not be amifs to take notice of the different forms derived from this fource, and explain the rules by which the mind conducts itself in the ule of them.

IV. When in any fyllogifm the major is a conditional propofition, the fyllogifm itself is termed conditional. Thus: "If there is a God, he ought to be worfhipped:-But there is a God:Therefore he ought to be worthipped." In this example, the major, or firft propofition, is conditional, and therefore the fyllogifm itself is also of the fame kind. And here we muft observe, that all conditional propofitions are made of two diftin&t parts: one expreffing the condition upon which the predicaté agrees or difagrees with the fub

jec

ject, as in this now before us, if there is a God; the other joining or disjoining the faid predicate and fubject, as here, he ought to be worshipped. The first of these parts, or that which implies the condition, is called the antecedent; the fecond, where we join or disjoin the predicate and fub ject, has the name of the confequent.

V. In all propofitions of this kind, fuppofing them to be exact in point of form, the relation between the antecedent and confequent must ever be true and real; that is, the antecedent muft always contain fome certain and genuine condition, which neceffarily implies the confequent; for otherwise the propofition itself will be falfe, and therefore ought not to be admitted into our reafonings. Hence it follows, that when any conditional propofition is affumed, if we admit the antecedent of that propofition, we must at the fame time neceffarily admit the confequent; but if we reject the confequent, we are in like manner bound to reject the antecedent. For as the antecedent always expreffes fome condition which neceffarily implies the truth of the confequent; by admitting the antecedent, we allow of that condition, and therefore ought also to admit the confequent. In like manner, if it appears that the confequent ought to be rejected, the antecedent evidently must be so too; because, as was juft now demonftrated, the admitting of the antecedent would neceffarily imply the admiffion alfo of the confequent.

VI. There are two ways of arguing in hypothetical fyllogifms, which lead to a certain and unavoidable conclufion. For as the major is always a conditional propofition, confifting of an antecedent and a confequent; if the minor admits the antecedent, it is plain that the conclufion muft admit the confequent. This is called arguing from the admiffion of the antecedent to the ad miflion of the confequent, and conftitutes that mood or fpecies of hypothetical fyllogifms which is diftinguished in the schools by the name of the modus ponens, inasmuch as by it the whole conditional propofition, both antecedent and confequent, is eftablished. "Thus: If God is infinitely wife, and acts with perfect freedom, he does nothing but what is beft:-But God is infinitely wife, and acts with perfect freedom:-Therefore he does nothing but what is beft." Here we fee the antecedent or firft part of the conditional propofition is established in the minor, and the confequent or ad part in the conclufion; whence the fyllogifm itself is an example of the modus ponens. But if now we` on the contrary suppose that the minor rejects the confequent, then it is apparent that the conclufion must also reject the antecedent. In this cafe we are said to argue from the removal of the consequent to the removal of the antecedent, and the particular mood or fpecies of fyllogifms thence arifing is called by logicians the modus tollens; because in it both antecedent and confequent are rejected or taken away, as appears by the following example. "If God were not a Being of infinite goodness, neither would he confult the happiness of his creatures:-But God does confult the happiness of his creatures: -Therefore he is a Being of infinite goodness."

VII. These two species take in the whole clafs

of conditioual fyllogifms, and include all the por fible ways of arguing that lead to a legitimate conclufion; becaufe we cannot here proceed by a contrary process of reasoning, that is, from the removal of the antecedent to the removal of the confequent, or from the establishing of the confequent to the establishing of the antecedent. For although the antecedent always expreffes fome real condition, which, once admitted, ne ceffarily implies the confequent, yet it does not follow that there is therefore no other condition; and if fo, then, after removing the antecedent, the confequent may ftill hold, becante of fome other determination that infers it. When we fay, If a flone is expofed fome time to the rays of the fun, it will contract a certain degree of heat; the propofition is certainly true; and, admitting the antecedent, we must alfo admit the confequent. But as there are other ways by which a stone may gather heat, it will not follow, from the ceafing of the before-mentioned condition, that therefore the confequent cannot take place. We cannot argue: But the ftone has not been expofed to the rays of the fun; therefore neither has it any degree of heat: Inafmuch as there are many other ways by which heat might be communicated to it. And if we cannot argue from the removal of the antecedent to the removal of the confequent, no more can we from the admifiion of the confequent to the admiffion of the antecedent: because, as the confe quent may flow from a great variety of different fuppofitions, the allowing of it does not determine the precife fuppofition, but only that some one of them muit take place. Thus, in the foregoing propofitions, "If a tone is expofed fome time to the rays of the fun, it will contract a certain degree of heat;" admitting the confequent, viz. that it has contracted a certain degree of heat, we are not therefore bound to admit the antecedent, that it has been fome time exposed to the rays of the fun; becaufe there are many other caufes whence that heat may have proceeded. Thefe two ways of arguing, therefore, hold not in conditional fyllogifms.

VIII. As, from the major being a conditional propofition, we obtain the fpecies of conditional fyllogifms; fo, where it is a disjunctive propofition, the fyllogifm to which it belongs is alfo called disjunctive, as in the following example:"The world is either felf-exiftent, or the work of fome finite, or of fome infinite Being:-But it is not self-exiffent, nor the work of a finite being:Therefore it is the work of an infinite Being.'

Now, a disjunctive propofition is that, in which, of feveral predicates, we affirm one neceflarily to belong to the subject, to the exclufion of all the reft, but leave that particular one undetermined. Hence it follows, that as soon as we determine the particular predicate, all the reft are of course to be rejected; or if we reject all the predicates but one, that one neceffarily takes place. When, therefore, in a disjunctive fyllogifm, the feveral predicates are enumerated in the major; if the minor establishes any one of these predicates, the conclufion ought to remove all the reft; or if in the minor all the predicates but one are removed, the conclufion muft neceffarily establish that one. Thus, in the disjunctive fyllogifm given above,

the

the major affirms one of the three predicates to belong to the earth, viz. felf-existence, or that it is the work of a finite, or that it is the work of an infinite Being. Two of these predicates are removed in the minor, viz. felf exiflence, and the work of a finite being. Hence the conclufion neceffarily afcribes to it the 3d predicate, and affirms that it is the work of an infinite Being. If now we give the fyllogifm another turn, infomuch that the minor may establish one of the predicates, by affirming the earth to be the production of an infinite Being: then the conclufion must re move the other two, afferting it to be neither felf. exiftent, nor the work of a finite being. Thefe are the forms of reafoning in thefe fpecies of fyllo gifms, the juftness of which appears at firft fight: and that there can be no other, is evident from the very nature of a disjunctive proposition.

IX. In the feveral kinds of fyllogifms hitherto mentioned, we may obferve, that the parts are complete; that is, the three propofitions of which they confift are represented in form. But it often happens, that fome one of the premises is not only an evident truth, but also familiar and in the minds of all men; in which cafe it is ufually omitted, whereby we have an imperfect fyllogifm, that seems to be made up of only two propofitions. Should we, for inftance, argue in this maner :"Every man is mortal:-Therefore every king is mortal:"-the fyllogifm appears to be imperfect, as confifting but of two propofitions. Yet it is really complete; only the minor (every king is a man] is omitted; and left to the reader to supply, as being a propofition so familiar and evident that it cannot escape him.

X. These feemingly imperfect fyllogifms are called enthymemes; and occur very frequently in reafoning, especially where it makes a part of common converfation. Nay, there is a particular elegance in them, because, not displaying the argument in all its parts, they leave fomewhat to the exercise and invention of the mind. We are thus put upon exerting ourselves, and seem to Thare in the discovery of what is propofed to us. Now this is the great fecret of fine writing, fo to frame and put together our thoughts, as to give full play to the reader's imagination, and draw him infenfibly into our views and courfe of reafoning. This gives a pleasure not unlike to that which the author himself feels in compofing. It befides shortens discourse, and adds a certain force and liveliness to our arguments, when the words in which they are conveyed favour the natural quicknefs of the mind in its operations, and a fingle expreffion is left to exhibit a whole train of thoughts.

XI. But there is another fpecies of reafoning with two propofitions, which feems to be complete in itself, and where we admit the conclufion without fuppofing any tacit or fuppreffed judgment in the mind, from which it follows fyllogiftically. This happens between propofitions, where the connection is fuch, that the admiffion of the one neceffarily, and at the firft fight, implies the admission also of the other. For if it fo falls out, that the propofition on which the other depends is felf-evident, we content ourselves with barely affirming it, and infer that other by a direct

conclufion. Thus, by admitting an univerfal propofition, we are forced alfo to admit of all the particular propofitions comprehended under it, this being the very condition that conftitutes a propofition univerfal. If then that universal propofition be felf-evident, the particular ones follow of courfe, without any farther train of reafoning. Whoever allows, for inftance, " that things equal to one and the fame thing are equal to one another," must at the fame time allow," that two triangles, each equal to a fquare whofe fide is three inches, are alfo equal between themselves." This argument, therefore,-"Things equal to one and the fame thing, are equal to one another:Therefore these two triangles, each equal to the fquare of a line of three inches, are equal between themselves"-is complete in its kind, and contains all that is neceflary towards a just and legitimate conclufion. For the first or univerfal propofition is felf-evident, and therefore requires no farther proof. And as the truth of the particular is infeparably connected with that of the univer fal, it follows from it by an obvious and unavoidable confequence.

XII. Now, in all cafes of this kind, where propofitions are deduced one from another, on account of a known and evident connection, we are faid to reafon by immediate confequence. Such a coherence of propofitions, manifeft at firft fight, and forcing itself upon the mind, frequently occurs in reafoning. Logicians have explained at fome length the several fuppofitions upon which it takes place, and allow of all immediate consequences that follow in conformity to them. It is how. ever obfervable, that thefe arguments, though feemingly complete, because the conclufion follows neceffarily from the fingle propofition that goes before, may yet be confidered as real enthymemes, whofe major, which is a conditional propofition, is wanting. The fyllogifm just mentioned, when represented according to this view, will run as follows:-" If things equal to one and the fame thing, are equal to one another; these two triangles, each equal to a fquare whose fide is three inches, are also equal between themselves. -But things equal to one and the same thing are equal to one another:-Therefore also these triangles, &c. are equal between themselves." This observation will be found to hold in all immediate confequences whatsoever, infomuch that they are in fact no more than enthymemes of hypothetical fyllogifms. But then it is particular to them, that the ground on which the conclufion refts, namely its coherence with the minor, is of itself apparent, and feem immediately to flow from the rules and reafons of logic.

XIII. The next fpecies of reafoning we shall take notice of here, is what is commonly known by the name of SORITES. This is a way of arguing, in which a great number of propofitions are fo linked together, that the predicate of one becomes continually the fubject of the next fol lowing, until at laft a conclufion is formed, by bringing together the fubject of the firft propofition, and the predicate of the laft. Of this kind is the following argument:-" God is omnipotent:-An omnipotent being can do every thing poffible:-He that can do every thing poffible,

can

ment (fays that accurate logician, Mr TATHAM), diligently practifed, and frequently repeated, on many individuals of the fame clafs or of a fimilar nature, noting their agreements, marking their differences, however minute, and rejecting all inftances which, however fimilar in appearance, are not in effect the fame, REASON, with much labour and attention, extracts fome general laws, refpecting the powers, properties, qualities, actions, paffions, virtues, and relations of real things. This is no hafty, premature, notional abftraction of the mind, by which images and ideas are formed that have no archetypes in nature: it is a rational, operative, experimental procefs, intituted and executed upon the conftitution of beings, which in part compofe the univerfe. By this procefs REASON advances from particulars to generals, from lefs general to more general, till by aeries of flow progreffion, and by regular degrees, it arrive at the most general notions, called FORMS or FORMAL CAUSES. And by affirming or denying a genus of a 'fpecies, or an accident of a fubftance or clafs of fubftances, through all the flages of the gradation, we form conclufions, which, if logically drawn, are AXIOMS, or general propofitions ranged one above another, till they terminate in thofe that are UNIVERSAL.

IV." Thus, for instance, the evidence of the external fenfes is obviously the PRIMARY PRINCIPLES from which all phyfical knowledge is derived. But, whereas nature begins with caufes, which, after a variety of changes, produce effects, the fenfes open upon the effects, and from them, through the flow and painful road of experiment and obfervation, afcend to caufes. By experiments and obfervations skilfully chofen, artfully conducted, and judiciously applied, the philofopher advances from one ftage of inquiry to another, in the rational investigation of the general causes of physical truth. From different experiments and obfervations made on the fame individual subject, and from the fame experiments and obfervations made on different fubjects of the fame kind, by comparing and judging, he difcovers fome qualities, caufes, or phenomena, which, after carefully diftinguishing and rejecting all contradictory inftances that occur, he finds common to many. Thus, from many collateral comparisons and judgments formed upon particulars, he afcends to generals; and by a repetition of the fame industrious procefs and laborious investigation, he advances from general to more general, till at laft he is enabled to form a few of the most general, with their attributes and operations, into AXIOMS or fecondary principles, which are the well-founded laws enacted and enforced by the God of nature. This is that juft and philofophic method of reafoning which found logic prescribes, in this as well as in other parts of learning; by which, through the flow but certain road of experiment and obfervation, the mind afcends from appearances to qualities, from effects to caufes, and from experiments upon many particular fubjects forms general propofitions concerning the powers and properties of phyfical body.

V. "AXIOMS fo investigated and established are applicable to all parts of learning, and are the indifpenfable, and indeed the wonderful expedients,,

by which, in every branch of knowledge, reafon pushes on its inquiries to the particular pursuit of truth: and the method of reafoning by which they are formed, is that of true and legitimate INDUCTION; which is therefore by Lord Bacon, the beft and foundest of logicians, called “the KEY of interpretation."

VI." Inftead of taking his axioms arbitrarily out of the great families of the categories (fee CATEGORY), and erecting them by his own fophiftical invention into the principles upon which his difputation was to be employed, had the analytical genius of Ariftotle presented us with the laws of the true INDUCTIVE LOGIC, by which AXIOMS, are philofophically formed, and had he, with his usual fagacity, given us an example of it in a fingle branch of fcience; he would have brought to the temple of truth an offering more valuable than he has done by the aggregate of all his logical and philofophical productions.

VII. "In all sciences, except the mathematics, it is only after the INDUCTIVE procefs has been industriously pursued and fuccefsfully performed, that DEFINITION may be logically and usefully introduced, by beginning with the genus, paffing through all the graduate and subordinate stages, and marking the specific difference as it defcends, till it arrive at the individual, which is the subject of the queftion. And by adding an affirmation or negation of the attribute of the genus on the fpecies or individual, or of a general accident on the particular fubftance fo defined, making the definition a propofition, the truth of the question will be logically folved without any farther procefs. So that inftead of being the first, as employed by the logic in common ufe, definition may be the last act of reafon in the fearch of truth in general.

VIII. "Thefe AXIOMS or general propofitions, thus inductively established, become another fpecies of PRINCIPLES, which may be properly called SECONDARY, and which lay the foundation of the fyllogiftic method of reasoning. When these are formed, but not before, we may safely admit the maxim with which logicians fet out in the exercife of their art, as the great hinge on which their reafoning and difputation turn: "From truths that are already known, to derive others which are not known." Or, to ftate it more comprehenfively, fo as to apply to probable as well as to scientific reasoning-" From truths which are better known, to derive others which are lefs known." Philofophically speaking, fyllogiftic reasoning is, under general propofitions to reduce others which are lefs general, or which are particular; for the inferior ones are known to be true, only as we trace their connection with the fuperior. Logically speaking, it is, To predicate a genus of a species or individual comprehended under it, or an acci dent of the fubftance in which it is inherent.

IX. "Thus INDUCTION and SYLLOGISM are the two methods of direct reafoning corresponding to the two kinds of principles, primary and fecon dary, on which they are founded, and by which they are refpectively conducted. In both me thods, indeed, reafon proceeds by judging and comparing, but the process is different throughout; and though it may have the fanétion of Aristo TLE, an inductive fyllogifm is a folecism. X. "Till