are two and three ; therefore five are even and odd. Here that is very falsely inferred concerning two or three in Union, which is only true of them divided.

The Sophism of Division is when we infer the fame Thing concerning Ideas in a divided Sense, which is only true in a compounded Sense ; as, if we should pretend to prove that every Soldier in the Grecian Army put an bundred thousand Persians to Flight, because the Grecian Soldiers did so. Or if a Man should argue thus ; five is one Number ; two and three are five; therefore two and three are one Number.

This sort of Sophisms is committed when the Word All is taken in a collettive and a distributive Sense, without a due Distinction ; as, if any one should reason thus; Ail the musical Instruments of the Jewish Temple made a noble Concert, The Harp was a musical Instrument of the Jewish Temple ; therefore the Harp made a noble Concert. Here the Word Al in the Major is collective, whereas such a Conclusion requires that the Word All should be distributive.

It is the same Fallacy when the universal Word All or No refers to Species in one Propofition, and to Individuals in another; as, All Animals were in Noah's Ark ; therefore no Animals perished in the Flood : Whereas in the Premiss all Animals signifies every kind of Animals, which does not exclude or deny the drowning of a thousand Individuals.

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VIII. The last sort of Sophisms arises from our Abuse of the Ambiguity of Words, which is the largest and most extensive kind of Fallacy; and indeed several of the former Fallacies might be reduced to this Head.

When the Words or Phrafes are plainly equivocal, they are called Sophifms of Equivocation; as, if we fhould argue thus, He that Jends forth a Book into the Light, defires it to be read; He that throws a Book into the Fire, fends it into the Light; therefore, be that throws a Book into the Fire defires it to be read.

This Sophifm, as well as the foregoing, and all of the like Nature are folved by fhewing the different Senfes of the Words, Terms or Phrafes. Here Light in the major Propofition fignifies the publick View of the World; in the minor it fignifies the Brightness of Flame and Fire, and therefore the Syllogifm has four Terms, or rather it has no middle Terms, and proves nothing.

But where fuch grofs Equivocations and Ambiguities appear in Arguments, there is little Danger of impofing upon ourfelves or others. The greateft Danger, and which we are perpetually exposed to in Reasoning, is, where the two Senfes or Significations of one Term are near akin, and not plainly distinguished, and yet they are really fufficiently different in their Senfe to lead us into great Miftakes, if we are not watchful. And indeed the greateft Part of Controverfies in the facred or civil Life arife from the different Senfes that are put upon Words, and the different Ideas which are included in them; as has been shewn at large in the first Part of Logick, Chap. IV, which treats of Words and Terms.

There is after all thefe, another Sort of Sophifm which is wont to be called an imperfect Enumeration, or a falfe Induction, when from a few Experiments or Obfervations Men infer general Theorems and univerfal Propofitions. But this is fufficiently noticed in the foregoing Chapter, where we treated of that fort of Syllogifm which is called Induction.

SECT.

SECT. II.

Two general Tefts of true Syllogifms, and Methods of folving all Sophifms.

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Efides the special Defcription of true Syllogifms and Sophifms already given, and the Rules by which the one are framed, and the other refuted, there are these two general Methods of reducing all Syllogifms whatsoever to a Teft of their Truth or Falfhood.

I. The first is, that the Premiffes must (at least implicitly) contain the Conclufion; or thus, One of the Premiffes must contain the Conclufion, and the other must shew that the Conclufion is contained in it. The Reafon of this Rule is this; When any Propofition is offered to be proved, it is neceffary to find another Propofition which confirms it, which may be called the containing Propofition; but because the second must not contain the firft in an exprefs manner, and in the fame Words*, therefore it is neceffary that a third or oftenfive Propofition be found out to fhew that the fecond Propofition contains the first which was to be proved. Let us make an Experiment of this Syllogifm. Whosoever is a Slave to his natural Inclinations is miferable; the wicked Man is a Slave to his natural Inclinations; therefore the wicked Man is miferable. Here it is evident that the major Propofition contains the Conclufion;

*It is confeffed that conditional and disjunctive major Propofitions do exprefly contain all that is in the Conclufion; but then it is not in a certain and conclufive Manner, but only in a dubious Form of Speech, and mingled with other Terms, and therefore it is not the fame express Propofition.

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for under the general Character of a Slave to natural Inclinations, a wicked Man is contained or included; and the minor Propofition declares it; whence the Conclufion is evidently deduced that the wicked Man is miferable.

In many affirmative Syllogifms we may suppose either the major or the minor to contain the Conclufion, and the other to fhew it; for there

is no great Difference. But in negative Syllogifms it is the negative Propofition that contains the Conclufion, and the affirmative Propofition fhews it; as, every wife Man masters his Paffions; no angry Man mafters his Paffions; therefore no angry Man is wife. Here it is more natural to fuppofe the minor to be the containing Propofition; it is the minor implicitly denies Wisdom concerning an angry Man, because mastering the Paffions is included in Wisdom, and the major fhews it.

Note, This Rule may be applied to complex and conjunctive, as well as fimple Syllogifms, and is adapted to fhew the Truth or Falfhood of any of them.

II. The fecond is this; As the Terms in every Syllogifm are ufually repeated twice, fo they must be taken precifely in the fame Senfe in both Places: For the greateft Part of Mistakes, that arife in forming Syllogifms, is derived from fome little Difference in the Senfe of one of the Terms in the two Parts of the Syllogifm wherein it is used. Let us confider the following Sophisms.

1. It is a Sin to kill a Man; a Murderer is a Man; therefore it is a Sin to kill a Murderer. Here the Word Kill in the firft Propofition fignifies to kill unjustly, or without a Law; in the Conclufion it is taken abfolutely for putting a

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Man to Death in general, and therefore the Inference is not good.

2. What I am, you are not; but 1 am a Man; therefore you are not a Man. This is a relative Syllogifm: But if it be reduced to a regular categorical Form, it will appear there is Ambiguity in the Terms, thus; What I am, is a Man; you are not what I am; therefore you are not a Man. Here what I am, in the major Propofition, is taken fpecifically for my Nature; but in the minor Propofition the fame Words are taken individually for my Perfon; therefore the Inference muft be falfe, for the Syllogifm doth not take the Term what I am both Times in the fame Senfe.

3. He that fays you are an Animal, fays true; but be that fays you are a Goofe, fays you are an Animal; therefore be that fays you are a Goofe, fays true. In the major Propofition the Word Animal is the Predicate of an incidental Propofition; which incidental Propofition being affirmative renders the Predicate of it particular, according to Chap. II. Sect. 2. Axiom. 3. and confequently the Word Animal there fignifies only buman Animality. In the minor Propofition, the Word Animal, for the fame Reafon, fignifies the Animality of a Goofe; thereby it becomes an ambiguous Term, and unfit to build the Conclufion upon. Or if you fay, the Word Animal in the Minor is taken for human Animality, then the Minor is evidently falfe.

It is from this laft generat Teft of Syllogifms that we derive the Cuftom of the Refpondent in anfwering the Arguments of the Opponent, which is to distinguish upon the major or minor Propofition, and declare which Term is used in two Senfes, and in what Sense the Propofition may be true, and in what Sense it is falfe.

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