353 



LOGIC. 



LOGOS. 



no elemeut can be dismissed, but any new one may be admitted. Thus 

 A,B))Y and X))AB allow A))Y andx))A; but not A,B,C))Y nor 

 X ) ) A B c. Again, A B ) ) y and x ) ) A, B do not allow A ) ) T nor X ) ) A ; 

 but they do allow A B c ) ) Y and x ) ) A, B, C. 



Elements may, under certain conditions, be transposed from one 

 term to another, without alteration of the import of the proposition. 

 Universal propositions allow the elements of vague terms to be trans- 

 posed : particular propositions allow the elements of full terms to be 

 transposed. In universal propositions the transposition is made directly 

 in negatives, by contraversion in affirmatives. In particular proposi- 

 tions the transposition is made directly in affirmatives, by contra version 

 in'negatives. As instances x ) ) A, B gives x a ) ) B ; A B ) ) Y gives B ) ) 

 T,"a; AB)-(Y gives B)-(AY; AB( )Y gives B( ) A Y; AB(-(Y 

 gives B ( . ( Y, a ; A, B ( ) Y gives A ( ) y, B, &c. And in all these 

 cases the result of transposition is identical with the original. 



Both extent and intent are to be considered in both sides of logic, 

 the mathematical and the metaphysical. A class may be an aggregate 

 or a compound ; the class animal is aggregate of man and bruts ; the 

 cla>* animal is compound (common part of ) the class body and the 

 class living. An attribute may be an aggregate or a compound : the 

 attribute useful is aggregate of the naturally and the artificially useful : 

 the attribute useful is compounded of, or at least has amony its com- 

 ponents, attainable and applicable. But the conveniences of thought, 

 though not its necessities, and whether by mere habit or by human 

 constitution is not a question of logic, dictate an almost exclusive 

 confinement of the notion of aggregation to that of class, and of the 

 notion of composition to that of attribute. Accordingly, intent is of 

 predominant importance in the metaphysical side of logic, and extent 

 in the mathematical. 



The mathematical form of thought builds upon the notions of con- 

 tained and excluded: the metaphysical form upon the notions of 

 taential and rejutgnant. The metaphysical form should be cultivated 

 because, right or wrong, human beings are made to be metaphysicians, 

 children most of all, uneducated persons more than educated. The 

 must be and the cannot be are the strong points of our mental constitu- 

 tions. We know all about can and cannot from our cradles : we never 

 feel the same assurance about is and is not. A philosopher, in a dark 

 age, may determine to set out with a knowledge of the naturally 

 possible and impossible ; but not even a philosopher ever pretended to 

 set out with a knowledge of the existent and non-existent. Logic 

 excludes actual metaphysics by declining to enter into the inquiry 

 whether this or that use of the metaphysical form of thouyht be true 

 or false in matter. But logic claims to interfere to give a logical cor- 

 rectness in the use of terms and relating notions : to prevent, for 

 instance, a person who, rightly or wrongly, makes reason an essential 

 of man, from pronouncing it to be therefore repugnant to the nature of 

 brute. 



Additional intent may diminish extent, but never increases it : 

 additional extent may diminish intent, but never increases it. By con- 

 tinual introduction of new attributes we may, if speaking of things 

 existing, not of possibilities of thought, curtail the widest class until we 

 have brought it down to an individual. Thus ieiny includes every- 

 thing ; material being is body ; living body is animal ; human animal is 

 man ; man of old time is ancient ; go on thus until we come to ancient 

 Roman general who conquered Gauls, and wrote his own campaigns, 

 and we have the individual Julius C;esar. 



If we read our cumular propositions by the notion of enumeration 

 of attributes, we have the following arithmetical reading by enumera- 

 tion of attributes, just as " every x is Y," &c., show arithmetical 

 reading by enumeration of the smallest * possible classes, that is, 

 individuals. 



x ) ) Y. All the attributes of Y are attributes of x. 

 x ( ( Y. Some attributes of Y are not attributes of x. 

 x ) ( Y. Everything wants either some attribute of Y, or some attri- 

 bute of x. 



X ( ) Y. Some things want neither any attribute of Y, nor any attri- 

 bute of x. 



x ( ) Y. Everything has either all the attributes of y, or all the 

 attributed of x. 



x ) ( Y. Some things want either some attributes of Y, or some 

 attributes of x. 



x ( ( Y. Some attributes of Y are all the attributes of x. 

 x ) ) Y. Any attributes of Y are not some attributes of x. 

 The complete inversion of the quantities will be perceived. We 

 now give a metaphysical nomenclature. 



x ) ) Y. x a dependent of Y ; Y an essential of x. 



x ( ( Y. x an independent of Y ; Y an inessential of x. 



x ) ( Y. x a repugnant of Y ; and Y of x. 



x ( ) Y. x an irrepugnant of Y ; and Y of x. 



x ( ) Y. x an alternative of Y ; and Y of x. 



* There is a termination to disaggregativc separation ; we cannot subdivide 

 individuals. But if there be a termination to decompositive separation, we 

 know nothing about it. We can disaggregate the class mankind into its con- 

 stituent non-interfering indivisibles, or individuals : MO cannot decompose 

 reason into attributes, which all will agree upon as being primary and non- 

 interfering, and not further separable. But this distinction is of no logical 

 imij .rt;mco. 



ABTg AND SCI. DIV. VOL. V. 



X ) ( Y. X an inalternative of Y ; and Y of x. 



x ( ( Y. x an essential of T ; Y a dependent of x. 



x ) ) Y. x an inessential of Y ; y an independent of x. 



The syllogisms are now described in a way which will suggest itself : 

 thus ( ) ) ) giving ( ), which read mathematically exhibits the com- 

 bination " A complement of a deficient is a partient," will, when read 

 metaphysically, give "an alternative of an inessential is an irre- 

 pugnant." 



In the article PREDICABLES we shall add something on the extension 

 which must follow the admission of contrary terms. In RELATION we 

 shall enter farther upon the doctrine of figure, which is of no import- 

 ance in any system in which only convertible relations are used, and 

 quantities and terms are converted together. In PROBABILITY we 

 enter upon the subject of belief. 



When reduced to so brief an abstract as we have here given, a 

 system of logic appears like a string of names. But the more names 

 the more ideas ; provided only that every name has meaning which is 

 not merely repeated in any other. So far as the invention of words is 

 analysis of ideas, or signifies the completion of such analysis, and 

 prevents it from being lost, so far it is augmentation of power over 

 ideas. Dr. Thomson well observes that " as the distinctions between 

 the relations of objects grow more numerous, involved, and subtle, it 

 [language] becomes more analytic, to be able to express them : and, 

 inversely, those who are born to be the heirs of a highly analytic 

 language, must needs learn to think up to it, to observe and distinguish 

 all the relations of objects, for which they find the expressions already 

 formed, so that we have an instructor for the thinking powers in that 

 speech which we are apt to deem no more than their handmaid and 

 minister." 



It is very common to discuss the utility of the subject, in an article 

 treating of it in general ; but of all arguments, that about the utility 

 of any branch of knowledge is the most useless. Allowing an in- 

 frequent exception here and there, those who have mastered the first 

 difficulties of any branch of knowledge are all convinced of its utility ; 

 and with those who have not, and who have the boldness to form an 

 opinion, there ia no basis for an argument. 



LOGISTIC. [PROPORTIONAL.] 



LOG'OS, \6yos, the Greek for a word, is used as a theological term, 



1. The Jeiulsli doctrine of (he Lorjos. 



The phrase, the Word or Memra of Jehorah 0?"T SlJ^g), occurs 

 repeatedly in the Chaldee Targums, where it commonly stands in the 

 place of njrP (Jehovah) in the Hebrew original. There are, however, 

 passages in which this phrase appears to denote a distinct personal 

 existence ; and many eminent critics, among whom are Bertholdt and 

 Wegscheider, are decidedly of opinion that the Targumists intended it to 

 apply to the Messiah ; " plainly showing it to have been their belief 

 that the Shechinah, or Word, as some of them indeed expressly say, 

 would employ the future Messiah, when he should be born, as the 

 instrument of his gracious designs, and would be joined to him in a 

 personal union." (Bertholdt, ' Christol. Jud.') 



Philo often speaks of the Logos, but his views on the subject are 

 involved in much obscurity. He seems, however, to have had the idea 

 of a two-fold Logos ; the one denoting a conception in the divine mind 

 according to which the world was created ; the other a personal exist- 

 ence, the Son of God, partaking of the divine nature, though inferior 

 to the Supreme God, the Creator of the world (Srmiov/ryas) , presiding 

 over the universe, the instructor and guide of man, the High Priest 

 and Mediator between God and man. These two ideas of the Logos 

 he often confounds together. The passages from Philo are collected in 

 Dr. J. P. Smith's ' Scripture Testimony to the Messiah," book ii., cap. 

 vii., sect. 4. 



See also the descriptions of Wisdom and the Word of God in 

 Prov. viii. ; Wisdom of Solomon,^x. 15-19 ; xi. 1-4 ; xviii. 15 (compare 

 1 Cor., xii. 4, 9, where the same actions are attributed to Christ) ; and 

 in other parts of the Wisdom of Solomon and Ecclesiasticus. 



These opinions are thought by some to represent the ancient Jewish 

 doctrine respecting the word of God, corrupted by a mixture of heathen 

 philosophy ; and by others to have been wholly borrowed either from 

 the Platonic philosophy or from the Magiau doctrine of diviuo 

 emanations and 



2. The Christian doctrine of the Loyos. 



The only examples of the theological use of this word in the New 

 Testament are found in the writings of John (Gospel, c. i. ; 1st Epistle, 

 :. 1 ; Rev., xix. 13). These passages are generally allowed to refer to 

 Christ ; but the sense in which Logos is to be taken, and the nature of 

 ihe connection between this Logos and the person of Christ, are 

 subjects of much dispute. 



The Trinitarian expositors assert that these passages can mean nothing 

 Jse than that the Logos is a distinct personal subsistence, which has 

 existed from all eternity in a union of nature and of essence with God, 

 which created the universe, and which was joined with a human nature 

 to form the person of Christ. 



The Ariau doctrine represents the Logos as an emanation from tlie 

 Deity, superior to ail other created beings, and which supplied the 

 ilace of a human soul in the person of Christ. 



