93? 



SYLLOGISM. 



SYMBOLS AND NOTATION. 



tss 



the reduction requires the major premiss to be simply converted A, 

 that the minor is a universal affirmative ; M, that the reduction re- 

 quires the transposition of the premises ; I, that the conclusion is a 

 particular affirmative ; S, that the conclusion must be simply con- 

 verted. We thiu change 



Some YS are 

 Every Y is z 

 Some zs are 



M.I r 



, V into < 



X8,J 



DAR 



Every T is z, 

 Some xs are YS, 

 Some xs are zs. 



A prvptr mood was one in which one of the premises spoke of a 

 Dingle subject, as in " All Frenchmen talk French, Pierre is a French- 

 man, therefore Pierre talks French." There was much discussion as 

 to whether such a proposition as " Pierre is a Frenchman " was a uni- 

 versal affirmative or not, it being obvious on all sides that, whether 

 or no, it would .have in deduction all the properties of a universal 

 affirmative. 



An cntkymeme is a syllogism in which one premiss is obviously im- 

 plied, and is the form in which argument is commonly given. For 

 example, " He isn't here; I don't see him," implies that the speaker 

 would affirm himself certain of seeing him if he were there, and is an 

 enthymeme which, with the suppressed premiss restored, makes the 

 i. .Hi. whig syllogism : 



Fig. 2. A All that is here is seen by me. 

 Camtilrti. K He is not seen by me. 



Therefore E He is not here. 



The nrite is a collection of Barbara syllogisms, in which the sup- 

 prtBBcd conclusion of the first is a premiss of the second, that of the 

 second a premiss of the third, and so on ; as in A is B, B ia c, c is D, 

 l> in K, therefore A is r.. Here are three syllogisms, namely, 



A is C A is D 



B is c c is D D is K 



Various attempt* were made to classify the manners in which com- 



i -gument is to be expressed syllogUtically. The only difficulty is 



to reduce the expressions to the pure form of simple assertion or nega- 



An oblique syllogism was one in which one of the oblique cases 



enters the premises in such a manner as to vitiate the purity of the 



form. For instance, 



The thought* of man govern his action*, 



John is a man, 

 Therefore John's thoughts govern his actions. 



As it stands, this is not strictly a syllogism, and some leas idiomatic 

 expression* must be adopted before it can be turned into one. As, 



(Every man) is 



John 

 Therefore John 



govern hu a. 



is a being, ftc. 



The same thing occurs in a modal ti/l/oyitm, which is one in which 

 some modifying expression gives more or less of force to one or both 

 l<rmuw. As 



Probably Every Y is x, 



Every Z is T, 



Therefore Probably Every z ia x. 



If we consider both matter and form, we have here merely a syllo- 

 gism In which one premiss in only probable. [PROBABILITY.] But, 

 conridcrmg form only, the perfect deduction may be made as follows : 



g r - a ( a thing which is more likely than 



Every z is Y, therefore every z is [a thing, 4c.] 



The iu'liirtire syllogism Is merely one in which one of the premises 

 is proved by induction, or by separate proof of every instance : as 

 when the ri are known to be A, B, and C, and no more, and Every Y is 

 X is shown by proving separately that A is x, B is x, c is X. There is 

 nothing peculiar to the syllogism here. [IsDCcnox.] 



The hy/i'i'lietiral syllogism (so called) is one in which the truth of 

 one proportion ia stated to depend solely on that of another ; so that 

 ill'- first can be affirmed as soon as the second is known to be true, 

 or the second can be denied as soon as the first is known to be false. 

 Thus, 



If A be B, c is D, 

 But A is n, therefore c is D. 



Or, If A be B, c Is D, 

 But c is not D, therefore A is not B. 



Whenever a proof is complete, except in one proposition when, for 

 example, we have fully made out that c is D, except only in this that 

 the proposition " A is B " is not yet proved, the first member of the 

 hypothetical syllogism lays down the state of the argument. When 

 all that will prove a proposition is true, the proposition itself is true, 

 whence there is only need to affirm the one doubtful premiss, to make 

 the conclusion a logical consequence. Again, when a proposition is 



fake, some part of any logical proof must be deniable : hence there is 

 only need to deny the conclusion in order to make the one doubtful 

 premiss logically deniable. 



The conditional syllogism is reducible to an hypothetical one. It is 

 when, under certain circumstances, the first member affirms a propo- 

 sition, as in Wherever A is B, c is D. 



The dilemma is a double or other compound syllogism, in which two 

 or more contradictory propositions form each a conclusion with other 

 propositions, so that from those other propositions necessarily follows 

 one or other of the conclusions : because of contradictory propositions 

 one must be true. It is not therefore a syllogism, but a collection of 

 them. For example, " He must either have been for, against, or 

 neuter : if for, he was unjust ; if neuter, he was mean ; if against, he 

 was false; therefore he must have been either unjust, mean, or false." 

 This presumes the existence of a premiss for each conclusion ; as for 

 example, that the cause is that of oppression, that he is so circum- 

 stanced that nothing but fear or favour could prevent him from taking 

 part with the right, and that he has pledged himself to the wrong. 



The rules of syllogism may be briefly condensed as follows : 



1. One at least of the premises must be affirmative, and one at least 

 universal ; 2, the middle term must enter universally in one of the 

 premises ; and 3, the conclusion must not speak of any term in a wider 

 sense than it was spoken of in the premiss in which it entered. A 

 term universally spoken of is either the subject of a universal affirma- 

 tive, or the predicate of any negative. 



The first rule is derived from observation, but might be demon- 

 strated. The second is seen thus : if the middle term were not uni- 

 versally spoken of in one premiss, there might be in reality no middle 

 term, or nothing with which to compare the major and minor term. 

 Thus if we attempt to infer anything from Every x. is Y, some YS are 

 not zs, we merely see that all the xs are so many of the YS, or make up 

 a part of the YS. Some of the YS (another portion, it may be) are not 

 zs, so that the common term does not exist, or may not exist. The 

 third rule is obvious, for no more can be made of any assertion than it 

 contains, and an argument which asserts something about every x from 

 premises which only mention some xs, must be illogical. 



The various species of fallacies must consist either in the introduc- 

 tion of unproved propositions, or an illogical use of those which are 

 proved. Wo do not feel it necessary to extend this article by entering 

 into the usual classification of them. 



SYLVIC ACID, (C^H, U 0,) a substance which with pinic acid 

 [PiNic ACID] constitutes the greater portion of colophony, or common 

 rosin. When this substance is digested in cold alcohol of specific 

 gravity 0'838, the piuic acid dissolves, but the sylvic acid remains in- 

 soluble in alcohol until it is boiled ; on cooling, it separates in crystals 

 of considerable size, the form of which, according to Unverdorben, is 

 a rhombic prism terminated by four facets, but Laurent represents it 

 as an acute rhomboid, the edges of which are usually serrated. 



Sylvic acid melts below 212; is insoluble in water, but dissolves 

 readily in hot alcohol and in ether, and is precipitated by water ; it is 

 soluble also in all proportions in the volatile and fixed oils. Concen- 

 trated sulphuric acid dissolves aud water precipitates it from the acid ; 

 by the action of nitric acid it is converted into another resinous acid 

 when it has been precipitated from alcohol by water ; ammonia dissolves 

 this acid readily, and the sylvate of ammonia formed, as well as that of 

 potash and of soda, is soluble in water ; most sylvates are however 

 insoluble in it, but many of them are dissolved by alcohol and 

 by ether ; the sylvate of magnesia especially is takeii up by alcohol ; 

 the sylvates of silver and lead are colourless and insoluble in 

 water. 



SYMBOLS, CHEMICAL. [CHEMICAL FORMULA.] 



SYMBOLS and NOTATION. The word symbol (from the Greek 

 ttfmMon, avnBo\ov) means " that which is taken with," and a symbol 

 is a mark which is always attached to some one particular meaning. 

 Notation (/iota, a known mark) is the method of selecting and assigning 

 meaning to symbols, aud the theory of notation (if it yet deserve the 

 name) includes the consideration and choice of symbols, with the 

 formation of rules of selection, so as to take the symbols which are 

 best adapted for the purpose. 



This subject Wght be treated in a very wide manner ; for all marks 

 with understood meanings are symbols, from written words to 

 direction-posts. A picture is a symbol, the force of which lies in the 

 resemblance to its object, and many of the earliest symbols must have 

 been pictorial. It is obvious that a general treatment of the subject 

 would hardly be within the power of any one person, and that its 

 extent would be enormous, though it would be desirable to have it 

 discussed in a more general form than has yet been attained, in order 

 that its different parts might receive aid from the rest. Symbols are to 

 the progress of civilisation precisely what mechanism is to that of the 

 arts, not a moving force, perfectly dead in themselves, but capable of 

 being made the medium by which the power is conveyed to its desti- 

 nation, and adapted to its object. They are the instruments of our 

 first thoughts and the originators of new ones. The process by which 

 the earliest symbols called out a yet higher intelligence than that 

 which produced them, which last was again employed iu perfecting the 

 symbols themselves, and so on alternately, exactly resembles what has 

 taken place iu the mechanical arts. The earliest and rudest tools were 

 first employed to make better ones ; and every improvement in the use 



