336f 



Mb DE morgan, ON THE SYLLOGISM, No. IV, 



possess some materials of the soil; of the foundation, not of the building, though the bricks 

 may partake of the nature of the foundation; of the rails, not of the locomotive, though both 

 may have iron in their structure. 



The canons of ordinary syllogism cannot be established without help from our knowledge 

 of the convertible and transitive character of identification: that is, we must know and use 

 the properties ' A is B gives B is A' and ' A is B and B is C, compounded, give A is C 

 Can these principles be established by concession of ' A is A, nothing is both A and not-A, 

 and every thing is one or the other'? All my attempts at such establishment end in 

 begging* the question, when closely scrutinised. The logicians do not make their deduction 

 in perfectly precise and formal method, so that a lapse may be clearly pointed out. I 

 suspect that the use of convertibility and transitiveness actually takes place, and must take 

 place, in every attempt to deduce the legitimacy of the two laws, as necessary consequences 

 of the three laws: and if my suspicion be correct, it follows that the two principles must be 

 assumed independently of the three. I cannot argue the question until I find some more 

 precise attempt to maintain the assertion: I suspect that 'it is as plain as that A is A' has 

 been confounded with ' it is true because A is A.' 



In the consideration of the proposition, identification of objects is in truth a relation 

 of concepts. In the ordinary books on logic, the relation before the mind is confusedly mixed 

 up with the judgment, the assertion or denial of the relation. The word is has two different 

 meanings: standing alone, it means identity affirmed; in the phrase is not, it means only 

 identify. I claim to recognise the distinction between relation and judgment, and to assign 

 to each notion its own symbol. Let X and Y be terms, and L a relation in which X may 

 or may not stand to Y, let X . . LY signify the assertion of the relation, and X . LY its 

 denial. This separation of relation and judgment is an important step towards the treat- 

 ment of syllogistic inference as an act of combination of relation ; as also towards the 

 knowledge that the ordinary canons of syllogism do actually embrace every case in which 

 one relation only is used, and that relation transitive and convertible. 



That all analysis of thought should be confined to expression under one class of re- 

 lations is the defence of a system formed under limited views, and a defence which nothing 

 but necessity could have originated. It is the. great principle of pebbles invented for 

 justification of arithmeticians who have never got beyond pebbles. Pure arithmetic, dealing 

 with nothing but the notion of number, has all its processes reducible of course to making 

 number more or less. The solution of a cubic j- equation to 153 figures is within the reach 



* It is not lawful to employ syllogism in deducing syllo- 

 gism from postulates which are affirmed to necessitate it: for 

 if all syllogism be invalid — and whether or no is the question — 

 it may establish itself on any basis. The quadrature of the 

 circle may be deduced from the Habeas Corpus Act by a 

 method which contains only one paralogism. I have heard 

 logic called the science which demonstrates demonstration; 

 it only analyses demonstration. So surely as no syslem of 

 truths can be established upon no truth to begin with, so 

 surely can no methods of transition or inference be estab- 

 lished without methods of inference to start with. If then the 

 very earliest demand the use of the transitive and convertible 



characters of the copula, these characters cannot be themselves 

 inferred: consequently, unless non-inferentially and immedi- 

 ately seen in the three principles, they must be adopted on 

 their own security. The moment this is done, the whole of 

 the common syllogism must be admitted under the extension 

 to every copula which is both transitive and convertible ; for 

 transitiveness and convertibility once separated from the three 

 principles of identification, and standing on their own footing, 

 the restriction of the copula to the identifying verb ' is,' no 

 matter how many its senses, is only arbitrary and lawless dis- 

 tinction. 



f " If the curiosity of any gentleman that has leisure" to 



