THE THEORY OF SYLLOGISM, ETC. 127 



lows ; — " Not as it stands ; for, as expressed, this reasoning is elliptical. Explicitly stated, 

 it is as follows : — 



What are equal to the same, are equal to each other; 



A and C are equal to the same (B) ; 



Therefore, A and C are equal to each other." 



I am quite at a loss to see how the second is an expanded form of the first. But I 

 see distinctly the composition of relation, * equal of equal is equal,' expressing the tran- 

 sitiveness of the copula equals, which, with its convertibility, renders it of equal validity 

 with is as the copula to be employed in a syllogism. 



Again, a recent and learned editor of Aldrich, the Rev. H. L. Mansel, observes of the 

 preceding, that "the reasoning is elliptical, and therefore, as it stands, material; though 

 owing to the suppressed premise being self-evident, its deficiency is apt to be overlooked ." 

 This suppressed premise is the major given above. But does it not then follow that the 

 ordinary syllogism is elliptical ? Is there not always the suppressed premise (as I feel 

 bound, on these authorities, to call it), " What are the same are each other ?" 



There is some want of distinctness in the use of the word material, as distinguished from 

 formal. When the last named writer makes it " material and therefore extra-logical " that 

 Alexander was the son of Philip because Philip was his father, he uses the word historically. 

 The formal connexion of relation and correlation exists, though Aristotle did not recognize 

 it as copular except when the relation is its own correlation, and then only in a limited 

 case. Certainly the matter, in the case of father and son, supplies the knowledge of the 

 correlative relation existing, but not the mode of using it in inference, when known to 

 exist. In this and a great many other instances, matter is opposed by writers, not to form, 

 but to what is recognized as form in the school of Aristotle : the assumption of course 

 being that that school exhausts the forms of thought. Historically speaking, the copula 

 has been material to this day : this I must continue to believe until it be pointed out 

 where the formal conditions have been separated from the matter, and made the instru- 

 ments of inference, independently of the separated matter. 



A certain indifference to close description of the copular relation is manifest in many 

 logical works, accompanied by negligence in its application ; and this may produce strange 

 consequences in literal translations. The proposition ' X is F, 1 may bear expression in 

 French as ' X doit etre F,' and in Latin as ' X debet esse F,' though both are rather 

 negligent forms for a strict work : but the English ' X ought to be F' is of a different 

 signification. Both* the English translations of the Port Royal Logic give a paralogism 

 for the instance cited in illustration of the definition of the word reasoning: " having judged 

 that true virtue ought to be referred to God, and that the virtue of the heathens was 

 not referred to him, we thence conclude that the virtue of the heathens was not true virtue." 

 Had the copula been as fully treated of as the terms, such inaccuracies could hardly have 

 occurred. 



* A new one has recently been published by T. S. Baynes, Edinburgh, 1850. 

 July 3, 1850. 



