86 PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



avowedly in abbreviation of combinations of fundamental symbols. Again, the complex 

 symbol should not be prior in invention to the simple ones ; nor should it be invented until the 

 simple ones have had their chance of good suggestion. 



For instance, in the old notation, the letters A, &c. are of compound meaning ; A is 

 universal and affirmative. If A and E had stood simply for affirmative and negative, and 

 two consonants, as B and N, for universal and particular, the distinction of figure might have 

 been symbolized. Barbara does not suggest the first figure, nor Camestres the second, 

 except by memory. But if the premise-consonants had been made to imitate the middle term 

 in location, the figure would have been seen in the word which would have resulted, whether 

 unmeaning letters had been added for euphony or not. Thus AE occurring as premises in the 

 second figure, in which the middle term is predicate of both premises, would have given 

 ABEBEB ; and so on. If some choice of liquids had been allowed for designation of par- 

 ticulars, and of other consonants for designation of universals, euphonic words might have been 

 invented, which would have been, by this time, as venerable as Bokardo or Felapton. Nor 

 would it have been difficult to have fitted on letters symbolic of the method of reduction into 

 the first figure. 



This suggestion, however, comes a few centuries too late : the following one is more to our 

 purpose. 



Symbols in which relative position is the whole or part of the symbol, whatever their 

 advantages may be in other respects, lie under one great disadvantage : abstraction is not sug- 

 gested, and can only be done awkwardly. The exponential symbol in algebra has this defect : 

 we cannot describe it independently of others, except by ( ) ( ', or some such contrivance. In 

 the more detailed notation of my former paper this fault was committed : thus XY, by mere 

 position of the letters, was made to indicate ' Some Xs. are Fs.' 



The distinctive characters of the proposition are made to be, usually, the terms, the copula 

 (affirmative or negative), and the quantity of the subject. But if the quantity of the predicate 

 be also symbolized, notice of the terms is not distinctively necessary : for every proposition 

 used has neither more nor less than two terms, and a term need not enter except to have its 

 quantity noted. The symbols of the terms, in fact, are only pegs on which to hang distinc- 

 tions: so that it is desirable that they should not be essential, though capable of introduction. 



The quantities of the terms give name to the proposition : which is usually called universal 

 or particular after its subject. This is arbitrary ; and it is open to us, by the same license, to 

 make the proposition take the name of its predicate. The enlargement of the proposition, 

 whether Sir William Hamilton's or my own, will probably require a new word to express the 

 distinction of propositions : for both have their double universals, and their double particulars, 

 which are not in the Aristotelian set. At present, however, I am not prepared to suggest 

 a term which would apply to both systems. 



Let the subject and predicate, when specified, be written before and after the symbols of 

 quantity. Let the inclosing parenthesis, as in X) or (X, denote that the name-symbol X, 

 which would be inclosed if the oval were completed, enters universally. Let an excluding 

 parenthesis, as in )X or X(, signify that the name-symbol enters particularly. Let an even 

 number of dots, or none at all, inserted between the parentheses, denote affirmation or agree- 



