176 OF SECONDARY PROPOSITIONS. [CHAP. XI. 



essential to the development of a theory of primary propositions, 

 but am disposed, though desiring to speak with diffidence upon 

 a question of such extreme difficulty, to think that the idea of 

 time is essential to the establishment of a theory of secondary 

 propositions. There seem to be grounds for thinking, that 

 without any change in those faculties which are concerned in 

 reasoning, the manifestation of space to the human mind might 

 have been different from what it is, but not (at least the same) 

 grounds for supposing that the manifestation of time could have 

 been otherwise than we perceive it to be. Dismissing, however, 

 these speculations as possibly not altogether free from presump- 

 tion, let it be affirmed that the real ground upon which the 

 symbol 1 represents in primary propositions the universe of 

 things, and not the space they occupy, is, that the sign of 

 identity = connecting the members of the corresponding equa- 

 tions, implies that the things which they represent are identical, 

 not simply that they are found in the same portion of space. 

 Let it in like manner be affirmed, that the reason why the symbol 

 1 in secondary propositions represents, not the universe of events, 

 but the eternity in whose successive moments and periods they 

 are evolved, is, that the same sign of identity connecting the 

 logical members of the corresponding equations implies, not that 

 the events which those members represent are identical, but that 

 the times of their occurrence are the same. These reasons appear 

 to me to be decisive of the immediate question of interpretation. In 

 a former treatise on this subject (Mathematical Analysis of Logic, 

 p. 49), following the theory of Wallis respecting the Reduction 

 of Hypothetical Propositions, I was led to interpret the symbol 1 

 in secondary propositions as the universe of" cases" or " conjunc- 

 tures of circumstances;" but this view involves the necessity of a 

 definition of what is meant by a " case," or " conjuncture of 

 circumstances ;" and it is certain, that whatever is involved in 

 the term beyond the notion of time is alien to the objects, and 

 restrictive of the processes, of formal Logic. 



