266 ADVANCEMENT OF LEARNING 



selves. And yet the attempt of Kamus in this way has not 

 been useless. 



There are still two other limitations of propositions, be 

 sides that for making them convertible the one for extend 

 ing and the other for producing them. For if it be just that 

 the sciences have two other dimensions, besides depth, viz. , 

 length and breadth, their depth bearing relation to their 

 truth and reality, as these are what constitute their solidity ; 

 their breadth may be computed from one science to another, 

 and their length from the highest degree to the lowest in 

 the same science the one comprehends the ends and true 

 boundaries of the sciences, whence propositions may be 

 treated distinctly, and not promiscuously, and all repeti 

 tion, excursion, and confusion avoided; the other prescribes 

 a rule how far and to what particular degree the propositions 

 of the sciences are to be reduced. But no doubt something 

 must here be left to practice and experience; for men ought 

 to avoid the extreme of Antoninus Pius, and not mince 

 cumin- seed in the sciences, nor multiply divisions to the 

 utmost. And it is here well worth the inquiry, how far 

 we should check ourselves in this respect; for we see that 

 too extensive generals, unless they be reduced, afford little 

 information, but rather expose the sciences to the ridicule 

 of practical men, as being no more fitted for practice than 

 a general map of the world to show the road from London 



7 The axioms in the text must not be understood as applying to the mathe 

 matical sciences, which being, as Coudillac observes, purely ideal, exact in their 

 conversion nothing more than a detailed exposition of the properties we have 

 already included in their definition ; but of the objective sciences, where, since 

 our knowledge of the subject is generally so imperfect as to render any direct 

 definition uncertain, we are obliged to involve ourselves in a chain of reasoning 

 to prove that the interchangeable attribute can be affirmed of the subject in its 

 whole extent, and that both possess no qualities which are not convertible with 

 each other. In establishing this reciprocal accordance of parts, it frequently 

 happens that, having to connect a series of propositions in a chain of mutual 

 dependence on each other, the first being proved by the second and the second 

 by the third, etc., we arrive at and rest the whole proof upon a conclusion 

 which is nothing else than the enunciation of the very proposition which we 

 are laboring to establish, instead of grounding the argument upon some univer 

 sally admitted principle or well -ascertained fact. This fallacy logicians term 

 a vicious circle, and is the error to which Bacon alludes in the text. Ed. 



