144 REASONING. 



language) for proving the minors necessary to complete the syllogisms; 

 the majors being the definitions and axioms. In ^hose definitions and 

 axioms are laid down the whole of .the marks, by an artful combina- 

 •tion of which men have been able to discover and prove all that is 

 proved in geometry. The marks being so few, and the inductions 

 which furnish them being so obvious and familiar ; the connecting of 

 several of them together, which constitutes Deductions, or Trains of 

 Reasoning, forms the whole diflftculty of the science, and, with a trifling 

 exception, its whole bulk ; 'and hence Geometry is a Deductive Science. 



§ 5. It will be seen hereafter that there are weighty scientific 

 reasons for giving to every science as much of the character of a De- 

 ductive Science as. possible ; for endeavoring to construct the science 

 from the fewest and the simplest possible inductions, and to njake 

 these, by any combinations however complicated, suffice for pro^dng 

 even such truths, relating to complex cases, as could be proved, if we 

 chose, by inductions from specific experience. Every branch of nat- 

 ural philosophy was originally experimental ; each generalization, 

 rested upon a special induction, and was derived from its own distinct 

 set of observations and experiments. From being sciences of pure 

 experiment, as the phrase is, -or, to speak more correctly, sciences in 

 which the reasonings consist of no more than one step, and are ex- 

 pressed by single syllogisms, all these sciences have become to some 

 extent and some of them in nearly the whole of their extent, sciences 

 of pure reasoning ; whereby multitudes of truths, already knowta by 

 induction from as many different sets of experiments, have come to be 

 exhibited as deductions or corollaries from inductive propositions of a 

 simpler and more universal character. Thus mechanics, hydrostatics, 

 optics, acoustics, and thermology, have successively been rendered 

 mathematical; and astronomy was brought by Newton within the 

 laws of general mechanics. Why it is that the substitution of this cir- 

 cuitous mode of proceeding, for a process apparently much easier and 

 more natural, is held, and justly, to be the greatest triumph of the in- 

 vestigation of nature, we are not, in this stage of our inquiry, .prej)ared 

 to examine. But it is necessary to' remark, that although, by this 

 progi-essive transformation, all sciences tend to become more and more 

 Deductive, they are not therefore the less Inductive ; every step in the 

 Deduction is still an Induction. The opposition is not between the 

 terms Deductive and Inductive, but between Deductive and Experi- 

 mental. . A science is Experimental, in proportion as every new case, 

 which presents any peculiar features, stands in need of a new-set of 

 observations and experiments, a fresh induction. It is Deductive, in 

 proportion as it can draw conclusions, respecting cases of a new kind, 

 by processes which bring those cases under old inductions; by ascer- 

 taining that cases which cannot be observed to' have the requisite 

 marks, have, however, marks of those marks. 



We can now, therefore, perceive what is the generic distinction be- 

 tween sciences which can be made Deductive, and those which must 

 as yet remain Experimental. The difference consists iji our having 

 been able, or not yet able, to discover marks of marks; If by our 

 various inductions we have been able to proceed no further 'than to 

 such propositions as these, a a mark of b, or a and h marks of one 

 another, c a mark of d, or c and d marks of one another, vnthout any- 



