164 KEASONING. 



merous, and complicated may be the processes necessary for bringing the 

 inductions together, even when each induction may itself be very easy and 

 simple. All the inductions involved in all geometry are comprised in those 

 simple ones, the formulae of which are the Axioms, and a few of the so-call- 

 ed Definitions. The remainder of the science is made up of the processes 

 employed for bringing unforeseen cases within these inductions ; or (in syl- 

 logistic language) for proving the minors necessary to, complete the syllo- 

 gisms ; the majors being the definitions and axioms. Cin those definitions 

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

 tion of which it has been found possible 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 difiiculty 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 Deductive Sci- 

 ence as possible ; for endeavoring to construct the science from the fewest 

 and the simplest possible inductions, and to make these, by any combina- 

 nations however complicated, sufiice for proving even such truths, relating 

 to complex cases, as could be proved, if w:e chose, by inductions from spe- 

 cific experience. Every branch of natural philosophy was originally exper- 

 imental ; each generalization rested on 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 mostly consist of no more than one step* 

 and are expressed by single syllogisms, all these sciences have become tdl 

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

 of pure reasoning ; whereby multitudes of truths, already known by induc- 

 tion 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, 

 therniology, 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 circuitous mode of proceeding for a process 

 apparently much easier .and more natural, is held, and justly, to be the 

 greatest triumph of the investigation of nature, we are not, in this stage 

 of our inquiry, prepared to examine. CBut it is necessary to remark, that 

 although, by this progressive transfonfiation, 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 teims 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 ascertaining that cases which 

 can not be observed to have the requisite marks, have, however, marks of 

 those marks. 



We can now, therefore, perceive what is the generic distinction between 



* Infra, book iii., ch. iv., § 3, and elsewhere. 



