24* On Some Processes of Scientific Reasoning. 



• The Science of Geometry certainly pursues the method of 

 Ideal Construction. Few mathematicians will agree with 

 Mr. Mill that Geometry deals with the forms of real material 

 objects. The subject-matter of Geometry is not the forms 

 of real objects, but Ideal Conceptions derived therefrom. No 

 material object fulfils the mathematical definition of a sphere 

 — that all points on its boundary are equally distant from a 

 certain point within the sphere — and consequently none of 

 the propositions proved for geometrical spheres are rigorously 

 true for material objects ; the more nearly a material object 

 fulfils the definition of an ideal sphere, the more nearly are 

 the properties of ideal spheres true for it, and the difference 

 between some real objects and ideal spheres may be so small 

 that, as far as our senses can detect, they rigorously possess 

 the properties of the ideal conceptions. So, there is no such 

 thing in nature as a straight line, — no lines such that if they 

 coincide in two points, they coincide everywhere between 

 those points, — although there are many material lines whose 

 difference from straight lines is imperceptible to the senses. 



The one Science which is as true of reals as of ideals is 

 Arithmetic, or, at all events, that branch of Arithmetic which 

 deals with Integral Number. Ten material bodies fulfil the 

 definition of ten as accurately as ten ideal spheres and the 

 deductions of Integral Arithmetic are absolutely true for 

 external objects. 



I now pass to the science of Dynamics. The fundamental 

 conceptions of this Science are those of Matter and Force. I 

 do not intend to discuss the various theories which have 

 been held as to the nature and origin of these conceptions, 

 but will endeavour, to the best of my ability, to give a clear 

 account of my own opinions on the subject. Without enter- 

 ing into the general subject of the nature of Knowledge and 

 Belief, it will be permitted me, I think, to divide Beliefs 

 into two classes — Beliefs which have received verification 

 from experience, and Beliefs which have not received such 

 verification, either because they are, from their nature, 

 incapable of it, or because the requisite experience has 

 never presented itself. Would it be allowable to define the 

 term Scientific Knowledge as denoting those Beliefs which 

 have been verified by experience ? 



Now, let us take such a belief as this— a table is before 

 me ; — how can I proceed to test that belief ? I may look at 

 the table ; I may touch it, and in other ways apply my 

 senses to test my belief. But what is proved when I look 



