The concepts and theories of modern physics / By J.B. Stallo.

  • John Stallo
Date:
1900
Catalogue details

Licence: In copyright

Credit: The concepts and theories of modern physics / By J.B. Stallo. Source: Wellcome Collection.

    267/376 (page 217)
    pose I select an exposition of the theory in the booh above referred to, the System of Logic of J. S. Mill, in whicli the fifth chapter of the second book “ On Demonstration and Necessary Truth ” contains an elab- orate statement of the author’s views on the basis and methods of geometrical science. “The foundation of all sciences, even deductive or demonstrative sciences,” says Mill* “is Induction; every step in the ratiocination of geometry is an act of induction. . . . The character of necessity ascribed to the truths of mathematics, and even (with some reser- vations to be hereafter made) the peculiar certainty at- tributed to them is an illusion; in order to sustain which it is necessary to suppose that those truths relate to, and express, the properties of purely imaginary ob- jects. It is acknowledged that the conclusions of ge- ometry are deduced, partly at least, from the so-called Definitions, and that those definitions are assmned to be correct representations, as far as they go, of the ob- jects with which geometry is conversant. Now, we have pointed out that, from a definition as such, no proposi- tion, unless it be one concerning the meaning of a word, can ever follow ; and that what apparently follows from a definition follows in reality from an implied assump- tion that there exists a real thing conformable thereto. This assumption, in the case of the definitions of geom- etry, is not strictly tnie; there exist no real things ex- actly conformable to the definitions. There exi.st no points without magnitude; no lines without breadth, nor perfectly straight; no circles with all their radii exactly equal, nor squares with all their angles porfectlv right. It will perhaps be said that the assumption does not extend to the actual, but only to the possible, exist- * A System of Logic (eighth ed.), p. 1G8 seq.