A new logic / by Charles Mercier.

  • Mercier, Charles Arthur, 1852-1919.
Date:
1912
Catalogue details

Licence: In copyright

Credit: A new logic / by Charles Mercier. Source: Wellcome Collection.

    432/458 (page 400)
    carries with it comparison of the terms of the ratios. These instances are comparable with the attempt of many logicians to assimilate Analogy to Induction ; or rather, to make it a kind of Induction. We have seen how difficult it is, in literary or qualitative Analogy, to avoid some assimilation of the terms of the compared relations; and how, in comparing the stillness of the harmless child to that of the harmless mouse, we feel that the Analogy is more appropriate than would be comparison with the still- ness of death, or the stillness of the air before a storm. Some comparison of the terms, as well as of the ratios, is unavoidable, we found, in literary Analogy ; and is not only unavoidable, but appropriate and satisfying. Wherein, then, lies the fallacy ? It lies in this : when Byron says the Assyrian came down like a wolf on the fold, we understand him to suggest that the Assyrian partook of the rapacity and savagery of the wolf; but this suggestion is made, not as an inference from our previous know- ledge, but as an addition to it. There is no reference here to constancy in experience ; and consequently no Induction. There is no substitution of one proposition for another which implies it; and consequently no Deduction. All that is put forward is a suggestion. It is not a positive assertion : it is not a conclusion : it is a covert assertion, or semi-assertion, that the Assyrian has the detestable and terrifying qualities of the wolf. There is no fallacy in making the suggestion: but to take the suggestion for proof, that would be fallacious. If we turn the suggestion into an argu- ment, and conclude that since the Assyrian came down like a wolf on the fold, therefore he is as savage as a wolf, then we perpetrate a fallacy; but so long as we receive the suggestion as a mere suggestion, it is not fallacious. Quantitative analogy is fallacious when the ratios compared and discerned to be alike, are in fact not alike. 1- ?46 is a 359 fallacious analogy. “ The ratio between the homologous sides of similar triangles is equal to the ratio between their areas is a fallacious quantitative analogy. This application of analogy is equally fallacious when like ratios are taken to be unlike, as when triangles on the same base and between the same parallels are allowed to be of different areas, or when the odds of 15 to 12 are chosen in preference to odds of 25 to 20.