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.

    348/458 (page 316)
    Now take the proposition, thus obtained from the major premiss of your syllogism, and make it the minor premissof a new syllogism, having the minor premiss of your old syllogism for a major. You will then obtain the premisses : All men are mortals ; Some non-vegetarians are men ; and from this you get the conclusion, ‘ Some non-vegetarians are mortals.’ This, by conversion, yields * Some mortals are non- vegetarians,’ and finally, by one more obversion, you arrive at the end of your long journey, and triumphantly attain the conclusion ‘ Some mortals are not vegetarians.’ Whether the importance of the result is commensurate with the time and trouble necessary to attain it, the reader must judge for himself; but if, notwithstanding the reduction to Darii, he is still unsatisfied with his syllogism, and cannot be convinced of its validity without reducing it to Barbara, he will be pleased to know that he is not at the end of his resources. All he has to do is to substitute for his major premiss the contradictory of his conclusion. By this means he gets a syllogism in Barbara, the conclusion of which contradicts his original major. Thus he reduces his syllogism to absurdity, a result not without further significance. It does seem that if a simpler method of ensuring the validity of a syllogism could be found, it would be preferable; and such a method is, I submit, found in the Method of Explication. By this method, we are authorised to replace any proposition by its reciprocal, and any term by its equivalent or its part. We may, therefore, replace ‘ mortals ’ by ‘ some mortals ’ and ‘ All men are mortals ’ by ‘ Some mortals are all men.’ ‘ Some men ’ are included, for the purpose of the argument, in ‘ all men ’, and may therefore be substituted for ‘ all men ’ ; and thus we get ‘Some mortals are some men.’ But ‘not vegetarians’ is given, in the major premiss, equivalent, for the purpose of the argu- ment, to ‘ Some men,’ and may therefore be substituted for ‘ some men.’ Hence we get, in three steps, ‘ Some mortals are not vegetarians.’ Thus the two processes, of deriving the conclusion, and assuring ourselves of its validity, are carried on simultaneously, and attained in three very simple steps; and all the many processes of reduction, together with their rules, the mne- monic verses which enable us to remember them, and the quaint