Items related to Logic in the application to language
Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1856 Excerpt: ...It proved the case, but it proved it something more. It may be said, however, that in this there is neither harm nor inconvenience, that a conclusion which is true concerning a whole is true concerning a part of that whole. It may be said, in short, that superfluities do no mischief--superflua non nocent. On the other hand, however, formulas ought not to be multiplied unnecessarily, and what is Darapti but an unnecessary appendage to Disamis and Datisi? which is--I. Some men are mortal. A. All nun are rational beings. I. Some rational beings are mortal. or--A. All men are mortal. I. Some men are rational beings. I. Some rational beings are mortal. The inference is the same, whatever be the order of the premises. Of these, one, provided it be universal, will give a particular conclusion. Two will do no more. It is clear, then, that there are such things in Logic as over-strong conclusions, conclusions which a smaller amount of premiss would have given equally well. Exteact. " Several of the usual syllogisms are more strong than need be in the premises, in order to produce the conclusion. Thus, Y) X and Y) Z being admitted as premises, the necessary conclusion is X Z. But if Y) X be weakened into Y X, the same conclusion follows. If we call a syllogism fundamental, when neither of its premises are stronger than is necessary to produce the conclusion, it is obvious that every fundamental syllogism which has a particular premise, gives at least as strong a conclusion when that particular is strengthened into a universal. But, except when strengthening the premise also enables us to strengthen the conclusion, in which case we have a new and different syllogism, it seems hardly systematic to mis up with fundamental arguments, syllogisms which have quantity o...
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