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Elementary Notions of Logic, Designed as Prolegomena to the Study of Geometry

Elementary Notions of Logic, Designed as Prolegomena to the Study of Geometry


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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. 1884 Excerpt: ... example of it would be--All birds are winged, Some bipeds are birds, ... All bipeds are winged. It will be easily seen that this rule has already been investigated in the case of immediate inference, and is the same law in another form as that which regulates conversion by limitation. (Cf. p. 40.) III.--Suppose we have given us as premisses--No M is P, No S is M. We can represent these graphically, thus: --From these figures we may gather that any variety o relation between S and P is consistent with the premisses. This might, in fact, be seen at a glance frorr the premisses themselves, for all they do is to deny any relation between the major and minor and the middle term. Hence they leave the relations between the major and the minor wholly undetermined. In this way we arrive at Rule III.--Two negative premisses prove nothing. IV.--Having examined the case-where both premisses are negative, it remains to be seen what law will hold in the case where one only of the premisses is negative. Take, for instance--No M is P, Some S is M. This can be represented thus: --Now, the only portion of S that we know anything about is that portion which is contained under M. Therefore the premisses will be equally well represented whether the line S stops at x or is produced to_y. Thus, since all the M lies outside P, it follows that all the S of which we have any knowledge also lies outside P; that is to say, that our conclusion from the above premisses must be negative--Some S is not P. A still stronger case would have been made if our minor premiss had been a Universal, instead of a Particular Affirmative: --No M is P, AUS is M; E for then we should have known that in our figure the line S could not be prolonged beyond the point x, and our conclusion would have been--No


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Product Details
  • ISBN-13: 9781151392282
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1151392286
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 77 gr


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