Selected Mathematical Works: Symbolic Logic + The Game of Logic + Feeding the Mind: by Charles Lutwidge Dodgson, alias Lewis Carroll. Lewis Carroll

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СКАЧАТЬ Some xy′ exist = Some x are y′ = Some y′ are x All x are y′ Some x′y exist = Some x′ are y = Some y are x′ All x′ are y Some x′y′ exist = Some x′ are y′ = Some y′ are x′ All x′ are y′ No xy exist = No x are y = No y are x All y are x No xy′ exist = No x are y′ = No y′ are x All y are x′ No x′y exist = No x′ are y = No y are x′ All y′ are x No x′y′ exist = No x′ are y′ = No y′ are x′ All y′ are x′ Some x are y, and some are y′ Some y are x and some are x′ Some x′ are y, and some are y′ Some y′ are x and some are x′

      

CHAPTER IV.

       INTERPRETATION OF BILITERAL DIAGRAM WHEN MARKED WITH COUNTERS.

      Table of Contents

      The Diagram is supposed to be set before us, with certain Counters placed upon it; and the problem is to find out what Proposition, or Propositions, the Counters represent.

      As the process is simply the reverse of that discussed in the previous Chapter, we can avail ourselves of the results there obtained, as far as they go.

      First, let us suppose that we find a Red Counter placed in the North-West Cell.

      We know that this represents each of the Trio of equivalent Propositions

      “Some xy exist” = “Some x are y” = “Some y are x”.

      Similarly we may interpret a Red Counter, when placed in the North-East, or South-West, or South-East Cell.

      Next, let us suppose that we find a Grey Counter placed in the North-West Cell.

      We know that this represents each of the Trio of equivalent Propositions

      “No xy exist” = “No x are y” = “No y are x”.

      Similarly we may interpret a Grey Counter, when placed in the North-East, or South-West, or South-East Cell.

      Next, let us suppose that we find a Red Counter placed on the partition which divides the North Half.

      We know that this represents the Proposition “Some x exist.”

      Similarly we may interpret a Red Counter, when placed on the partition which divides the South, or West, or East Half.

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