where the only Proposition, represented by them all, is “Some not-y are not-x,” i.e.
Deleuze inverts this priority: identity persists, but is now a something produced by a prior relation between differentials (dx rather than not-x).
But to represent any Particular Proposition, at least three Diagrams would be needed (in order to include all the possible cases), and, for “Some not-x are not-y”, all the four.
Against Herbart and Fries, Bolzano thinks that contraposition requires a supplementary premise: From “all X are Y”, it is possible to deduce “all not-Y are not-X” only if we add as premise “the idea not-Y is not empty”.
The fact is, “The Logicians” have somehow acquired a perfectly morbid dread of negative Attributes, which makes them shut their eyes, like frightened children, when they come across such terrible Propositions as “All not-x are y”; and thus they exclude from their system many very useful forms of Syllogisms.
Thus, the Diagram, here given, exhibits the two Classes, whose respective Attributes are x and y, as so related to each other that the following Propositions are all simultaneously true:—“All x are y”, “No x are not-y”, “Some x are y”, “Some y are not-x”, “Some not-y are not-x”, and, of course, the Converses of the last four.
pg023Secondly, let us suppose that we have selected a certain Adjunct, which we may call “x,” and have divided the large Class, to which we have assigned the whole Diagram, into the two smaller Classes whose Differentiæ are “x” and “not-x” (which we may call “x′”), and that we have assigned the North Half of the Diagram to the one (which we may call “the Class of x-Things,” or “the x-Class”), and the South Half to the other (which we may call “the Class of x′-Things,” or “the x′-Class”).
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To begin with, if x ≠ 0, then x2 ≠ 0, so that, if x2 = 0, then necessarily not x ≠ 0.
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It is trivial that if x is identical to y at a time, then x and y would have all the same parts, whether or not x and y are sums.
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but that law of logic that ordains – in simplified form – that something cannot be "x" and "not x" at the same time.
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X is said to be ⊢-consistent iff not X ⊢ 0.
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The first eight modes of the first figure are obtained by going through all permutations with ‘not X’ instead of ‘X’ (with X for A, B, C); the second eight modes are obtained by using a rule of contraposition on the conclusion:
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But suppose also that in fact the act with the best consequences in this situation is not x but y.
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In one 14-minute test that Dr. van Gorp administers on a computer, letters pop up at varying intervals, and students must press a button whenever they see a letter that is not X.
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In an expert-panel decision on the safety of some technology, the technology may be either safe (X = 1) or not (X = −1).
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So we can say that ‘most’ indicates a function that maps ⟨X, Y⟩ to T iff the number of things that both Y and X map to T exceeds the number of things that Y but not X maps to T.
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Harvey flatly denies fronting any money to Showtime, providing one of those moments in reporting about this company when all signs point to X and he says “Absolutely not X.”
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But I will not be able to formulate thoughts about X and Y unless I am acquainted with X and Y.
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(“This party is Rated R . . . not X.
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For example, since there are no centaurs, the open sentence ‘Centaur(x)’ is not true of any objects of any kind, and so ‘∃x Centaur(x)’ is not ontologically committed to any kind of entity.
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