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Three-valued logic

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Notes

  1. ‘Crosses’ is used here “tenselessly” — i.e., in the sense of “crossed, is crossing, or will cross.”

  2. More precisely, S is accepted if and only if ‘S is true’ is accepted.

  3. The distinction between sentences and statements will be ignored, because we have passed over to consideration of a formalized language in which it is supposed that a given sentence can be used to make only one statement.

  4. Cf. Alonzo Church'sIntroduction to Mathematical Logic (Princeton, N.J.: Princeton University Press, 1956), p. 141. Intuitionist logic is not a truth-functional logic (with any finite number of truth-values). However, the rules given above hold (except when both components are “middle” in the case of rules b and c) provided truth is identified with intuitionist “truth,” falsity with “absurdity,” and middlehood with being neither “true” nor “absurd.”

  5. In this paper, ‘three-valued logic' means the system presented at the beginning. Of course, there are other systems, some of which represent a more radical change in our way of speaking.

  6. Philosophic Foundations of Quantum Mechanics (University of California, 1944).

  7. Ibid., pp. 29–34.

  8. A. Einstein, B. Podolsky, N. Rosen, “Can Quantum Mechanical Description of Reality Be Considered Complete?” Physical Review, 47:777 (1935).

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  9. For example, Hempel writes in his review of the previously cited work by Reichenbach (Journal of Symbolic Logic, volume 10, p. 99) : “But the truth-table provides a (semantical) interpretation only because the concept of truth and falsity, in terms of which it is formulated, are already understood: they have the customary meaning which can be stated in complete precision by means of thesemantical definition of truth.” (Italics mine.)

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  1. Princeton University, USA

    Hilary Putnam

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  1. Hilary Putnam
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Putnam, H. Three-valued logic. Philos Stud 8, 73–80 (1957). https://doi.org/10.1007/BF02304905

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