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Noughty bits: the subatomic scope of negation

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Abstract

Since Fodor 1970, negation has worn a Homogeneity Condition to the effect that homogeneous predicates (e.g., (1), (2)) denote homogeneously—all (1) or nothing (2)—to characterize the meaning of (1)–(2) when uttered out-of-the blue, in contrast to (3)–(4):

  1. (1)

    The mirrors are smooth.

  2. (2)

    The mirrors are not smooth.

  1. (3)

    The mirrors circle the telescope’s reflector.

  2. (4)

    The mirrors do not circle the telescope’s reflector.

It has been a problem for philosophical logic and for the semantics of natural language that (5)–(6) appear to defy the Principle of Excluded Middle while (7)–(8) do not—

  1. (5)

    Smooth(m)

  2. (6)

    ¬Smooth(m)

  1. (7)

    Circle(m)

  2. (8)

    ¬Circle(m).

An impoverished logical form (5)–(8) has been the occasion to embellish all else—Boolean algebra, lexical presuppositions, Strongest Meaning Hypothesis, trivalence, supervaluation, double strengthening, etc., enriching the semantics and pragmatics with what remains a special theory of negation, which may be dismissed when the logical syntax and semantics of negation reflects that negated sentences are also tensed sentences.

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Authors and Affiliations

  1. Department of Linguistics, University of Southern California, MC-1693, Los Angeles, CA, 90089-1693, USA

    Barry Schein

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  1. Barry Schein
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Correspondence to Barry Schein.

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For discussion sine qua non, much thanks to Elena Herburger, Yael Sharvit and Anna Szabolcsi, and thanks too to audiences at the University of Arizona, Tucson and Stanford University and to two anonymous reviewers for sound and critical advice.

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Schein, B. Noughty bits: the subatomic scope of negation. Linguist and Philos 39, 459–540 (2016). https://doi.org/10.1007/s10988-016-9194-3

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