In a similar vein, in the present note we submit a novel argument showing that the assumption of a linguistic logic is not obligatory for those accepting logicality. From a philosophical perspective, the essence of the argument is that one can invoke logicality without “trepidation” (Gajewski 2002, p. 4) since a substantive characterization of the deductive system is not necessary. In particular, what we would like to show is that the same logical principle that justifies the analytic status of the ungrammatical exceptive construction (1) also justifies the analytic status of a suitably derived variant of (1). The crucial observation is that this variant is clearly grammatical. We understand this observation to suggest that logicality isn’t necessarily paired with a peculiar (or “exotic”; Abrusán 2019, p. 342, Del Pinal 2021, p. 23) deductive device.
In order to present the logic of our argument, let us begin with the analysis of one of the acceptable sentences with exceptives in universal quantification, namely (5a). For illustration, let us denote by P the unary predicate of smoking; obviously we have that x ∈ smoke if and only P(x) holds. In order to derive the relevant variant of (5a), we assume a very general equivalence between conjunction and universal quantification, which we describe in (13). We take it that the formula in (14b) is an adequate variant of (5a). In particular, what this variant expresses is that any collection of students such that they all smoke must necessarily exclude John. This, according to our understanding, captures the content of (5b) fairly accurately. In addition, we submit that (14a) provides one possible natural language translation of the logical variant. For concreteness, in order to translate (14b) into natural language, we are assuming that the relevant domain D consists of three students (say Alice, Bob, and John). Note that this assumption is made for the mere sake of simplicity, since the cardinality of D should not affect any grammaticality issue. Under this assumption, then, our translation appears straightforward.
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Let us now turn to the analysis of the ungrammatical construction with exceptives in existential quantification, namely (1). In this case, we submit that the formula in (16b) constitutes an adequate propositional variant of the representation in (4b), which provided the logical reason for the unacceptability of (1). This formula again derives from (4b) with the assumption that existential quantification is equivalent to generalized disjunction. Let us also consider a natural language translation of this variant, sentence (16a), where we assume again that |D| = 3. Our take is that the sentence so construed is acceptable – certainly less deviant than standard examples with exceptives and existentials such as (1).
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As is easy to check, the logical variant now under consideration crucially amounts to a contradiction. Our observation is that the source of this contradiction is the same as that of the contradiction in the original formula in (4b). We would like to emphasize that the analogy between (16b) and (4b) is, according to our understanding, not a mere superficial resemblance. In fact, it is a principle of classical logic that the disjunction satisfies the following weakening principle, which is importantly analogous to the upward monotonicity of the existential quantifier: If ϕ holds, then ϕ∨ψ holds for any choice of ψ. More generally, if a disjunction holds (or equivalently, if an existential formula is true over a certain domain), there is no way to make it false by adding other disjuncts (equivalently, by expanding the domain). We conclude that it cannot possibly be the case that a logical system that realizes the analytic status of (4b) does not also realize the analytic status of (16b) (we suspect that this conclusion is also valid for the other cases). The difference in grammaticality between (1) and (16a) is more plausibly related to the possibility of making the latter sentence informative via modulation of its nonlogical material (in line with the account of Del Pinal 2019, 2021; see also Pistoia-Reda and Sauerland 2021 for a possible extension). Assuming different representations is pointless if one doesn’t have a different logic underlyingly.
To make the latter suggestion more precise, consider a context in which the speaker wants to convey that adding John to the relevant group of people actually changes something with respect to what counts as smoking. This makes the content associated with the sentence informative: it prevents the contradiction via modulation of the meaning of the predicate. Note that this possibility immediately follows, for instance, from Del Pinal’s more pragmatic version of the logicality approach. According to this account, when an analytic interpretation is due to a dependency between nonlogical terms, a reinterpretation strategy, i.e. rescale or ‘ℜ’ in symbols, can apply to modulate the meaning of at least one of the occurrences of the predicate, thus removing the analyticity. Such a strategy is easily shown to be ineffective when the analytic interpretation is actually due to the functional vocabulary, like in the case of (1), and we have a single occurrence of the predicate. On the other hand, if we focus on our variant, it is easy to realize that the strategy is indeed sufficient to remove the contradiction that is literally expressed in that case. The contradiction would be removed, for instance, by specifying (with \(\{x : \mathfrak{R}^{+}_{c} (P(x)) \}\subseteq \{ x : P(x)\}\)) the meaning of the second occurrence of the predicate. But then the acceptability of our natural language translation (16a) is clearly expected.
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