Abstract
In the first exposition of the doctrine of indeterminacy of translation, Quine asserted that the individuation and translation of truth-functional sentential connectives like ‘and’, ‘or’, ‘not’ are not indeterminate. He changed his mind later on, conjecturing that some sentential connectives might be interpreted in different non-equivalent ways. This issue has not been debated much by Quine, or in the subsequent literature, it is, as it were, an unsolved problem, not well understood. For the sake of the argument, I will adopt Quine’s background assumption that all the semantic features of a language can be reduced to the speakers’ dispositions toward assent and dissent, as far as only the truth-conditional core of the meaning of sentences is concerned. I will put forward an argument to the effect that the speech dispositions of most, if not all, English (French, Italian, etc.) speakers constrain a unique translation of their connectives. This argument crucially relies on an empirical conjecture concerning the behaviour of these operators.
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Notes
Note that the ordered pair <a, d> assigned to some sentence by M is not to be confused with the stimulus meaning of that sentence, at least if we stick to the definition of stimulus meaning given by Quine himself (1960, p. 32). Quine says that a stimulation s belongs to the positive (negative) stimulus meaning of p, if and only if s prompts assent to (dissent from) p. Given the definition of Quine’s technical notion of prompting, if a sentence s is always assented to, then both its positive and its negative stimulus meaning are empty. While, for reasons that will become clear later on, I need to be entitled to say that, in such a case, the set a is identical with the set of all stimulations.
This point is accounted for more thoroughly below, in Sect. 4.5.
By ‘binary operator’ I mean any linguistic context that yields a complete sentence when joined to two other sentences. It does not have to consist of a single word, and it can be syntactically discontinuous. Thus, complex structures like ‘not (... and ...)’ or, ‘neither ... nor ...’ are included as well.
The letters ‘p’, ‘q’, ‘r’, and ‘s’ are used as variables ranging over sentences. A sequence like ‘p & q’ means ‘the result of the concatenation of p, &, and q’.
The double quotes ‘ “ ’ and ‘ ” ’ are used for quasi-quotations, in the sense of Quine (1951, § 6).
In the demonstrations presented in this paper, I will omit the steps that are obvious from the point of view of elementary logic or set theory.
H.G. Callaway asserts that Quine claims that ‘observation alone will not allow discrimination between a linguistic community making use of classical logic and one making use of intuitionistic logic’ (1992, pp. 65–66). Alan Berger’s interpretation is in this respect identical (1980, p. 264). This claim can be refuted: as noted above, we can distinguish intuitionists from speakers that make use of classical logic just by observing the way they use negation. And it does not express Quine’s view, simply because there is no trace of it in the texts quoted by those critics, where Quine does not mention translation but speculates on the acquisition of truth-functions on the part of a child learning his or her mother tongue (Quine 1974, pp. 75–78).
My description of Quine’s position is actually simplistic, but my present aim is not philological. Nonetheless, some clarification is maybe necessary. As for the above mentioned maxim ‘impose your logic to the native’, Quine would probably assert that it is not ‘a substantive law of speech behavior’ (Quine 1960, p. 74), which I would interpret as meaning that the uniformity caused by the adoption of this maxim—namely the fact that almost all speakers of all languages seem to adopt truth-functional operators—must not be mistaken for a linguistic universal: it is not something linguists can discover, rather it is imposed by their own methodology, see similar considerations of Quine’s on the so-called Gestalt maxim (1969a, p. 34; 1970, p. 9) and the principle of charity (Quine 1969b, p. 318; see Pavan 2009, pp. 132–141). I subscribe this claim of Quine’s, but something of his position on the translation of sentential operators eludes me. Is he claiming that the translation of negation is determinate even without the adoption of the maxim, or rather that the maxim entails that the translation of negation is determinate, unlike the translation of conjunction and disjunction? In any case my position is different. I take conjunction, disjunction and negation to be on a par: even after the adoption of the maxim, something has to be added in order for their translation to be determinate.
Here and elsewere, I am assuming that the English ‘if’ is a material conditional, and this might be questioned. This is a dispensable shortcut, since if ‘or’ and ‘not’ are taken to be truth-functional, which is less controversial, then there is in English a device for expressing a material conditional.
An example is provided below, see footnote 17. I do not want to claim that when there is concomitant variation between p and q, it is indeterminate whether they are equivalent or not. I just claim that Quine’s criterion is inadequate, by his own standards. On the contrary, once we have identified an operator \(\Leftrightarrow\) that is determinately translatable as the material biconditional, we can devise a satisfactory criterion of cognitive equivalence for occasion sentences: p and q are equivalent if and only if \(\left[\left[p\Leftrightarrow q\right]\right]^+=S\). And the main argument of this paper entails that this can be done.
There is a trace of this issue in Donald Davidson. At some point he deduces a formula mentioning an un-interpreted operator |, and he points out that if we assume | to be truth-functional, then it cannot be but Scheffer’s stroke, and that therefore p|q is equivalent to “not (p and q)” (Davidson 2005, p. 72). But this is of no help with the problem I am addressing. It is likewise true that if we assume • to be truth-functional, then it cannot be anything but disjunction, but we still do not know whether we are bound to take it to be truth-functional. Davidson’s argument, as well as mine, presupposes that, all else being equal, among all the mappings from Jungle onto English, those that find a counterpart of the English sentential operators among Jungle operators are to be preferred over the others. But he does not show that there can be only one candidate.
Its cognate ‘\(\left[\left[{\rm C}(\approx\approx p)\right]\right]^-=\left[\left[{\rm C}(p)\right]\right]^-\)’ can be deduced: \(\left[\left[{\rm C}(p)\right]\right]^-=\left[\left[\approx{\rm C}(p)\right]\right]^+=\left[\left[\approx{\rm C}(\approx\approx p)\right]\right]^+=\left[\left[{\rm C}(\approx\approx p)\right]\right]^-\).
This is more than a mere notational simplification. I wanted to take the idea that all this can be done in radical translation as seriously as possible. Since the determination of the scope of an operator in an unknown spoken language would not be an easy task, I tried to minimise the number of nested operators inside the sentences to be tested. On the notion of radical translation see Quine (1960, § 7).
All this is reminiscent of Michael Dummett (2004, Chaps. 3–4), with the difference that he speaks in terms of ‘verification’, while the formulation of (4) only involves a weaker and non-factive ‘justifying’.
More formally: let ‘B a ’ be the familiar belief operator of doxastic logic, for some agent a; “\(\odot p\leftrightarrow p\)” is not always true, but, “\(B_a\odot p\leftrightarrow B_ap\)”, quite plausibly, is.
I observe that, in such a case, the compound \(\sim\odot p\) is a v-negation which is clearly not semantically equivalent to the classical negation ∼ p.
‘[...] thought, as John B. Watson claimed, is primarily incipient speech’ (Quine 1995, p. 88).
Exceptions are possible, but we should expect them to be rare and not systematic (Quine 1960, § 13, p. 69).
A Davidsonian theory of meaning can accomplish this in two ways. The fact can be explained in terms of the logical form of the relevant sentences, as with Davidson’s analysis of action sentences, which entails that the following schema is a theorem of a theory of meaning of English (Davidson 1980, pp. 105–122).
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‘If John kissed Mary passionately then John kissed Mary’ is true.
Alternatively it could be attributed to entailment relations between elements of the lexicon, and accounted for by specific ‘non-logical axioms’ introduced in the truth definition (Callaway 1988, p. 17).
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Acknowledgments
An early version of this paper was presented during a seminar at the University of Milan on March 22nd 2007. I am grateful to the people who attended the lecture, in particular Paolo Casalegno, Fabio del Prete, Elisa Paganini and Clotilde Calabi. I wish also to thank two anonymous reviewers for their comments. The paper is dedicated to the memory of Paolo Casalegno.
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Pavan, S. Sentential Connectives and Translation. Erkenn 73, 145–163 (2010). https://doi.org/10.1007/s10670-010-9243-1
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DOI: https://doi.org/10.1007/s10670-010-9243-1