Hodges' Theorem Does Not Account for Determinacy

Hodges’ Theorem Does Not Account for Determinacy of Translation. A Reply to Werning Hannes Leitgeb Department of Philosophy University of Salzburg 29 June 2004

Running head: Hodges’ Theorem and Determinacy Article type: Critical Note Address: Department of Philosophy, University of Salzburg, Franziskanergasse 1, A-5020 Salzburg, Austria Tel.: (++43)662 8044 4084 Fax: (++43)662 8044 4074 E-mail: [email protected]

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Hodges’ Theorem Does Not Account for Determinacy of Translation. A Reply to Werning ABSTRACT. Werning applies a theorem by Hodges in order to put forward an argument against Quine’s thesis of the indeterminacy of translation (understood as a thesis on meaning, not on reference) and in favour of what Werning calls ‘semantic realism’. We show that the argument rests on two critical premises both of which are false. The reasons for these failures are explained and the actual place of this application of Hodges’ theorem within Quine’s philosophy of language is outlined.

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Introduction

Recently, Werning[11] has put foward an interesting argument against Quine’s thesis of the indeterminacy of translation, which we are going to take here just as a thesis on the indeterminacy of meaning, not of reference; instead of ‘translation’ we might just as well say ‘synonymy relation’ or ‘sameness of meaning relation’ (just as Quine often does; see [7], pp.52f, [9], pp.76f). The essential ingredient of Werning’s argumentation is claimed to be a theorem by Hodges[3]. In applying this theorem to refute the indeterminacy thesis, Werning makes use of the following two critical premises (which are discussed in the subsequent sections): (P1) The meaning of each observation sentence in ObsL is identical to its stimulus meaning. (P2) For every natural language, if the meaning function ν, defined on a set Y of well-formed expressions of the language, is a cofinal extension of the meaning function µ, defined on a set X of well-formed expressions of the language, then ν is a cofinal Fregean extension of µ. As we want to show now, Werning’s argument does not prove the indeterminacy of translation thesis to be false. Section 2 is devoted to a brief reconstruction of Werning’s argument. In section 3 we are going to find that P2 is plainly false, and that Werning’s argument also cannot be saved by a simple adaptation of P2 (even more so if P1 is presupposed, as is done by Werning). Section 4 points out why we think that P1 is also false. Accordingly, there are actually two reasons why Werning’s argumentation fails. Moreover, Quine himself neither claimed P1 nor P2 to be true; as far as Quine’s disapproval of P1 is concerned, one has first to clarify the context of the intended application of P1 in order to acknowledge that fact. We conclude that not just Quine’s indeterminacy thesis is left undefeated, but 2

also that Quine cannot be accused of being inconsistent, i.e., of believing P1, P2, the other background assumptions, and the indeterminacy of translation thesis. The paper ends with a consideration of what role an application of Hodges’ theorem might really play in a philosophy of language such as Quine’s.

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Werning’s Argument

Since my criticism is directed at premises P1 and P2, I will not consider every detail of Werning’s[11] argument. A short sketch of the general line of the argument will be sufficient as background. For the explanation of the technical terms – some of which are also explained below – see Hodges[3] or Werning[11]. Werning[11], p.162, restates Hodges’ theorem in the following form (cf. theorem 14 and corollary 15 in [3]): (Hodges’ Theorem) Given a language with grammar G, let X be a cofinal subset of the set of grammatical terms GT (G). Then, if µ is a compositional and Husserlian meaning function with domain X, there is, up to isomorphism, exactly one total Husserlian and compositional Fregean extension of µ. According to Werning’s intended application of the theorem, the variables are instantiated as follows: consider an arbitrary natural language L, or perhaps a “large” fragment L of a natural language, such that L is the subject of some Quinean field linguist. Let ObsL be the set of observation sentences of L. Finally, let LObs be the union of ObsL with the set of all subexpressions of the observation sentences in ObsL . Now, LObs is used as the above “given language with grammar G”, X is ObsL , and µ is identical to the meaning assignment µobs for ObsL . In order to make use of Hodges’ theorem, Werning accepts P1 as a premise (see [11], the abstract on p.145, and p.153): (P1) The meaning of each observation sentence in ObsL is identical to its stimulus meaning. Since the assignment of stimulus meanings to the observation sentences in ObsL is determined factually and uniquely (cf. Quine[5]), Werning can thus conclude that the assignment µobs of meanings to the observation sentences in ObsL is also determined factually and uniquely. Because ObsL is, by the construction of LObs , a cofinal subset of LObs , and µobs is assumed to be both compositional and Husserlian, Hodges’ theorem entails that there is (up to isomorphy) one and only one total Husserlian and compositional

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Fregean extension µ∗obs of µobs , where ‘total’ means that LObs is the domain of µ∗obs . Thus, also µ∗obs is determined factually. But, obviously, the fact that µobs can be extended uniquely to some type of assignment for LObs does not show by itself that the latter assignment can be argued to be the unique “actual” meaning assignment νLObs on LObs (where νLObs should be the restriction of the “actual” meaning assignment νL on L to the set LObs ⊆ L). The identification of µ∗obs and νLObs has to be justified, and it is indeed justified by Werning on the basis of premise P2 (see [11], p.155): (P2) For every natural language, if the meaning function ν, defined on a set Y of well-formed expressions of the language, is a cofinal extension of the meaning function µ, defined on a set X of well-formed expressions of the language, then ν is a cofinal Fregean extension of µ.1 Since every meaning assignment on LObs may be assumed to be an extension of µobs , and since every such assignment is thus also a cofinal extension of µobs by the fact that ObsL is a cofinal subset of LObs , it follows from P2 that every meaning assignment on LObs is even a cofinal Fregean extension of µobs . Given the further assumption that every meaning assignment on LObs is Husserlian and compositional, Werning can conclude from the uniqueness part of Hodges’ theorem that every meaning assignment for LObs is isomorphic to µ∗obs , i.e., their corresponding synonymy relations coincide. But that seems to constitute sufficient reason for regarding µ∗obs as the “actual” meaning assignment νLObs on LObs which is (up to isomorphy) determined uniquely and factually. Therefore, Quine’s indeterminacy of translation thesis seems to be false as regards the members of LObs . In how far this also constitutes an argument against the indeterminacy of translation thesis for L, i.e., for the total underlying natural language, is discussed in our section 3, where we are going to show that P2 is false. In any case, Werning considers his argument to be an argument in favour of what he calls ‘semantic realism’, i.e., “the assertion that the expressions of natural languages, up to isomorphism. . . , have determinate meanings, which themselves are metaphysically independent from expressions” (Werning[11], p.146). As noted above, we do not want to give the impression that Werning aims at disproving the inscrutability of reference, which is indeed not the case. In the subsequent sections we are only interested in the determinacy 1

P2 is nearly identical to the formulation in Werning[11], p.155, with only one proper exception: we prefer ‘well-formed expression’ over Hodges’ term ‘grammatical term’, which is often also used by [11]. By ‘grammatical term’, Hodges does not only refer to singular or general terms, but to all well-formed, i.e., grammatical expressions of arbitrary syntactic type.

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or indeterminacy of meaning-assignments, which is also the main topic of Werning[11], who tries to show that there are factually and uniquely determined assignments of “real meanings”. For the same reason, Werning’s distinction of translation meanings, which are just the linguistic images under translation mappings, and neuronal meanings, which are his actual meaning entities, will not play a role in this paper.2

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P2 vs. The Context Principle

Werning, p.155, calls P2 the “context principle” and on p.156 a “generalization” of Frege’s principle. Indeed, Frege’s context principle can be regarded as the following confirming instance of P2: for every natural language, (i) the meaning function ν, defined on the total set of well-formed expressions of the language, is a cofinal extension of the meaning function µ, defined on the set of sentences of the language, and (ii) ν is even a cofinal Fregean extension of µ. What does this amount to? Ad (i): the set of sentences of a natural language is certainly cofinal in the superset of all well-formed expressions of a natural language, i.e., every well-formed expression of a natural language is a syntactic part of some sentence of the language; thus ν is a cofinal extension of µ. Ad (ii): that the meaning function ν on the language is a Fregean extension of µ means that two expressions of the language have the same meaning if and only if they can be substituted for each other arbitrarily in arbitrary sentences without turning a sentence (non-sentence) into a non-sentence (sentence) and without changing the meaning of sentences (see [3], p.17, for the detailed formulation3 ); let us simply grant (ii) now for the sake of the argument. While Frege’s context principle as sketched above seems to be rather plausible, P2 is certainly not plausible by itself since it is much stronger than Frege’s principle. On the other hand, Werning needs this stronger principle and not Frege’s, because he intends to apply the former not to the set X of sentences of L, but rather to the smaller set X = ObsL of observation sentences of L, i.e., those sentences that “command the subject’s assent or dissent outright, on the occasion of a stimulation in the appropriate range”, where “the sentence must command the same verdict from all 2 Note that when Werning[11] says on p.169 that “the thesis of the indeterminacy of translation stands”, he obviously does not think of meaning, but of reference. 3 According to the precise formulation, it is not really one sentence that is substituted for another, but both are used to replace one and the same variable in a common linguistic expression. However, we are going to stick to the more straightforward manner of referring to such substitutions, just as [11] does on p.156.

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linguistically competent witnesses of the occasion” (Quine[7], p.3). Y is set identical to LObs . In order to apply P2 it is important that X is cofinal in Y , and that is the main reason why Werning suggests to choose Y to be the set of all those expressions that are observation sentences or occur in observation sentences as proper syntactic parts. Moreover, if Quine is right, the closure of LObs under all syntactic operations contains “most expressions of the language”, including what is usually regarded as theoretical terms, as Werning[11], p.164, summarizes Quine’s position. Werning himself prefers to be neutral concerning the question of whether most or even all primitive expressions of a natural language actually occur as a syntactic part of at least one of its observation sentences. But note that if the vocabulary of Y were drastically smaller than the vocabulary of its underlying natural language, the argument from above would leave vast room for the indeterminacy of translation outside the borders of Y . In that case, Werning[11], p.146, could not really say that he “defends semantic realism against Quine’s (1960) sceptical challenge”, since the latter is not directed towards some small fragments of natural languages but towards the natural languages themselves. In any case, we are simply going to grant that X = ObsL and Y = LObs , and therefore also that X is cofinal in Y , which is all that is needed for the application of P2, and also of Hodges’ theorem. For simplicity, we might concentrate on the most interesting possible case, i.e., where L is identical to the syntactic closure of Y = LObs . However, none of the subsequent critical considerations depends on that point. Unfortunately, P2 is much too strong.4 Just think of the following example: let X be a subset of the set of logically true sentences that are members of a set Y ⊆ L of expressions, such that every expression of Y occurs within at least one member of X as a syntactic part; think of L, and thus of Y and X, as being interpreted by some typical Carnapian intensional meaning assignment ν, such that the ν-image of every sentence in L is the proposition expressed by that sentence, i.e., the set of worlds in which the sentence is true. X is cofinal in Y by assumption; note that this assumption can be satisfied easily: e.g., every well-formed expression in Y is a syntactic part 4 It is important not to mix up P2 with Hodges’ theorem (as stated at the beginning of section 2). Hodges’ theorem is a mathematical theorem that is provable and thus true. On the other hand, P2 is a factual hypothesis. Hodges[3] does not state a principle such as P2 at all. Of course he studies abstract versions of Frege’s context principle as well as their formal consequences, but when he speaks of “Frege’s context principle” he only thinks of the case X = set of sentences and Y = set of all expressions of a language (see [3], p.16), where ‘language’ may be assumed to denote natural languages and their formalized counterparts.

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of some sentence A of L, and every sentence A of L is a syntactic part of the sentence A ∨ ¬A which is a potential member of the set X (and of Y ). Therefore, the restriction of ν to Y is a cofinal extension of the restriction of ν to X. Let µ be that latter restriction, and assume P2: thus ν on Y must be a cofinal Fregean extension of µ. But then every two expressions of Y have the same ν-meaning if and only if they can be substituted for each other arbitrarily in arbitrary members of X without turning a member (non-member) of X into a non-member (member) of X and without changing the µ-meanings of the latter expressions. But since every member of X is logically true, every two members of X always have the same µ-meaning, i.e., the set of all worlds. Therefore, every substitution of an Y -expression A for an Y -expression B that transforms a member of X into another one can never lead to a change of µ-meanings. On the other hand, if there is a substitution of A for B, or vice versa, such that membership in X is changed, P2 entails that A and B cannot have the same ν-meaning. So for every two expressions A, B of Y , either there is one of these latter membership-changing substitutions and thus ν(A) 6= ν(B), or there is no such substitution and ν(A) = ν(B). We see that the assignment of meanings according to ν only reflects syntactic issues concerning X, which is absurd, and which leads to plain inconsistency if different sets X and Y of the above kind are considered. It is surely not the Carnapian intensional framework that can be blamed for that result, but P2. Hence, by reductio, we see that P2 is false, and the argument from above does not go through.5 Where is the crucial difference between this latter falsifying instance of P2 and our former confirming instance of P2, i.e., Frege’s context principle? While the set of sentences of a language is, presumably, sufficiently representative of the whole language in order to reflect every single distinction or coincidence of expression meaning, our subset of the set of logically true sentences is not; the meaning assignment on the latter set is simply much too coarse-grained in that respect. What about the intended application of P2 in the above argument against Quine’s indeterminacy thesis? Is the set of observation sentences, together with the meaning assignment µobs on this set, sufficient for determining identity and difference of meaning for every expression of LObs ? Consider any expression that is a part of some observation sentence in ObsL : presumably, as Frege has taught us, the meaning of this expression is indeed determined completely by the meaning of all the 5

In personal communication, M. Werning has sketched two weakenings of P2. However, for the reasons stated in this section, we do not think that any weakening could ever succeed as long as it entails that the (stimulus) meaning of observation sentences determines completely the meaning of their subexpressions.

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sentential contexts of L in which it occurs; but is it plausible to assume that its meaning is already determined completely just by the meaning of the observation-sentential contexts in which it occurs? Independently of whether that is the case or not, we now lack Werning’s original reason for an affirmative answer to the question, since P2 has failed. But it is highly probable that the answer is negative anyway, and even more so if P1 is presupposed, i.e., if it is assumed that µobs assigns stimulus meanings to observation sentences: if there were a unique “actual” meaning assignment νLObs on LObs at all, νLObs would be likely to be underdetermined empirically by µobs , just as empirical theories are underdetermined by observation. This is precisely one aspect of the indeterminacy of translation thesis: “There is an evident parallel between the empirical underdetermination of global science and the indeterminacy of translation. In both cases the totality of possible evidence is insufficient to clinch the system uniquely.” (Quine[7], p.101; cf. also Quine [6]). Independently of how “large” the vocabulary of LObs is in comparison to the vocabulary of L (recall our considerations on the choice of Y above), LObs is a non-trivial set of expressions of L, while ObsL restricts sentential contexts to observation-sentential contexts and, according to P1, µobs restricts the meaning of these observation-sentential contexts to (pairs of) stimulation patterns. The other aspect of the indeterminacy thesis – the very aspect in which the indeterminacy thesis differs from the thesis of the empirical underdetermination of theories – is the claim that there is no such unique “actual” meaning assignment on L at all, that there is no “fact of the matter” which could ever decide between rival translation manuals. If that is the case, then for precisely the same reasons as stated before it is very likely that the different possible meaning assignments on L do not coincide on LObs , because LObs is a non-trivial set of expressions of L. The only difference would be that this were now an ontological issue, not an epistemological one. Of course, it remains open whether the indeterminacy of translation thesis is true or not. But, in any case, we lack a good reason for regarding the unique total Husserlian and compositional Fregean extension µ∗obs of the (stimulus) meaning assignment µobs as “the” unique and factually determined meaning assignment on LObs , or in fact as a proper meaning assignment on LObs at all. At best, µ∗obs may be regarded to assign some kind of “empirical” meaning, i.e., “meaning-in-the-observational-set-LObs ”, to expressions, which differs from meaning in the standard sense, i.e., “meaningin-the-respective-natural-language-L”. Werning[11] does not indicate this distinction. We are going to return to empirical meaning or content in the Conclusions section. 8

There is evidence that Quine believed Frege’s context principle to be true, even though one has to be aware of the fact that Quine could not accept talking of the meaning of sentences in a literal sense. But there is surely no evidence whatsoever that he believed in a principle like P2.

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P1 vs. The Meaning of Observation Sentences

So let us turn now to the question of whether “the” meaning of an observation sentence can be identified with its stimulus meaning, as is claimed by P1. Prima facie it seems that Quine did indeed think so6 : Werning[11], p.154, quotes from Quine’s reply in Hahn et al.[2], pp.427f, to Putnam’s[4] claim that, according to Quine, the stimulus meaning of an observation sentence could not be called the meaning of the individual sentence: “On the contrary, I did intend the stimulus meaning to capture the notion of meaning–for the linguistic community in the case of an observation sentence, and for the individual speaker in the case of many other occasion sentences. It was the meanings of standing sentences that were elusive.” However, on the very same page, Quine adds the subsequent qualification of Putnam’s and of his own statement: “. . . what Putnam misses is my distinction between taking an occasion sentence holophrastically and taking it analytically, i.e., analyzed. When the infant or the field linguist learns one of his early observation sentences by ostension, he learns it holophrastically. . . it is holophrastically that their stimulus meanings are their meanings”; at a later stage, “a semantic wedge is indeed driven between the stimulus-synonymous sentences ‘Lo, a rabbit’, ‘Lo, rabbithood’, ‘Lo, undetached rabbit parts’, and the rest” (Quine, in: Hahn et al.[2], p.428). Thus, according to Quine, while the stimulus meaning of an observation sentence can be identified with its meaning if the sentence is taken holophrastically, i.e., as a single-word expression (“as a monolithic whole”, Quine[8], p.109), this is no longer possible if the observation sentence is not taken holophrastically, i.e., if it is taken analyzed as being syntactically composed of meaningful parts. If taken piecemeal, an observation sentence is theory-laden; if there is “the” uniquely determined meaning of it at all, it consists in more than just a subject’s disposition to assent or dissent to the sentence given certain stimulations, and in that 6 Just like Werning[11] we are going to ignore the obvious problem that the stimulus meaning of a sentence is only determined relative to single subject, because stimulation (types) are not subject-invariant, while proper meanings are generally regarded to be subject-invariant. See Quine[7], pp.40–44, and Quine[10], for Quine’s most elaborate accounts of stimulation and intersubjectivity.

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case “the” meaning of the sentence cannot be identified with its stimulus meaning. Let us – with Werning, who does not want to draw into question any of Quine’s premises (Werning[11], p.146) – assume that Quine is right concerning his account of observation sentences and stimulus meanings: can we take observation sentences in the context of P1, and in the context of the argument from above, holophrastically, or do we rather have to take them as being analyzed? In order to apply Hodges’ theorem, the syntactic structure of the sentences of ObsL has to be fixed uniquely; by means of the substitution function, syntactic parts of sentences have to be substituted for other subsentential well-formed items; the meaning of expressions is to be determined by their occurrence as syntactic parts of observation sentences (compare the proof of the existence part of Hodges’ theorem: see e.g. [11], p.174). Therefore, given that Quine is right, and in a context like the one above, observation sentences must be taken analyzed; hence P1 is false. Accordingly, while ‘Lo, a rabbit’, ‘Lo, rabbithood’, and ‘Lo, undetached rabbit parts’ have the same stimulus meaning, and thus the same meaning if taken holophrastically, they do not have the same meaning if taken analyzed. When the competent English speaker considers ‘Lo, a rabbit’, ‘Lo, rabbithood’, and ‘Lo, undetached rabbit parts’ as not being synonymous, it is always presupposed that these sentences are taken analyzed. If someone replied to this point by saying “no, for me ‘Lo, a rabbit’, ‘Lo, rabbithood’, and ‘Lo, undetached rabbit parts’ are indeed even synonymous”, then this would only show that some non-standard notions of synonymy and meaning are put to use. Quine himself indeed cannot say that e.g. ‘Lo, a rabbit’ and ‘Lo, rabbithood’ are not synonymous though stimulus-synonymous, simply because he does not accept synonymy as a proper, determinate and scientific notion. So when he speaks in the quotation above of a “semantic wedge” that is driven between ‘Lo, a rabbit’ and ‘Lo, rabbithood’ after the introduction of analytical hypotheses, what does he refer to? Perhaps something along the following lines: assume that while there are empirically adequate analytical hypotheses by which ‘Lo, a rabbit’ is mapped to ‘Lo, a rabbit’ and ‘Lo, rabbithood’ to ‘Lo, rabbithood’ (think of the homophonic translation), and while there are also empirically adequate analytical hypotheses by which ‘Lo, a rabbit’ is mapped to ‘Lo, rabbithood’ and ‘Lo, rabbithood’ to ‘Lo, a rabbit’, there are no empirically adequate analytical hypotheses by which both ‘Lo, a rabbit’ and ‘Lo, rabbithood’ are mapped to one and the same observation sentence (say, ‘Lo, a rabbit’). If that is the case, there is a semantic difference between ‘Lo, a rabbit’ and ‘Lo, rabbithood’ in the sense that no analytical hypotheses support an empirically adequate 10

translation mapping by which the two sentences have the same translation, although the sentences are synonymous if taken holophrastically, i.e., they are stimulus-synonymous. Stimulus-synonymy thus does “pretty well” (cf. Quine[5], pp.62f) as a substitute for synonymy of occasion sentences, but just as long as these sentences are regarded as unstructured building blocks. In order to apply Hodges’ theorem, these sentences have to be taken analyzed, which entails that their stimulus meanings are not to be identified with their meanings. This leaves us with two remaining possible cases: (i) analyzed (observation) sentences have factually determinate meanings, these meanings are “laden” with analytical hypotheses that go beyond the empirical data, and thus the meaning of an observation sentence as taken analyzed is not to be identified with its stimulus meaning; (ii) analyzed (observation) sentences do not have factually determinate meanings at all, and a fortiori the stimulus meaning of an observation sentence as taken analyzed should not be regarded as its meaning. Case (i) is the realistic option, while case (ii) is the anti-realistic one. Since Quine is sceptical with respect to meanings, we may presume that he is in favour of the latter possibility (although he does not say so explicitly in his reply to Putnam quoted above). Note that as far as ‘Lo, a rabbit’, ‘Lo, rabbithood’, and ‘Lo, undetached rabbit parts’ are concerned, it is the sentences that do not have the same meaning if taken analyzed: therefore, it is not legitimate to disregard the issue just by expressing one’s intention of not attacking the inscrutability of the reference of terms. Quine’s classical version of the indeterminacy of translation thesis is, contrary to his inscrutability or ontological relativity thesis, indeed a thesis on the level of sentences and not on the level of singular or general terms: but if Hodges’ theorem is to be applied, these sentences have to be taken analyzed, and if taken analyzed the stimulus meanings of these sentences cannot be regarded as their meanings. This is also not a point concerning the question of whether the grammatical structure of sentences can be fixed independent of meanings or not: the point is that even if the former is the case, the meanings of sentences qua analyzed expressions still cannot be identified with their stimulus meanings. If µobs really assigned stimulus meanings to the members of ObsL , the fact that µ∗obs from above is an extension of µobs would entail that µ∗obs still assigned the same (stimulus) meanings to ‘Lo, a rabbit’, ‘Lo, rabbithood’, and ‘Lo, undetached rabbit parts’, although, as we have just pointed out, these sentences do not have the same meaning qua analyzed linguistic items. One must therefore not misinterpret the transition from µobs to µ∗obs as the transition from (i) a “provisional” holophrastic assignment of one and the same stimulus meaning to the three sentences, (ii) to a “definite” analyzed 11

assignment of pairwise distinct meanings to the sentences. We see that Quine did not hold P1 true, given the context in which P1 is to be understood; more importantly, if he had held P1 true in the respective context, he would not have done so justifiedly. A final afterthought on P2 : Since P1 is now found to be false, it is not clear at all whether there is an assignment µobs of meanings (not stimulus meanings) to the observation sentences in ObsL that is determined factually and uniquely. Thus, it is also not clear at all whether µ∗obs is determined factually. Therefore, the whole point of applying P2 in order to derive the falsity of the indeterminacy thesis, or the truth of the determinacy thesis concerning meaning assignments, has vanished.

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Conclusions

The upshot of our considerations in section 3 is that P2 is false; moreover, and even more so if we are also given P1, it is unlikely that P2 can be “amended” in a way such that some small variation of the original argument might still be applicable: even if the the expressions in LObs have uniquely determined meanings, the (stimulus) meanings of observation sentences are likely not to carry sufficient information in order to determine them. In section 4 we have found that the stimulus meanings of observation sentences are not even sufficiently informative in order to determine “the” proper meanings of observation sentences uniquely if the latter are taken analyzed; since they have to be taken analyzed in order to apply Hodges’ theorem, P1 is false, too. We see that P2 and P1 fail for related reasons. Quine’s thesis of the indeterminacy of translation is left undisputed. Moreover, Quine did neither claim P2 nor P1 to be true, where in the latter case the intended context of P1 has to be taken into account. It remains to be seen whether any other use can be made of Hodges’ theorem as far as Quine’s philosophy of language is concerned. Perhaps µ∗obs from above can be regarded as assigning some “weaker” kind of meaning, say, empirical content, to linguistic expressions, rather than proper meaning. The former would be determined completely by all observational data concerning the assent or dissent to observation sentences given certain stimulations, whereas the latter transcends these data. Such empirical contents would not account for the determination of the truth conditions of sentences and thus would not be identical to what is often discussed under the term ‘meaning’, but they might still be philosophically relevant entities. E.g., they might be related to the study of empirical confirmation. It is open

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in how far the usual principles for meaning, such as the context principle, still apply to these empirical contents. As far as the assignment of such empirical contents is concerned, µ∗obs is perhaps to be preferred to Quine’s assignment of stimulus meanings to sentences. While the latter is only defined for sentences – though not only for observation sentences – the former is also defined for some subsentential expressions, i.e., those of LObs ; while every two true eternal sentences may be assumed to have the same stimulus meaning, they do not necessarily have the same images under µ∗obs (given that these eternal sentences are members of LObs or at least members of some syntactic closure of LObs ). Such an improvement over the plain assignment of stimulus meanings is even acknowledged by Quine[7], p.54, when he says that “cognitive equivalence”, i.e., stimulus-synonymy, of observation sentences can first be used in order to define cognitive equivalence of terms, such that “slight progress can then be made toward cognitive equivalence of standing sentences. Certainly they should be rated cognitively equivalent if one can be got from the other by supplanting a component term by a cognitive synonym.” Though Quine does not forget to add: “But this does not cover all the pairs of standing sentences that we would want to regard as cognitively equivalent.” The assignment of empirical content by means of µ∗obs can perhaps further be improved by defining a mapping µ∗∗ obs in the ∗∗ (B) if and only if (i) µ∗ (A) = µ∗ (B) and way, such that µ∗∗ (A) = µ obs obs obs obs (ii) there is a correlation of the subexpressions of A with the subexpressions of B such that each two correlated expressions have the same µ∗obs -image (as would be in line with Carnap’s[1] notion of intensional isomorphism). This may then be considered as the positive outcome of Werning’s[11] application of Hodges’[3] theorem to Quine’s theory. But that outcome also has its shortcomings: while the relation of cognitive synonymy in Quine’s[7] sense might be sufficient for serving some purposes in the philosophy of language, it is utterly useless as far as the interest of philosophers of science in empirical content is concerned: in order to make use of the empirical content of sentences or theories for the study of empirical confirmation, it is not such much relevant whether the empirical content of A is identical to the empirical content of B, but rather what the empirical content of A is like, i.e., in which circumstances A (or perhaps ¬A) is confirmed. Quine’s assignment of stimulus meanings, i.e., of pairs of sets of stimulations, does indeed give a partial answer to that question – notwithstanding Quine’s confirmational holism. On the other hand, this is not the case for the mapping µ∗obs as constructed according to Hodges[3], p.9, starting from the synonymy relation that is defined in the proof of Hodges’[3] lemma 13: images under that mapping are not set-theoretic constructions on stimulations but equiv13

alence classes of linguistic expressions (see also the corresponding proof of theorem 16 in [11], p.174).7 Moreover, even if µ∗obs were defined in a way, such that the µ∗obs -images were constructions on stimulations, since there is only up to isomorphism exactly one total Husserlian and compositional Fregean extension of µ, there would be no guarantee at all that µ∗obs could serve the purpose of determining or “constraining” the empirical content of sentences or theories adequately; perhaps one of its isomorphic twins would rather do the job. Acknowledgments: I want to thank Markus Werning for interesting discussions on the topic, and Johannes Brandl, as well as two anonymous referees, for valuable remarks on the paper.

References [1] Carnap, R.: 1956, Meaning and Necessity, The University of Chicago Press, Chicago. [2] Hahn, L.E. and P.A. Schilpp (eds.): 1986, The Philosophy of W.V.Quine, Open Court, La Salle, Illinois. [3] Hodges, W.: 2001, “Formal Features of Compositionality,” Journal of Logic, Language, and Information 10, 7–28. [4] Putnam, H.: 1986, “Meaning Holism,” in: Hahn[2], pp.405–426. [5] Quine, W.V.O.: 1960, Word&Object, The M.I.T. Press, Cambridge, Massachusetts. [6] Quine, W.V.: 1970, “On the Reasons for Indeterminacy of Translation,” The Journal of Philosophy LXVII, 178–183. [7] Quine, W.V.: 1992, Pursuit of Truth, Harvard University Press, Cambridge, Massachusetts. [8] Quine, W.V.: 1993, “In Praise of Observation Sentences,” The Journal of Philosophy XC, 107–116. 7

So that mapping µ∗obs does not assign “neuronal meanings” to linguistic expressions, contrary to what is said in Werning[11], p.165. For the same reason, meaning assigment according to that particular mapping is “anti-realistic” in the sense of [11], p.161, contrary to the “realistic” intentions of [11]. Of course there might also be isomorphic “realistic” meaning assignments, but these have not been defined by Hodges or Werning.

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[9] Quine, W.V.: 1995, From Stimulus to Science, Harvard University Press, Cambridge, Massachusetts. [10] Quine, W.V.: 1996, “Progress on Two Fronts,” The Journal of Philosophy XCIII, 159–163. [11] Werning, M.: 2004, “Compositionality, Context, Categories and the Indeterminacy of Translation,” Erkenntnis 60, 145–178.

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