Translational Indeterminacy and Substitutional Quantifiers

In the paper which follows we DENY Quine’s thesis of Translational Indeterminacy on the level of observational terms by outlining a procedure for confirming analytical hypotheses.

Translational Indeterminacy and Substitutional Quantifiers

by James D. Carney (Arizona State University) and Zak Van Straaten (University of the Witwatersrand)

published in: Foundations of Language Vol 11 No. 4 July, 1974. D. Reidel Publishers, Dordrecht, Holland and Boston, U.S.A.


In Word and Object and in other places Professor Quine presents his thesis of translational indeterminacy. It is the thesis that:

Manuals for translating one language into another can be set up in divergent ways, all compatible with the totality of speech dispositions, yet incompatible with one another. In countless places they will diverge in giving, as their respective translations of a sentence of the one language, sentences of the other language which stand to each other in no plausible sort of equivalence however loose. (1)

Quine’s argument for his thesis has been the object of considerable criticism, ranging from the claim that he has no argument for his thesis if we take at face value his own behaviouristic criterion of meaning;(2) to the claim that if we follow out the consequences of his thesis the result is that no one can know what he means.(3)

Most of these criticisms, we believe, rest on the example of an everyday observational term such as Quine’s ‘Gavagai’ which Quine uses in one place to explain and defend his thesis. Indeed Quine has recently said that his ‘Gavagai’ example has played too central a role in the discussion of his indeterminacy of translation thesis.(4) Critics judge the thesis on the basis of its examples, so that if the thesis is unreasonable for ‘Gavagai’, then the thesis is unreasonable. Quine’s counter to this is that his thesis is better grounded in the fact that physical theory is empirically undetermined, with the result that there could be two or more theories logically incompatible and empirically equivalent with respect to possible observational evidence. In this case the totality of possible observations of nature may be compatible with systems of translation from one physical theory to another which can specify sentences that are mutually compatible. And if critics see this they are more likely to concede the thesis on the level of everyday observational terms such as ‘Gavagai’. Whether physical theory is undetermined by all possible observation and whether, thus, indeterminacy can break out on the level of physical theories will not be considered in this paper. Nor will the questions as to whether there are methodological objections to Quine’s thesis. We shall rather try to deny Quine’s thesis on the level of observational terms by outlining a procedure for confirming analytical hypotheses. This procedure relies on a certain extensional language in which the quantifiers are interpreted as substitutional quantifiers, If the results of this paper are correct, then one consequence is that, either theories cannot be logically incompatible and empirically equivalent or indeterminacy or translation does not move from the upper levels of theories down to everyday talk about the objects around us.

We begin with what in this paper is being identified as the thesis of translational indeterminacy.


In any natural language there will be observational terms, learned by the method of ostension, where the spatio-temporal objects provide the reinforcing stimuli; for example (for most of us) terms such as ‘mama’, ‘water’, ‘red’, ‘round’, ‘earlier than’, and ‘rabbit’. In Quine’s well-known example, a linguist attempts to translate such terms e.g., ‘gavagai’ from the unknown language, Foreign, to the home language, Familiar. (5) A linguist first considers the sentence ‘There is a rabbit’ as a possible translation for ‘Gavagai’ and he can go about establishing this hypothesis inductively. We suppose that ‘Gavagai’ is an observation sentence, that is, it is one on which all the speakers of Foreign give the same verdict when given the same concurrent stimulation. (6) We can determine the range of stimulation that would prompt assent or dissent to ‘Gavagai’ (the stimulus meaning of the sentence), and the range that would prompt assent or dissent to ‘There is a rabbit’ in Familiar (its stimulus meaning) and if they are identical we can translate one into the other. The import of such a ‘translation’ is that the two sentences are stimulus-synonymous.

The stimulus-synonymy of ‘Gavagai’ and ‘Rabbit’ does not, however, guarantee that ‘gavagai’ and ‘rabbit’ are coextensive.(7) Even supposing that ‘gavagai’ is a general term, it is possible that the object to which ‘gavagai’ applies are not rabbits after all, but mere stages of brief temporal segments of rabbits. Thus in order for a linguist to confirm his analytical hypothesis that ‘gavagai’ means ‘rabbit’, he must first determine how the user of Foreign individuates or conceptualizes his experiences, if ‘gavagai’ is a term of divided reference as is ‘rabbit’. Does the speaker of Foreign apply the term to enduring and homogenous three dimensional objects in space and time or does he individuate his experience in terms of stages (‘gavagai’ as true of a number of individuals, each of them being a brief stage, a particular temporal, spatial spread, bearing a rabbit kinship relation to each other). Perhaps the individual to which ‘gavagai’ applies are detached parts of a rabbit, not homogenous object. The possible ways a Foreigner might individuate his experiences are almost limitless. The Foreigner may be an immaterialist and organize his experience in terms of qualities, space, and time, or ‘gavagai’ might even be a singular term naming a Goodman-like particular, a rabbit fusion, the single though discontinuous portion of the world that consists of rabbits.

The thesis of indeterminacy, as understood in this paper, is that more than one analytical hypothesis for the term ‘gavagai’ and for synonymity-hypothesis for the sentence ‘Gavagai’ (‘Rabbit’, ‘Rabbit stage’, and ‘Undetached rabbit part’) can be compatible with the totality of possible observations of the Foreigner’s speech dispositions to respond to stimulations and that this has nothing to do with normal uncertainty of inductive inferences. To clear up the question of the reference of a term, if the term is a term of divided such as ‘rabbit’, one may of course try to ask questions such as “Is this gavagai the same as that one?” while making the appropriate ostensive gestures and in this way try to make progress towards settling which analytical hypothesis for ‘gavagai’ is likely to be correct. But for this to work linguist must verify an analytical hypothesis relating his notion of identity of a Foreigner’s expression. But here also the translation of a Foreigner’s expression as ‘is the same as (identity)’ can be as compatible with behaviour as one which, say, translates that expression as ‘belongs with.’ (8) Consequently we are left with an inscrutability of reference with respect to the Foreigner’s terms; we cannot even determine what expressions in Foreign are quantifiers or the identity sign, if they have such logical terms. Assuming that the recognition of assent of dissent is unrelated to analytical hypotheses, the only analytical hypotheses we can possibly confirm are those treating truth-functional connectives. (9) Outside of these hypotheses, the question as to which is the correct analytical hypothesis for any linguistic expression is without significance. “The point is… that there is not even… and objective matter to be right or wrong about.” (10)

There are important consequences of our inability to confirm analytical hypotheses. (1) We cannot even establish stimulus synonymity of non-occasional sentences (occasional sentences being sentences for which stimulation can prompt assent or dissent), since to do this we must rely on analytical hypothesis. And more than one set of analytical hypotheses, and more than one set of analytical hypothesis for Foreign-to-Familiar translation is possible. Two or more Foreign-to-Familiar dictionaries and grammars can each be compatible with the speech dispositions of the speaker of Foreign. Thus the translation of non-occasional sentences using these different manuals can result in contrary sentences, each of which is a translation of a given sentence in Foreign. (2) Our inability to confirm analytical hypotheses prevents the successful conjecture that terms are stimulus-synonymous. If we could detect logical terms, then we would pick out the predicates and logical terms in, say, ‘All F’s are G’s’ in which case the confirmable fact that ‘All F’s are G’s’ and ‘All G’s are F’s’ is ‘stimulus-analytic’ in Foreign, (11) – the speaker asserts it, or nothing, after every stimulation, come what stimulation – establishes the stimulus-synonymity of F and G in Foreign. In turn, if we can detect the logical structure of ‘This is a gavagai’, its being stimulus-synonymous with ‘This is a rabbit’ would confirm that ‘gavagai’ is stimulus-synonymous with ‘rabbit’. But our confirming abilities are limited to analytical hypotheses treating truth-functional connectives.

It goes without saying that linguists from one culture are generally in agreement with respect to the correct manuals for Foreign. As the ‘gavagai’ example has been explained, two or more of our English linguists would not hesitate in entering “‘gavagai’ means ‘rabbit’” in their manuals. The reason for this, according to Quine, is that linguists from culture are influenced by shared presuppositions which are not inductively verified by observing a person’s current dispositions to respond verbally to stimulations. For example, if our linguists go on to translate ‘gavagai’ as ‘rabbit’ they would be influenced by their natural expectation that any people in rabbit country would have some brief expression for “the most conspicuously segregated wholes” that could best be translated ‘rabbit’. Or else they would be influenced by the maxim that observational terms denote enduring and relatively homogenous objects moving as a whole against contrasting backgrounds. (12)Charles Landesman has recently argued that one can have strong evidence for such presuppositions (13). For example, the first assumption may be supported by psychological laws of least action for which there can be physiological correlates. If these physiological states are species invariant, then we would have evidence for the first assumption. However Quine’s thesis of indeterminacy on either level does not imply that behavioural evidence is all the evidence that there is for analytical hypothesis. Rather evidence to prove or disprove the thesis is restricted to the bounds of speech dispositions, for the thesis is that rival manuals for translating one language into another can each conform to all speech dispositions and yet yield disparate translations.


It seems reasonable that if the linguist can confirm analytical hypotheses covering quantifiers, identity and other logical terms, then he can ask the appropriate questions that would provide the necessary verbal behaviour for inductively confirming other analytical hypothesis treating observational terms such as ‘gavagai’. Once analytical hypotheses at this level are admitted nothing in principle should rule out confirming or disconfirming analytical hypotheses at all levels; thus rival sets of analytical hypothesis for Foreign can be eliminated, and consequently contrary sentences, each candidate for a translation of a sentence in Foreign are eliminated.

We now sketch a language in which the quantifiers are to be construed as substitutional by anyone learning or detecting the language. This language can be detected or learned from us but users of Foreign if it is part of Familiar, or we can detect or learn it from the users of Foreign if it is part of Foreign. In what follows, we will suppose that this language if part of Foreign. If the linguist can inductively detect the elements of this language, then this will allow him to confirm analytical hypotheses covering logical terms including identity, and thus eliminate indeterminacy.

The language, L, is made up of the following materials: truth-functional statement connectives, quantifiers, individual variables, and the identity sign. It also comprises predicates and individual constants sufficient to distinguish one concrete object from another, a concrete object being an individual in space and time. For this purpose the language will contain the following kinds of predicates: terms for shape (e.g. round), terms for temporal relations (e.g. earlier than), terms for spatial relations (e.g. between), and, if necessary, terms for sensible qualities (e.g. red). The individual constants will be indicator terms (e.g. this, that, there) which can act as names for each individual in the immediate sensory environment at any time. All the predicates, it will be supposed, can be learned by the method of ostension.

If the user of Foreign had such a language, how could it be inductively confirmed which expressions are quantifiers, which are predicates, and so on? The presence of truth-functional connectives could be confirmed by assent and dissent behaviour. Quine makes the point that there are no assent and dissent behavioural conditions for interpreting a Foreigner’s expression as objectual quantifiers and variable (because we could not distinguish vacuous names from real names, a point we return to in a moment). But granting this point does not rule out the possible existence of empirical conditions for interpreting a Foreigner’s expression as a substitutional quantifier. The substitutional interpretation of an existential quantifier expression, (Ex) Fx, would be ‘Some substitution instance of Fx is true’, while for the universal quantifier it would be ‘all substitution instances of Fx are true’. The objectual interpretation would be, respectively, ‘There is something which is F’ and ‘Everything is F’ – the customary interpretation of quantifiers. While there are no assent and dissent conditions for interpreting a Foreigner’s expression as an objectual existential or universal quantifier, there can be such conditions for interpreting a native’s expression as a substitutional quantifier, and such conditions are easy to formulate. For example, having settled on a candidate for existential substitutional quantifier and variable, a behavioural condition for our being correct is that the Foreigner is disposed not to dissent from each of the sentences obtainable by dropping the quantifier and substituting for the variable. A second condition is that the Foreigners be disposed to assent to the whole whenever disposed to assent to one of the sentences obtainable by dropping the quantifier and substituting for the variable. As in the case of truth-functional connectives, such test conditions are inductive and do not yield the highest level of certainty, but they provide reasonable inductive evidence, and this is as far as we need to go in confirming analytical hypotheses (if this is possible).

The occurrences of the indicator terms in the subject position when substitutional quantifiers are dropped is not sufficient for judging correctly that these terms in such a position are names for environmental objects rather than vacuous names such as ‘Santa’ or ‘Pegasus’. Quine has pointed out that “the very notion of a singular term appeals implicitly to classical or objectual quantification”. What counts as conclusive evidence that an expression a is used as a name of an object is if in the language one affirms (Ex) (x = a), where the quantifier is interpreted objectually. (14) But this does not in fact block detecting singular terms in L. Ways are available. First, the fact that an expression appears in the subject position of atomic sentences and can be replaced with behavioural gestures would confirm that the expression names an object and is not a vacuous term such as ‘Pegasus’. Second, to confirm that the expression is a vacuous name, we should expect that in such cases each stimulation would leave the speaker of L prepared to assent to the given sentence or to assent to its negation. Such a response would confirm that the term is a vacuous name. Detecting what expressions are predicates should now offer no special problems. Quine point outs that in translating Foreign expression such as ‘red’ and ‘round we would be in the same predicament as with ‘gavagai’, in that neither the method of teaching these terms nor the use of the terms by the Foreigners would indicate whether they are used before ‘is’ or after ‘is’. (15) The latter is true for L but is not for L(sq) – L with quantifiers substitutionally construed. If they occur in the predicate position, then they are to be construed as concrete general terms, terms true of many concrete objects; and if they occur in the subject position, then they are abstract singular terms, names which purport to name single abstract objects. But with quantifiers and variables in hand, the way these terms true of many objects since they appear in the predicate position.

Let us now suppose that ‘gavagai’ or any other concrete general term is admitted to L(sq). We need to see now if we can settle whether ‘gavagai’ in this language is a name for a concrete object, and, if so, how the Foreigner individuated the objects of his experience. Its appearance in the predicate position and the Foreigner’s affirmation that if x is gavagai then it has spatial and temporal properties will confirm that the term is a concrete general term. If one can now ask the simple question, ‘Is this gavagai the same as that one?’ then one could adjudicate between sets of hypotheses concerning how the Foreigner individuate the objects of his experience, as enduring homogenous objects, parts, stages, and so on. This is true for objectual identity, i.e. a sign satisfying strong reflexivity, substitutivity, and Leibniz’s Law, where the quantifiers are interpreted objectually. In asking such simple identity questions which use objectual identity, we are in effect asking if this and that individual is the same individual. And an affirmative answer to such questions tells us that for the Foreigner this and that individual are indistinguishable in the language, in terms of any properties, including relational ones. In asking simple identity questions using substitutional identity, one would be asking if the demonstrative singular term ‘this’ names the same object as the term ‘that’. In receiving an affirmative answer, we are told that names for what ‘this’ and ‘that’ name can be interchanged in sentences in the language without affecting truth-value, for what ‘a is (substitutionally identical to) b’ implies, is that every substitutional instance of ‘Fa if and only if Fb’ is true, not that for any a and b, Fa if and only if Fb. Being told the former by the Foreigner would be of little help unless L(sq) satisfies two conditions: It must be extensional and, at least with respect to indicating and separating individuals or our experience, it is sufficiently rich in predicates.


Supposing that there can be an extensional language L rich enough in predicates to demarcate concrete objects of experience, this language, together with indicator terms, could be a part of Foreign. The presence of the quantifiers interpreted as substitutional quantifiers can be empirically detected in terms in L which can act as singular terms for all the individuals in the immediate sensory environment of the Foreigners. The detection of these terms does not fall back on interpreting quantifiers as objectual, but either on their replaceability by ostensive gestures when they appear in atomic sentences, or on their elimination as vacuous names by the failure of atomic sentences to be stimulus-analytic. The predicates are detectable via their grammatical position and their being learned by ostensive method. With the introduction of a term such as ‘gavagai’, position and dissent or assent, when spatial and temporal predicates are applied to the gavagai extension, would confirm that the term is a general concrete term. Since the language in question is rich enough in predicates to separate and distinguish individual of experience, identity questions, interpreted as substitutional identity, will aid inductively in confirming how the Foreigner individuates his experience. If now on can translate sentences in L construed substitutionally, L(sq), into sentences of a L construed objectually, L(oq), then our identity questions will not need to fall back on the above set of predicates.


Substitutional quantifiers are not part of the standard grammar of classical logic because: (a) they cannot apply, for obvious reasons, to an empty universe or an infinite universe; (b) they cannot apply to those objects in a non-empty finite universe which lacks names; (c) they are not eliminable in favour of objectual quantifiers in a system and cannot be characterised as merely simulated quantifiers since the quantifiers since the quantifiers in a system are not introduced by contextual definition. This means that the substitutional quantifiers cannot be a special instance of the objectual ones with the set of names as the domain and the variables taking names as values; and (d) Gödel’s strong completeness result for a standard predicate calculus cannot be obtained when the quantifiers are substitutionally construed. (16)

Because of (a) and (b), Translation from L(sq) to L(oq) is suspect. For example, if every individual in the domain of discourse does not have a name, (Ax)Fx, substitutionally interpreted could be false since in the latter interpretation (Ax)Fx is true if and only if everything is F. And for a translation from L(sq) to L(oq) to be successful, truth-value must be preserved. The possible sentences from L(sq) that could resist translation into L(oq) are those containing vacuous names, those related to an empty universe, and those related to an infinite universe, and those related to a universe with nameless objects. We have suggested two ways to eliminate the alternative that sentences in L(sq) contain vacuous names, and we do not need to account for sentences related to infinite or empty universes since we can confirm that L(sq) deal with neither. And confirmation of indicator terms will assure us that L(sq) is sufficiently rich in names for the observable objects in the immediate environment.

James D. Carney, Arizona State University
Zak Van Straaten, University of the Witwatersrand, Johannesburg


^1 Word and Object, The MIT Press, 1960, p.27
^2 Steven Davis, ‘Translational Indeterminacy and Private Worlds’, Philosophical Studies XVII (1967) 38-45
^3 M.C. Bradley, ‘How Never to Know What You Mean’, The Journal of Philosophy LXVI, No. 5, March 1969 pp. 199-124
^4 ‘On the Reasons for Indeterminacy of Translation’, Journal of Philosophy (1970) 178-185
^5 Word and Object, Chapter II, ‘Translation and Meaning’.
^6 Quine, ‘Epistemology Naturalised’, Ontological Relativity and Other Essays, Columbia University Press, pp. 85-86.
^7 Word and Object, p. 68.
^8 ‘Ontological Relativity’, Ontological Relativity, p.33
^9 ‘Existence and Quantification’, Ontological Relativity, pp. 104-105.
^10 Word and Object, p.73.
^11 Ibid., p.55.
^12 Ibid., p.74.
^13 Charles Landesman, ‘Scepticism About Meaning: Quine’s Thesis of Indeterminacy’, Australian Journal of Philosophy (1970) 320-337.
^14 ‘Existence and Quantification’, p. 94.
^15 ‘Ontological Relativity’, p.39.
^16 See Quine, ‘Existence and Quantification’, pp. 91-94, and Dunn and Belnap, ‘The Substitution Interpretation of the Quantifier’, Nous 11, No. 2, May 1968.