Jason Bridges

Phil340,W02-lecture 16 notes



Final paper topics will be given out on Thursday

Second papers will be available for pick-up by the end of the week.


So far we’ve looked at various aspects of the notion of linguistic meaning, and at various views about how these aspects are to be understood, and about how they connect both with each other and with other non-linguistic phenomena, notably, psychological phenomena like beliefs and intentions.

We are going to finish off by looking at doubts that have been raised about the very idea of linguistic meaning.  These are arguments designed to show that our talk of meaning in one way or another does not have the substance we are inclined to accord it.

We will begin with Quine’s argument for what he used to call the inscrutability of reference and now calls the indeterminacy of reference.

Afterward, we will look at an even more corrosive doubt voiced by Kripke in an attempt to interpret Wittgenstein.


I. Quine on indeterminacy: preliminaries

What is the indeterminacy of reference?  There is unfortunately some confusion in the secondary literature over what the thesis is even supposed to be, let alone how it is to be argued for.

Two theses, both held by Quine, must be distinguished.  Recall first of all the ideas of reference and extension, and how they manifest in axioms of a theory of meaning.  [Axioms for referring expressions.  Simplified version of axioms for predicates, and how this motivates the notion of extension.]


The two theses are:

For any theory of meaning x for L, there exists another theory of meaning y for L such that: x and y differ systematically in the references and extensions they assign to expressions of L, and yet x and y entail precisely the same set of T-sentences.


For any language L, there is no fact of the matter about what the referring expressions of L refer to, or about what the predicates of L have in their extension.


Commentators differ over which of these to call the thesis of the indeterminacy of reference.  But clearly it is only appropriate to so call the latter, for it is only the latter that gives voice to the idea that reference is indeterminate, that there is no fact about what any expression refers to.  What we shall see is that the first thesis is a crucial step in Quine’s argument for indeterminacy, but it certainly does not get one there all by itself.  Just for expositional sake I shall call the first thesis the availability of systematic reference permutation.


We’ll talk more about the former in a moment.  Let me quickly first say something about the latter, about the indeterminacy of reference properly so called.  The claim is simply that there are no such facts as:

“Kripke” refers to Kripke.

“Snow” in English refers to snow.

The predicate “is white” in English is true of white things.

No such sentence is true.   But nor are they false.  There are no facts about reference or extension.  This is obviously a radical and apparently disturbing claim.  In Quine’s view it is not really either: as we shall see, it’s the natural upshot of viewing the phenomena of meaning and communication in an unprejudiced way.


Another preliminary point: Quine doesn’t talk about theories of meaning at all.  He prefers to talk about translations.  So he would put the former thesis in something like the following way: For any translation of language L into language M, there exists a different translation of L into M that differs in its reference assignments to expressions of L but not in what it says or implies about whole sentences of L.

But in talking this way Quine is making a mistake.  In fact, translations properly so-called needn’t say anything about reference at all.  Reference is a notion that has its home in theories of meaning, not in translations.



A theory of meaning for O in M entails for every sentence of O a statement in M of what that sentence means.  (It is Davidson’s view, as we have discussed at length, that such a theory must respect the following constraints:…)

A translation manual from O to M provides a way of generating, for every sentence of O, a sentence in M that has the same meaning.

These are crucially different demands, although they may not seem so at first.  The crucial difference is this: translations manuals do not say what sentences in O mean.  Thus there is no reason for them to be subject to Davidson’s constraints.



“La neige est blanche” in French is true iff snow is white.

“La neige est blanche” in French is translated in English by “Snow is white”

The second sentence says nothing about what “La neige est blanche” means.  It does not give the truth-condition of that sentence.  Of course, if one understands the quoted English sentence, one will be in a position to derive, from the fact that the French sentence has the same meaning, the truth condition of it.  But the translation sentence does not explicitly state that fact.

This is made vivid by reflecting on the fact that translation manuals can be stated in languages different from either the language being translated or the language its being translated into.  That is, the real parallel with a theory of meaning for O in M is a theory of meaning from O1 to O2 in M.

“La neige est blanche” in French is translated in German by “Der Schnee ist weiss”.

Here it’s quite obvious that one could be told this sentence and understand it but not thereby know the truth-condition of the French sentence.  The earlier sentence, in which the meta-language of the translation manual is the same as one of the object-languages, no more states a truth-condition that this one.


Translation manuals do not state the meanings of an object language.  They simply associate two object languages together (and they may do so in a language different from either).

So the ‘axioms’ of a translation manual will be different from those of a theory of meaning.  Forgetting about the complications about mass-terms we discussed earlier:


“Snow” refers in English to snow.

“La neige” in French is translated in English by “snow”.


In the second of these there is no mention of reference at all.  Translation manuals simply don’t need to talk about truth, reference or any semantic notion but that of synonymy.  And synonymy is a relational expression: it can be stated to hold between pairs of expression without anything at all being said or implied about what further semantic properties these expressions might have on their own.

So if we are to find in Quine an argument to the indeterminacy of reference, we must reinterpret what he says in terms of theories of meaning, although he himself does not talk that way (and would in fact be loathe to do so).  I’m going to talk explicitly in terms of Davidsonian-style theories of meaning, because that’s the kind of compositional theory of meaning we’ve discussed here.

Next time, we’ll see that Stroud thinks it’s not a mere slip, but extremely revealing, that Quine speaks in terms of translation.


II. The argument

We can gloss Quine’s argument for the indeterminacy of reference as follows:

1.      Systematic reference permutations are always available (see above).

2.      The only evidence in principle available to an interpreter of a given speaker’s language is utterances by that speaker of whole sentences.

3.      There are no facts about what a speaker’s expressions mean that are not in principle available to an interpreter.

4.      Therefore, reference is indeterminate (from 1, 2 and 3).


The soundness of this argument turns on four things: whether premises 1-3 are true, and whether the inference from them to the conclusion is sound.

I shall talk about each in turn, the three premises today, and the inference next time.


III. First premise

Quine argues for the availability of systematic reference permutations in two ways.


1.  First, through the famous example of “gavagai”.

Suppose we are radically interpreting some language.  We observe that the speaker in question always says, “Gavagai,” when a rabbit scampers by, and refuses to say, “gavagai” otherwise.  We are thus inclined, given the principle of charity enjoining the ascription of true beliefs about simple stuff, to suppose that the speaker’s sentence is true iff a rabbit is present.


Fair enough.  Quine wouldn’t have anything to say about this yet.  But now suppose we take the step of adopting the following axiom:

“gavagai” is a common noun whose extension is the class of all rabbits.


No actual, rigorous theory of meaning would use a premise quite like this (wouldn’t make uncritical use of that semantic category), but that’s not to the point.

With this axiom, coupled with theorems for dealing with sentences composed of one word—which, might for example, see these sentences as short for sentences having more words, say words meaning, “are present”—we could entail the axiom:

The sentence, “Gavagai!” is true iff a rabbit is present.

This is the result we sought.


But suppose instead we, perversely, decided to opt for this axiom:

“gavagai” is a common noun whose extension is undetached rabbit parts.

We’d still get the same truth condition, for undetached rabbit parts are present iff rabbits are present….


Same result with any of the following:

“gavagai” is a common noun whose extension is the class of all temporal stages of rabbits.

“gavagai” is a mass term referring to rabbit-stuff.

“gavagai” is a referring expression referring to the total sum of rabbits on the earth.

These axioms all portray the term, “gavagai”, as functioning in very different ways, as having different references and/or extensions.  But all of this, according to Quine, is consistent with the premise that the sentence, “Gavagai!” is true iff a rabbit is present.  For whenever a rabbit is present, then there is something in the environment that falls into the extension or reference of any of these proposed expressions.  And whenever a rabbit is not present, none of the expressions apply.


One might object that Quine is here missing that we are trying to construct a theory of meaning for the whole language, one that gives the right truth-conditions for every sentence, not just this one.  And so we have to understand the semantic properties of “gavagai” in such a way as so as to give it the proper role in every sentence in which it occurs.

But Quine would say we could do so in any of these cases, simply by changing our interpretation of other terms accordingly.


Suppose we came up with the hypothesis that the expression, “boogaloo” means ‘is the same as’.  Then we could ask the speaker whether this gavagai is the same as that one.  So we point to a rabbit’s foot and then the same rabbit’s ear.  Or to different one’s  Here it would seem we’d have a method for deciding between the first two choices….  (chart it out)

But in fact the second hypothesis can still be accommodated to this data.  All we do is change our hypothesis about “boogaloo”, holding that it means ‘belongs with’.

Similar compensatory judgments, says Quine, are always available.


Now, it has been argued by Gareth Evans that this example doesn’t succeed, that there is a type of data that Quine does not think of.  These are sentences combining terms like “gavagai”.  Say, “thewly” is asserted by itself iff a red thing is present.  Then we might look into the conditions under which “thewly gavagai” is asserted.  When a wholly red rabbit is present?  When a rabbit that is not red but has a red part is present?  And one sees how this would go.


I’m not going to get into this discussion here.  It’s moot for our purposes, for Quine has a different and unassailable way of making his point.


2.  The notion of a proxy function.

A proxy function is a one-to-one mapping of every object in the universe onto another object in the universe (doesn’t actually have to be one-to-one or onto objects in the same universe, but ignore these complications.)  Such functions exist; infinite numbers of them do, even if we can’t specify them fully.  So for example there’s the function that maps….


So let p be a proxy function.  Let T be a theory of meaning for a language L.  Then let T* be the theory of meaning for L such that: whenever according to T a name n refers to an object x, then according to T* n refers to p(x); whenever according to T a predicate is true of an object x, then according to T* the predicate is true of p(x).

Then T and T* will assign identical truth conditions to all sentences.


For consider:

If T entails: “Sally is a gloomy person” iff Sally is a gloomy person

Then T* entails: “Sally is a gloomy person” iff the proxy of Sally is the proxy of a gloomy person.

Same truth conditions!


To make this clearer, consider the relation, “is the shadow of” (an example I got from Davidson, I believe).  This won’t work as a proxy function because not every object has (or is) a shadow, but setting this aside, we’d get:

On T*: “Sally is a gloomy person” iff the shadow of Sally is the shadow of a gloomy person.


So systematic reference permutations are indeed always available.