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Field's Challenge

Hartry Field http://www.nyu.edu/gsas/dept/philo/faculty/field/photo.jpg On the radical versions of deflationism that I prefer, it doesn't make sense for X to ask whether one of Y's sentences is true as Y really intended it, but only whether it is true as X understands it
—Hartry Field, p. 406n of "Disquotational truth and factually defective discourse." Philosophical Review, 103:405–452, 1994.

Field's Challenge

Field's picture is something like this: We speak two different languages. I translate your language, $ {\mathcal L}' $ , into mine, $ {\mathcal L} $ , via a translation function $ *:{\mathcal L}'\rightarrow {\mathcal L} $ , and you translate my language into yours via a translation function $ {@}:{\mathcal L}\rightarrow{\mathcal L} $ . I compare my beliefs with my version of yours; you compare your beliefs with your version of mine. There is, according to Field, no way to get across the linguistic barrier.

I am, here and below, using Field's choice of symbols in discussing his work (pp. 421–422 of "Are our logical and mathematical concepts highly indeterminate?" In French et al., eds., Philosophical Naturalism, 391–429. Notre Dame, 1994).

Field's Challenge

In the quote, Field says we cannot arrive at a common "understanding." Since I don't know what an understanding is, I have no quarrel with that, but in fact he argues for a much stronger claim.

Field's Challenge

Field's Claim
One cannot have good reason to believe that the translation of a predicate has the same extension as the original predicate.
He holds that we can't even reach agreement about what objects satisfy predicates.

Field's Challenge

Suppose you have a predicate, $ \text{Wolf}' $ , in your language that I have observed you to apply to all wolves I have observed you to observe and to nothing else. I might reasonably decide to set $ \text{Wolf}{'}^{*} $ , my translation of your term, to Wolf, but I do not have enough evidence to do so: I might, with equal propriety set $ \text{Wolf}{'}(x)^{*} $ to $ \text{Wolf}(x)\lor\text{TasmanianWolf}(x) $ : A Tasmanian wolf is a marsupial that resembles a wolf. It is disputed whether or not the Tasmanian wolf is extinct. I have no access to Tasmanian wolves, and so I am in no position to show you one.

Field's Challenge

I am not in a position to conclude that $ \text{Wolf}=\text{Wolf}{'}^{*} $ , that is, that it is appropriate to translate your $ \text{Wolf}' $ as Wolf, but only that $ \text{Wolf}\subseteq \text{Wolf}{'}^{*} $ , that is, that I must choose a translation $ \text{Wolf}{'}^{*} $ such that the wolves are among the $ \text{Wolf}{'}^{*} $ s.
more...close
Field has argued, for an arbitrary predicate $ ' $ $ W' $ , that in principle all I can have reason to conclude about a proposed translation $ W $ is that
\[ W\subseteq W'^{*}. \]
Similarly, you will at best be able to conclude
\[ W'\subseteq W^{@}. \]
I can then translate your conclusion to obtain
\[ W'^{*}\subseteq W^{@*}, \]
which I can combine with my conclusion above:
\[ W\subseteq W'^{*}\subseteq W^{@*}. \]
If I could somehow conclude that
\[ W'^{@*}\subseteq W, \]
all the inclusions would be equalities, and I would have a reason to take my translation to be correct.

Field uses numbers, not wolves, and hyperfinite numbers, not Tasmanian wolves, but that, so far as I can see, makes no difference.

Obvious Reply to Field

The obvious reply to the argument is that I can ask you whether or not, for example, your term wolf could apply to any marsupials.

That reply won't do, since we speak different languages. I will apparently have to translate my question, then translate your answer. Field will, quite reasonably, argue that the indeterminacy of the translation will render the (translated) answer to the (translated) question useless.

Ground Rules

Field's argument relies heavily on an implicit theory of what can count as evidence that a translation is good. For example, I might conclude that I have good reason to translate your $ \text{wolf}' $ by wolf because we speak a common language, and your word sounds like—is homophonic with—mine. Why does Field reject, along with many other possibilities, that we have good reason to adopt the homophonic translation?

Radical Translation

Quine actively pursued a program of analyzing what we could learn about the language of another by engaging in radical translation: translating the foreign language without assuming that the speaker or the language had anything in common with the translator or the translator's language.

Word and Object. M. I. T., 1960.

Radical Translation

Radical translation was ideally to be based solely on the observed behavior, including the linguistic behavior, of the foreign speaker. After all, Quine thought, we do learn language solely on the basis of observed behavior, including linguistic behavior. In fact, behavior alone is not enough. One needs at least one propositional attitude to get started. Quine chose assent and dissent.

Radical Translation

Quine used radical translation to argue against a traditional theory of linguistic meaning. He showed that radical translation does not preserve the semantic relations postulated by the theory (most notably, reference), and concluded that those relations cannot play a role in language acquisition and, therefore, in language use.

Radical Translation and Field

Field's notion of translation seems to be Quine's radical translation, but why? Field's project is intended to support a form of deflationary semantics. Like Quine, he uses radical translation to attack traditional components of semantic theories. The argument I have been discussing attacks the utility of extensions of predicates for purposes of semantics.

Radical Translation Is Usually Dismissed

There is comparatively little interest in radical translation today. Some, I think, dismiss it for Moorean reasons, but the main reason is that the downfall of behaviorism took radical translation with it: We do not acquire language solely on the basis of observed behavior, including linguistic behavior: we exploit innate tendencies and the considerable cognitive and perceptual similarities that exist between us and those from whom we learn a language.

New Niche for Radical Translation

If the Quinean project is moribund, why should Field and I still care?
  1. We are both interested in how language can be used to communicate about mathematics. In that
  setting, the move away from behaviorism makes comparatively little difference. Cognitive and
  perceptual similarities may help in learning how to use "rabbit," but they do not seem to help in
  learning "set" or "number," especially when one focuses on such notions in their fully abstract
  mathematical sense.

New Niche for Radical Translation

If the Quinean project is moribund, why should Field and I still care?
  2. Just as it is of interest to know not only what language is used to convey, but also its literal
  meaning, it is of interest to know what part of that literal meaning is conveyed solely in virtue
  of the publicly available features of the language, and that part of what is conveyed is just the
  part that is preserved by radical translation. That is of interest in itself, since that is the
  part of what is conveyed that is conveyed solely in virtue of the use of language, and because it
  will presumably be useful in sorting out what is conveyed as a result of such extralinguistic
  features of communication as common innate mechanisms and perceptual systems.

Quine's Radical Translation Doesn't Work

Davidson pointed out that Quine's proposed method of radical translation can't work.
We can't assume that the person whose language we are translating shares our beliefs and desires.

Quine's Radical Translation Doesn't Work

Since we can't assume that the person whose language we are translating shares our beliefs and desires, translation cannot proceed by trying to make everything the person asserts come out true, since we surely disagree about some things. We need some way to simultaneously arrive at theories of translation, belief and desire.

Quine's Radical Translation Doesn't Work

In order to simultaneously arrive at theories of translation, belief and desire, Davidson argues, assent and dissent are not enough: assent and dissent give us no information about preferences and desires. He advocated using "prefers true" instead of assent and dissent.

The structure and content of truth. Journal of Philosophy, 87:279–328, 1990.

Radical Translation Characterized

Davidson calls his proposal "radical interpretation" to distinguish it from Quine's radical translation, but I am more interested in what the two projects share—
Both represent attempts to arrive at a theory of an unknown language based solely on publicly observable evidence plus a minimal assumption of some intensionality.

Quine and Davidson also assume versions of what has been called a principle of charity. I make no explicit use of such an assumption.

Radical Translation Characterized

Since there is disagreement about what can be assumed for purposes of radical translation, we need a criterion. Here is the radical translation criterion I propose:
If we cannot attribute a language to a subject or cannot proceed to translate the language of a subject without an assumption, we are entitled to that assumption in radical translation.

Rules

The first interesting consequence of the radical translation criterion: Since we cannot translate a language unless it obeys rules,
We can take the person speaking the language being translated to be speaking it in accordance with a system of rules.
So much for rule skepticism.
It is necessary, to get this right, to take account of competence/performance issues.

Radical Communication

In order to translate someone's language, we must take that person to be a language user, and, therefore, to be capable of translating us. When we observe a language user for purposes of translation, we will normally, in turn be observed back. Thus, anyone whose language we attempt to translate will normally be in a position and will have the ability to translate us back, and that possibility follows from the radical translation criterion.

Radical Communication

We have just shown that anyone whose language we translate will have the ability to translate us, even within the limitations of radical translation. Is that enough to ensure communication? It is not. But the radical translation criterion will therefore require that we put in place enough additional structure to ensure that communication is possible, since communication is constitutive of language use.

Plan of the rest of the talk

Two-way translation is not enough

Next, I shall show that translations in both directions are not enough. To do that, I describe a counterexample. That will suggest a characterization of communication.

New requirement

After that, I propose a "new requirement" consonant with the radical translation criterion that can be added to radical translation or interpretation to make it possible to ensure communication. Radical translation or interpretation employing the new requirement is radical communication.

Two-Way Communication

Suppose you and I speak "the same" language and that we have more or less the same beliefs and preferences. In that case, I will be able to arrive at a translation of your language using only assent and dissent, and a similar remark will apply to you.

If we each adopt the homophonic translation of the other, then communication will clearly be possible, whatever exactly communication turns out to be.

Actually, that simple example won't do, since if I want to speak your language, there will be no way to tell when I am doing so. For that reason, let us assume that you speak English, while I speak Pig Latin. I continue to call the natural translation homophonic, since porcuphonic is barbarous and khoirophonic is pretty awful.

The Antihomophonic Translation

Suppose now that I, in attempting to translate your language, begin by reversing your assent and dissent, so that I take your normal attitude toward declarative sentences you utter to be denial. A bit of thought shows that I can arrive at a good translation of your language. I'll illustrate the point by pretending that your language is first-order logic.

The Antihomophonic Translation

Translation Table
Your term My translation  
$ c $ $ c $ name
$ R $ $ \lnot R $ relation
$ \lnot $ $ \lnot $ negation
$ \land $ $ \lor $ and
$ \lor $ $ \land $ or
$ \forall $ $ \exists $ for all
$ \exists $ $ \forall $ there exists

The Antihomophonic Translation. An Example

Suppose, for example, you assert "Peter is white, but some rabbits are not," $ W(p)\land(\exists x)(R(x)\land\lnot W(x)) $ .

I will, in accordance with the translation, take you to be denying "Eterpay isn'tway itewhay, unlessway allway abbitsray areway itewhay" [Peter isn't white, unless all rabbits are white], $ \lnot W(p)\lor(\forall x)(\lnot R(x)\lor\lnot\lnot W(x)) $ , which denial is logically equivalent to your assertion.

The Antihomophonic Translation

The homophonic and antihomophonic translations meet the criteria proposed by Quine and Davidson equally well. Both account for your assents and dissents and the inferential relations within your language equally well. On all criteria concerning your behavior, they are fully interchangeable.

Two-Way Translation Is Not Enough

Suppose you translate me using the homophonic translation, while I translate you using the antihomophonic translation. I wish to tell you that "Eterpay isway itewhay" [Peter is white]. The sentence of your language that I take to say that is "Peter is not white." That is not the right thing for me to say, as can be verified by checking what you tell me you took me to say: The sentence of my language you translate as "Peter is not white," which is what I said, is "Eterpay isway otnay itewha" [Peter is not white], the negation of what I intended.

Two-Way Translation Is Not Enough

It is obvious what has gone wrong, of course. The point is that what has gone wrong is not something that has gone wrong with a single translation. What has gone wrong can be described in various ways, but each of them involves two translations, or one of us speaking the language of the other, or my use of a principle about what propositional attitudes you will impute to me, all of which go beyond what has traditionally been considered in discussing radical translation or interpretation.

What We Have Here Is a Failure to Communicate

Whatever exactly communication is, it has clearly failed in the present case. The radical translation criterion therefore allows us to supplement the usual list of techniques and assumptions to block such failures in some minimal way. My proposal involves two components.

Radical Communication

The appropriate setting in which to discuss how language is constrained by observable behavior is not the linguist attempting to translate the language of a foreign informant, but the languages and translations of a group of people each translating the others. For most purposes, it is enough to consider a "group" of two people and their two translations.

The New Requirement

The new requirement is that translating back and forth should leave you more or less where you started, that is, that communication be possible. More precisely:

For any two people in the group, who speak languages $ {\mathcal L}' $ and $ {\mathcal L} $ , and who translate each other via translation functions $ *: {\mathcal L}'\rightarrow {\mathcal L} $ and $ @: {\mathcal L}\rightarrow{\mathcal L}' $ ,

  For any sentence $ \phi $ of $ {\mathcal L} $ , $ \phi^{@*}\approx\phi $ ,
  and, in the other direction,
  for any sentence $ \phi ' $ of $ {\mathcal L}' $ , $ \phi '^{*@}\approx\phi ' $ .

Of course, the idea rests on a suitable choice of the equivalence $ \approx $ . I discuss that below.

Back to Field

We mentioned earlier that we could solve Field's problem if only we could show that $ W'^{@*}\subseteq W $ . But that will follow from the new requirement, so long as the new requirement holds not only at the level of sentences, but also of predicates, and $ W'^{@*}\subseteq W $ follows from $ W'^{@*}\approx W $ . As we shall see, it will be reasonable to require that of $ \approx $ on grounds concerning communication in any case.

Back to Field

Of course, Field is right that no amount of behavioral evidence can guarantee that my translation of your predicate is coextensive with your predicate—that was clear anyway, since conjectures based on evidence never come with guarantees. But he concludes that that introduces an irreducible indeterminacy in radical translation that cannot be overcome in principle. That may be, but it does not introduce such indeterminacy in radical communication.

Back to Field

Part of our commitment to communication is a commitment to keeping synchronized the extensions of our predicates that we take to be translations of each other. My predicate wolf does not include Tasmanian wolves. It may be that for some of you wolf does include Tasmanian wolves or that it is indeterminate whether or not it does. Nonetheless, we can be quite sure that we can agree on what wolves are: when disagreements arise, we can reach an agreement.

Back to Field

It is the possibility of maintaining communication by reaching agreements, no, stronger, it is the fact that it is constitutive of language use that we can normally do so, that is part of radical communication and omitted from standard pictures of radical translation. The evidence omitted by Field that my translations of your terms are appropriate translations and your translations of my terms are appropriate is evidence that we ensure that translations in both directions are appropriate.

Back to Field

The evidence that we ensure that translations in both directions are appropriate is just as external and behaviorally based as any, but it only becomes available when we consider translation back and forth. Though I have been arguing in terms of examples concerning you and me, everything would go through for an observer watching two language users communicating by translating each other. Such results would be applicable to you and me.

Back to Field

I have made my points about communication in terms of translating one and the same sentence back and forth, something we do not ordinarily do. That is just intended to make the case that radical communication is, in principle, possible. The kinds of exchanges that are actually relevant are more complex, but can be seen to involve closely related elements. They include asking questions and giving answers, and such locutions as "How do you say," "What did you mean by," "I think we're talking at cross purposes," and "we need to distinguish between."

Radical Communication

Of course, radical communication is good for more than just answering Field's rather special worry. The kind of equivalence I suggested we can obtain between predicates across translation to answer Field extends throughout language, and that yields a notion of a kind of synonymy that is defined not only within, but between languages, a type of synonymy that is useful for reflecting the kind of communication we in fact establish. I should immediately add that my claim about synonymy does not conflict with Quine's arguments against synonymy: He disputes the existence of a notion of synonymy that is of any use for establishing translations. My notion is specified only with respect to a system of translations that is already in place.

Radical Communication

Of course, radical translation has been based on a picture on which we first speak languages and then learn to translate. Radical communication suggests that what it is to speak a language is, in part, to have in place a system of translations of and by other language users.

Radical Communication

Though I haven't even indicated how today, radical communication can be used to show more: That is usually just assumed on the basis of a principle of charity.
Sentential connectives are easy. It is in the case of the quantifiers that this does real work. That follows from our having a common notion of identity. It does not, of course, mean that we agree on what entities exist. For any name in your language, I can introduce one in mine that is co-referential with it, and similarly for predicates. That requires substantial ideas going beyond what I have discussed today.
A term may $ \text{refer}' $ without referring. Though the term I introduce will be co-referential with yours, it need not be $ \text{co-referential}' $ with yours. Analogously for predication.

Equivalence

The new requirement depends on a notion of equivalence. Since the equivalence I propose is not simple, I shall build up to it with a series of proposals that do not work.

Identity

We can obtain identity using homophonic translation, but it will not, in general, be possible: If one language has two interchangeable names for something and another language only one, it will not be possible to go from the first language to the second and back and keep track of which of the names was used.

Synonymy

Synonymy would do all we want if there were a way to determine synonymy in a foreign language via radical translation. Whatever equivalence we use must be definable within the strictures of radical communication, and I shall actually define it that way. That means I cannot rely on the notion of synonymy.

Stimulus Synonymy

Two sentences of a language are stimulus synonymous if they prompt the same response—assent, dissent, or neither—under all stimulus conditions. That is definable from the perspective of radical communication, but it is too coarse: "grass is green" and "snow is white" are stimulus synonymous, and it is too individual: we shall need a notion that takes account of a whole group of language users. I'll handle the second problem first.

The notion is Quine's, as is the next. For brevity, I'm ignoring competence/performance issues and second intensions, here and below.

Social Stimulus Synonymy

Changes from stimulus synonymy are bold.
Two sentences of a language are socially stimulus synonymous if for each user of the language they prompt the same response under all stimulus conditions.

I know Newton was a bachelor; Terry may not. But Newton was a bachelor and Newton was an unmarried male are stimulus synonymous for Terry and for me, and hence socially stimulus synonymous.

Radical Social Stimulus Synonymy

Radical communication is not concerned with groups of people who speak a single language, but with groups of people each of whom speaks a different language. So I modify social stimulus synonymy as follows, with changes bold:
Two sentences of a language are radically socially stimulus synonymous for a group if they prompt the same response under all stimulus conditions and that remains true of their translation into any other language obtained using a single translation function built from the translation functions used by the group.

Structural Equivalence

Now, I turn to the first problem: for, for example, the group of people in this room, "grass is green" and "snow is white" are not just stimulus synonymous, but even radically socially stimulus synonymous.

In discussing radical interpretation, Davidson notes that the definition of truth required by his theory must be finitely axiomatizable so that it is realizable in a person. I make use of a similar consideration: the translation functions under consideration must be explicitly computable functions, that is, computable functions that are computed by an explicitly given algorithm.

Structural Equivalence

Say that two linguistic elements (words, phrases, grammatical transformations, whatever) of a language are of the same grammatical category with respect to a translation algorithm from that language if they are of the same data type with respect to the translation algorithm, that is, if wherever it makes sense to feed one to a part of the algorithm, it makes sense to feed to feed the other.

What the linguistic elements and grammatical categories are will depend on the translation. For actual translation algorithms, insofar as we understand them, the grammatical categories are grammatical categories in a standard sense.

Structural Equivalence

Fix a language and a translation algorithm. Let $ a $ and $ b $ be two linguistic elements of the same grammatical category. Sentence $ \psi $ is the result of substituting $ b $ for $ a $ in sentence $ \phi $ if applying the translation algorithm to $ \phi $ and to $ \psi $ results in the same inputs to every computation that does not depend on a prior computation that had $ a $ or $ b $ as an input, except that input $ a $ is replaced by input $ b $ .

Structural Equivalence

Let $ E $ be an equivalence relation on the sentences of a language, and fix a translation algorithm $ \dagger $ from that language.
Two linguistic elements with respect to $ {\dagger} $ are structurally $ E $ -equivalent if the result of substituting one of the linguistic elements for the other in any sentence is $ E $ -equivalent to the original sentence.

Final Answer: Radical Structural Social Stimulus Synonymy

This is the equivalence relation I propose for use in the new requirement:
Two linguistic items are radically structurally socially stimulus synonymous (structurally synonymous) for a group of language users if they are structurally radically socially stimulus synonymity-equivalent with respect to every translation algorithm from the language that is used by the group.

In plainer English, two linguistic items are structurally synonymous if the result of replacing one by the other in any sentence is stimulus synonymous to the original sentence, and the translations of the pair of sentences using any of the translation functions of the group are also stimulus synonymous.

-- ShaughanLavine - 22 Sep 2005