Random thoughts on random topics

Berlin

On transitivity of translation

Part of the argumentation in Davidson’s ‘On the Very Idea of a Conceptual Scheme’ centers around transitivity of the translation relation. The point Davidson is trying to make here, I think, is that if there exists a translation from L1 into L2, that translation itself can be stated in either L1 or L2, and consists in an accurate mapping of sentences from L1 onto sentences of L2. If the translation is stated in L1 then, by assumption, it can also be stated in L2 (after all, there is a mapping from all of L1 into L2, i.e., also of the L1-sentences describing the mapping). So we can safely assume that if there is a translation from L1 into L2, it can be formulated in L2. Now suppose there is a translation from L2 into L3: that, again is a mapping, in this case of L2-sentences onto L3-sentences. That mapping includes those L2-sentences that describe how to translate L1-sentences into L2-sentences. So what we have then is (among other things) a set of L3-sentences that tell us which L2-sentences are translations of which L1-sentences, and L3-translations of the L2-sentences. But that means we have a translation of L1 into L3. (More neatly: if a translation is a homomorphism from L to L’, then we know that if there is a homomorphism from L1 to L2 and a homomorphism from L2 to L3, then there is a homomorphism from L1 to L3, viz.: the composition of the two.)

Of course the above argument only works if we assume that translations are total, i.e., that they map all sentences of L onto sentences of L’ and vice versa. What if we drop that assumption? First of all we have to ask ourselves whether we are still dealing with translation in such a case. But let that pass, and suppose we have a mapping of all the sentences of L1 onto a proper subset of sentences of L2, i.e., there are parts of L2 that have no counterpart in L1. Notice that the formulation of the translation can not be in the latter set (for that would mean that the translation would be statable in L2, but not in L1, which is absurd.) Now assume we have a translation from L2 into L3: the only way in which that would not give us a translation of L1 into L3 (by the reasoning above), is by being restricted to exactly that part of L2 that does not contain the L1-to-L2 translation. But that would mean that it really isn’t a translation of L2 as such: it must leave out a proper part of L2. Of course, such a mapping could exists, but we would lack any justification for calling it a translation. (And if we would insist that we could call it that, then we actually are assuming what we set out to prove, viz., the failure of transitivity of translation.)

Note that the fact that in actual cases there are bound to be discrepancies between languages, i.e., things in L that don’t have an exact counterpart in L’, or things in L’ that lack a counterpart in L, does not really affect this line of argumentation. The central point is that the translation itself concerns such a substantial part of both languages, that that by itself guarantees transitivity to a sufficient degree.

Martin Stokhof
from: Radical Interpretation Discussion Board
date: 11-2004

Random thoughts on random topics

Oslo, Opera House

The need for uncertainty

Suppose there were creatures with the following features. If something is the case, they believe it; if something is not the case, they believe it is not the case; they do not entertain any other thoughts, more specifically they don’t have thoughts of the form ‘Suppose A were (not) the case …’, ‘If B had not been the case …’, and so on. Would we say that these creatures had knowledge? They could serve as reliable oracles, as perfect encyclopaedias, but we wouldn’t want to say that they knew anything. So knowledge presupposes (among other things) our ability to be uncertain, to entertain suppositions, to consider situations that we know to be counterfactual.

Does this mean that the concept of an omniscient interpreter à la Davidson is incoherent? Not necessarily. Perfect knowledge about the world is compatible, at least so it seems, with counterfactual uncertainty, and hence with having the concept of being wrong. 

Martin Stokhof
from: Aantekeningen/Notes
dat
e: 13/10/2000, 09/08/2001

Random thoughts on random topics

Lisbon

Uninterpreted content

Theodore Schatzki’s analysis of dispersed and integrative practises implies that normativity arises, not at the higher order level of rules, or practises, or institutions (at least not exclusively), but at the very basic level of individual interaction with the environment. This view is reinforced by various analyses of know-how and expertise.

What is interesting to note, especially with regard to Davidson and Gadamer, who actually are in the same boat here, is that uninterpreted content then plays a key role. We need such content in order for normativity to have a basis on which the language-based practises may build.

For Gadamer this is anathema: all experience is linguistic and exists only in and through language. For Davidson it presents a problem too, although it may not be immediately obvious that it does. For doesn’t Davidson avail himself of a primitive causal relationship between the world and us? And doesn’t he reject any form of mediation (linguistic or otherwise) between ourselves and the world?

But unmediated content is not the same as uninterpreted content as we use the phrase here. For in Davidson’s view our causal interaction with the world results in beliefs, and beliefs and (sentence) meanings are indistinguishable in terms of structure and content. So Davidson’s unmediated content is highly structured, in such a way that it is immediately expressible (given a suitably expressive language, of course): definitely not the uninterpreted content of everyday expertise. In fact Davidson seems committed to the same kind of linguistic view on experience that Gadamer embraces explicitly.

Martin Stokhof
from: Aantekeningen/Notes
date: 21/11/2006

Random thoughts on random topics

Amsterdam

Davidson, indeterminacy and charity

The point seems to be this: given that we have a shared ontology due to the application of the Tarskian framework (as the theoretical framework in which we formulate concrete theories of meanings for concrete languages) and charity, which implies shared beliefs, why don’t we have a shared vocabulary and a shared theory of reference concerning this vocabulary? 

The point seems to be this: given that we have a shared ontology due to the application of the Tarskian framework (as the theoretical framework in which we formulate concrete theories of meanings for concrete languages) and charity, which implies shared beliefs, why don’t we have a shared vocabulary and a shared theory of reference concerning this vocabulary? 

The question boils down to what follows from the assumptions mentioned about reference. Let’s start with the use of the Tarskian framework. For Davidson this follows from the assumptions he makes concerning the nature of meaning (extensionalism) and the function of a semantic theory (explanation of competence); cf., ‘Truth and Meaning’ for the details. So his view is that if we want a theory of meaning for a language, it has to have that particular form. And that in its turn presupposes that in any language we find a shared logical machinery, consisting of propositional connectives, quantificational apparatus (and the basic distinctions brought along by that) and the logical rules governing their behaviour. But that is all, in particular it does not involve any assumptions concerning the reference of the non-logical vocabulary. Of course, reference is used in stating the Tarskian truth theory, but there it is used only as an auxiliary notion. What the theory defines, or accounts for, is (our knowledge of) truth conditions of sentences. It does so using the auxiliary notion of reference of sub-sentential expressions, but, and this is the important point: it does not define truth on the basis of an independent account of reference. And as Davidson points out, any account of truth along these lines leaves reference essentially underdetermined (a point also made by Putnam and several others): two sentences may have the same truth conditions under different assignments of references to their sub-sentential expressions. (If the sentences are from different languages, we have two translatable sentences which do not allow us to infer any shared reference; if the sentences are from the same language, this means that synonymy does not guarantee unique reference; and as a special (but most important) case we have that it is possible to assign to one and the same sentence the same truth conditions based on attributions of different references to one or more of its component expressions.)

Then charity. Notice that charity, too, concerns sentences, not words. In interpretation, i.e., in actually trying to construct a Tarskian theory of truth for a given language, the empirical data we start from are utterances made in a context (situation). The assumption that truth plays the same role for the speakers of the language we are interpreting as it does for us, these data can be viewed as utterances of sentences held true in that situation. A specific (to be determined!) subset of those will be utterances of sentences held true about that situation, i.e., utterances of sentences that are held true on the basis of certain aspects of the situation in which they are uttered. Each and every sentence uttered is supposed to express a belief. So certain sentences uttered in a situation express beliefs of the speaker about that situation. This is where charity comes in: it allows us to proceed on the assumption that the belief that the speaker expresses in these sentences (but remember, we do not know of every sentence in advance whether it belongs to this set) is a belief that we hold about the situation as well. This is supposed to give us enough common ground to work our way into the language. But, and this is the important point, just as two sentences can have the same truth conditions, yet not share reference of sub-sentential expressions, beliefs too can be shared without a shared set of objects, properties and relations that can be attached in a unique way as references to the expressions that occur in the sentences that are used to express these beliefs.

So neither the Tarskian framework nor charity allows us to venture beyond the level of sentences/beliefs and be confident that we will return with a unique ontology in this particular sense. But for Davidson the conclusion is not that hence there is a relativity of ontological schemes, but rather that the idea behind it, viz., that the beliefs we hold and the meanings of the sentences we use to express those beliefs, are built up from referents in this particular way, is misguided in the first place. In combination with the holistic nature of language and belief that Davidson clearly endorses, this assumption would lead to relativism. But there is, according to Davidson, no reason to make it in the first place.

Martin Stokhof
[from: Radical Interpretation Discussion Board
date: 10-2003]