Reduction and translation

These are very rough notes for myself.

The translatability of B-talk to A-talk as either a necessary or a sufficient condition for a reduction of Bs to As is generally rejected. Translatability can be symmetric, so it obviously can't be a sufficient condition. And it is generally thought that translations are so hard to come by, even in cases where it is very plausible that there is a reduction, that we shouldn't ask the reductionist for a translation. As an example, it seems pretty plausible that being oval is not a fundamental property. But the hopes of a reduction of being oval to more fundamental geometric concepts are pretty slim. We can start: An oval is a convex domain with a twice differentiable boundary approximating a non-circular ellipse. But if we try to explain the respects in which the oval approximates the ellipse, I expect at some point we would have to throw up our hands and say: "In the way definitive of an oval!"

It should not surprise us if there were no good translations. Words are rarely precisely redundant, and I suspect that cases of non-trivial synonymy are pretty rare. Certainly, few of the things listed in a thesaurus are genuine synonyms, i.e. words expressive of the same concept. Similarly, translation between different languages is rarely exactly right. For instance, "Il neige" and "It is snowing" are unlikely to express the same proposition. Here is one reason to think this. The boundaries of "neiger" and "to snow" are vague, and the behavior of the corresponding concepts near the boundaries will be determined by use. But different linguistic communities occupy different physical and social environments, and it is unlikely that the boundaries will be exactly the same. The same is likely to be true for most ordinary sentences, though the effect is probably decreasing with globalization.

However, I think there is a somewhat neglected option for translation. Instead of translating to an actual language, one can translate to a counterfactual language. And for purposes of testing hypotheses about ontological commitment, that should be enough.

We could imagine a community that has practices that outwardly and normatively resemble our practices of artifact production, use and possession. But they never say anything that commits them to the existence of these. They have other ways of talking. Maybe they say "It is chairing here" in circumstances that correspond to those in which we say "There is at least one chair here." They also describe the intensity of a chairing with a non-negative integer: "It is chairing here with intensity three" corresponds to our "There are three chairs here." They have some ways of talking that correspond to our possession practices. "It is Smithly chairing here with intensity three" corresponds to our "Smith owns three chairs here." They also have ways of talking that correspond to our talk of clear identity. Thus, they say "It is t₀ly chairing with intensity two at t₁" correspondingly to our "Two chairs that existed at t₀ exist at t₁."

Now here is a move that I like. It might turn out that some of our sentences have no corresponding sentences in that community. This will be a problem for the reductionist, unless those very sentences are ones that lead to logical problems in our community. For instance, it might turn out that one cannot translate all diachronic identity sentences about chairs. But that could be an asset if the untranslatable sentences are precisely the ones that lead to ship of Theseus problems. And this could, further, provide an asymmetry that could help fix the direction of reduction: in our language we can get paradoxes, while in theirs maybe we can't. We could, then, simply say that the untranslatable sentences (or maybe now we should call them "quasi-sentences") in our language are nonsense.