Reductions as Explanations?

In the SEP article on “Definitions,” Anil Gupta formulates the idea of “reduction” in the traditional account of definitions: “the use of a formula Z containing the defined term is explained by reducing Z to a formula in the ground language.” This struck me as strange, and got me thinking about the role of explanation in motivating and comparing between proposed reductions of a term.

Do we reduce a term to a base in order to explain the use of the term? I always thought that the main three reasons to reduce a term t were: (1) to increase the simplicity of the theories in which t occurs; (2) to demonstrate that (at least some well-formed) sentences containing t are contentful (or have a certain sort of content); and (3) to demonstrate that (at least some well-formed) sentences containing t do not lead to contradiction or paradox. I might have also have included (4) to demonstrate that a set of presuppositions (preferably minimal) are sufficient to make uses of t contentful (or contentful in a certain way, e.g., “cognitively”). There is no explicit mention here of explanation. Still, there is something like an explanatory bonus when a reduction satisfies (2)-(4). When a reduction demonstrates that sentences containing t are contentful, it also explains, or can later be used to explain, that same fact. Similarly for (3) and (4). Note that this really is a bonus, not the main purpose of the reduction. This is because we don’t, in general, try to explain some alleged state of affairs when we have real doubts whether it obtains, and (2)-(4) are good motivators only if we do have real doubts about the contentfulness, consistency, and theoretical baggage of uses of a term. So, in order to be strongly motivated, the sort of explanatory function of reductions that I have already described must be secondary.

I’m not sure what Gupta means when he talks about explaining the “use” of a sentence or formula. I thought that when we wanted to explain why a word (or a sentence containing it) has one use rather than another, we do etymology. Maybe we do some psycholinguistics to find out whether the word is an onomatopoeia, or why certain concepts are lexicalized and others aren’t. Reduction seems to be besides the point here.

Do reductions have some other explanatory role? Am I missing something?

A Test for Ambiguity... Tewtally Pwned

I’m reading Zwicky and Sadock’s (1973) paper on “Ambiguity Tests and How to Fail Them” for a paper on the ontology of senses (of linguistic expressions) that I’m working on.* They discuss different types of arguments for or against a sentence (or a crucial expression in the sentence) being ambiguous. One type, called “inconstancy under substitution” caught my eye. Fully spelled out, I think inconstancy under substitution arguments work something like this:

1. F is synonymous with G / F is a hypernym of G / G is a hypernym of F.
2. “… F …” has distinct understandings p and q.
3. “… G …” has p, but not q / “… G …” has an understanding that is acceptable if p, but no understanding that is acceptable if q / “… G …” has an understanding that is acceptable only if p, but none that is acceptable only if q.
4. Therefore, “… F …” is ambiguous between p and q.

Some comments: as it stands, the conclusion doesn’t logically follow from the premises. It’s hard to say what the implicit premise is that makes the conclusion seem warranted. At any rate, I don’t want to question the validity of this line of argument here. The big problem is antecedently establishing the first premise. Intuitively, the fact that substitution of G for F does not transform the possible understandings in the appropriate way** is evidence for the semantic relation not obtaining between F and G. To take one of the relations, it seems that we come to call F and G synonyms because of their intersubstitutability across diverse sentential and conversational contexts. Granted, of course, that intersubstitutability can fail in certain sorts of contexts without telling against the synonymy of the two terms; the argument from inconstancy of substitution (which does not involve reference to conversational contexts) works precisely when the sentential context is of such a sort. But we need to be able to identify those contexts prior to making the judgment that F and G are synonymous. But this entails that we can already recognize that, in the context quoted in the argument, F is ambiguous between the reading with which G is synonymous and some more idiomatic reading. So it seems that in order for us to establish the soundness of the premises of an argument from inconstancy of substitution, we must already be in a position to know that the conclusion is true.
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* - The first paper I’ve started to work on since graduating from Bard. Kind of exciting.
** - The appropriate way when F and G are synonymous would be that “… F …” can be understood precisely in all the ways that “… G …” can. The appropriate way when F is a hypernym of G would be that there is a certain one-to-one correspondence between the understandings of “… F …” and the understandings of “… G …”, such that an understanding of the latter is acceptable only when the corresponding understanding of the former is acceptable, or something like that.

Happy Birthday!

Yom huledet sameach, Israel!

Today, in the Jewish calendar, is the 60th anniversary of the birth of the modern Jewish state of Israel. It is a very happy day in Israel, immediately following Yom Hazikaron, Israel's Memorial Day. It is a very happy day, as well, for Jews the world over who think that the state of Israel should exist.

Did anybody else find it strange that, on Yom Hazikaron and Yom Haatzmaut, the New York Times should be airing this video? Israel's treatment of its own Arab citizens is troubling in many respects, and the Times' video is nuanced and, as far as I can tell, not inaccurate. But wouldn't it be outrageous if the Times covered the Fourth of July with, say, a story about our shabby treatment of the Native Americans, or the history of our government's indifference to the intimidation of non-white voters? Isn't that exactly what's going on here? For everything a season, guys.

The Particularity of Love

Now and again I hear or read something saying that we should or do love what we love “in its particularity.” This sometimes gets the implicitly metaphysical gloss that we should love people, especially, just for “who they are” and sometimes gets the explicitly metaphysical gloss that the reason why we love whom and what we love is that it possesses its own haecceity
. Since I don’t believe in haecceities yet, and since I don’t know what to do with “who they are” in this context, I never put much stock in this particularity idea.

Harry Frankfurt has cleared it up for me:

“The significance to the lover of what he loves is not that his beloved is an instance or exemplar… For a person who wants simply to help the sick or the poor, it would make perfectly good sense to choose his beneficiaries randomly from among those who are sick or poor enough to qualify. It does not matter who in particular the needy persons are. Since he does not really care about any of them as such, they are entirely acceptable substitutes for each other. The situation of a lover is very different. There can be no equivalent substitute for his beloved… It cannot possibly be all the same to the lover whether he is devoting himself disinterestedly to what he actually does love or – no matter how similar it might be – to something else instead.” (The Reasons of Love, 44)

I’m still not sure whether the particularity idea is true, but now I know roughly what would count as a counterexample to it.

My question here is: How does the particularity idea sit with the fact that there are such things as what we love about individuals? It sure seems that, if I love certain things about an individual, then, if the individual were not to have those things I love about it (or if I were to come to believe that the individual did not have those things), I would not love the individual. When I tell my girlfriend what I love about her – how funny she is, how affectionate she is – part of what I am telling her is why, in part, I have come to love her. My beloved’s having what I love about it, or my believing that it has what I love about it, is a necessary condition for my having come to love it, if not also for my continuing to love it.

But while this is a necessary condition, a consequence of the particularity idea is that it can’t be sufficient. What we love about an individual is not alone what makes us love it, either in fact or as a matter of duty. For what we love about individuals are properties, and properties are typically things that numerically distinct individuals can share. But if I need not, either in fact or as a matter of duty, love a numerically distinct qualitative duplicate of my beloved, then what I love about my beloved – certain properties of the sort shared by its doppelganger – is neither what causes me nor what obligates me to love it.