Ch. 3: Naturalness, Explanation, and Equivalence

According to Sider, theories based on non-joint carving classifications may be unexplanatory even if true (23). Consider, for example, two true theories T and T* where T is more joint-carving than T*. According to Sider, T is more explanatory than T* because of how much better it carves at the joints than T*.

I’m skeptical of this proposal for largely Hirschian reasons (cf. Hirsch 2017, ms). I take Sider to be saying that T* is less explanatory than for objective reasons: that to describe the world using Twould result in an objectively inferior description. But why isn’t Tjust less explanatory for practical reasons?—i.e., that it’s just easier for us to formulate our theories in T rather than in T*? Imagine two linguistic communities, call them L and L*L-speakers speak our language—English—and L*-speakers speak some strange and bizarre version of it. Now compare two theories offered by L-speakers and L*-speakers respectively,

TL: The glass shattered only if the baseball shattered it.
T*L*: The glassable shattered only if the bageball shattered it.

where ‘glassable’ means ‘the glass or the table’ and ‘bageball’ means ‘the baseball or the bagel’.

Now, as theories, both TL and T*L* are true. In particular, T*L* is true because its strange disjunctive predicates are all true. But, so says Sider, Tis the more explanatory theory. Why? Because its predicates, namely ‘glass’ and ‘baseball’, somehow carve better at the joints than ‘glassable’ and ‘bageball’. But what joints? Of course, us English speakers would and should prefer a theory formulated in rather than L*, but why is this a mark of objectivity? Why should this make Tthe more objective theory? Perhaps, with Sider, we ought to say that T*Lis unexplanatory (and hence less objective) because its carvings seem arbitrary: glasses and tables and baseballs and bagels don’t go together in any natural way. Well, prima facie maybe they don’t; maybe they don’t go together in any meaningful, worldly way,  but regardless, it seems the explanatory power of the theory remains unchanged; T*Ldoesn’t leave anything out: the glass or the table shattered only if the baseball or the bagel shattered it. And that’s just true!

Consider another example. Imagine a species of humans with extraordinary computational ability; surely any joint-carving discrepancies in the logical equivalence below would be negligible to these extraordinary humans:

Screen Shot 2017-06-18 at 9.01.22 PM

Indeed when these extraordinary humans see the formalism flanking the left side of the equivalence symbol, they process it immediately as p. Now, would Sider say that the more complicated formalism is less joint-carving then p? More precisely, if both formalisms were invoked in two true theories—one theory which used only and the other which used the more convoluted formalism—would the theory using only be more explanatory? Perhaps we would, at first, be skeptical of the extraordinary humans strange preference for the more complicated formalism: why use it to describe a theory when is just more simple, more elegant, more easier to parse (especially when the formulas get really long and complicated)? But to the extraordinary humans, the complicated formalism isn’t hard to parse at all; to them it’s read just fine without any hesitation; to the extraordinary humans, the more complicated formalism is more beautiful and that’s why they prefer to use it in their theories.

Now, if I’m understanding Sider correctly, I believe he would say that the extraordinary humans are just getting something wrong: a theory’s syntactical simplicity is a guide to more better, more objective theories; the theory written in the more convoluted formalism, though true (and equivalent to the simpler theory) is explanatorily inferior. If this is really what Sider is suggesting, then I’m not sure I can buy it—at least not just yet. In the two examples above, the explanatorily robustness of a theory seems only to be a feature of our preferences rather than a feature of its objective virtues. As equivalent and true theories differing only in syntactical complexity (or lack thereof) both encode the very same information. One might be more simple to use and handle than the other, but does this really entail that one may be more explanatory and, hence, more objective than another?

Should we not find it suspiciously anthropocentric for ‘dog’ to just carve better (but not perfectly) at the joints than, say, ‘trog’, i.e., ‘the tree or the dog’?


One thought on “Ch. 3: Naturalness, Explanation, and Equivalence

  1. Hi Louis,

    I really liked this post. As someone who has not read ‘Writing the Book on the World,’ I found this discussion easy to follow; you’ve done a good job paraphrasing Sider’s ideas while simultaneously proposing your own. I also have not read the article by Hirsch you are referencing; I can’t seem to find it anywhere, but I think I am tracking what you are saying nonetheless. If you don’t mind pointing me in the direction of Hirsch’s article I would like to read it.

    That being said, I think the explanatory value of a language goes beyond mere subjective preference, contrary to what you seem to be suggesting. To demonstrate what I mean, let’s build some context around your two sentences. Suppose a detective is investigating a crime scene and sees a broken window and a baseball on the floor nearby. In court, the detective must give her testimony to the jury. She can say either of your sentences:

    TL: The glass shattered only if the baseball shattered it.

    T*L*: The glassable shattered only if the bageball shattered it.

    where ‘glassable’ means ‘the glass or the table’ and ‘bageball’ means ‘the baseball or the bagel’.

    As jurors, we know that the glass is shattered. If we hear TL, then we can logically conclude that the baseball shattered it, and so we can convict Jimmy the Slugger of breaking the window. If we hear T*L*, we can conclude that either the baseball or the bagel broke the window, and so we cannot decide whether to convict Jimmy the Slugger or Papa Rino the baker based solely on the detective’s testimony.

    In both TL and T*L*, the detective was intending to convey the same information, that the baseball broke the window. But because of the explanatory impotence of L*, she was unable to get her message to the jury, and so Jimmy the Slugger walked free.

    P.S. The second half of your post is the most interesting part to me. When you say, “to the extraordinary humans, the more complicated formalism is more beautiful and that’s why they prefer to use it in their theories,” I am curious as to what you think grounds aesthetic beauty. Do you think it has objective grounds or is merely subjective preference?

    Regarding the convoluted vs simple syntax discussion: it seems like Sider might want to say that a simpler syntax that conveys the same meaning “matches” the structure of the world better and so has an additional explanatory virtue that makes it preferable. Again, I have not read the book so I cannot say for sure, but this post is making me excited to pick it up!


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