Ch. 3: Simple Axiom

Sider writes:

Lewis denied laws as generalizations in the best system—the deductive system, cast in a language whose predicates express natural properties and relations, that best balances the virtues of simplicity and strength. The restriction on the language of the best system is essential; otherwise, as Lewis (1983b, p. 367) points out, a simple and maximally strong theory could be given with a single, simple axiom, ∀xFx, where F is a predicate true of all and only things in the actual world. All true generalizations would be counted as laws.

I’d like to get a bit more clear about just why this “simple axiom” would prove illicit by Lewis’s lights. The thought seems to be that this predicate does not express a perfectly natural property or relation. But why should this be? For illustration, assume supersubstantivalism. By assumption, every actual entity is simply a chunk of the spacetime manifold. Thus, F is guaranteed to apply to all actual entities just in case F expresses the property “is a portion of the spacetime manifold”. Doesn’t this seem to be a perfectly natural property?

The point may be more obvious if we ignore the supersubstantivalist assumption and just stipulate that the actual world is composed of all and only the material objects. Thus, so long as F has the value “is material,” it applies to every actual entity. But on superficial examination this seems to me entirely licit: isn’t “is material” a perfectly natural property, or at any rate as good a candidate as any we have?

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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’?

Ch. 1 & 2: Theory, Ideology, and Structure

I found the epistemology of structure offered in Section 2.3 the most interesting of these first two chapters so my post will discuss some issues that arise therein. I’ll quickly summarize some material then follow-up with some (mostly rambling) comments and questions.

Sider says structure is a posit. In particular, he says that posits are more justified when they’re unifying. Accordingly, he distinguishes two sorts of unification:

Ideology. The set of our undefined words/concepts/notions.
Example. The identification of inertial and gravitational mass. The same notion of mass is countenanced in both laws. Instead of containing two notions of mass, there is just one notion: mass. 

Unification of Fundamental Principles.  The set of our fundamental laws. [Do the ‘fundamental laws’ cover both metaphysical and physical laws?]
Example. The orbiting of the planets was shown to require no new fundamental laws: elliptical orbits follow from the second law and law of gravitation. 

He also adds that:

While both sorts of unification seem to count in favor of a posit, too much of the former sort without any of the latter seems rarely to be pursued. We like to keep our posits few in number, but we also want them to obey a small number of fundamental laws, from which much else can be derived (13).

Following Quine, Sider holds that one should believe the ontology of one’s best scientific theory. But Sider goes further and extends this slogan to ideology: regard the ideology of one’s best theory as joint-carving. Thus:

Search for the set of concepts and theory stated in terms of those concepts <I, TI>.

Go back to the example of mass. It seems Sider wants to say that, all things considered, one ideology can be more fundamental than another. For example, an ideology that contains only the word ‘mass’ compared to an ideology which contains both ‘inertial mass’ and ‘gravitational mass’ (but not ‘mass’) will be the more fundamental ideology. And it will be more fundamental because the former is more unifying than the latter without sacrificing theoretical virtue (17). But, as Sider would surely concede, the physics says there is no difference between ‘inertial mass’ and ‘gravitational mass’; indeed, both are equivalent to one another, hence, equivalent to ‘mass’. And if they are equivalent, how, then, could the ‘mass’ ideology be more fundamental than the ‘inertial mass’ and ‘gravitational mass’ ideology? After all, the ‘inertial mass’ and ‘gravitational mass’ ideology has the same consequences about mass as the more fundamental ‘mass’ ideology. Again, I think Sider would just say that the former (inferior) ideology just doesn’t carve quite perfectly at the joints because it contains too much syntactical structure, given that less—i.e., one term: ‘mass’—will do. But again, the two notions of mass are equivalent with the singular notion: mass. So does one ideology really carve more accurately—more better—than the other? Is that what Sider thinks?

There’s another passage that confused me:

The Quinean thought also rationalizes changes in beliefs about what is fundamental. The special theory of relativity led to (at least) two such changes. First, we came to regard electromagnetism as a single fundamental force, rather than regarding electricity and magnetism as separate fundamental forces. [footnote omitted] And second, we came to regard spacetime as lacking absolute spatial and temporal separation. These changes weren’t ontic: changes in which entities are accepted. Nor were they merely doctrinal: changes in view, but phrased in the old terms. The changes were rather ideological: we revised our fundamental ideology for describing the world (16–17, emphasis mine).

These changes weren’t ontic? I would have thought that they were. For example, the ideological shift from ‘space’ and time’ to ‘spacetime’ seems to yield the following ontic shift: there being two kinds of substances (space and time) to there being only one kind of substance (spacetime). If this isn’t right, I guess it isn’t clear to me what exactly generates the ontic changes. Is it the ideology, the theory, or is it the pair <I, TI>? Maybe an example will clarify things. Take the following:

Suppose I believe the ontology of our best theory of time which, for sake of example, we’ll say is the Special Theory of Relativity (STR). STR is a scientific theory; it makes certain predictions. The predictions it makes entail new additions to reality and new omissions: things we previously thought to exist don’t exist according to STR. Suppose STR’s new additions to reality include past, present, and future entities and say that STR’s omissions include absolute space, absolute time, temporal asymmetry, intrinsic direction, change, and so on. Now, we would of course say that the changes here are ideological, but wouldn’t we also say that they are ontological as well? Our set of concepts is the ideology and STR is our theory; STR is stated in terms of those concepts and those concepts have ontological implications. [Is that right?] Suppose further that we believe STR but we find it lacking in some respects: we don’t think it carves perfectly at the joints because it says nothing about the direction of time (and we think direction is joint-carving). Indeed, we’re just the kind of philosopher who thinks scientific theory isn’t satisfactory until it can reconcile its image with the manifest; and the manifest image suggests that time has a direction. What we do is add to the ideology of STR. Suppose we add a new topological structure that builds-in a direction to time (à la Tim Maudlin’s Theory of Linear Structures). It seems an ontological posit follows from our ideological posit: spacetime now has something it previously lacked: direction.