NoR 2.5b: Inductive concepts and Reference Magnetism

This is one of a series of posts setting out my work on the Nature of Representation. You can view the whole series by following this link

In the previous post, I argued that a default-disposition to use concept c in inductive generalization means that simpler properties are favoured as the denotation of c. This is a result absolutely in keeping with all the earlier examples of drawing out specific predictions from radical interpretation, being derived from normative and architectural assumptions.

In this post, I want to connect this idea of “simpler” properties with “natural properties’ (i.e. those which are somehow “close to” the fundamental or perfectly natural features of the world). Specifically, I want to articulate the perspective this gives us on the influential claim that natural properties are reference magnets.

We get the connection between claims about simplicity in the previous post and claims about naturalness, if we add one additional (and unforced, and contentious) claim to the mix. The claim is explicit in Lewis’s discussion of theoretical virtues in the context of laws of nature, and is that the canonical language–the one that gives us a level playing field on which to measure compact expressibility of theories–was one which contained only broadly logical resources and predicates for every metaphysically fundamental property and relation. Given this, if we follow Lewis in defining a property’s degree of naturalness as the length of its shortest definition in this canonical language, then F will be simpler than G iff F is “more natural” than G (i.e. has a lower degree of naturalness) So given the full Lewisian treatment of simplicity, we derive a version of the famous Lewisian “reference magnetic” constraint on interpretation: that all else equal, interpretations that ascribe more natural properties are to be favoured.

(Compare the discussion of naturalness and simplicity in my “Eligibility and Inscrutability” and the discussion of alternative canonical bases in my “Lewis on Reference and Eligibility”. Both those discussions take place in the context of the foundations of the linguistic representation, and I was concentrating on simplicity as it applied to the theorist’s interpretation not the subject’s inductive inferences. But the connection is the same).

Now, even if we take this final step, the naturalness constraint here is not the one that appears in most of the literature. It does not imply that there is a general bias towards interpreting a general concept as natural. In order for the above to kick in, the concept must be one of those that we are default-disposed to deploy in inductive inferences. A fortiori, there’s no immediate extension of these considerations to a “naturalness” constraint on reference-fixing for concepts in other categories (quantifiers, singular terms, connectives, etc)—even if we allow, with Sider, that the semantic values of such terms can be ranked by naturalness. If we are to secure that result, I think the way to go would be to argue that we are default-disposed to induct on complex general terms as well as simple ones. If “all”, “and”, “that” and the like figure in inductive complex general terms, then just as before pressure arises to interpret them as denoting the simplest entities in their respective category, and given the final step above, this will favour the most natural candidate referents. This is still selective: if “or”, for example, never figures in inductive complex general terms, no naturalness constraint on its denotation will arise.

I’ve encountered many who think the whole idea of natural properties being reference magnets is prima facie weird and unmotivated. But the discussion to this point should undercut that idea. Its source is exactly the same as (I have argued) other kinds of theories of reference–a first-order normative theory paired with assumptions about cognitive architecture. It is no ad hoc primitive piece of metaphysical prejudice, but something that falls out of the story given suitable auxiliarly background.

We need not accept that background, and charting the various points at which one can get off the boat .

  1. We can resist the Lewisian package on simplicity by refusing to take that final step and identify the simplicity-measuring language with a language populated with metaphysically fundamental predicates. If we still allow there is a “canonical” simplicity-measuring language, then properties picked out by the atomic predicates in that language will be predicted to be “reference magnets” for inductive concepts, for exactly the same reasons as before.
  2. If we resist the Lewisian package by refusing to identify simplicity with elegance-in-a-canonical-language, then we won’t get a picture isomorphic to Lewis’s. But if there is still a distinctive systematic contribution that properties make to the simplicity of (interpreted) theories in which they figure, so that we can grade properties as more or less simple, than we still get a reference-magnetic thesis, but framed around simplicity (treated now as a working primitive) and detached from naturalness.
  3. If we resist the Lewisian package at its first step, by giving a different account of the theoretical virtues that doesn’t cite simplicity among those, we won’t get this. But still, a parallel discussion may be conducted. Some (e.g. Sider) express sympathy for the idea that naturalness itself is virtue of theories. That would give a rather more direct route to the conclusion that naturalness is reference-magnetic in this context! But even if one sets aside simplicity and naturalness, if some properties are more suited to figure in explanations than others–than all else equal, those will be favoured as referents.

As this illustrates, one has to work quite hard not to get a reference-magnetic thesis out of these considerations—though what property exactly turns out to be magnetic will be sensitive to the fine details of one’s account of the explanatory virtues.

The connection between radical interpretation, induction and Lewis’s naturalness constraint has been suggested before (Pautz 2013, Weatherson 2013), and I was led to the above story by thinking through these author’s writings. But my account is not based around what Weatherson calls “inductive dogmatism” (nor is Weatherson’s own, in its published version). That theory cuts out the background of IBE. No connection is made, then, to considerations of simplicity or other theoretical virtues. In their place is an epistemology specifically of induction, of the shape that Goodman suggested. Here, faced with an enumerative inference, the major theoretical question is just this: which properties make an inference with the enumerative inductive form good (call those the projectable properties). On this reading, what forges a link to Lewisian naturalness is the thesis (not to my knowledge ever endorsed by Lewis) that the projectable properties are those that are natural enough (rather than, as in Goodman himself, those that are historically entrenched in inductive practice).

What we get from this picture is the thesis that there is a cut-off (maybe a vaguely defined one) in the hierarchy of more or less natural propeties, with those more natural than the threshold being suited to figure in induction, and those less natural than threshold not. That is problematic (and particularly problematic as Lewis exegesis). Green is projectable, being positively charged and located before the midpoint of history or negatively charged and after the midpoint is not. But on various accounts (including Lewis’s) the latter will be more natural than the former.

If we think things through starting from IBE, the account we derive makes relative simplicity/naturalness the key factor. If we try to move directly to characterizing Goodman’s “projectability” in terms of a threshold of naturalness, an absolute notion of “being natural enough” plays the key role. I think the former is much nicer.

 

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