## Lewis on magnetism: Reply to Janssen-Lauret and Macbride

In my 2014 paper "Against Magnetism", I argued that the meta-semantics Lewis defended in "Putnam's Paradox" and pp.45-49 of "New Work" is (a) unattractive, (b) does not fit what Lewis wrote about meta-semantics elsewhere, and (c) was never Lewis's considered view.

In a paper forthcoming in the AJP, Frederique Janssen-Lauret and Fraser Macbride (henceforth, JL&M) disagree with my point (b), and present what they call "decisive evidence" against (c). Here's my response. In short, I'm not convinced.

Let's review some background. In "Putnam's Paradox" and pp.45-49 of "New Work", Lewis defends a theory I'll call Magnetised Global Descriptivism, or MGD for short. MGD is a theory of how words get their meaning. According to MGD, the correct interpretation of a language is the one that strikes the best balance between two desiderata: (1) making the sentences that are accepted by the speakers true (alternatively, the sentences that would be accepted in some kind of limit of enquiry), and (2) assigning objectively natural referents to the language's non-logical terms.

Let me go through the three reasons I offered (in "Against Magnetism") for thinking that Lewis did not endorse MGD, and comment on what JL&M say about them.

Obvious faults. I find MGD highly unattractive, and mentioned several problems with it in my paper. The problems are rather obvious, and surely didn't (all) escape Lewis. JL&M don't address any of them. Presumably they don't agree these problems would have stopped Lewis from accepting the theory. I think they would, but I won't go through all of them again. But I'll mention one, because Lewis also mentions it, and his response is instructive. The problem is that MGD is a non-starter unless we hold fixed the meaning of logical vocabulary (and the rules of compositional semantics). An urgent task for anyone who endorses MGD is therefore to explain how the meaning of logical vocabulary is determined -- that is, why logical vocabulary can be treated as "old vocabulary". Lewis has the following to say about this.

...perhaps the old vocabulary is just the first-order logical vocabulary. Putnam seems to assume this, but without telling us why that vocabulary is special, or how it got its reference. [p.224]
...the applicability of the model theory depends on treating exactly the first-order logical vocabulary as 'old' language, with antecedently determinate reference. As Robert Farrell has emphasised, Putnam has no right to give this vocabulary special treatment. Perhaps he only did it for the sake of the argument, giving away points just because he would not need them. [p.230]

To me, these passages strongly suggest that Lewis didn't see the problem as a challenge to his own view. That would be strange if Lewis endorsed MGD, as JL&M claim.

Lack of fit. Lewis wrote a lot about how natural languages get their meaning. Among other things, his PhD thesis and first book were on that topic. The answer he gave everywhere except in "Putnam's Paradox" and pp.45-59 of "New Work" is not MGD. Rather, Lewis suggested that the interpretation of natural languages is determined by conventions of use, which in turn boil down to certain beliefs and expectations in the relevant community. Once the beliefs and expectations are fixed, the interpretation of the language is fixed as well (to the extent that it is). Lewis also had an account of what determines the content of beliefs and expectations; that account looks even less like MGD, for Lewis didn't believe in a language of thought whose sentences could constitute a speaker's "total theory" and whose non-logical terms would stand in need of interpretation.

What do JL&M say about this lack of fit? They deny it. They don't even see a tension. I thought that I had explained in detail how MGD contradicts what Lewis wrote elsewhere about language, but apparently the message didn't come across. "Schwarz doesn't explain the alleged contradiction", JL&M say. As a reminder, here are three points of contradiction. (There are many more.)

• MGD assigns no role to the conventions that ground linguistic meaning on Lewis's own account.
• MGD makes meanings objectionably intransparent to competent users, in a way that goes against the central point of semantics, to explain and systematise linguistic behaviour.
• MGD only gives sensible results for expressively rich languages, and only if we hold fixed the meaning of logical expressions and the rules of compositional semantics. Lewis's own account has none of these limitations.

JL&M argue that far from contradicting Lewis's other writings on language, MGD nicely complements it. The idea is that Lewis's earlier writings only explained how entire sentences get their truth-conditions; they don't explain how individual words get their reference. That's the gap MGD is supposed to fill:

Because early Lewis only discussed the truth-conditions of sentences, and admitted he lacked an account of reference, it's difficult to see how the account of reference in 'Putnam's Paradox', magnetized global descriptivism, can 'contradict', as Schwarz claims, what Lewis wrote elsewhere on language.
Lewis's proposal [...] in 'Putnam’s Paradox' doesn’t conflict with what he'd written before. Appeal to making ideal theory come true supplements his earlier account, which had gone no further than assigning truth-conditions: choose an assignment of reference that makes ideal theory come out true relative to the assignment of conventionally established truth-conditions.

I don't understand this proposal. The supposed combination of views would be coherent if truth-conditions and reference were entirely independent. One could then tell one story about truth-conditions, and an entirely different story about reference. But that's surely implausible. In any case, MGD is not just a theory of reference. The interpretation it singles out as correct is supposed to tell us what the sentences of a language mean, not just what the individual words refer to. (Remember we need to hold fixed the meaning of the logical expressions and the compositional semantics for MGD to get off the ground.)

Here's what JL&M might have in mind: Lewis's earlier account of language did not fix the meanings of subsentential expressions; the conventions Lewis identifies as determining the truth-conditions of sentences are compatible with many assignments of meanings to subsentential expressions. What Lewis then came to accept is that the true meanings of subsentential expressions are the most natural ones among the various candidates.

That's a coherent view. (I mentioned it in my paper.) But it's not MGD. It has traded Global Descriptivism as a theory of how sentences get their truth-conditions for Lewis's convention-based account. And it has reduced the role of naturalness to breaking ties between different grammars producing the same truth-conditions. In my paper, I had set aside this view as uninteresting and unmotivated. I stand by these judgements. Why would one want subsentential semantic values to be objectively natural, rather than, say, simple to manipulate in linguistic theorising? What problem would that solve? Recall also that Lewis is explicit that subsentential semantic values are not referents, but more complex set-theoretic constructions.

The proposed view also doesn't make much sense of "Putnam's Paradox". Putnam's paradox is not about reference or subsentential semantic values. The paradox Lewis tries to dissolve is Putnam's claim that our total theory cannot possibly be false. This is a claim about the truth-values of sentences, not about subsentential semantic values. The naturalness constraint on meanings is supposed to force some sentences to become false that would otherwise have come out true.

To sum up:

• MGD is not just a theory of how subsentential expressions get their meaning. It is also a theory of how sentences get their meaning.
• This theory is markedly different from the theory Lewis defended elsewhere.
• One could coherently combine Lewis's convention-based metasemantics with a naturalness constraint on subsentential semantic values, but this is not what Lewis defends in "Putnam's Paradox" (or pp.45-49 of "New Work"), and there is no other reason to think it was Lewis's view.

The distancing. In both papers in which Lewis defends MGD, the defence is accompanied by a caveat. Here is the caveat in "Putnam's Paradox" [p.222]:

I shall acquiesce in Putnam's linguistic turn: I shall discuss the semantic interpretation of language rather than the assignment of content to attitudes, thus ignoring the possibility that the latter settles the former. It would be better, I think, to start with the attitudes and go on to language. But I think that would relocate, rather than avoid, the problem; wherefore I may as well discuss it on Putnam's own terms. [Footnote: For a discussion o f the 'relocated' problem and its solution, see the final section of my 'New Work for a Theory of Universals']

Here is the corresponding passage in "New Work":

You might well protest that Putnam's problem is misconceived, wherefore no need has been demonstrated for resources to solve it. Putnam seems to conceive of language entirely as a repository of theory, and not at all as a practice of social interaction. We have the language of the encyclopedia, but where is the language of the pub? Where are the communicative intentions and the mutual expectations that seem to have so much to do with what we mean? In fact, where is thought? It seems to enter the picture, if at all, only as the special case where the language to be interpreted is hard-wired, unspoken, hidden, and all too conjectural. I think the point is well taken, but I think it doesn't matter. If the problem of intentionality is rightly posed there will still be a threat of radical indeterminacy, there will still be a need for saving constraints, there will still be a remedy analogous to Merrill's suggested answer to Putnam, and there will still be a need for natural properties. Set language aside and consider instead the interpretation of thought...

What follows is a lengthy discussion of how mental states get their content. Nothing remotely like MGD figures in that discussion.

To me, these passages clearly indicate that Lewis disagreed with a presupposition of Putnam's Paradox: that the correct interpretation of a language is determined by what makes total theory come out true (Global Descriptivism, understood as a metasemantics), rather than by the attitudes in the relevant linguistic community. Both passages also explain why Lewis nonetheless goes on to address Putnam's paradox on Putnam's own terms: he thinks a somewhat analogous problem arises in his own account of how mental states get their content, and that appealing to objective naturalness helps with that problem.

What do JL&M say about these passages? According to JL&M,

Lewis meant what he said in 'Putnam's Paradox'. He was a global descriptivist who adopted reference magnetism to fend off radical indeterminacy of reference, modulo the caveat that content magnetism is first required to fend off radical indeterminacy of content at the level of thought.

In the remainder of JL&M's paper, the caveat is ignored altogether. So JL&M seem to interpret Lewis as saying that objective naturalness is needed not only in the correct theory of how words get their meaning, but also (and "first") in the correct theory of how mental states get their content. Surely this is not what Lewis is saying in the passages just quoted.

Interlude. I claim that in "Putnam's Paradox", Lewis defended a theory (namely MGD) which he didn't actually endorse. JL&M find this unbelievable. Why would Lewis defend a particular answer to a puzzle if he thought the correct answer is completely different?

Well, I said something about this, but apparently I didn't say it clearly enough. Here is what I think was going on.

To begin, Lewis was responding to a puzzle raised by Putnam. The puzzle presupposes a certain view of how words get their meaning. Lewis rejected that view. But he thought that given the presuppositions of Putnam's paradox, MGD is a good response. So on my interpretation, Lewis accepted MGD as a good response to Putnam's paradox, given the terms of the paradox.

Still, why would Lewis give this response, rather than point out that the presuppositions are mistaken? For two reasons.

First, as his says himself, he thought a somewhat analogous puzzle arises in his own account of how mental states get their content, which in turn affects how words get their content. And he liked a somewhat analogous solution to that puzzle.

(But it's important not to overstate the analogies. For example, the puzzle that arises for Lewis's theory of intentionality has nothing to do with reference. The decision-theoretic permutation argument Lewis gives in "New Work" vaguely resembles familiar permutation arguments for the indeterminacy of reference, but what is being permuted in Lewis's argument are assignments of propositional attitudes, not assignments of referents.)

Second, Lewis plausibly regarded Putnam's Global Descriptivism as a crude approximation to his own meta-semantics. The approximation simplifies the attitudes that ground meanings to just one: acceptance of a sentence. On Lewis's own account, any sentence that is widely accepted in a community is likely to be true (on the correct interpretation of the sentence). So if we had to work with the simplified basis of which sentences are accepted, a natural way to fill in the story is to say that the correct interpretation should, as much as possible, make the accepted sentences come out true.

Moreover, since Lewis accepted that objective naturalness plays a role in determining the content of attitudes, which in turn determine the interpretation of language, he also accepted that objective naturalness (indirectly) constrains the interpretation of language. Indeed, I suspect he thought that 'the sky is blue' means that the sky is blue partly in virtue of the fact that blue is more natural than grue. Not because there is a direct naturalness constraint on referents, but indirectly via the interpretation of the attitudes that give the sentence its meaning. (I speculate a bit about how this indirect route might go in my paper. It's far from obvious, especially because Lewis says so little about how exactly the naturalness of certain properties is meant to constrain the probability and utility functions that give content to our mental states.)

I mention all this because JL&M assume that on my interpretation, Lewis should reject MGD whenever he discusses Putnam's paradox in correspondence. They go on to cite various passages from letters in which Lewis doesn't do that, and treat that as "decisive evidence" against my interpretation.

Evidence from correspondence. I won't go through all the letters cited by JL&M. I don't think any of them undermines my interpretation of Lewis. Some of them seem completely irrelevant, such as this passage from a letter to Teller:

I'm not sure what you’re proposing. It might be this: (1) that imperfect naturalness of some properties is to be understood in terms of definability from perfectly natural properties; then for words to have imperfectly natural referents is the same as for them to be definable from words, if such there be, with perfectly natural referents. ... (1) is fine with me; it makes explicit something I've supposed, but left out because I didn't have details -- a theory of simplicity of definitions -- to offer.

So Lewis is "fine" with the idea that imperfect naturalness can be understood in terms of definability from perfect naturalness. I have no idea how that is meant to show that Lewis endorsed MGD.

In other letters, Lewis explicitly discusses Putnam's argument, and suggests, for example, that inegalitarianism about properties "would provide the necessary constraints on reference" to escape the paradoxical conclusion. I don't see why Lewis shouldn't have said that. On my interpretation, this is precisely what Lewis thought, although he also thought that Putnam's argument rests on an oversimplified metasemantics.

In a 2001 letter which may or may not be about Putnam's argument, Lewis states that "[f]airly determinate content of thought (or language) ... requires reference magnetism". Again, this is perfectly compatible with my interpretation of Lewis's views. Yes, Lewis did think that the content of our attitudes, and indirectly the content of our language, is partly fixed by constraints of objective naturalness. Admittedly, "reference magnetism" is a somewhat misleading label for the ideas presented in "New Work" from page 50 onwards, which describe how naturalness enters into the determination of mental content. So one might take Lewis's use of that label to suggest that he later switched to a completely different account on which the content of mental states is determined by assigning referents to mentalese words. But that would be a big change of opinion. I'd need to see a lot more evidence for it.

JL&M also cite a letter to Forrest from 1988, which actually supports my interpretation. The topic of the letter is Putnam's argument. Lewis writes:

Once the over gruesome interpretations are out by inegalitarianism, I would hope that fit can do the rest of the job. Fit is something like making ideal theory come true. I'm not sure how much farther we can go while joining Putnam in ignoring the difference between interpreting thought and interpreting language.

Overall, I don't find anything in JL&M's paper that really challenges the interpretation I offered in "Against Magnetism".

PS. The strongest piece of evidence against my interpretation that I know of is something JL&M don't mention: footnote 6 of "Many but Almost One". Here Lewis discusses the problem that in the vicinity of any cat there are countless aggregates of matter that equally deserve the name 'cat'. He adds:

I do not think reference is entirely up to our choice. Some things are by their nature more eligible than others to be referents or objects of thought, and when we do nothing to settle the contest in favour of the less eligible, then the more eligible wins by default; see Lewis (1984) [i.e., "Putnam's Paradox"].

I mention this passage in footnote 7 of "Against Magnetism", but falsely claim that it is only about thought. (I'm not sure how that happened. Maybe I parsed "referents or objects of thought" as "referents of thought or objects of thought"? That's grammatically possible, but I don't think it's what Lewis had in mind.)

I'm not entirely sure what to make of this passage. As I said, I think it's the strongest piece of evidence against my interpretation of Lewis. But it's far from conclusive, especially given that every alternative interpretation I can think of (such as the interpretation defended by JL&M) clashes with much more of Lewis's writings, besides attributing views to him that have obvious and serious faults.

Also, as I said earlier, Lewis may well have thought the upshot of his complicated and indirect metasemantics is a kind of reference magnetism that resembles MGD, but without running into all the problems for MGD that I raised in my paper. That is, for all I'm suggesting, Lewis may well have thought that 'blue' means blue partly in virtue of the objective naturalness of blue, but not because there's a brute naturalness constraint on the reference of words. The true story is much more complicated, and wouldn't fit in a footnote.

# on 19 July 2019, 18:47

“The supposed combination of views would be coherent if truth-conditions and reference were entirely independent. One could then tell one story about truth-conditions, and an entirely different story about reference. But that's surely implausible.”

Isn’t this a fairly popular position? That is, isn’t this just to say that there’s a difference between the indeterminacy of translation (a thesis about the assignment of meaning to sentences) and the inscrutability of reference (a thesis about the meanings to terms)? And fixing the former needn’t fix the latter?

# on 19 July 2019, 19:08

Thanks Bryan. I agree fixing truth-conditions doesn't fix reference. But I would have thought that if something fixes truth-conditions and something fixes reference, then these two things should be closely related to one another. Also, while one can come up with a semantics in which "dogs bark" is true iff dogs bark even though "dogs" refers to planets and "bark" to eating ice-cream, this won't be an intuitively plausible semantics. If we want a plausible semantics, the referents and the truth-conditions must be coordinated in a particular way.

# on 19 July 2019, 19:23

Hmm. I’m not so sure. The truth condition you assign to ‘dogs bark’ will be some set of worlds. In exactly those worlds planets will get up to certain antics. So if we have ‘dogs’ refer to planets and ‘bark’ refer to the relevant antics, then don’t we have the requisite coordination? What is missing?

# on 19 July 2019, 19:28

Maybe a way of putting it that centers your debate with JLM: I can see how one might think conventions of trust and truthfulness fix the truth conditions of ‘dogs bark’. But I’m less clear about how they fix that we are talking about dogs rather than dog-complements, undetached dog parts, or numbers. Is there a straightforward story?

# on 20 July 2019, 08:10

Ah, right, no there isn't. The conventions only settle truth-conditions of sentences, not subsentential semantic values. On this, JL&M and I agree. Lewis also says as much.

JL&M suggest that Lewis endorsed MGD as an account of how subsentential semantic values are determined. This I deny, for a number of reasons. One is that MGD is also an account of how truth-conditions are determined, and this part of MGD is not equivalent to the convention-based account. Another is that at the only places where Lewis defends MGD, his main concern is with truth-values of sentences, not with subsentential semantic values. Another is that combining the convention-based account for truth-conditions with an MGD account for subsentential semantic values, even if it were possible, would likely lead to a very strange semantics; for example, if there's a convention to use 'a is F' iff a is F but the nearby property G is more natural than F, then the semantics will say that 'a is F' is true iff a is F although 'a' refers to a and 'F' refers to G. This is what I meant by the MGD referents and the conventional truth-conditions being uncoordinated.

On my interpretation, Lewis did not have a particular account of how subsentential semantic values are determined. (He /did/ have an account of why we are talking about dogs when we say 'dogs bark', but his theory of aboutness doesn't involve subsentential semantic values.) He may have liked the idea that the correct assignment of subsentential semantic values is the objectively most natural one among those that generate the right truth-conditions. But that's not MGD, and there's no clear textual evidence that Lewis endorsed it. (It's the hypothesis I'd set aside in my paper as unmotivated and uninteresting.)

Hope this clears things up a little.

# on 20 July 2019, 12:14

Wolfgang, you’ve said here a couple of times that magnetised global descriptivism (MGD) is a view about truth conditions, not about reference. But me and JL don’t think of MGD that way, and we’re certain that Lewis didn’t either.

Here’s how Lewis introduced global descriptivism in ‘Putnam’s Paradox’: ‘The intended interpretation will be the one, if such there be, that makes the term-introducing theory come true. (Or:... come near enough to true. Or: the intended interpretations will be the ones, if such there be.... with in- determinacy if there are more than one.) But this time, the term-introducing theory is total theory! Call this account of reference: global descriptivism’ (1984: 224). Now Lewis goes onto argue that global descriptivism leads straight to unpalatable indeterminacy of reference. He concludes, ‘Global descriptivism stands refuted. It may be part of the truth about reference, but it cannot be the whole story. There must be some additional constraint on reference’. The additional constraint that Lewis comes up with, to add to global descriptivism so understood, is reference magnetism, ‘This constraint looks not to the speech and thought of those who refer, and not to their causal connections to the world, but rather to the referents themselves’ (227).

What’s important for present purposes is that there is nothing here to suggest or require that global descriptivism + reference magnetism is a thesis about truth conditions; there isn't because it’s about reference, as Lewis explicitly says several times. Since MGD’s about reference rather than truth-conditions, it’s possible for Lewis to tell a distinct but compatible story about how truth-conditions are settled, as we argue at the end of our paper: ultimately that truth-conditions of a public language are owed to the contents of the mental states of speakers that share the language as a matter of convention and that the referents of the words of public language are the most natural assignments of reference which cohere with the assignments of contents to speakers. This I take to be the point that Bryan was agreeing with in his comments above.

There’s a lot more to say about this and about the other points you raise, but I’ll stop here since this is clearly a major disagreement between us.

# on 20 July 2019, 12:47

Thanks Fraser. It's interesting that you think what Lewis wants to secure in "Putnam's Paradox" is determinacy of reference. I think what he wants to secure is the realist assumption that our (ideal) total theory could be false. This is what Lewis says he wants to do at the start of the paper, and he comes back to it at various points throughout. The two issues are related because Putnam assumes the theory in question is expressed in standard first-order logic. On that assumption, the truth-value of sentences is determined by the referents of the non-logical expressions. Lewis agrees that there will always be some choice of referents that makes the total theory true (provided the theory is consistent and the universe is large enough). So Global Descriptivism alone is unpalatable, not because it leads to indeterminacy of reference, but because it leads to Putnam's incredible claim that our ideal total theory is guaranteed to be true. MGD is supposed to block that result. This would make no sense if MGD had no consequences for the truth-values of sentences.

Exegetical points aside, don't you agree that in a plausible semantics, the truth-conditions of sentences and the referents of subsentential expressions must be closely connected? Don't you find it problematic that on your view, 'a is F' could be true iff a is F (that's the truth-conditions) even though 'a' refers to a and 'F' refers to a property G that's different from F (and more natural)? To make this consistent, one would need highly non-standard compositional rules, certainly nothing like the rules Lewis outlines e.g. in "General Semantics". If we rule out bizarre compositional rules, then an assignment of referents comes close to assigning truth-conditions. For example, once we say that 'dogs' refers to dogs, and 'bark' refers to barking, there won't be many plausible options for what the truth-conditions of 'dogs bark' might be.

# on 20 July 2019, 16:58

Hello Wolfgang, I'm following up on a couple of these points. First, we see no textual evidence that magnetised global descriptivism is a theory of how sentences get their meaning, or that, as you say, Putnam's paradox is not about reference'. Lewis says otherwise: The main lesson of Putnam's Paradox, I take it, is that this purely voluntaristic view of reference leads to disaster' (Lewis 1984: 226). He does not mention sentence meaning in Lewis 1984. He also says, global descriptivism ... leads straight to Putnam's incredible thesis. For any world (almost), whatever it is like, can satisfy any theory (almost), whatever it says' (Lewis 1984: 226). Here he describes a maximal object (a world) satisfying a very long description (theory). He thinks there is no way the theory can be false because the world always satisfies it through creative permutation of referents. There will be more material in the Lewis book we are writing about this topic.

I'd also like to clarify that magnetised global descriptivism isn't our view. We argue that it is Lewis's view, and that it is legitimate for him to hold it because is compatible with early Lewis's convention-based philosophy of language. (Both of us actually think MGD is false, though for different reasons from yours, Wolfgang. E.g. see Janssen-Lauret 2016, Synthese, against global descriptivism).

But we think that truth-conditions and reference are intelligibly connected for Lewis, as we say in the last paragraph of our paper, by the following recipe: choose an assignment of reference that makes ideal theory come out true relative to the assignment of conventionally established truth-conditions. You suggest as a RAA of this view that the following might occur: " 'a is F' could be true iff a is F (that's the truth-conditions) even though 'a' refers to a and 'F' refers to a property G that's different from F (and more natural)", but we think that is ruled out by the recipe. On our interpretation, Lewis doesn't think that you could legitimately assign some property G to the predicate which is more natural than the most natural property consistent with the assignment of truth-conditions. He thinks that we should assign the most natural referent that is compatible with the assignment of truth-conditions. Since, as you set up the case, G doesn't cohere with the assignment of truth conditions, the assignment of G, rather than F, to the predicate is ruled out.

# on 20 July 2019, 19:34

“Don't you find it problematic that on your view, 'a is F' could be true iff a is F (that's the truth-conditions) even though 'a' refers to a and 'F' refers to a property G that's different from F (and more natural)?”

Isn’t this meant to be a virtue? ‘Dogs are spheres’ is true iff dog-complements are sphere-complements. But ‘dogs’ refers to dogs (and not dog-complements) and ‘spheres’ to spheres (and not sphere-complements).

# on 21 July 2019, 07:53

I'm clearly not getting across the "coordination" problem. Here's a more concrete example.

Consider a community that speaks a fragment of English consisting of noun phrases for animal kinds ("dogs", "birds", etc.) and verb phrases for properties like having fur, having wings, etc. (They also have first-order logical machinery: quantifiers, boolean connectives, etc.) The conventional truth-conditions of their sentences are just like in English. So "all birds breathe fire" is true iff all birds breathe fire.

Now, people in this community have misleading evidence that birds breathe fire. So their total theory includes the false sentence "all birds breathe fire". That's the only thing the community gets wrong. So their theory also includes true sentences like "no dog breathes fire", "no cat breathes fire", and so on.

If we follow the MGD recipe for assigning reference, we should look for an assignment that strikes the best compromise between naturalness of referents and making the total theory true. The problem Putnam raised was that we can always find some assignment that makes total theory true. However, such an assignment will often involve highly gerrymandered referents. MGD excludes such assignments. But in the present case, it's easy to make the entire theory true. We simply need to find some relatively natural property that only birds have, and assign it as referent to "breathe fire". Let's take the property of using air sacs for respiration.

So by following the MGD recipe for determining reference, we might say that "birds" refers to birds, and "breathe fire" refers to using air sacs for ventilation. (And of course "all" means all, etc.) And yet the conventional truth-conditions for "all birds breathe fire" are that all birds breathe fire.

This is what I mean when I say that the assignment of reference should be coordinated with the assignment of truth-conditions, in a way it is not if we let truth-conditions be determined by conventions and referents by MGD. A semantics according to which (a) "birds" refers to birds, (b) "breathe fire" refers to using air sacs, and (c) "all birds breathe fire" is true iff all birds breathe fire is not a plausible semantics.

(The case is not like that of dog-complements and sphere-complements.)

# on 21 July 2019, 09:15

What exactly is the difference here between the case you describe and the dog-complements? On your view, the conventional truth conditions of 'birds breathe fire' have it that the sentence is true if and only if bird complements exhibit an appropriately caused heat pattern. In the story you tell, those truth conditions are the result of functionally applying the meaning of 'breathe fire' to the meaning of 'birds'. (Notice that your proposed semantics follows the pattern that you said you found problematic, because 'birds' refers to 'birds' and not to bird-complements.) One difference here is that the bird story that you told---but not the dog story---requires deviantly interpreted construction rules to make the assignment of truth conditions consistent. But if our problem is the inscrutability of reference and not the indeterminacy of translation, then even holding fixed the construction rules does not solve it, as the dog story shows. One way to think about this: we can build interpretations of the construction rules into the total theory and still get a lot of deviant interpretations.

# on 21 July 2019, 18:36

@bryan: I think we may be talking past each other. I agree that fixing truth-conditions doesn't fix referents, even if we hold fixed the compositional rules. The relevant complaint I have about JL&M's interpretation is only about /the specific method/ by which they think Lewis wants to secure determinacy of reference, namely by means of MGD. And here I was making what I hope is a simple and obvious point: if we want a sensible compositional semantics, then we can't independently assign truth-conditions and subsentential semantic values; for a given assignments of truth-conditions, the vast majority of possible assignments of subsentential values is ruled out, if we want a non-deviant compositional semantics.

That's all I wanted to say. I'm not claiming that there is a single assignment of subsentential values that non-deviantly creates the stated truth-conditions. There are lots, no doubt. But there are many more that don't. And this means that we can't tell two entirely different stories about what fixes truth-conditions and about what fixes subsentential values. In particular, we can't say that conventions fix truth-conditions while MGD fixes referents. My last example was meant to illustrate how this combination of views can concretely lead to a semantics that requires a deviant compositional grammar.

# on 21 July 2019, 20:23

Wolfgang, you haven’t responded to our previous point, so here’s something else. In my and JL’s paper (section 2) we provide evidence from the letters that Lewis did allow reference magnetism a role in determining reference, contra your claim that ‘objective naturalness plays essentially no role in Lewis's theory of language' (2014:21). In particular we quote from a letter to Teller in which Lewis discusses Teller’s suggestion that naturalness provides a constrain on reference. Lewis says that understood correctly, Teller’s suggestion, as Lewis clarifies it in his letter, is ‘fine with me’. Nevertheless you claim that this letter is ‘completely irrelevant’ because really it only tells us that Lewis conceived less natural properties as being defined in terms of natural properties. But you’re leaving out half of Lewis’s point, the bit to do with reference.

Lewis begins his discussion with the line, Concerning your suggestion about naturalness as a constraint on reference’, a line which you omit here in your blog but is clearly relevant to establishing the provenance of the subsequent remarks. Lewis then proceeds to write, even in the part you do quote, that ‘for words to have imperfectly natural referents is the same as for them to be definable from words, if such there be, with perfectly natural referents’. Here Lewis isn’t just saying that imperfect naturalness can be defined in terms of natural properties but about the consequence of this for how we conceived of words that have imperfectly natural referents. As me and JL continue in our paper, If Lewis hadn't believed what he wrote in `Putnam's Paradox', he'd have responded to Teller's suggestion of naturalness as a constraint on reference that naturalness was no such thing. In your blog, you don’t respond to the exegetical reasoning here in section 2 or elsewhere in our paper. Again, a lot more to say, but I’ll stop there.

# on 22 July 2019, 11:16

@Fraser: I have addressed these points in the blog post. On my interpretation, Lewis agrees that a good response to Putnam's challenge, granting the presuppositions of the challenge, is to impose a direct naturalness contraint on reference.

What Lewis says he is "fine" with in the letter still seems irrelevant to me. The relevant point '(1)' has two parts; I quote:

(1a) "that imperfect naturalness of some properties is to be understood in terms of definability from perfectly natural properties;"

(1b) "then for words to have imperfectly natural referents is the same as for them to be definable from words, if such there be, with perfectly natural referents"

(1b) is entailed by (1a). (Which is why Lewis correctly begins with "then".) That is, (1b) doesn't add anything to (1a); it merely spells out a consequence. So when Lewis says he is fine with (1), he doesn't really say more than that he is fine with (1a).

# on 22 July 2019, 12:04

On a more general note, I should mention that I am far from certain about the interpretation I've presented in my paper. My credence is around 80-90%. So I really appreciate the discussion and pointers at possible new evidence.

(I am around 99% sure Lewis didn't endorse the theory he defends in PP, however, for the three reasons I mentioned.)

# on 22 July 2019, 18:51

Wolfgang, I don't think you have addressed these points in your blog. For example, you say that 'Putnam's Paradox' isn't about reference but we've provided evidence to the contrary and I don't think you've provided an alternative reading of these passages.

WIth regard to the Teller letter. First of all, you're leaving off the beginning of Lewis’s sentence, viz. ‘Concerning your suggestion about naturalness as a constraint on reference'. Lewis then proceeds to disambiguate this suggestion, and under disambiguation (1), Lewis endorses Teller's suggestion, i.e. a suggestion about naturalness as a constraint on reference. He says not just that ‘(1) is fine with me’ but also that ‘it makes explicit something I’ve supposed’. You also leave out this latter part of what he says.

The disambiguation (1) which Lewis endorses indeed has two clauses, I’ll keep your labelling.

(1a) "that imperfect naturalness of some properties is to be understood in terms of definability from perfectly natural properties;"
(1b) "then for words to have imperfectly natural referents is the same as for them to be definable from words, if such there be, with perfectly natural referents"

You say that (1b) just follows from (1a) so when Lewis says (1) is fine with him, he just means to endorse (1a). But (1b) mentions referents and words, while (1a) doesn’t, so it’s not obviously equivalent. E.g. (1a) could be about real definition on wholly abstract properties, (1b) could not.

But, more importantly (1b) is incompatible with your interpretation of Lewis, because it assigns naturalness a role in constraining reference, which you deny. This is what Teller suggests and Lewis endorses.

Since you think that Lewis endorses (1a) and that (1b) just follows from (1a), it looks like you think that Lewis is committed to (1b) too! But that's contrary to your view.

# on 23 July 2019, 06:07

@Fraser:

- Of course PP is /also/ about reference. My point was that it is not /just/ about reference: the main aim of the presented theory to secure that the sentences in our total theory may be false.

- I really don't see the problem with (1b). Nothing in (1b) implies MGD, or anything else I claim Lewis didn't accept.