Lewis on meaning and fundamental O-terms

I thought after finishing my PhD thesis I would spend less time thinking and writing about Lewis for a change. But just then, Brian started his Lewis blog raising all kinds of interesting issues, like how to handle theoretical terms in multiply realised theories. I think Lewis's early suggestion to treat the terms as empty in those cases is much worse than he realised (than he realised even later, when he dropped the suggestion). I hope to say more about that later.

This entry is about a somewhat related question that came up on David Chalmers's blog: how Lewis's account of theoretical terms can serve as a general theory of meaning.

One of the most puzzling things about Lewis's theory of meaning is that throughout his career, he told two apparently very different stories about how our words get their meaning. I'll try to explain how I think the two stories go together.

Here's the descriptivist story:

Our words are associated with descriptions, or 'theories'. The relevant theory is usually a folk theory, commonly known in our linguistic community. This theory defines the words with which it is associated: if the (ramsified) theory is uniquely realized by objects x1,...,xn, then the defined words denote x1,...,xn. Moreover, the sense of the words is the function from all worlds to the realizers at those worlds, if there are any. (The worlds should be centered because the theory may contain indexicals, like "Aristotle stands at the causal origin of our use of the name 'Aristotle'").

Something like this can be found in "An Argument for the Identity Theory" from 1966 and "Ramseyan Humility" from around 2001, and in lots of papers from in between, for example in "Psychophysical and Theoretical Identifications" (1972), "Putnam's Paradox" (1984), "Naming the Colours" (1997), and, most detailed, in "How to Define Theoretical Terms" (1970).

The second story is the use story:

The semantic properties of linguistic expressions are determined by their conventional use: by conventions to only utter sentences in certain circumstances, e.g. "it's raining" when it's raining. For each sentence, this determines a set of circumstances, that is, of centered possible worlds. Call this set the truth conditions of the sentence. A compositional grammar for English is any -- preferably systematic, nice, natural and simple -- theory that delivers those truth conditions. The grammar need not trace our cognitive processing, nor does it need to assign, say, London as semantic value to "London": what matters is only that it assigns to all sentences the truth conditions that match our intentions and expectations towards utterances of the sentence.

Something like this can be found, for example, in "Convention" (1969), "Languages and Language" (1975), "Index, Context and Content" (1980), On the Plurality of Worlds, pp.40-50 (1986), and "Meaning without use" (1992).

It is highly unlikely that Lewis regarded the two stories as rivals and continuously changed his mind about which one is true. We need a unified story that includes them both.

An important clue to this end is that the use story dominates Lewis's writings in the philosophy of language and formal semantics, whereas the descriptivist story mainly comes up in papers on metaphysics. (One might argue that HTDTT is a paper on language; but I think it's no accident that Lewis put it in the "Ontology" section of his Papers I and not in the "Language" section. In the language section, we only get the use story.)

Here's how I think the unified story goes:

To explain why linguistic expressions, say "it's raining", have a meaning -- and why they have the particular meaning they have --, we must look at how these expressions are used. "It's raining" means that it's raining because members of our linguistic community generally try to utter that sentence only when it's raining, and because this is common knowledge among us. An utterance is true if it takes place in the circumstances conventionally associated with the sentence.

To follow our linguistic conventions, members of our community have to know, at least implicitly, which sentences are true in which circumstances.

Now as we happen to speak a fairly rich language, we can often express these truth conditions in all kinds of ways: we can say that "it's raining" is true iff it's raining, but also that it's true iff water falls from the sky in a particular manner. Let's call an expression T definable by O-expressions, where the O-expressions are any expressions, if the truth conditions for all sentences containing T can be expressed by clauses containing only O-expressions.

From a semantical point of view -- if our question is how words in general get their meaning --, it isn't very interesting that some expressions are definable in terms of others. We could speak a less rich language where no expression is definable in terms of other expressions, like a fragment of English that only contains the expressions "it's raining", "it's snowing", "I", "am", "hungry", and "not". There would still be an interesting question as to how these words get their meaning, and the answer would still be the use story.

However, from a metaphysical point of view, definability is very interesting indeed. If, for example, it turns out that we can define phenomenal expressions in terms of functional/physical expressions, we can make an argument for the identity theory based on this. Which is exactly what Lewis does. In a similar way, he uses definitions of causation, laws of nature and objective chance as key steps in his arguments for Humean Supervenience.

Nowadays, metaphysics is often understood as being primarily about modal relations. Lewis himself defines materialism and HS as modal supervenience claims. Then one can ask whether B-truths might supervene upon A-truths even though B-terms are not definable by A-terms. The answer is yes: In a Chalmers-style type-F monism, the phenomenal supervenes on the physical without the phenomal being definable in terms of the physical. In my view, metaphysics should better be understood as being about analytical relations. The common modal definition of materialism cuts across the really important question in this area which divides dualism and type-F monism on the one side from behaviourism and analytical functionalism on the other side. (I find "non-reductive materialism" hard to classify because I don't quite see how it is supposed to work. I suspect most non-reductive materialists, Papineau for example, are actually type-F monists once the dust has settled.)

Dave says that isolating a set of basic expressions in terms of which all others can be defined is one of the deepest questions in philosophy. I think that's right, but maybe not for Dave's reasons. For I don't believe that there is a unique set of such basic expressions. We are familiar with small sets of interdefinable terms: { "part", "overlap", "fusion"}, {"and", "or", "not" }. I think it's quite likely that this occurs also on a very large scale.

To my knowledge, Lewis never explicitly discusses this issue, but I think he is committed to the same view.

For one, as Dave notes in the comment linked to above, there are very few expressions (or small families of expressions) Lewis took to be undefinable, maybe only logical and mereological expressions. But surely not all other terms are definable in terms of those. In fact (and importantly, I think), no other expression at all is definable in terms of those.

Secondly, if one looks at Lewis's definitions, they don't seem to go in a common direction, towards a set of absolutely fundamental expressions: phenomenal terms are defined using causation; causation by certain counterfactuals; those counterfactuals in terms of local events and laws of nature; laws of nature in terms of simplicity, strength and fit of theories; fit of theories in terms of objective chance; objective chance in terms of ideal subjective probabilities; and so on and on.

Thirdly, Lewis always emphasizes that the "old terms" in a theoretical definition are not meant to be epistemologically or conceptually basic terms like the logical positivist's "obvservational terms": "An O-term can have any epistemic origin and priority you please. It can belong to any semantic or syntactic category you please" (HTDTT, p.79).

Fourthly, Lewis does not need basic O-terms in his philosophy of language, or anywhere else. He would need them if he wanted to base his theory of meaning on something like the descriptivist story. Clearly, the descriptivist story alone doesn't work as a theory of meaning, as it presupposes old terms with a fixed meaning. Even the 'Global Descriptivism' Lewis talks about in "Putnam's Paradox" assumes that a different, non-descriptivist story fixes the meaning of the logical vocabulary.

Perhaps one could build a theory of meaning around the descriptivist story: suppose we have a good non-descriptivist story about how a certain very limited fragment of our language gets its semantic properties. Then perhaps we could use the descriptivist story to explain how all the other expressions get their meanings. I think Dave accepts something like this, though probably not, or not directly, for public language. At any rate, Lewis's theory looks completely different. Lewis's account of meaning is based on the use story, which directly covers at least a very large fragment of our language.

Perhaps it's important that all this is about public language, not about the intentionality of mental states. Lewis never uses anything even remotely like the descriptivist or the use story in his account of mental content.


# on 27 October 2005, 02:05

Thanks, Wo. That's really interesting and useful.

Let's distinguish three questions. (i) Is Lewis committed to there being some class (or classes) of fundamental O-terms? (ii) If so, what terms are plausibly in this class, according to Lewis's commitments? (iii) Does this class have a special role to play in Lewis's account of meaning or content?

Re (i): You say that Lewis' analyses don't seem to go in a common direction. I'm not sure about that. I think Lewis would have been very bothered had his analyses turned out to be circular: e.g. going from the phenomenal to the causal to the nomic to the spatiotemporal to the phenomenal. So it does look like he's at least committed to there being some relatively small class of O-terms in which everything can be defined. And his philosophical method seems to be inclined toward making this class as small as possible. So I'm inclined to think that Lewis would hold that there is some really quite small class of O-terms in terms of which everything can be defined.

Of course there may be more than one such minimal class. At the very least, we'll have a class of basic families such that one can choose different basic terms within a family. And there may be a bit more variation than this. Still, Lewis's general orientation seems to suggest that he regards many candidates for fundamental O-terms (experience, causation, law, etc) as non-basic "simpliciter". That is, it's not the case that we might equally well take these terms as basic and then use them to analyze the terms that we've in fact used to analyze them. So this tends to point toward pretty serious restrictions on the basic classes.

(ii) The pattern of analysis you suggest above tends to suggest a candidate view, on which Lewis thinks that spatiotemporal terms are basic and not to be analyzed in terms of further O-terms. Certainly these play a crucial role in grounding the regularities that are at the basis of his analyses of laws, theories, causation, etc. And I don't see much in Lewis that promises to serve as an analysis of these notions. Of course the view that these are basic also fits very nicely with the his Humean supervenience, on which everything supervenes on distributions in space and time. Lewis presumably also holds something close to the claim that everything is a priori entailed by sentences describing distributions in space and time. So whatever vocabulary is needed to state these sentences might be a candidates for fundamental O-terms, according to Lewis. That presumably involves spatiotemporal notions plus logic, maybe some mathematics, and maybe a bit of "categorical" stuff, e.g. enough to characterize the instantiation of primitively distinct fundamental natural properties.

I don't know what he'd say about the Matrix-style argument for the nonbasicness of spatiotemporal notions, and their analyzability in terms of dispositions to cause experiences and the like. I suspect he'd have wanted to reject the arguments. If not, we'd have been left with some sort of "Naming the Colors"-style circle in the base, which presumably wouldn't be a good thing.

I'm not quite sure where ideal subjective probabilities and related epistemic notions fit in here. Presumably Lewis doesn't think that these are in the supervenience/entailment base. Rather, I presume they play a role in helping to explain how statements outside the base are entailed by statements in the base. And I presume that Lewis has some story about what these epistemic claims are themselves true in virtue of (though I'm not sure what it is). So I think it's more natural to say that these aren't fundamental O-terms for Lewis. But I'm a bit unclear on just what their status is.

(iii) OK, so it looks like what Lewis says about the theory of meaning doesn't commit him to fundamental O-terms playing a special role. Still, if his commitments from elsewhere do commit him to there being some pretty fundamental O-terms, then one can't help but wonder whether a theory of meaning ought to say something distinctive about them. I suspect that there are different strands in Lewis's thought that may be in some tension with each other here -- it would have been interesting to know what he'd say. I also think that a lot of these issues recur at the level of mental content, but the relationship between these issues and Lewis's view of mental content is even harder to figure out.

# on 27 October 2005, 11:32

I agree that my interpretation isn't exactly obvious, and that perhaps there were different strands in Lewis's thought on this matter.

However, since Lewis was very familiar with (and sympathetic to) logical empiricism, I think it's likely that he accepted that we can at least come close to analysing lots of non-phenomenal terms in phenomenal or observational terms. If I recall correctly, what he says in "Policing the Aufbau" and "Statements partly about observation" at least points in that direction.

Suppose Lewis believed that, say, spatiotemporal notions can be analysed in terms of phenomenal and causal notions, and also that all notions whatsoever can be analysed in terms of spatiotemporal notions. (Unlikely, of course.) Then the latter analysis would be metaphysically far more interesting for him, as it makes it probable that a very austere physical description of the world suffices to settle all facts, which Lewis very much liked to believe. By contrast, Lewis wouldn't have had much use of the other analysis. This could explain why he only mentions analyses in that direction when discussion other people's views. (I don't believe that this explanation will suffice, but maybe it could be part of a full explanation.)

You raise an interesting question about the Humean basis: Let HB be a sentence that specifies the spatiotemporal distribution of all fundamental physical properties. Let R(HB) be the Ramsey sentence of HB in which all names of fundamental properties are replaced by existentially bound variables, together with a claim saying that the values of those variables are perfectly natural. Arguably, Lewis took HB to a priori entail all other truths. Did he also believe that about R(HB)? You seem to think so. I'm rather inclined to doubt it.

# on 29 October 2005, 05:19

I suspect that Lewis would have been at least a bit concerned if spatiotemporal notions could be analyzed in terms of phenomenal and causal notions and vice versa. That's the sort of thing that in other cases leads him to look for a common analysis base for both. Perhaps continuity and related topological concepts might serve as a common analysis base in this case, as these concepts aren't obviously subject to the arguments that suggest spatiotemporal notions aren't primitive. Although then it's not entirely obvious that we have enough structure in the base to ground the analysis of everything else.

As for R(HB), I think that at least one point, he took something like this to be an a priori entailment base (though one would need to add the claim that each of the natural properties are distinct). The nature of the fundamental natural properties is something that I talked to Lewis a fair amount about. I was hoping to get him to concede that they have some substantial nature of which we're ignorant. But he took the line that they are distinct from each other, and that's that. I.e., there's property1, property2, and so on, and nothing more to say (at least in case when the properties involve the same value-ranges, e.g. the real numbers). That's a sort of structuralism about the natural properties, I suppose (though it still allows one to rigidify on the properties and invert them in different structurally identical possible worlds). That would suggest that if HB a priori entails everything, then so does R(HB).

Of course he talks about this sort of thing more in "Ramseyan Humility". My recollection of that paper is that his discussion there leaves open the possibility that fundamental properties have a further nature that we don't know about, though I think the discussion is also compatible with the structuralist view above (as long as we allow transworld identity for properties). He does say that if there's something we don't know, it's also something we can't state. So even if he took the "further nature" view, we'd at least have the view that R(HB) a priori entails all true sentences.

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