Monthly Archives: August 2006

Existence and just more theory

I’ve been spending much time recently in coffee shops with colleagues talking about the stuff that’s coming up in the fantastically named RIP Being conference (happening in Leeds this weekend). Hopefully I won’t be treading on toes if I draw out one strand of those conversations that I’ve been finding particularly interesting.

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The story for me begins with an old paper by Hartry Field. His series of papers in the 70’s is one of the all-time great runs: from “Tarski’s theory of truth” through “Quine and the correspondance theory”, “Theory Change”, “Logic, meaning and conceptual role”, “Conventionalism and Instrumentalism in semantics” and finishing off with “Mental representation”. (All references can be found here). Not all of them are reprinted in his collection Truth and the absence of fact, which seems a pity. The papers I mentioned above really seemed to me to lay out the early Fieldian programme in most of the details. Specifically, in missing out the papers “Logic, meaning …” and “Conventionalism and instrumentalism…”, you miss out on the early-Field’s take on how the cognitive significance of language relates to semantic theory; and the most interesting discussion I know of concerning what Putnam’s notorious “just more theory” argument might amount to.

The “just more theory” move is supposed to be the following. It’s familiar that you can preserve sensible truth conditions, by assigning wildly permuted reference-schemes to language (see my other recent posts for more details and links). But, prima facie, these permuted reference schemes are going to vitiate some plausible conditions of what it takes for a term to refer to something (e.g. that the object be causally connected to the term). Now, some theorists of meaning don’t build causal constraints into their metasemantic account. Davidson, early Lewis and the view Putnam describes as “standard” in his early paper, are among these (I call these “interpretationisms” elsewhere). But the received view, I guess, is to assume that some such causal constraint will be in play.

Inscrutability argument dead-in-the-water? No, says Putnam. For look! the permuted interpretation has the resources to render true sentences like “reference is a relation which is causally constrained”. For just as, on the permuted interpretation “reference” will be assigned as semantic value some weirdo twisted relation Reference*, so on the same interpretation “causation” will be assigned some weirdo twisted relation Causation. And it’ll turn out to be true that Reference* and Causation* match up in the right way. So (you might think), how can metasemantic theories tell you rule in favour of the sensible interpretation over this twisted one? For whichever no matter which of these we imagine to be the real interpretation of our language, everything we say will come out true.

Well, most people I speak to think this is a terrible argument. (For a particularly effective critique of Putnam—showing how badly things go if you allow him the “just more theory” move—see this paper by Tim Bays.) I’ll take it the reasons are pretty familiar (if not, Lewis’s “Putnam’s paradox” has a nice presentation of a now-standard response). Anyway, what’s interesting about Field’s paper is that it gives an alternative reading of Putnam’s challenge, which makes it much more interesting.

Let’s start by granting ourselves that we’ve got a theory which really has tied down reference pretty well. Suppose, for example, that we say “Billy” refers to Billy in virtue of appropriate causal connections between tokenings of that word and the person, Billy. The “Wild” inscrutability results threatened by permutation arguments simply don’t hold.

But now we can ask the following question: what’s special about that metasemantic theory you’re endorsing? Why should we be interested in Reference (=Causal relation C)? What if we tried to do all the explanatory work that we want semantics for, in terms of a different relation Reference*? We could then have a metasemantic* theory of reference*, which would explain that it is constrained to match a weirdo relation causation*. But, notice, that the relation “S expresses* proposition* p” (definable via reference*) and “S expresses proposition p” (definable via reference*) are coextensional. Now, if all the explanatory work we want semantics to do (e.g. explaining why people make those sounds when they believe the world is that way) only ever makes appeal to what propositions sentences express, then there just isn’t any reason (other than convenience) to talk about semantic properties rather than semantic* ones.

The conclusion of these considerations isn’t the kind of inscrutability I’m familiar with. It’s not that there’s some agreed-upon semantic relation, which is somehow indeterminate. It’s rather that (the consideration urges) it’ll be an entirely thin and uninteresting matter that we choose to pursue science via appeal to the determinate semantic properties rather than the determinate semantic* properties. You might think of this as a kind of metasemantic inscrutability, in contrast to the more usual semantic inscrutability: setting aside mere convenience, there’s no reason why we ought to give this metasemantic theory rather than that one.

Now, let’s turn to a different kind of inscrutability challenge. For one reason or another, lots of people are very worried over whether we can really secure determinate quantification over an absolutely unrestricted domain. Just suppose you’re convinced that there are no abstracta. Suppose you’re very careful to never say anything that commits you to their existence. However, suppose you’re wrong: abstracta exist. Intuitively, when you say “There are no abstracta, and I’m quantifying over absolutely everything!” you’re speaking falsely. But this is only so if your quantifiers range over the abstracta out there as well as the concreta: and why should that be? In virtue of what can your word “everything” range over the unrestricted domain? After all, what you say would be true if I interpreted the word as ranging over only concreta. I’d just take you to be saying that no concreta exist (within your domain; and that you were quantifying over absolutely everything in your domain. Both of these are true, given that your domain happens to contain only concreta!

Bring in causality doesn’t look like it helps here; neither would the form of reference-magnetism that Lewis endorsed, which demands that our predicates latch onto relatively natural empirical kinds, help. Ted Sider, in a paper he’s presenting at the RIP conference, advocates extending the Lewis point to make appeal to logical “natural kinds” (such as existence) at this point. However, let me sketch instead a variant of the Sider thought that seems more congenial to me (I’ll sketch at the end how to transfer it back).

My take on Lewis’s theory is the following. First, identify a “meaning building language”. This will contain only predicates for empirical natural kinds, plus some other stuff (quantifiers, connectives, perhaps terms for metaphysically basic things such as mereological notions). Now, what it is for a semantic theory for a natural language to be the correct one, is for there to be a semantic theory phrased in the meaning-building language, which (a) assigns to sentences of the natural language truth-conditions which fit with actual patterns of assent and dissent; and (b) is as syntactically simple as possible. (I defend this take on what Lewis is doing here).

Now, clearly we need to use some logical resources in constructing the semantic theory. Which should we allow? Sider’s answer: the logically natural ones. But for the moment let’s suppose we don’t want to commit ourselves to logically natural kinds. Well, why don’t we just stipulate that the meaning building language is going to contain this, that, and the next logical operator/connective? In the case of predicates, there’s the worry that our meaning-building theory should contain all the empirical kinds there are or could be: since we don’t know what these are, we need to give a general definition such as “the meaning building language will contain predicates for all and only natural kinds”. But there seems no comparible reason not simply to lay it down that “the meaning building language will contain negation, conjunction and the existential quantifier).

Indeed, we could go one further, and simply stipulate that the existential quantifier it contains is the absolutely unrestricted one. The effect will be just like the one Sider proposes: this metasemantic proposal has a built-in-bias towards ascribing truly unrestricted generality to the quantifiers of natural language, because it is syntactically simpler to lay down clauses for such quantifiers in the meaning-building language, than for the restricted alternatives. You quantify over everything, not just concreta, because the semantic theory that ascribes you this is more eligible than one that doesn’t, where eligibility is a matter of how simple the theory is when formulated in the meaning-building language just described.

Ok. So finally finally I get to the point. It seems to me that Field’s form of Putnam’s worries can be put to work here too. Let’s grant that the metasemantic theory just described delivers the right results about semantic properties of my language; and shows my unrestricted quantification to be determinate. But why choose just that metasemantic theory? Why not, for example, describe a metasemantic theory where semantic properties are determined by syntactic simplicity of a semantic theory in a meaning building language where the sole existential quantifier is restricted to concreta? Maybe we should grant that our way picks out the semantic properties: but we’ve yet to be told why we should be interested in the semantic properties, rather than the semantic* properties delivered by the rival metasemantic theory just sketched. Metasemantic inscrutability threatens once more.

(I think the same challenge can be put to the Sider-style proposal: e.g., consider the Lewis* metasemantic theory whereby the meaning-building language contains expressions for all those entities (of whatever category) which are natural*: i.e. are the intersection of genuinely natural properties (emprical or logical) with restricted domain D.)

I have suspicians that metasemantic inscrutability will turn out to be a worrying thing. That’s a substantive claim: but it’s got to be a matter for another posting!

(Major thanks here go to Andy and Joseph for discussions that shaped my thoughts on this stuff; though they are clearly not to be blamed..).

Rigidity and inscrutability

In response to something Dan asks in the comments in the previous post, I thought it might be worth laying out one reason why I’m thinking about “rich” forms of rigidity at the moment.

Vann McGee published a paper on inscrutability of reference recently. The part of it I’m particularly interested in deals with the permutation argument for radical inscrutability. The idea of the permutation arguments, in brief, is: twist the assignments of reference to terms as much as you like. By making compensating twists to the assignments of extensions to predicates, you’ll can make sure the twists “cancel out” so that the distribution of truth values among whole sentences matches exactly the “intended interpretation”. So (big gap) there’s no fact of the matter whether the twisted-interpretation or rather the intended-interpretation is the correct description of the semantic facts. (For details (ad nauseum) see e.g. this stuff)

Anyway, Vann McGee is interested in extending this argument to the intensional case. V interesting to me, since I’d be thinking about that too. I started to get worried when I saw that McGee argued that permutation arguments go wrong when you extend them to the intensional case. That seemed bad, coz I thought I’d proved a theorem that they go over smoothly to really rich intensional settings (ch.5, in the above). And, y’know, he’s Vann McGee, and I’m not, so default assumption was that he wins!

But actually, I think what he was saying doesn’t call into question the technical stuff I was working on. What it does is show that the permuted interpretations that I construct do strange things with rigidity. Hence my now wanting to think about rigidity a little more.

McGee’s nice point is this: if you permute the reference scheme wrt each world in turn, you end up disrupting facts about rigidity. To illustrate suppose that A is the actual world, and W a non-actual one. Choose a permutation for A that sends Billy to the Taj Mahal, and a permutation for W that sends Billy to the Great Wall of China. Then the permuted interpretation of the language will assign to “Billy” an intension that maps A to the Taj Mahal, and W to the Great Wall of China”. In the familiar way, we make compensating twists to the extension of each predicate wrt each world, and the intensions of sentences turn out invariant. But of course, “Billy” is no longer a rigid designator.

(McGee offers this as one horn of a dilemma concerning how you extend the permutation argument to the intensional case. The other horn concerns permuting the reference scheme for all worlds at once, with the result that you end up assigning objects as the reference of e in w, when that object doesn’t exist in w. I’ve also got thoughts about that horn, but that’s another story).

McGee’s dead right, and when I looked at (one form of) my recipe for extending the permutation argument to waht I called the “Carnapian” intensional case, I saw that this is exactly what I got. However, the substantial question is whether or not the non-rigidity of “Billy” on the permuted interpretation gives you any reason to rule out that interpretation as “unintended”. And this question obviously turns on the status of rigidity in the first place.

Now, if the motivation for thinking names were rigid, were just that assigning names rigid extensions allows us to assign the right truth conditions to “Billy is wise”, then it looks like the McGee point has little force against the permutation argument. Because, the permuted interpretation does just as well at generating the right truth conditions! So what we should conclude is that it becomes inscrutable whether or not names are rigid: the argument that names are rigid is undermined.

However, maybe there’s something deeper and spookier about rigidity, above and beyond getting-the-truth-conditions-right. Maybe, I thought, that’s what people are onto with the de jure rigidity stuff. And anyway, it’d be nice to get clear on all the motivations for rigidity that are in the air, to see whether we could get some (perhaps conditional) McGee-style argument against permutation inscrutability going.

p.s. one thing that I certainly hadn’t realized before reading McGee, was that the permuted interpretations I was offering as part of an inscrutability argument had non-rigid variables! As McGee points out, unless this were the case, you’d get the wrong results when looking at sentences involving quantification over a modal operator. I hadn’t clicked this, since I was working with Lewis’s general-semantics system, where variables are handled via an extra intensional index: it had quite passed me by that I was doing something so kooky to them. You live and learn!

Varities of Rigidity

This post over on metaphysical values by Ross Cameron has got me thinking about reference and rigidity.

There’s a familiar distinction between singular terms that are “de facto” rigid and those that are “de jure” rigid. Paradigm example of the former: “the smallest prime”; paradigm example of the latter: “Socrates” (or, variables).

I’m not sure exactly how “de jure” rigidity is typically characterized. I’ve seen it done through slogans such as: what the name contributes to the truth conditions expressed by sentences in which it figures is just the object it stands for. I’ve seen it done like this: a name is de jure rigid if its rigidity is “due to” the semantics of language, and not to metaphysical facts about the world.
Those two definitions seem to come apart: “the actual inventer of the zip” is plausibly de jure rigid in the second, but not the first, sense.

Let’s concentrate on the first sense of de jure rigidity (so a constraint on getting this right is that actualized descriptions won’t count as de jure rigid in this sense). How could we tighten it up? Well, the task is pretty easy if your semantic theory takes the right shape. For example, suppose you have a semantic theory which in the first instance assigns structured propositions to sentences, and then says what truth conditions these propositions (and thus sentences) have. Then you can say precisely what it is for “name to contribute an object” to the truth conditions of sentences in which it figures: it’s for you to shove an object into the structured prop associated with the sentence.

Notice two things:
(1) this is a semantic characterization: you can read off from the semantics of the language whether or not a given term is de jure rigid. (In this sense, it’s like the characterization of “rigidity” as “referring to the same thing wrt every world”).
(2) this is a local characterization: it only works if you’re working within the right semantic framework (the structured-props one). You can’t use it if you’re working e.g. with Davidsonian truth theories, or possible world semantics.

This raises a natural question: how can we capture de jure rigidity in this, that and the next semantic framework? What interests me is what we can do to this end, working with a general semantics in the sense of Lewis (1970). I can’t see any way to read off de jure rigidity from semantic theory.

But if we appeal to metasemantics (i.e. the theory of how semantic facts get fixed) it looks like we have some options. Suppose, for example you’re one of the word-first guys: that is, like early Field, Fodor, Stalnaker et al, you think that the metasemantic story operates first at the level of lexical items (names, predicates), and then we can offer a reduction of the semantic properties of complex expressions (e.g. definite descriptions, sentences) to the semantic properties of their parts. The de jure rigid terms will be those whose semantic properties are fixed in the following way:

(1) term T refers (simpliciter) to an object X.
(2) term T has the as intension that function from worlds to objects, which, at each world w, will pick out the entity that is identical to what T refers to (simpliciter).

So here’s my puzzle: this looks like a characterization that’s turns essentially on the word-first metasemantic theory. Fair do’s, if you like that kind of thing. But I’m more sympathetic to metasemantic theories like Lewis’s, where the semantic properties of language get determined holistically. If you’re an “interpretationist” (and if you haven’t got the semantic characterizations to help you out, because you’re working with a trad possible world semantics), is there any content in the notion of de jure rigidity? More on this to follow.

“Timid modal fictionalism”

Just reading this very interesting paper by Brit Brogaard comparing timid modal fictionalism with “holistic ersatzism” a la Nolan, Sider, et al (I’ve just noted that Sider credits this paper by Leeds’ very own Joseph Melia as one source of the idea). Still thinking about the content at the moment, something about the terminology in this area re-struck me.

As currently used, modal fictionalisms are positions that endorse something like the following biconditional

Possibly P iff According to the fiction of possible worlds, P*

Strong modal fictionalism is the natural thought that we see this biconditional as in the service of possibility-talk to talk about what holds according to a fiction. That is a fictionalism about modality.

Timid modal fictionalism is a view that denies this. Rather, we take modality as primitive (or reduce it in some other way), and read the biconditional left-to-right as partially defining the content of the fiction.

But is this really a modal fictionalism at all (in the sense of a fictionalism about modality)? When I first read this stuff, this issue threw me totally—I didn’t understand what the point or purpose of timid fictionalism was meant to be—until I realized that it is really a kind of fictionalism about possibilia and worlds-talk. So it’s not a modal fictionalism (/fictionalism about the modal operators), timid or otherwise; it’s a possibilia-fictionalism, as strong as you like.

I guess I can see why Rosen chose those names (you might take the domain of modality to cover modal operators+worlds-talk+possiblia-talk, and then modal fictionalism is strong or timid to the extent that it’s a fictionalism about all or only some of those bits of modal talk). The cogniscienti will be well aware of what’s intended: but it wasn’t what the terminology suggested to me at first.

This is the best job in the world

…. because you can do it at the cricket.

England playing Pakistan. In the sun at Headingley (a short bus ride from the office). Sun shining, final day of the test match. Lots of support for both sides. A pile of philosophy papers, books lying around. Lots of interesting stuff about vagueness, composition, monism etc to puzzle about between wickets falling (which they did regularly). I’m particularly intrigued by this paper at the moment.

England won by about 130 runs just before tea, allowing time to come back and sort email and blog before coming home.

Semantics for nihilists

Microphysical mereological nihilists believe that only simples exist—things like leptons and quarks, perhaps. You can be a mereological nihilist without being a microphysical mereological nihilist (e.g. you can believe that ordinary objects are simples, or that the whole world is one great lumpy simple. Elsewhere I use this observation to respond to some objections to microphysical mereological nihilism). But it’s not so much fun.

If you’re a microphysical mereological nihilist, you’re likely to start getting worried that you’re committed to an almost universal error-theory of ordinary discourse. (Even if you’re not worried by that, your friends and readers are likely to be). So the MMN-ists tend to find ways of sweetening the pill. Van Inwagen paraphrases ordinary statements like “the cat is on the mat” into plural talk (the things arranged cat-wise are located above the things arranged mat-wise”). Dorr wants us to go fictionalist: “According to the fiction of composition, the cat is on the mat”). There’ll be some dispute at this point about the status of these substitutes. I don’t want to get into that here though.

I want to push for a different strategy. The way to do semantics is to do possible world semantics. And to do possible world semantics, you don’t merely talk about things and sets of things drawn from the actual world: you assign possible-worlds intensions as semantic values. For example, the possible-worlds semantic value of “is a cordate” is going to be something like a function from possible worlds to the things which have hearts in those worlds. And (I assume, contra e.g. Williamson) that there could be something that doesn’t exist in the actual world, but nevertheless has a heart. I’m assuming that this function is a set, and sets that have merely possible objects in their transitive closure are at least as dubious, ontologically speaking, as merely possible objects themselves.

Philosophers prepared to do pw-semantics, therefore, owe some account of this talk about stuff that doesn’t actually exist, but might have done. And so they give some theories. The one that I like best is Ted Sider’s “ersatz pluriverse” idea. You can think of this as a kind of fictionalism about possiblia-talk. You construct a big sentence that accurately describes all the possibilities. Statements about possibilia will be ok so long as they follow from the pluriverse sentence. (I know this is pretty sketchy: best to look at Sider’s version for the details).

Let’s call the possibilia talk vindicated by the construction Sider describes, the “initial” possibila talk. Sider mentions various things you might want to add into the pluriverse sentence. If you want to talk about sets containing possible objects drawn from different worlds (e.g. to do possible world semantics) then you’ll want to put some set-existence principles into your pluriverse sentence. If you want to talk about transworld fusions, you need to put some mereological principles into the pluriverse sentence. If you add a principle of universal composition into the pluriverse sentence, your pluriverse sentence will allow you to go along with David Lewis’s talk of arbitrary fusions of possibilia.

Now Sider himself believes that, in reality, universal composition holds. The microphysical mereological nihilist does not believe this. The pluriverse sentence we are considering says that in the actual world, there are lots of composite objects. Sider thinks this is a respect in which it describes reality aright; the MMN-ist will think that this is a respect in which it misdescribes reality.

I think the MMN-ist should use the pluriverse sentence we’ve just described to introduce possibilia talk. They will have to bear in mind that in some respects, it misdescribes reality: but after all, *everyone* has to agree with that. Sider thinks it misdescribes reality in saying that merely possible objects, and transworld fusions and sets thereof, exist—the MMN-ist simply thinks that it’s inaccuracy extends to the actual world. Both sides, of course, can specify exactly which bits they think accurately describe reality, and which are artefactual.

The MMN-ist, along with everyone else, already has the burden of vindicating possibilia-talk (and sets of possibilia, etc) in order to get the ontology required for pw-semantics. But when the MMN-ist follows the pluriverse route (and includes composition priniciples within the pluriverse sentence), they get a welcome side-benefit. Not only do they gain the required “virtual” other-worldly objects; they also get “virtual” actual-worldy objects.

The upshot is that when it comes to doing possible-world semantics, the MMN-ist can happily assign to “cordate” an intension that (at the actual world) contains macroscopic objects, just as Sider and other assign to “cordate” an intension that (at other worlds) contain merely possible objects. And sentences such as “there exist cordates” will be true in exactly the same sense as it is for Sider: the intension maps the actual world to a non-empty set of entities.

So we’ve no need for special paraphrases, or special-purpose fictionalizing constructions, in pursuit of some novel sense in which “there are cordates” is true for the MMN-ist. The flipside is that we can’t read off metaphysical commitments from such true existential sentences. Hey ho.

(cross-posted on Metaphysical Values)