Monday, September 10, 2012

Is Lewis's ontology qualitatively or ideologically parsimonious?


David Lewis believes in lots of things.  He believes in human beings, and animals and plants; he believes in tables, and statues and universities; he believes in planets, and solar systems and galaxies.  And he believes in sets of such things, and sets of sets of such things, and sets which have only other sets as members.  And so on.  But so far, so mundane: there’s nothing there that plenty of philosophers don’t believe in.  But Lewis also believes in unicorns, and gods, and ghosts, and golden mountains.  Lewis thinks there’s a talking donkey who spends his days giving a completely accurate account of your life.  Lewis thinks that somewhere there is an infinite sequence of intrinsic duplicates of you doing a conga line.

That’s a pretty wild ontology.  Unless you’re a philosopher who believes in something that, as a matter of fact, just could not exist, then Lewis believes in everything you believe in and – chances are – an awful lot more.  How is this ontological extravagance to be justified?  Lewis offers two different answers to this justificatory challenge.  His more commonly mentioned answer is as follows.

The Cost-Benefit Response:
It is indeed a lavish ontology that is proposed.  It is a cost to accept that there are so many things: it is a pro-tanto reason not to accept the proffered theory that it posits so many things.  But this cost is outweighed by the benefits afforded by the theory.  If it is true then it provides for a reduction of the modal, an ontological identification of propositions and properties with sets of individuals, and so on.  These benefits outweigh the admitted ontological costs.  So on the balance of costs versus benefits, the theory should be accepted, and the lavish ontology embraced.

Here Lewis is admitting that his ontology comes at a price, but that it is a price worth paying.  But elsewhere he refused to admit that there is even a price to be paid.  He offers instead the following answer to the justificatory challenge.

The No-Cost Response:
The extra things postulated are just more things of the same kind that we all already believed in.  To believe in more kinds of thing is a cost, but to believe in more tokens of a kind of thing you already believe in is no additional cost.  Thus the postulation of this additional ontology is not even a cost that needs to be paid.  It is not even a pro-tanto reason not to accept the proffered theory that it posits so many things, given that they are things of a kind with things postulated by the theory’s salient rivals anyway.

The former response sees the ontology as a cost to be outweighed, the latter doesn’t even acknowledge it as a cost.  Lewis distinguishes between a principle of quantitative parsimony which tells you to minimise the number of things postulated, and principle of qualitative parsimony which tells you to minimse the number of kinds of things postulated.  He admits the latter as a good rule, but doesn’t think he is breaking it; he admits to breaking the former, but doesn’t recognize it as a good rule to be obeyed.

I’m not interested here in which response to the justificatory challenge Lewis would do better to rely on.  My question here is: is Lewis correct when he says, in the No-Cost Response, that his theory is a pro-tanto offense only against quantitative parsimony and not against qualitative parsimony?

Joseph Melia argued that Lewis was wrong: that his ontology sinned against qualitative parsimony as well.  Indeed, that Lewis’s ontology maximally sins against qualitative parsimony, since it admits the existence of things for any kind of thing that there could be.  The only way to do worse on qualitative parsimony would be to believe in some kinds of thing that couldn’t exist.  But provided that we’re only concerned with theories that refrain from postulating impossibilia, Lewis’s proposed ontology is maximally qualitatively unparsimonious: for every kind of thing there could be, Lewis believes in things of that kind.

John Divers responds on Lewis’s behalf.  Lewis believes in sets and individuals, the end.  Actuality consists of individuals and sets, and the admission of the reality of logical space requires merely the postulation of more individuals and sets.  Thus the number of kinds of thing you need to acknowledge by accepting Lewis’s ontology is the same as what we’d need to acknowledge to give a good account of actuality anyway: two.  Thus Lewis does not sin against qualitative parsimony, as he claimed.

How are we to judge this dispute between Divers, on behalf of Lewis, and Melia?  It comes down, seemingly, to a really thorny issue: at what level do we draw the kinds?  Sure, at one level Lewis is merely asking us to believe in things of a kind with what we already believe: individuals (we all believe in those, right?), and the sets that you get by taking those individuals as ur-elemete (and most of believed in sets anyway – and if you don’t, well just believe in Lewis’s ontology minus the sets!).  But on another level, Lewis isn’t just introducing us to new individuals, he’s introducing us to new kinds of individuals.  He believes in unicorns; so there’s a kind of thing – unicorn – that Lewis is asking us to believe in that we didn’t already believe in.

At one level, everything is of a kind: entity.  Read thus, the rule of qualitative parsimony only ever tells us to (ceteris paribus) choose a theory that doesn’t postulate anything at all over one that does: it will never select between theories that each say that there is something.  That’s pretty useless.  At the other extreme, there’s a kind for every way for things to be: hence, a kind F for every predicate F (at least, every satisfiable predicate).  Read thus, the rule of qualitative parsimony will collapse into the rule of quantitative parsimony, for every new token thing you admit will also be to admit a new kind of thing.

For there to be an interesting rule of qualitative parsimony, we have to find a middle level: a way of dividing things into kinds such that it isn’t automatic that everything is of a kind nor that no two things are of a kind.  (Or better: that for any two things, there’s a kind that one falls under that the other doesn’t.)  But then the question is: at what level do we draw the kinds?  How can we do this in a principled manner?  Divers and Melia draw the kinds at different levels, but who is right?  What facts about reality even speak to one way of drawing the kinds as the correct way (or at least, the correct way for the purposes of weighing theories with respect to qualitative parsimony)?

If you believe in ontological categories, you’ve got an answer: draw the kinds at the level of the categories.  So the principle of qualitative parsimony amounts to saying: (ceteris paribus) choose the theory that postulates the fewest ontological categories.  So take someone like E.J. Lowe, who thinks the things in reality divide into four ontological categories: the substantial particular, the substantial universal, the non-substantial particular, and the non-substantial universal.  On the current proposal, Lowe should view the principle of qualitative parsimony as telling him: believe in whatever kinds of thing you like provided the things fall into one of these four categories – but (ceteris paribus) don’t accept a theory that postulates a fifth category of thing, and (ceteris paribus) prefer a theory that postulates fewer categories of thing.

But personally, I don’t find this very helpful.  The same problem as before just comes back at a different point.  When I think of Lowe’s four ontological categories (e.g. – I’m picking on Lowe’s view, but I think the same thing about every proposal on ontological categories that I’ve encountered), I simply wonder why that is the right way to divide things up.  By a non-substantial universal, Lowe means an Armstrongian universal like redness; by a non-substantial particular he means a trope, like the redness of this postbox.  Why isn’t that one ontological category: property?  By a substantial particular he means kinds like electron.  Why aren’t the universals, tropes and kinds all part of the same ontological category: abstracta?  This is just exactly the same problem as before: where to make the divisions.  But instead of asking directly where to make the divisions for the purposes of qualitative parsimony, we’re assuming we make the divisions at the level of ontological categories and instead asking where to make those divisions instead.  I don’t find the detour illuminating, having as little an intuitive grasp of where the ontological categories are as I have of what matters with respect to qualitative parsimony.

I suggest a rethinking of the principle of qualitative parsimony.  I think we should qualitative parsimony as derivative on a more fundamental norm of theory choice: ideological parsimony.  Qualitative parsimony is a virtue just insofar as it facilitates ideological simplicity.

So consider a debate between a compositional nihilist and a universalist.  The former, let us suppose, claims an advantage with respect to qualitative parsimony, since the universalist believes in a kind of thing – a complex object – that the nihilist does not believe in.  The universalist responds, suppose, that she is at no disadvantage with respect to qualitative parsimony since she is only believing in more things of the same kind the nihilist believes in: concrete individuals.  I think that it’s fruitless to try and settle whether, for the purposes of theory choice by qualitative parsimony, mereologically simple concrete individuals are of a kind with mereologically complex complex individuals.  In some sense, complex objects are a new kind of thing, and in another sense they aren’t: the question we should be asking, I think, is whether their admission requires more ideological resources.  And in this case, it plausibly does, because while the nihilist can eschew the ideology of mereology, the universalist needs to admit amongst their fundamental ideological primitives some mereological notion.  Thus, as Ted Sider (inspired by Cian Dorr) argues, there is a pro tanto reason to be compositional nihilists, for it minimizes the ideological complexity in reality.  I think that a drive to ideological simplicity is really what’s behind the drive to qualitative parsimony, and this lets us get a grip on what the relevant level of kinds is: admitting the Xs constitutes admitting a new kind of thing, in the relevant sense, when describing reality if there are Xs requires greater primitive ideological resources than describing reality does if there are no Xs.

In that case, it doesn’t look too good for Lewis, for even though he’s only introducing us to new individuals and sets of individuals, as Divers says, it nonetheless looks as though we’re going to need new ideological resources to describe those individuals.  We’re going to need new primitive predicates to describe things that instantiate alien properties since, ex hypothesi, those predicates aren’t definable in terms of a logical construction of actually instantiated predicates.  We’re going to need new spatio-temporal ideology to describe those worlds where things aren’t related spatio-temporally but rather are related in a manner ‘analogous’ to spatio-temporal relatedness.  We’re going to need new ideology to describe the ectoplasm ghosts the absence of which allows actuality to be a physicalistically acceptable world.  So it’s looking like Melia is right: the postulation of these new kinds of thing is a sin against qualitative parsimony.  Divers is right that it’s just more individuals, but that doesn’t matter, since they are individuals that are not describable just with the ideological resources we would have needed to describe actuality.

But whether this is really so depends on another question that I don’t know the answer to.  When judging what ideological resources you need, do you only count what you need to describe what there is, or do you need ideology enough to describe the ways things could have been?  For Lewis of course, there’s no difference: what there is includes all that there could have been.  But what about for those of us who think that how things are as a whole could have been different?  Does the mereological nihilist who thinks there could have been composite objects but there just happen not to be get to claim an ideological advantage over the universalist, or does one need to reject the very possibility of composition to claim such an advantage?

Parity with ontological parsimony suggests that you should only count the ideology you need to describe things as they are.  After all, no one would think that it is a sin against ontological parsimony to think that there could have been immaterial minds; it’s only believing in them that counts against ontological parsimony.  In which case, why should the possibility of having to describe things using some mereological notion matter: it only matters whether describing things as they are requires such notions.

Nonetheless, I can’t shake the feeling that ideological parsimony is different from ontological parsimony in this respect.  That the contingent mereological nihilist is at no advantage over the universalist, only the necessitarian nihilist.  After all, a theory of reality is not complete without a description of how things could have been: so your fundamental theory of reality will have to talk about what could have occurred but doesn’t – and so if there could have been complex objects, you will need to invoke mereological notions to describe that possibility.  So you can’t completely eschew speaking mereologically: your fundamental theory will still need its mereological primitives, even if it only ever uses them within the scope of a modal operator.  I find it intuitive that in that case you still incur the ideological cost: you still have to see reality in mereological terms, even if just to say that actuality is mereologically less complex than it could have been.  To really not have anything to do with the ideology of mereology you must not need to resort to it at any point in your description of reality – whether of how things are or how they could be – you must be a necessitarian nihilist.  (I’m assuming here that how things could be really is a part of the theory of reality.  If you were an expressivist or other kind of anti-realist about the modal I suppose you would deny this.  But since those views are false . . .)

If that is right, then things start to look better for Lewis.  In believing in possibilia, Lewis just thinks that the story of how things are and could be is the story of how things are unrestrictedly: so for him, the ideology needed to describe how things are, simpliciter, is the ideology required to describe how things actually are and how they could have been.  But if we were committed anyway to the ideological resources needed to describe both reality and the possible ways reality could be, this won’t be an ideological expansion, and Lewis won’t be sinning against ideological parsimony – hence against qualitative parsimony – after all.

20 comments:

Jason said...

Yeah, looks right to me.

Here's a geeky question on the Lewisania: how is ideological parsimony (as you're thinking about it) interacting with his stuff on natural properties? From one perspective, he needs (pre-Parts of Clsses) just first-order logic, a set membership predicate, a parthood predicate, and a Naturalness predicate. Then other questions of 'kinds' just become questions about Ramsey sentences describing worlds using just the above resources. Are we counting the ideology this way, or are we counting each additional natural property as more ideology?

Joshua said...

Hi Ross,

I'm not sure the Lewis is off the hook yet. On many ersatzist views, the possibility of an alien property is captured by a mere description of an uninstantiated property role. But, on Lewis's view, you not only have to describe the uninstantiated property role, but you also have to say which property is fulfilling that role in any particular possible world. That extra bit is going to require more ideological resources than the typical ersatzist needs.

Ross Cameron said...

Jason: I was thinking each additional natural property should count as more ideology.

Joshua: maybe I need to hear more, but it sounds like the ersatzist project is not fully capturing the project of giving a complete description of reality. Nor is it meant to: they're trying to do something different - to account for the truth of true English modal claims. What you say might be fine for that more modest project, but once they want to engage in the project of fully describing reality they also need to tell us how exactly roles are realized in alternate possibilities.

Matthew West said...

Yes, I think you have the principles right. To put it in my terms, it is the overall simplicity of your theory of everything that counts, not the simplicity of parts of that theory. Making a particular ontological commitment may make your overall theory simpler (or not) and that is the basis on which parsimony should be judged.
The issue you did not touch on is existence. The challenge here is that at an ontological level you have to admit things into existence if you want to talk about them, since you can't talk about them unless you admit them into existence. This is a very weak form of existence and I think a lot of people confuse this with whether you can kick something or not. So personally I am quite happy to draw the line of existence between those things that could possibly exist and those that could not possibly exist. It seems to me relatively harmless not to be able to talk about such things in ones ontology.

Jason said...

If we think each natural property is extra ideology, then I'm thinking there's going to be something in the neighborhood of what Joshua is saying: people who think there are fewer (or no) possible alien properties will be more parsimonious, which looks wrong to me.

But I think Lewis should resist that. He could, if he wanted, trade in natural properties for universals --- just an extra bit of ontology --- and a predicate 'is a universal'. If he did that, then the question of what universals there are looks like a purely ontological question, along the lines of 'what mereological sums there are'. But if we're granting that the number of mereological sums shouldn't matter, then we ought to think the number of universals shouldn't matter either. Or, to put it another way, the point of qualitative parsimony is to say that counting res has no bearing on theory choice. But if Lewis goes the universals option, seeing what natural properties there are is just counting res.

Ross Cameron said...

It looks exactly right to me that if you postulate fewer or no possible alien properties then you're at an ideological advantage!

On the second thing - I'm not sure. How does having the universals help secure ideological parsimony, because we still have to be able to describe them. I can't tell you how things are by saying that a instantiates U - I have to also tell you whether U is the universals or REDNESS or the universal of CHARGE, etc.

(Cf. Sider on truthmakers: you can tell me that A, B, C and D exist - but until you tell me that A is the state of affairs of Ball being red, etc, I don't know much about how reality is at all. So you still need that ideology to describe those truthmakers: the truthmaker theorist can't merely do with the ideology of first-order logic.)

Richard Woodward said...

Hi guys,

So I'm coincidentally writing a paper on this right now. Some thoughts.

Let's start with Jason's opening gambit. I'm not sure I understand the idea that there is a perspective from which Lewis only needs predicates for set-membership, parthood and naturalness. Incidentally, this is pretty much exactly how John thinks of it (though naturalness is off the table in his discussion).

I was thinking in line with Ross: each perfectly natural property is part of the fundamental ideology of Lewis's theory. So the crux of the matter is that Lewis is asking us to believe in a whole lot of extra kinds that other theories don't postulate. But note that the issues is about unicorns or talking donkeys (contra Melia). Those kinds are reduced, within the Lewisian picture, to perfectly natural ones. So in that sense, Lewis's commitment to unicorns et al isn't a commitment (in context) that matters with respect to theory choice given that those commitments are nothing over and above the previous commitment to the more basic kinds with which unicorns et al are identified.

I guess one thought is that "is an electron" (or whatever) is definable within Lewis's theory: x is an electron iff x is a member of a specific set, say {a, b, c...}. But it's not clear this gets you off the hook: we've now got something that satisfies the primitive predicate "x is a member of {a, b, c...}" and Lewis's opponents don't believe in any satisfier of that predicate, so Lewis has more ontological commitments of a qualitative nature. Moreover, there is something weird about the names.

Notice the analogy with the universals case. It's true that "is red" isn't a primitive predicate for the universals guy: x is red iff x instantiates redness. But we've just traded one kind for another: before we had a basic commitment to red things, now we have a basic commitment to things which instantiate redness.

Perhaps there are tricks here though: the kind of ramsification stuff Jason alluded stuff might allow us avoid the worry mentioned above. But I've not thought that through and I'd need to see the details.

What I do think is that its crucial to get clear on whether the perspective Jason mentions --- call it the Divers perspective --- makes sense. If it does make sense, I think the Melian objection fails in both spirit and detail. But my suspicion is that the Melian objection fails in detail only. The spirit of the objection survives once its relocated as an issue about perfectly natural alien properties.

Bit of trivia: the point Jason makes about universals --- once you believe in one, its no extra cost to believe in more --- goes back to Russell in the Problems of Philosophy: "having admitted one universal, we have no longer any reason to reject others"

Rich Woodward said...
This comment has been removed by the author.
Rich Woodward said...

Incidentally: Jason, why do you think that it's wrong to think that theories which postulate no (natural) alien properties are more parsimonious than Lewis's theory?

Lewis's theory says that there are things are a certain kind --- the things which are F, or the members of a a given set --- and is thereby ontologically committed to things of that kind. The other theory isn't and is thereby more parsimonious, no?

Joshua said...

I think that when I wrote my initial post, I was conflating two criticism. One is the one that Jason suggests. If we think that there is a bit of primitive ideology for every fundamental alien property, then the nomological role essentialist will be on better footing than Lewis simply because she believes in fewer fundamental alien properties than Lewis does (she believes in one alien property/alien role whereas Lewis believes in many alien properties/alien role).

But, another criticism I had in mind would involve a bit more machinery than the typical ersatzist would want to accept. Suppose we adopt the following Sider-inspired view. There are several ersatz pluriverses each one of which contains just as many alien properties as Lewis has (many/role) but only one of which grounds modality. The one that grounds modality is a matter of convention. On this view, there are just as many alien properties as on Lewis's view. But, there are (arguably) fewer primitives. Lewis needs a primitive to express each alien property and more primitives to describe the various roles those alien properties can fulfill. However, the Sider-inspired metaphysician only needs second order quantification (to quantify into the pluriverse) and whatever primitives are required to describe the various roles for fundamental properties. In particular, this metaphysician does not need a primitive for each alien property.

I guess this objection requires more machinery than I was originally thinking. But, maybe this helps us to see what kind of ersatzist view you have to adopt to have a view that is more parsimonious than Lewis's.

Ross Cameron said...

Let me think more about ersatzism tomorrow, Joshua - but for now: I'm really not getting the first criticism.

It seems exactly right to me that the nomological role essentialist will be on better footing than Lewis simply because she believes in fewer fundamental alien properties. Why is that a bad result? Fewer=better!
The complaint sounds to me like saying: you can't object to the introduction of bare substrata because then the substance-attribute theorist would be worse off than the bundle theorist. Ummm . . . yeah! In that respect, at lease.

Rich Woodward said...

Ross, can you explain a bit more on how you were thinking of the relationship between qualitative parsimony and ideological parsimony?

Suppose that my favourite theory T has a primitive predicate F but also entails no sentence which implies that there are Fs. What the theory does do is entail various sentences which imply that there could have been Fs.

Now we compare T with your favourite theory T*. Your theory contains F too but entails not only sentences which imply that there could have been Fs but that there are indeed Fs.

Finally, we have Jason's favourite theory T** which doesn't have F as a primitive.

My initial verdict is that your favourite theory and my favourite theory both have an ideological commitment that Jason's favourite theory avoids. So on the grounds of ideological parsimony, we have reason to prefer T** to its competitors. But at the same time, your theory says that there are things of a certain kind, the Fs, and my theory doesn't. So your theory has an ontological commitment that my theory avoids. So on the grounds of ontological parsimony, we have reason to prefer T to T*. But the relevant parsimony looks to be qualitative. And we've already granted that T and T* are on a par from an ideological point of view. So considerations of qualitative parsimony give us something that considerations of ideological parsimony don't: a reason to prefer T to T*. And that suggests that they aren't the same thing.

Or do you think that we DON'T have reason to prefer T to T* because there is no ideological advantage and so considerations of qualitative parsimony aren't being used to improve ideology?

Joshua said...

Ross, my first point was simply this: Even if we grant that a complete description of reality requires a description of possibility, the Lewisian may still have a less parsimonious view if (1) the Lewisian accepts that there are many possible fundamental properties for each possible role and (2) the anti-Lewisian says that there is only one/role and (3) for each possible fundamental property there is an extra bit of ideology to express that possible property. I didn't think this first point was any different from what Jason suggested at the beginning of his first post.

Ross Cameron said...

Joshua: I agree with everything you say in that last comment. Where we disagree, I think, is that I think that is just the right result. How ideologically parsimonious your theory is should be determined in part by how rich you think the space of possibilities is. So yeah: the Lewisian you're considering is less parsimonious than the anti-Lewisian you're considering, and so there's a pro-tanto reason to accept the latter's theory. I don't see a problem. (Sorry, I feel I'm being obtuse - I'm really not trying to be. If there's something I'm just missing, sorry!)

Ross Cameron said...

Rich, I don't think ideological parsimony and qualitative parsimony are the same thing - but what I was suggesting is that qualitative parsimony in and of itself isn't something to care about: it's only a virtue insofar as it sometimes allows us to achieve ideological parsimony. So if admitting things of kind K (or the poss of things of kind K) doesn't require the adoption of new ideology to describe them, I think that is no cost to theory: refusing to admit the (possibility of the) Ks is good only when admitting Ks would require additional ideology.

So yes, I think 'qualitative parsimony' selects your theory over mine. But I don't think we should care, since they are equivalent wrt ideological parsimony. By contrast, we should prefer Jason's on those grounds.

(There might be a reason to prefer your theory on other parsimony grounds, like quantitative parsimony - I'm staying neutral on whether that is a genuine virtue.)

Ross Cameron said...

Joshua: on the Sider-esque version of ersatzism you're considering: okay, I can see where you're going there. So sure, maybe there are some ways of being actualists that are more ideologically parsimonious than Lewisian realism. All I really want is that Lewis isn't sinning against ideological parsimony *just* by believing in all this possibilia. There are at least some actualist positions that will be just as unparsimonious by way of their needing to describe the possibilities.

Ross Cameron said...

(Remember, though, that the actualists I was restricting my attention to were ones who were realist about the possible - so discounting expressivism etc. I'm not sure the conventionalist character you're considering counts.)

Anonymous said...

--might there be fundamentality considerations which are such that, if added, put Lewis at a disadvantage?
--how do ideological commitments work? Lewis needs the added ideology to describe the non-actual worlds: their structure and inhabitants.
But compare someone like a plantingan about possible worlds. On this picture, reality is a bunch of complex abstracta --the maximal ones being the worlds, with parts, the states of affairs, which have constituents, the particulars, properties, and relations-- and the concrete cosmos. Even though all the merely possibly instantiated properties are constituents of states of affairs (which are parts of worlds), do they count as ideological commitments, given that they're uninstantiated, and thus aren't used to give the structure and inhabitants of worlds (if, say, the subject-constituents of states of affairs are haecceities)? Might there be an advantage (for the ersatzist, and a disadvantage for Lewis) to be found here? (Of course, there are also modal primitives for ersatzers.)
(Does anything in this second comment make sense?)

Anonymous said...

thanks for posting.

Tobias said...

Why the contingent Nihilist has no ideological advantage:

There are two versions of the view:
i) Composition-facts are fundamental and so are facts to the effect that collections don't compose
ii) There is some condition, C, such that things compose something iff they satisfy C. Plus, contingently, nothing satisfies C.

Note that the contingent Nihilist of the i)-variety needs the ideology of composition in their (non-modal) *negative* fundamental facts.

Note also that the contingent Nihilist of the ii)-variety will probably need some weird ideology to describe C and needs to appeal to that ideology in her (non-modal) fundamental *negative* facts.