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.