Tuesday, April 24, 2007

Comesaña on Whether There Could Be Exactly Two Things

(X-posted at GAF.)

I just read Juan Comesaña’s ‘Could There Be Exactly Two Things?,’ forthcoming in Synthèse. As Comesaña reminds us, Universalism—the view that whenever there are some things, there is something which is a sum of them—is obviously at odds with the idea that there could be exactly two things (indeed, incompatible with that idea given minimal further assumptions).

Comesaña contends (i) that we intuit that there could be exactly two things; and (ii) that this tells against Universalism. I have some doubts about (ii), and I found the discussion of it at the last two paragraphs of the paper less than completely satisfying. But, more importantly, I have not found anything in support of the assertion of the claim in (i). Everybody would agree that there are scenarios such that, in most ordinary contexts, to describe them with ‘There are exactly two things’ would be true (or true enough). Universalists typically contend, however, that this is compatible there being strictly speaking more than two things there, and familiarly invoke contextual quantifier domain restriction, in a rule-governed, independently motivated manner, or so she argues. Maybe there is something defective in this move by Universalist, but Comesaña does not say. And in the absence of this, (i) seems to me to be ungrounded, and thus unsuitable for a case against Universalism.

What do people think?

16 comments:

Juan said...

Hi,

Thanks for the comment on the paper.

Two small things: First, far from being obviously at odds with the possibility of exactly two things existing, Universalism is compatible with the existence of exactly two things, as long as those two things overlap. What is incompatible with the existence of exactly two things (and, more generally, with what I call Primitive Cardinality in the paper) is Universalism together with the reflexivity of the part relation and the Principle of Weak Supplementation. (As I note in the paper, moreover, some philosophers are committed to denying Weak Supplementation.)

Second, I agree that more discussion of the ecumenical resolution of the problem is needed. The thing is, I don't have anything new to say about that. As I put it in the paper:

"I have little to say about the first resolution. The general form of the strategy has a distinguished philosophical pedigree, but it is suggestive that many participants in ontological disputes resist this kind of ecumenical reinterpretation of their position. If so, charity bids us to consider the other options. "

Juan said...
This comment has been removed by the author.
Juan said...

Oops, I didn't see you parethentical remark about the assumptions needed to show the incompatibility. That takes care of my first comment (although I do think that calling attention to what is needed to generate the incompatibility is important).

Dan López de Sa said...

Many thanks for the comments!

I didn't see you parethentical remark about the assumptions needed to show the incompatibility. That takes care of my first comment.

The typo in my remark probably didn't help, sorry. I’ve now corrected ‘giving’ for ‘given.’

As to the main point, I understood that the “ecumenical,” first solution you discuss in the paper was “to claim that the conflict is merely apparent, and that both Primitive Cardinality and Classical Extensional Mereology are correct” as if “for example, there are two notions of ‘thing’, say thing* and thing#.” (p. 2)

But this is not the line that I said universalists such as David Lewis or Ted Sider would take: the relevant instances of Primitive Cardinality are, strictly speaking, false. And our intuitions with respect to them are respected and accounted for by independently motivated mechanisms of domain restriction and the pragmatics of counting-talk. Or so they might say. In so far as I can tell, you do not consider this in the paper, nor give reasons of why this familiar move shouldn’t work.

Juan said...

As to the main point, I understood that the “ecumenical,” first solution you discuss in the paper was “to claim that the conflict is merely apparent, and that both Primitive Cardinality and Classical Extensional Mereology are correct” as if “for example, there are two notions of ‘thing’, say thing* and thing#.” (p. 2)

But this is not the line that I said universalists such as David Lewis or Ted Sider would take: the relevant instances of Primitive Cardinality are, strictly speaking, false. And our intuitions with respect to them are respected and accounted for by independently motivated mechanisms of domain restriction and the pragmatics of counting-talk. Or so they might say. In so far as I can tell, you do not consider this in the paper, nor give reasons of why this familiar move shouldn’t work.


I think they are both variants of the same move. The move consists in claiming that the sentence "There could have been exactly two things" is ambiguous, and it is true in one disambiguation and false in the other. The Lewis-Sider implementation of the move consists in saying that the sentence could express one of these two different propositions:

[quantifiers wide open] There could have been exactly two things.
[quantifiers restricted (to, for instance, simples)] There could have been exactly two things.

As I said, I don't have anything terribly new to say about strategies of this kind. But here's a thought: they all involve attribution of confusion to one or more of the participants in the ontological dispute. The less confused the participants are, the less effective this strategy is.

Dan López de Sa said...

According to the view I had in mind, the sentence ‘There could have been exactly two things’ would not be ambiguous but, strictly speaking, just false. So it cannot be an implementation of the “ecumenical” solution you mention: it has it that the conflict between Primitive Cardinality and Universalism (given the rest of assumptions) is indeed genuine—and the former has to go.

This is nonetheless compatible with the sentence being true enough, in Lewis’ sense, and thus perfectly and appropriately assertable, in a lot of contexts—what accounts for the “pre-theoretical intuitions” with respect to it (or so the move has it), without invoking any confusion on part of any competent ordinary user of the sentence.

(Of course, if Universalism is right, then an ontologist who “theoretically” claims that the sentence is, strictly speaking, true would indeed be holding a false view. But here things are as one would expect: this by itself is hardly a reason against Universalism!)

Juan said...

As I understand the quantifier-restriction move, there is no such thing as the sentence 'There could have been exactly two things,' just as there is no such thing as the sentence 'All the beer is in the fridge.' Saying that a sentence is true enough is saying that it is false, but there is another related sentence that is true. But nevermind that--suppose that we are referring to the quantifiers-wide-open reading of the sentence. Saying that the attraction of the claim that there could have been exactly two things is due to the fact that, although false, the sentence is true enough still involves attributing some degree of confusion to the participants in the discussion: I, for one, still think that the sentence is simply true, not just true enough, even after considering the quantifier-restriction move.

Dan López de Sa said...

I, for one, still think that the sentence is simply true, not just true enough, even after considering the quantifier-restriction move.

Right. So, as I said, if Universalism is right, then someone like you who claims that the sentence is, strictly speaking, true would indeed be holding a false view.

But here things are as one would expect: this by itself is hardly a reason against Universalism. For the move is intended to account for “pretheoretical intuitions” regarding the sentence, which are to the effect that it is perfectly and appropriately assertable in a lot of ordinary contexts—and so it seems to do—; not to accommodate the incompatible theoretical views characteristic of the anti-universalist!

Juan said...

For the move is intended to account for “pretheoretical intuitions” regarding the sentence, which are to the effect that it is perfectly and appropriately assertable in a lot of ordinary contexts—and so it seems to do—; not to accommodate the incompatible theoretical views characteristic of the anti-universalist!

There are hughe methodological issues here and, on pain of repeating myself, I don't have anything radically new to say about those. Let me nevertheless point to a couple. I very much doubt that there is a neat distinction between "pretheoretical intuitions" and theoretical commitments, but why do you say that my committment to the claim that there could have been exactly two things is theoretical? Is it because of the fact that it survives the quantifier-restriction move? In that case, the quantifier-restriction move wins by fiat: either the "intuition" goes away, or, if it doesn't, it's no longer an intuition!

Dan López de Sa said...

Yeah, I think you’re absolutely right: there are lots of complexities in assessing whether universalism is indeed right or not, after all. I didn’t want to get into them here either, nor defend universalism in full. My only point was that precisely getting into them would be required in order to get a (prima facie) a case against universalism. Such a case does not get started, in my view, by merely pointing that “pre-theoretically” people would think there are situations naturally and correctly described by an instance of Primitive Cardinality—not even supplemented with the contention that anti-universalists reject universalism.

As you said in a comment above, it is indeed interesting to call attention to what is needed to generate the incompatibility between Primitive Cardinality and universalism, and I’ve very much liked the way you explicitly state this in detail in the paper. My complaint is only that, in the absence of a discussion of those huge issues you mention, it might seem at best an overstatement to conclude “that CEM cannot be a true theory of the part-whole relation.”

Juan said...

My complaint is only that, in the absence of a discussion of those huge issues you mention, it might seem at best an overstatement to conclude “that CEM cannot be a true theory of the part-whole relation.”

Here are some consequences of CEM that have been taken (correctly, in my view) to be prima facie arguments against it: that there is a sum of my nose and the Eiffel Tower and that it doesn't have a place for objects that can change their parts. Of course, there can be (and there have been) arguments concerning whether this prima facie case can be overcomed in favor of CEM--but that doesn't mean that the consequences are not prima facie bad for CEM. I point out a different kind of consequence: not that it entails the existence of too many, or too few objects, but that it imposes cardinality restrictions that seem arbitrary.

Perhaps many of the same moves deployed in the other disputes can be applied to this case, perhaps not. But, again, that doesn't mean that it cannot be the basis for a prima facie case against CEM.

Dan López de Sa said...

Yes, I agree again: it could be the basis for a prima facie case against CEM. As I said, however, whether there is finally such a case or not will depend on the discussion of the issues that you do not seem to address in the paper, in so far as I can see. That was my only point.

Juan said...

Maybe we just disagree on what it takes for something to be a prima facie case. If, after full discussion of all the possible defenses it still is the case that the consequence is unnaceptable, then I take it that we have not only a prima facie case, but a definitive case. As things stand, I think we have a prima facie case.

Pablo said...

Interesting discussion! I agree with Dan’s criticisms and do not have much to contribute to the debate, but I have a doubt about the way Dan construes the move of quantifier domain restriction (QDR):

According to the view I had in mind, the sentence ‘There could have been exactly two things’ would not be ambiguous but, strictly speaking, just false. So it cannot be an implementation of the “ecumenical” solution you mention: it has it that the conflict between Primitive Cardinality and Universalism (given the rest of assumptions) is indeed genuine—and the former has to go.
This is nonetheless compatible with the sentence being true enough, in Lewis’ sense, and thus perfectly and appropriately assertable, in a lot of contexts

Do you think this view you have in mind is Sider’s or Lewis’? I think it might be Sider’s, given that he uses the notion of “quasi-truth” or “true-enough” in related cases (see his “Presentism and Ontological Commitment”) What about Lewis? Do you have in mind any specific reference in which Lewis construes the QDR in this way –as implying that the guy who restricts the quantifier is saying something strictly speaking false? I tend to understand the QDR move as follows: there is one sentence that expresses different propositions in different contexts. In ordinary contexts, ‘there might be exactly two things’ expresses a true proposition (there might be exactly two things of the ordinary sorts we are familiar with); in the philosophy room the same sentence expresses a false proposition (there might be exactly two things of any sort). By ‘expressing a propositon’ here I mean both semantically express and pragmatically convey. In any case, what ordinary speakers say in ordinary contexts is strictly true, and not only quasi-true or loosely speaking true. If the true proposition is only pragmatically conveyed, it is still the case that the speaker says something true (by saying also something false). I thought this was Lewis view, but please tell me if you think it is not.

Another point: I do not see why the QDR move implies attributing some degree of confusion to the participants in the ontological debate. There would be confusion if (i) an ordinary speaker entered the philosophy room and somehow carrying his context with him claimed that there could be exactly two things, (ii) the philosophers in the room took him to be one of theirs and said ‘You are wrong! There could be exactly two things’. But this is not what happens in ontological disputes, given that all participants in those disputes share a context that makes quantifiers be wide open. So, there is no risk of confusion. I think this is another way of putting Dan’s point that “an ontologist who “theoretically” claims that the sentence is, strictly speaking, true would indeed be holding a false view”.

Finally, I am curious about this: do you think the kind of evidence we have for universalism is really so different from the one we have for primitive cardinality? In a sense, Lewis argument for universalism could also be traced down to intuitions about particular cases: we have the intuition that if the different parts of my computer make up a whole thing, a very similar set of parts will also make up a whole thing. And you can construe a sorties series of cases such that for any two contiguous cases, we have the intuition that it would be arbitrary to draw the line between them rather than at some contiguous point. And these seem to be ordinary intuitions about particular cases…I am too confused?

Juan said...

I agree with Pable regarding QDR, as can be seen in my comments above.

I still think that the defense of Universalism that appeals to QDR involves attribution of confusion (or else is innefective): someone who thinks that Universalism is incompatible with the existence of exactly two things is, according to the QDR friend, confused. Otherwise, how on earth is QDR relevant to whether Universalism is true or not?

And I do stand by the claim that the kind of evidence that we have for primitive cardinality is different than the evidence that we have for Universalism. The key point is that you need the argument from vagueness to get from judgments about particular cases to Universalism--and the argument from vagueness is, of course, up to the neck in heavy-duty theoretical commitments.

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