One of the upshots of the last section is that there are still two standing Contingency Arguments, the Exact Number and Even Number argument. Furthermore, I argued that the case in favor of the Incompatibility Premises of such arguments is compelling—I will return to this. Universalists need to take issue with the Possibility Premises. Let me first indulge in a quick consideration that I find not completely unconvincing—and will play a role later on. The Contingency Arguments are modus tollens arguments. But, echoing Putnam,Footnote 17 “one philosopher’s modus tollens is another philosopher’s modus ponens”. That is, one can argue along the following lines:
Incompatibility Premise. If universalism is necessary, then there is no possible world w such that w is \(\phi \), for some condition \(\phi \);
Necessity Premise. Universalism is necessary;
Conclusion. There is no possible world w such that w is \(\phi \).
Clearly, the point would be to have independent arguments in favor of either the Possibility or the Necessity premises and evaluate their respective strengths. Here are some possible arguments in favor of the Necessity Premise above. Universalism is a metaphysical thesis. Metaphysical theses are, if true, necessarily true.Footnote 18 Thus, universalism is necessary—if true at all. Another somewhat related argument appeals to metaphysical laws.Footnote 19 Universalism is a metaphysical law. Metaphysical possibility is compatibility with metaphysical laws.Footnote 20 There is no possible world w such that w is \(\phi \), for every \(\phi \) in the Possibility Premises. I don’t mean to endorse the arguments. Nor do I need to. As it will be clear soon enough it is their sheer existence and availability that is relevant in the present context. In effect, I don’t want to discuss this or other possible arguments in favor of the Necessity Premise at any length. My intention is rather to focus on the arguments for the Possibility Premises of the standing Contingency Arguments.Footnote 21 And I will argue that none of them are compelling.
Let me start from the Possibility Premise (5). Comesaña (2008) writes that it
[D]erives from our particular pre-theoretical judgments that there could have been exactly two things, three things, and... (Comesaña, 2008. 34).
Given that, to my knowledge, the Even Number argument has never been put forth in the literature there is no argument in favor of its Possibility Premise. And yet, I suspect that many would consider it the most plausible Possibility Premise of them all. What is this metaphysical privilege bestowed upon odd numbers, this oddity of being odd? But, as I said, this is just a suspicion. Be that as it may, we may look at arguments for the Possibility Premise (2) of the Junk argument to construct a similar argument in favor of (7). Bohn (2009b) and Bohn (2010) contend that junky worlds pass a three-step possibility test:
[I] argue (i) that junky worlds are (positively) conceivable and (ii) that junky worlds are logically consistent (in the sense of there being mereological models of them involving no controversial mereological principles) and (iii) that their possibility has been defended by such serious thinkers (Bohn, 2010: 296–297).
He claims that the conjunction of (i) conceivability, (ii) consistency, and (iii) advocacy, “provides prima facie evidence for the possibility of junky worlds (Bohn, 2010: 297)”.Footnote 22 Finally, Bohn contends, when faced with the fact that junky worlds pass the three-step possibility test above, universalists cannot simply assert the necessity of universalism, and should therefore try to explain the counterexamples—i.e. the problematic worlds—away (more on this later on).Footnote 23 In light of this, one can construct the following argument for the Possibility Premise of the Even Number argument—and for the Possibility Premise of the Exact Number argument for that matter: possible worlds in which there is an even number of objects pass the three-step possibility test. And this is prima facie evidence for their metaphysical possibility. An infamous example of such a world is arguably Max Black’s two-sphere world in Black (1952). On the face of it, the two-spheres world is populated only by two simple iron spheres. Black’s world seems to pass the three-step possibility test with flying colors. It has been conceived and advocated, and it is consistent. We thus seem to have two arguments in favor of the Possibility Premises: one argument from pre-theoretical intuitions, and one broad conceivability argument from the three-step possibility test mentioned above. Faced with these arguments, one question is whether universalists can explain the problematic possible world away as Bohn would put it. By “explaining it away”, I take it, Bohn (2010: 298) means that universalists should explain why, worlds that at first sight provide counterexamples to the necessity of universalism, do not really do so at a closer scrutiny. I will get to this shortly.
Before that, I think it is important to realize that explaining away—in the sense delineated above—is in fact not the only strategy that is available to universalists—pace Bohn. They can simply push back on his insistence that one should explain the problematic words away, for it is explicitly predicated on the premise that if universalists don’t explain the problematic worlds away, then they are simply asserting—Bohn’s own words—the necessity of universalism. But as we saw, this is not the case. Universalists have themselves independent arguments for their Necessity Premise. We saw two of them, from the nature of metaphysical theses, and from a certain conception of metaphysical laws and metaphysical possibility. So, they really don’t have to explain the worlds away. They could simply claim that at this stage in the dialectic, it is a matter of (i) weighting arguments in favor of the necessity of universalism against the plausibility of a pre-theoretical intuition on the one hand, and (ii) weighing arguments in favor of the necessity of universalism against the three-step possibility argument on the other. As for (i), I simply have to confess that I am not convinced about the use of intuitions to adjudicate metaphysical questions. In fact, one may simply hold that an argument always trumps an unsupported intuition. In any case, I will return to the pre-theoretical intuition argument later on. As of now, I want to focus on (ii). Here my contention is that, on the face of it, the case from the three-step possibility argument is rather weak. As Cotnoir writes:
I do not think Bohn’s three criteria are sufficient for (or even provide good evidence for) metaphysical possibility (Cotnoir, 2014: 650).
This is because the three-step possibility test is itself rather weak.Footnote 24In the absence of any details about the notion of conceivability at hand, it is way too easy to pass the test. And those who endorsed the Possibility Premises have provided no such details, despite the enormous body of work dedicated to the issue.Footnote 25 Serious philosophers have conceived and advocated all sorts of situations and worlds: against pluralism worlds with only one object, against materialism worlds with disembodied souls, against sortal essentialism worlds in which humans become animals, trees, even abstract objects like melodies, and so on. My bet is that for any claim that is allegedly necessary, you will find serious philosophers that conceived and advocated situations that provide a counterexample to it. As Hill puts it:
[S]imple, undisciplined conceiving is not a reliable test for possibility. On the present account of conceiving, it is possible to conceive of anything, including logical contradictions (Hill, 2016: 328).
Michels (2020) voices the same attitude, and provides an example:
[W]ithout any qualification of what we mean by conceivability, there is no way to exclude the conceivability of metaphysically impossible states of affairs, such as that of water being an element. Given a naïve, unqualified notion of conceivability, the conceivability of a state of affairs does not entail its metaphysical possibility (Michels, 2020: 7).
To further stress the point, those who endorsed the Possibility Premises of the Contingentist Arguments because they were persuaded by broad conceivability arguments have provided us no explicit detail to the point that the conceivability in question is substantially different from the simple, unqualified, naïve conceivability Hill and Michels are warning us against. In effect, Hill continues:
If we are to have a reliable test for possibility, we must rely instead on what I will call constrained conceiving—conceiving that is compatible with the laws of logic, the principles that are constitutive of concepts, and any other propositions that are assumed to be necessary in the relevant context (Hill, 2016: 328, italics added).
But this is clearly grist for the universalist mill. For the universalist has already provided arguments for her Necessity Premise. She could simply claim that, at this stage, it has not be shown that the conceivability at hand is Hill’s constraint conceivability—and thus not a reliable guide to (metaphysical) possibility. She could actually push the point further: given her arguments for the Necessity Premise one of the proposition that should be considered necessary in the relevant context is exactly universalism.
I am prepared to concede that at this point we should give the contingentists the opportunity to fill in some details about conceivability in order to beef up their case for the Possibility Premises. In what follows I will argue that plausible ways to fill in such details will also give the universalist a leeway to explain the problematic worlds away, as per Bohn’s request.
The argument starts by recognizing that conceiving, whatever it is, is a mental representation. And the standard view has it thatFootnote 26
[T]here are two candidate codings for mental representations (one of them being, according to some, reducible to the other): the linguistic and the pictorial (Berto and Shoonen, 2018: 2697).
Now, if the conceivability at stake in the Possibility Premises is a question of forming a linguistic representation, then it is very plausible that we can conceive the impossible. We can have a linguistic representation of logical contradictions, or a linguistic representation according to which water is an element.Footnote 27 It is noteworthy that Berto and Shoonen (2018) almost equate this linguistic notion of conceivability with Hill’s “simple, undisciplined” conceivability. This kind of conceivability is not a guide to metaphysical possibility exactly because, in this very broad and simple sense, we can conceive the impossible. This leaves a broadly pictorial notion of conceivability. Berto and Shoonen (2018) relate this pictorial notion of conceivability with Chalmer’s positive conceivability,Footnote 28 Yablo’s imaginability,Footnote 29 and Hill’s constraint conceivability. It is important to note that they all have some sympathies for the view that this kind of conceivability is a somewhat reliable guide to possibility. I am going to concede this much—a very generous concession indeed.Footnote 30 This is because I think that, even if universalists concede this, they will have a way to explain the problematic worlds away. Here is why.
Suppose I were to ask you to picture a world \(w_1\) with only two spheres—to stick to Black’s infamous example—and to picture a world \(w_2\) with the same two spheres together with their mereological sum. You would picture “the same world”. Try it. Draw what you pictured, that is, draw \(w_1\) and \(w_2\). Now compare the drawings. As far as picturing goes, there is nothing in \(w_1\) that is not in \(w_2\). In light of this I now ask you: how can you be sure that you pictured \(w_1\) instead of \(w_2\)? But note that this is crucial. For \(w_2\) clearly does not constitute a counterexample to the necessity of universalism. In general, a world with m simples and a world with m simples together with all their the mereological fusions are pictorially indistinguishable. This amounts, I contend, to explain the problematic world away. When you say that you conceived—that is, you pictured—of a world in which there are only two spheres (i.e. \(w_1\)), the universalist replies that you really conceived—that is, you pictured—of a world in which there were two spheres and their sum (i.e \(w_2\)).Footnote 31
This still leaves the pre-theoretical intuition argument open—at least for those who are not skeptical about the use of intuitions in metaphysics. To conclude the paper I offer one final strategy to resist the Contingency Arguments on behalf of universalists—yet I do not want to claim that this is the only strategy available. The strategy I have in mind starts by recognizing with Varzi that
[W]e quantify over everything, since the meaning of “everything” is set by the domain of the quantifiers; yet counting is selective. And we may set different standards for counting, but we must avoid omissions and repetitions.Footnote 32 (Varzi, 2010: 287, italics added).Footnote 33
Once we acknowledge a distinction between existence and (selective) counting, so the thought goes, two readings of the Possibility Premise(s) become available. Let me clearly disambiguate these two readings—I will mostly discuss a particular instance of (5) for the sake of simplicity:
(5-Existence) For any natural number n, there is a possible world w such that the exact number of objects that exist in w is n;
(5-Count) For any natural number n, there is a possible world w such that, under a given counting policy, counting the objects in w results in a count of exactly n objects.
I will first argue that, if (5) is read as (5-Count), then universalists can recognize the existence of the allegedly problematic worlds. In effect, Varzi himself suggests different counting policies that are compatible with the existence of such worlds. The first one is any counting policy compatible with what Varzi calls the Minimalist View:Footnote 34
(M) An inventory of the world is to include an entity x if and only if x does not overlap any other entity y that is itself included in that inventory. Varzi (2010: 285).
There is clearly a counting policy compatible with the Minimalist View (M) such that, e.g. counting the objects in Black’s world, results in a count of exactly 2 objects. First, count the 2 spheres. Then, notice that according to the Minimalist View, once you counted the 2 spheres, you should not count anything else, for everything else overlaps the spheres. Most importantly, you should not count their sum. Thus, universalists can account for the truth of (5), if (5) is read as (5-Count). As for another example, consider an even more stringent counting policy in Varzi (2010):
(A) An inventory of the world is to include an entity x only if x is mereologically atomic (Varzi, 2010: 300).
It should be clear that universalism is not in any tension with the claim there is a possible world w such that, under the counting policy in (A), counting the objects in w results in a count of exactly n objects. This is because, according to (A), one should count only atoms. And clearly, the problems for universalists are due to their countenancing the existence of composite objects. In either case, the way out of the Possibility Arguments is to note that there is a reading of (5), namely (5-Count), according to which universalists can indeed accomodate the relevant pre-theoretical intuition. As a matter of fact, the right thing to say in these circumstances would be that the Incompatiblity Premise is false—more on this in a second.
Finally, I want to argue that, if (5) is read as (5-Existence), then universalists have all the rights to simply discard the alleged pre-theoretical intuition. (5-Existence) is supposed to cash out a pre-theoretical intuition about a purely quantificational notion of existence. According to universalists, we quantify over both parts and wholes, that is, things that are built up from parts according to some specific laws of composition. If so, it should be granted that the relevant laws of composition play a crucial role in matter of existence. Any pre-theoretical intuition, such as the one at hand, that disregards completely such laws of composition can hardly be thought to carry any decisive weight. The result is that if (5) is read as (5-Existence), the pre-theoretical defense of the Possibility Premise is hardly compelling. To put it differently: it is hard to establish whether the alleged pre-theoretical intuition that underpins the Possibility Premise (5) is a pre-theoretical intuition about existence (5-Existence) or counting (5-Count). In the latter case, the Incompatibility Premise (4) is false. In the former case, universalists can—and should—simply discard the Possibility Premise (5) itself.Footnote 35
The conclusion I want to draw is the following. Insofar as the only arguments in favor of the Possibility Premise of the Contingentist Arguments are the ones I explored in the paper,Footnote 36 I think universalists are in good shape. They can claim that that the universe has to be odd.