Are the categorical laws of ontology metaphysically contingent?

Are the categorical laws of ontology metaphysically contingent? I do not intend to give a full answer to this question in this paper. But I shall give a partial answer to it. In particular, Gideon Rosen, in his article “The Limits of Contingency” (2006), has distinguished a certain conception of metaphysical necessity, which he calls the Non-Standard conception, which, together with the assumption that all natures or essences are Kantian, is supposed to entail that many laws of ontology are metaphysically contingent (Rosen 2006: 20, 27). Now, the argument Rosen gives supports the conclusion that all categorical laws of ontology are contingent. I shall argue that the Non-Standard conception and the thesis that all natures are Kantian are incompatible with each other and that, if the Non-Standard conception is true, there must be at least one metaphysically necessary categorical law of ontology, and I shall identify such a law. Thus my contribution to the question of the title of the paper will be that not all categorical ontological laws can be contingent if the Non-Standard conception is true.


1
Are the categorical laws of ontology metaphysically contingent? I do not intend to give a full answer to this question in this paper. But I shall give a partial answer to it. In particular, Rosen (2006) has distinguished a certain conception of metaphysical necessity, which he calls the Non-Standard conception, which, together with the assumption that all natures or essences are Kantian, is supposed to entail that many laws of ontology are metaphysically contingent (Rosen 2006: 20, 27). 1 Now, the argument Rosen gives supports the conclusion that all categorical laws of ontology are contingent. I shall argue that the Non-Standard conception and the thesis that all natures are Kantian are incompatible with each other and that, if the Non-Standard conception is true, there must be at least one metaphysically necessary categorical law of ontology, and I shall identify such a law. Thus my contribution to the question of the title of the paper will be that not all categorical ontological laws can be contingent if the Non-Standard conception is true.
In Sect. 2 I shall explain what I mean by the categorical laws of ontology, and I shall explain the Non-Standard conception of metaphysical necessity and the Kantian character of natures. In Sect. 3 I shall argue for the incompatibility of the Non-Standard conception and the thesis that all natures are Kantian, and in Sect. 4 I shall argue that if the Non-Standard conception is true, there must be at least one metaphysically necessary categorical law of ontology. Section 5 is a brief conclusion.
2 By the laws of ontology, or ontological laws, I will understand synthetic a priori claims about basic matters of ontology that are standardly regarded as metaphysically necessary. Such laws entail the existence of a distinctive sort of objectperhaps conditionally on the existence of things of a more basic sort. This is, indeed, Rosen's conception of an ontological law (2006: 20). 2 Examples of putative categorical ontological laws (as opposed to conditional ones) are the following claims: There are sets; For any two distinct things x and y, there is a set containing just x and y (the Pair Set Axiom) 3 ; There are numbers; Any number of things compose another one; Some things compose another one and some do not compose anything. Examples of putative conditional ontological laws are the following: If there are sets, there are members of sets; If x is a persisting object that exists at a certain time, it has a momentary part that exists wholly at that time.
What is metaphysical necessity? For Rosen, metaphysical necessity is synthetic, alethic, and non-epistemic. Rosen calls any synthetic, alethic, and non-epistemic modality a real modality. And he thinks that metaphysical necessity is the strictest real necessity, which means that what is metaphysically necessary is necessary in every real sense (Rosen 2006: 16). I shall assume, with Rosen (and others), that this is indeed the case. 4 Rosen distinguishes two conceptions of metaphysical necessity: the Standard and the Non-Standard. Rosen never properly defines the Standard conception, but it is part of it that all the laws of ontology are metaphysically necessary (2006: 20). This is not so on the Non-Standard conception. What is the Non-Standard conception?
The Non-Standard conception is the view that correct conceivability, that is, logical consistency with propositions that express the natures of things, is both necessary and sufficient for metaphysical possibility (2006: 24). Indeed, on the Non-Standard conception, a proposition is metaphysically possible if and only if it is logically consistent with the natures of things, it is metaphysically necessary if and only if it is logically required or entailed by the natures of things, and it is metaphysically impossible if and only if it is logically inconsistent with the natures of things (2006: 24, 37). 5 Occasionally Rosen suggests that, on the Non-Standard conception, a proposition is metaphysically impossible if it is inconsistent with the natures of things it concerns (2006: 24). I suppose this qualification is in order to secure certain impossibilities. For instance, it is plausible that it is impossible that water is an element. But that water is an element is not inconsistent with the nature of gold, or with the nature of nearly everything else. But I do not think the qualification is necessary. For to say that a proposition is metaphysically impossible if and only if it is logically inconsistent with the natures of things can be understood to mean that it is metaphysically impossible if and only if it is logically inconsistent with all natures taken collectively (since that water is an element is inconsistent with the nature of water, it is thereby inconsistent with all natures taken collectively); similarly, to say that a proposition is metaphysically possible if and only if it is logically consistent with the natures of things can be understood to mean that it is metaphysically possible if and only if it is logically consistent with all natures taken collectively, and to say that a proposition is metaphysically necessary if and only if it is logically required or entailed by the natures of things can be understood to mean that it is metaphysically necessary if and only if it is logically required or entailed by all natures taken collectively-of course, if one such nature entails a certain proposition, all do when taken collectively. I think this way of understanding the theory is better than the one that makes reference to what propositions concern. 6 For Rosen a nature is a condition that specifies what it is to be a certain thing or a certain kind of thing, and a nature is Kantian if and only if it is consistent with it that nothing instantiates it (2006: 25). 4 Of course, that metaphysical necessity is the strictest real necessity is controversial (see, for instance, Clarke-Doane 2019). But I need not discuss the assumption that metaphysical necessity is the strictest real necessity, for such an assumption will play no role in my argument. 5 Rosen assumes that the bearers of metaphysical necessity are propositions (2006: 13, 16). I do not question such assumption. 6 Cf. Fine 1994: 9, where he identifies metaphysically necessary truths with those that are true in virtue of the nature of all objects whatever.
How are the Non-Standard conception and the assumption that all natures are Kantian supposed to entail together that all categorical ontological laws are metaphysically contingent? Consider the Pair Set Axiom, Rosen's main example of an ontological law. Rosen argues that even if it follows from the nature of sets that if they exist, the Pair Set Axiom is true, given the Kantian character of the nature of sets, it is consistent with the nature of sets that they do not exist. But, on the Non-Standard conception, if it is consistent with the nature of sets that they do not exist, it is metaphysically possible that sets do not exist, and therefore it is metaphysically contingent that the Pair Set Axiom is true (2006: 25). Of course, this generalizes, and so the argument supports the conclusion that if all natures are Kantian, then all categorical ontological laws are metaphysically contingent on the Non-Standard conception. 7 In my view, the Non-Standard conception, as Rosen defined it (2006: 24, 37), does not include and does not entail the idea that all natures are Kantian. 8 I shall develop my argument that the Non-Standard conception is incompatible with the idea that all natures are Kantian under the assumption that the Non-Standard conception does not include and does not entail the idea that all natures are Kantian. If this is incorrect, and the Non-Standard conception was meant to include or entail the claim that all natures are Kantian, then the lesson of my argument should be that the Non-Standard conception is incoherent.

3
In this section I shall argue that the Non-Standard conception and the thesis that all natures are Kantian are incompatible with each other.
If all natures are Kantian, the nature of metaphysically necessary propositions is Kantian. If so, the nature of metaphysically necessary propositions is consistent with its having no instances. That is, it is consistent with the nature of metaphysically necessary propositions that no proposition is metaphysically necessary. Now, if all natures are Kantian, given that the nature of metaphysically necessary propositions is Kantian, it is consistent with every nature that no proposition is metaphysically necessary. Indeed, if all natures are Kantian, no nature can entail the existence of anything. For natures specify what it is to be a certain thing or a certain kind of thing, and so, if all natures are Kantian, that Gs exist cannot be part of the nature of Fs. For if the nature of Fs specifies what it is to be F, and that nature is Kantian, all that can be part of their nature is that if Fs exist, Gs exist-but this is short of entailing the existence of Gs (cf. Footnote 7 above). 7 Note that Rosen does not need to argue that no other nature entails the existence of sets. For given that natures specify what it is to be a certain thing or a certain kind of thing, if every nature is Kantian what any nature can entail is at most that sets exist if its instances exist, but this is short of entailing the existence of sets. So, on the assumption that all natures are Kantian, no nature entails the existence of sets (or the existence of anything else for that matter). 8 Michels (2019: 537), on the contrary, asserts that the idea that all natures are Kantian is part of the Non-Standard conception, but he does not provide textual evidence, nor does he discuss the issue. Now, if it is consistent with every nature that no proposition is metaphysically necessary, and the Non-Standard conception is true, then it is consistent with every nature that nothing-no proposition-is required by any nature.
But it is not consistent with every nature that nothing is required by any nature. For that nothing is required by any nature goes against the very nature of natures. Natures, or essences, specify what it is to be a certain thing or a certain kind of thing, and therefore they impose requirements that must be satisfied by their instances. So it is in the nature of natures that they require something of their instances. But then it is not consistent with the nature of natures that natures require nothing of their instances. 9 Thus, the conjunction of the Non-Standard conception and the thesis that all natures are Kantian entails something incompatible with the nature of natures. This means that if both the Non-Standard conception and the thesis that all natures are Kantian are true, there are no natures.
But if there are no natures, it is not true that all natures are Kantian (for the thesis that all natures are Kantian is not meant to be vacuously true).
And if there are no natures, the Non-Standard conception is not true. For either some proposition is metaphysically necessary or some proposition is metaphysically contingent. But nothing can be either on the Non-Standard conception if there are no natures. Therefore, if there are no natures, the Non-Standard conception is not true. 10 Of course, my argument in this section presupposes that metaphysically necessary propositions have a nature, and that natures have a nature. Are these assumptions justified? Yes. For a nature is simply a condition that specifies what it is to be a certain thing or a certain kind of thing. And there must be something that it is to be a metaphysically necessary proposition-whatever that might be. And since a nature is simply a condition that specifies what it is to be a certain thing or a certain kind of thing, this is the nature of natures, and so natures have a nature. Thus the assumptions that metaphysically necessary propositions have a nature and that natures have a nature are justified.
To conclude, neither the Non-Standard conception nor the thesis that all natures are Kantian can be true if the other one is true. Thus, the Non-Standard conception and the thesis that all natures are Kantian are incompatible with each other.

4
As we saw in the previous section, if the Non-Standard conception is true, there are natures, and the nature of natures requires that they require something of their instances. So, if the Non-Standard conception is true, there is a nature that requires that natures require something of their instances. And, on the Non-Standard conception, that there is a nature that requires that natures require something of their instances means that it is metaphysically necessary that natures require something of their instances. But if it is metaphysically necessary that natures require something of their instances, it is metaphysically necessary that there are natures. Therefore, if the Non-Standard conception is true, it is metaphysically necessary that there are natures.
But that there are natures, if true, is a categorical law of ontology: it is a claim about the basic structure and content of the world and, if true, it entails the existence of a distinctive kind of object, namely natures. Natures, or essences, are conditions that specify what it is to be a certain thing or a certain kind of thing. These conditions are properties, and such properties need not be conceptualized as universals, tropes, classes, or any other kind of entities that are sometimes thought to be what properties are; therefore, the claim that there are natures need not entail the existence of universals, tropes, or classes, or other such entities. But, however deflationary our conception of properties may be, natures or essences are a distinctive kind of properties, since they are the properties that define what things, and kinds of things, are.
Thus, that there are natures is a categorical law of ontology, and if the Non-Standard conception is true, it is metaphysically necessary that there are natures. Therefore, if the Non-Standard conception is true, there is at least one metaphysically necessary law of ontology, namely that there are natures.

5
I have arrived at two conclusions in this paper. Firstly, the Non-Standard conception and the thesis that all natures are Kantian are incompatible with each other (as I said above, if the Non-Standard conception is meant to include the claim that all natures are Kantian, one should conclude that the Non-Standard conception is incoherent). Secondly, if the Non-Standard conception is true, there must be at least one metaphysically necessary categorical ontological law, namely that there are natures. Thus, not all categorical ontological laws can be contingent if the Non-Standard conception is true.