On Parfit’s Ontology

Parfit denies that the introduction of reasons into our ontology is costly for his theory. He puts forth two positions to help establish the claim: the Plural Senses View and the Argument from Empty Ontology. I argue that, first, the Plural Senses View for ‘exists’ can be expanded to allow for senses which undermine his ontological claims; second, the Argument from Empty Ontology can be debunked by Platonists. Furthermore, it is difficult to make statements about reasons true unless these statements include reference to objects in reality. These arguments show the instability of Parfit’s claimed metaethical advantages over naturalism.


Introduction
When theories require the addition of abstract objects into their ontology, this is often taken to be a cost for these theories. In this context, abstract objects (abstracta) are those that do not exist in space-time; concrete objects (concreta) are those that do. Derek Parfit (2011Parfit ( , 2017a argues that his irreducibly abstract 1 objects -reasons -are not costs for his theory because existence truths about reasons are true in a 'non-ontological sense'. 2 By this, he means that they are not made true by corresponding to any part of reality, so that we do not need to introduce reasons into our ontology at all. 3 In this manner, Parfit holds that, when we say there exist or are reasons in his 'non-ontological sense', we do not mean that they exist in the way in which medium-sized dry goods exist in space and time, nor as objects that are merely possible, existing in possible worlds. Nor do we mean, as some Platonists hold, that they exist like numbers in some non-spatio-temporal reality. For claims about reasons to be true, Parfit holds, we do not need to populate a world with objects at all. Furthermore, Parfit claims, some other truths, such as mathematical truths and logical truths, are also true in this 'non-ontological sense'. This is not to say that these are fictional truths, or deflated truths. Parfit emphasizes that these truths are 'in the strongest sense', true (479).
Parfit's claims here matter for at least three reasons. First, the metaethical space may be radically reconfigured if Parfit is correct. If existence just needs to be understood in particular ways to allow for objective truth without ontological commitment, then a strong motivation for naturalist and nominalist theories would be undermined. Second, other cognitivists have found conceptions of 'non-ontological' moral properties and objects appealing. 4 Finally, theorists such as Gibbard and Railton are now convinced that their metaethical views are compatible with, or converge to, Parfit's own on the basis of these ontological claims (Gibbard 2017;Railton 2017). 5 In this essay, I argue that this style of ontologically cost-free cognitivism is not established by Parfit's arguments. My primary purpose is to establish the claim that Parfit does not have the resources to show that abstracta do not come with ontological commitments. More particularly, I use two independent arguments to show that Parfit does not avoid ontological costs, and I think these arguments put pressure on others who want to adopt similar cognitivist positions. My secondary purpose is to argue that Parfit's views on truth suggest that positions such as his are ontologically committal for abstracta. I argue that, if one wants to maintain the attractive position that claims about concreta and claims about abstracta are both true in the strongest sense, then this will lead to ontological commitment. In contrast, it has historically been a central motivation in favour of naturalist metaethical positions that they do not need to make contentious ontological appeals. One role that this discussion could play is reviving this parsimony motivation for naturalist metaethics.
In Section 2, I argue that Parfit's Plural Senses View is incomplete. Unless he can motivate the claim that the correct ontology contains only concrete objects, he is merely question-begging when he claims abstract objects exist in a non-ontological sense. This is because he does not show that abstract objects could not exist in an alternative ontological sense.
In Section 3, I specify what this alternative ontological sense would mean and how it would differ from Parfit's non-ontological sense. In the process, I address Parfit's claim that the discussion is confused because there is 'No Clear Question' about abstract ontology.
In Section 4, I consider objections to the alternative ontological sense concerning existence, defending it against claims that the ontological sense is ill-formed or that it is part of a merely verbal distinction.
In Section 5, I address Parfit's objection to this sense, specifically that it is undermined by what I call his Argument from Empty Ontology. I claim that the Platonist can reject or debunk the intuition behind the Argument from Empty Ontology.
In Section 6, I make a positive argument to show that Parfit's claims about truth do commit him to abstract ontology. He holds that claims about concreta and abstracta are both true in the strongest sense. However, the strong theories of truth -broadly speaking, so-called 'inflationary' theories -are ontologically committal and the weak theories -broadly speaking, so-called 'deflationary' theories -will not vindicate his claims about concreta (and furthermore are also not strong senses of truth).
In Section 7, I discuss the implications of this discussion. Since Parfit's positive arguments for adopting his ontologically cost-free position fail, and since there are difficulties in determining how a theory of truth would not lead towards a more ontologically costly position, I hold that the metaethical rapprochement evidenced in Parfit (2017a) and Singer (2017) rests on an insecure foundation.

Making sense together
Parfit holds that existence claims can be read in different 'senses'. For the sake of argument, I grant that they can be understood and distinguished in the way he describes. I also grant his claim that existence claims can be read in multiple ways, i.e. that 'exists'-style verbs can have different ontological implications -although this is a controversial thesis. 6 In this section, I argue that his arguments give us no reason to reject the claim that (at least some) abstracta could exist in an ontological sense, a claim he requires in order to reconfigure the metaethical landscape. In other words, his arguments do not help show that abstracta come without a cost when considering a contrasting metaphysical view (which we can broadly speaking call Platonist, following Parfit and the debate in philosophy of mathematics). 7 There are two categories of objects that can be said to exist: concreta and abstracta. Furthermore, Parfit holds that there is a distinction between ways in which something can be said to exist: ontologically or non-ontologically. These cross-cutting distinctions give us four (potential) 'narrow' types of existence claims. Parfit endorses two: the ontological existence of concreta and the nonontological existence of abstracta. If any of these four potential narrow types of existence holds for any object (abstract or concrete), then that object can be said to exist in a 'wide sense': 8 Plural Senses View: There is one wide, general sense in which we can claim that there are certain things, or that such things exist. We can also use these words in other, narrower senses. For example, if we say that certain things exist in what I call the narrow actualist sense, we mean that these things are, at some time, actually existing concrete parts of the spatio-temporal world…There are also, I have claimed, some abstract entities, such as some logical and normative truths, which exist in a distinctive, non-ontological sense. (719, my emphasis) The wide sense of existence holds of any object (concrete or abstract) about which one can make positive true claims (734-735). 9 The 'narrow actual-ist sense' 10 is used in true existence claims about concreta that are part of one's ontology in the spatio-temporal part of the actual world. 11 The 'narrow, non-ontological sense' is used in true existence claims about abstracta that are not part of one's ontology. Thus, they neither exist concretely in space and time, nor do they exist in any non-spatio-temporal part of reality.
It could be that Parfit is simply stipulating that abstracta and concreta exist in these narrow senses. However, this would be rather unsatisfying, leaving us with no reason to accept these ontological claims. Furthermore, mere stipulation would undermine the putative agreement that Parfit has developed with other more naturalist metaethical views (Gibbard 2017;Parfit 2017a;Railton 2017).
More weakly, it could be that Parfit is pointing attention to the possibility that these ontological claims could be consistently held in the space of metaethical positions. Although he writes that he believes there are such abstracta (e.g. on p. 487), he might not be trying to convince us that abstracta do in fact exist in the non-ontological sense. He would be right to draw attention to this position, since this kind of non-ontological moral realism is a historically unusual metaethical view. However, since he appeals to the truth of this view in the dialectic with other metaethicists, simply pointing out that it is a possibility would undermotivate their common ground.
However, Parfit need not be in either of these unsatisfying positions. We should construe him as offering reasons and arguments to hold that the existence of non-ontological abstracta is more plausible or more likely to be true than the existence of ontological abstracta. I think that there are two arguments that we could (re)construct which could support his claims. However, I ultimately find neither successful. This matters because the traditional motivation for the denial of abstracta, a view which often goes by 'naturalism' or 'nominalism', is that abstracta are ontologically committal. So the most important question is not whether it is more plausible that abstracta are ontologically committal or non-committal, it is whether the possibility that abstracta are committal should motivate a move towards rejecting abstracta (and perhaps making morality mind-dependent in the manner of, for instance, Street 2017). Examining these arguments can help us determine whether this motivation remains.

Alternatives for abstracta
The first argument is an argument from elimination. Abstracta, including reasons, logical objects and mathematical objects, can be said (truly) to exist; so in which 'sense(s)' can this be the case? For Parfit, existence claims for abstracta, such as 'There is a number of people in Britain', are true in the wide sense, since we can make positive true claims about such numbers (regardless of whether we do know the particular number at the time this claim is made). It cannot be true in the narrow actualist sense because this is correctly said only of concreta, and we are considering abstract objects. Thus, we are left with the narrow, non-ontological sense, which, he claims, is correctly applied to some abstracta, including numbers, valid arguments and reasons. We can formalize this as follows: (1) Abstracta can correctly be said to exist.
(2) All things which can correctly be said to exist do so in some narrow sense. (3) Abstracta do not exist in a narrow, actualist sense. (4) ∴ Abstracta exist in a narrow, non-ontological sense (by elimination).
The response to such an argument is equally clear: this argument form is only valid under the implicit assumption that there are no other narrow senses by which these existence claims about abstracta could be true. As hinted at above, there is a large amount of logical space that is left for other senses. For instance, his narrow, actualist sense about concreta could be contrasted with a narrow, possibilist sense also of concreta. But, even with the addition of such a sense, Parfit need not be troubled, since this would only apply to existence claims about concreta, not abstracta.
But there could be another sense: a narrow, ontological sense which holds of abstracta when they are said to exist in reality, but non-spatio-temporally. That reality extends beyond space and time is at least conceptually possibleon some readings of Plato, Platonic Forms are part of reality, but not in space or time. As noted above, we can call those who endorse the addition of abstracta (to non-spatio-temporal reality) Platonists.
Mathematical Platonists would hold that mathematical abstracta exist in the wide sense (one can have positive true beliefs about them) but also in a narrow, ontological sense for abstracta. In this manner, accepting the truth of their existence commits one to adding more to one's ontology, albeit in non-spatiotemporal reality. Another way of putting this point is that, in contrast to Parfit's narrow, non-ontological sense, true existence claims in a narrow, ontological sense have terms (for abstracta) that refer to objects in reality. On Parfit's view, the statement 'There is a number of Little Pigs in the famous children's story' is true without needing to refer to something abstract in our ontology (i.e. the number 3). However, for Mathematical Platonists, this statement would be made true in an ontological sense by an object in some non-spatio-temporal part(s) of reality (i.e. the number 3). In Section 6, I discuss some reasons for thinking that Platonism about abstracta is a plausible position for the kind of irreducible normativity that Parfit claims.
If we can understand this distinct ontological sense for abstracta, then this argument from elimination is no longer (formally) valid, since it could be that true existence claims about abstracta need not be understood in his narrow, non-ontological sense. Both his non-ontological sense and the introduced ontological sense could apply to any given existence claim about abstracta, so he needs further argument to show that his sense applies in general. For this reason, he cannot rule out that reasons exist in reality, and that he incurs the theoretical cost of introducing them into our ontology. 12 In short, the challenge is that there is a coherent possibility that there could be non-spatio-temporal parts of reality. Parfit's response to this challenge is that 'We may find it hard to understand this claim' or that 'We can vaguely understand the possibility that space and time are not metaphysically fundamental' (484). 13 But whether Parfit finds it hard to comprehend or not is not a challenge, conceptually or metaphysically. It is true that, as we do not experience any part of reality that is not spatio-temporal, it is difficult for us to show or demonstrate that there are such parts of reality. But that does not prove that such views are false, let alone incoherent. We can illuminate this by comparing this claim to claims which have structural similarities.
For instance, Parfit calls himself a Possibilist (Appendix J). The Actualist holds that there is nothing beyond the actual world, whereas Parfit qua Possibilist claims that there are also (in the wide sense) merely possible objects and/or worlds. From the Actualist's point of view, it may also be 'hard to understand' Parfit's claim -after all, merely possible objects don't exist in actuality, so how do they exist? Parfit and some others are motivated to accept that there are possibilia in reality because when making certain judgements, such as counterfactual judgements, we seem to commit ourselves to them.
However, the Possibilist may stand in a similar relation to the Actualist as the Platonist to the Nominalist. The Possibilist might claim against the Actualist that some of our judgements commit us to a reality containing possibilia. Similarly, the Platonist might claim against the Nominalist that, when making certain normative judgements, or mathematical judgements, we seem to be committing ourselves to a reality containing certain abstracta.
Here is another similarity. We cannot experience non-spatio-temporal parts of reality or detect them through empirical means, since all that we sense is, by definition, spatio-temporal. We also cannot experience non-actual parts of reality or detect them through empirical means, since all that we sense is, by definition, actual. As Parfit holds, 'We [Possibilists] believe that being actual is ontologically very different from being merely possible' (728); similarly, Platonists believe that there being abstracta is ontologically very different from there being (merely) concreta. In particular, they would both be (ontologically) in different parts of reality -namely, non-spatio-temporal regions and spatiotemporal regions.
Obviously, it may be simpler to imagine possible worlds which are metaphysically similar to the actual world than non-spatio-temporal regions of reality. This is part of why Plato appeals to metaphors and myths (such as comparing the Sun with the Form of the Good) when discussing the Platonic heaven of abstract objects. However, simply because it is challenging to expli-cate what such an ontology would look like should not lead us to reject the view as impossible. Once again, my intention is not to show here that Platonism is true, just that saying that it is a difficult or challenging question does not mean that it is not what Parfit calls a 'Clear Question'. If it is conceptually or metaphysically coherent, I believe that we should accept that there is a 'Clear Question' about whether abstracta exist in an ontological or non-ontological sense just as there is a 'Clear Question' about whether or not there are possibilia -something clear enough that Parfit even thinks he has the answer.

How sensible is this sense?
How could Parfit respond to the possibility of an ontological sense? In this section, I discuss a first type of response, following Manley (2009), which tries to show that the distinction between non-ontological and ontological senses for abstracta is problematic. Perhaps, in appealing to the 'unclarity' of the ontological question, Parfit means that the question is problematic in one of these ways. In particular, Parfit could argue that the distinction is either (a) illformed or (b) a merely verbal distinction, without any substance. Manley says that these are diagnoses that could be offered of some ontological debates, and Parfit has the resources to offer both of these objections, although I think that both charges can be decisively answered.
Let us begin with the claim that the introduced sense is somehow ill-formed. Parfit holds that claims such as the claim that 'Abstracta exist ontologically' are unclear like the claim 'There are some headaches which are correct, and others which are mistaken' (477). This latter sentence seems to be a case where the claim is unclear because a category mistake is being made; headaches are not the type of entity which admit of correctness. 14 For instance, one might think that this could be because 'correct' (respectively, 'mistaken') is a normative predicate and headaches do not admit of normativity in this manner.
However, taking this position requires that it is acceptable to the parties in the debate that it is a category mistake to attribute ontological existence to certain types of abstracta. Otherwise, it would not be unclear in the way that the headache attribution may be unclear. But this is not acceptable to the parties involved: in fact, this is what is at issue between an ontological quietist like Parfit and more ontologically profligate Platonists. Merely asserting that this is a category error is not sufficient in a dialectical situation where it is a live question. The Platonist would not accept that it is a category error to attribute ontological existence to some abstracta; this is precisely what she believes to be true! For Parfit to say that her theories are incomprehensible would certainly not be granted.
Here is another possibility: it could be unclear because of the unverifiability of headaches, due to their only being present in the phenomenology of a particular individual. I am not sure that this is the case; headaches could have complex neural bases which are in principle empirically discoverable. Let us grant the objector this point and set it aside. The analogous charge would be that we cannot determine -empirically, for instance -whether or not abstracta add to our ontology. In at least the empirical sense, it is accurate to say that we cannot determine the answer; this is why we consider arguments in metaphysics.
Perhaps Parfit intends this to be unclear in some further, distinct way, but then it is up to him or others to explain this distinct way.
We can now consider a second strategy which Parfit could use to object to the narrow, ontological sense; namely, that it appears distinct from his narrow, non-ontological sense, but that this apparent distinction cannot be understood or collapses under examination. This point can be drawn from an exchange between Dorr and Parfit.
Dorr (2008, 61)  Parfit is correct in holding that, if Dorr's thesis was that numbers are not part of space-time, then this would not be a denial of mathematical Platonism, since Platonists agree that numbers are not part of space-time. But this is not Dorr's thesis at all; he is explicit that it is 'obvious' that numbers are not concrete. And it is not mysterious what Dorr holds: Dorr's claim is that there are no numbers in reality, i.e. he denies that there are (a) non-spatio-temporal parts of reality or (b) objects in such parts. In the very first sentence of that essay, Dorr states his thesis: the view that "the world of material objects is the whole of reality" (58, emphasis his). To determine what he is denying, we need only negate this claim. That there are numbers in reality is precisely what Platonists assert and Nominalists deny.
So although Parfit claims that it is not explained what the difference between Platonism and Nominalism is, we can see that at least one way of drawing the distinction is whether or not the spatio-temporal parts of reality exhaust reality. This is unsurprising, since it corresponds directly to whether there are true existence claims understood in a narrow, ontological sense for abstracta or whether all existence claims about abstracta must be understood in Parfit's narrow, non-ontological sense. As Dorr suggests, one way of allowing abstracta into our ontology is to admit that there must be non-spatio-temporal parts of reality.

Getting something from nothing
The second argument that Parfit might offer grants that there could be this ontological sense for abstracta and that it differs from Parfit's senses but that this is an unnecessary distinction, a point which he thinks is shown by a thought experiment. This thought experiment, Parfit thinks, helps establish that the ontological sense is empty; no abstracta exist in this ontological manner as I suggest they could. I call it the Argument from Empty Ontology: A proof [that abstract numbers exist non-ontologically] may be possible partly because it is not true that numbers exist in an ontological sense. We can accept Dorr's claim that there could not be a priori arguments which showed that anything exists in such a sense. But this sense of 'exists' is not, I have claimed, the only important sense. If nothing had ever existed in any ontological sense, there would not have been any stars or atoms, nor would there have been space, or time, or God. But it would have been true that nothing ever existed. As we can also claim, there would have been the truth that nothing existed in an ontological sense. This truth would have existed in a different non-ontological sense. And there would have been many other truths, such as the truths that there are prime numbers greater than 100. (485, his emphases) The thought experiment is quite simple. Abstract objects, like numbers, truths about them, and truths about the world, would exist ('in a non-ontological sense') even if there were an empty ontology. From this we can infer that existence claims about abstracta are true without requiring any ontology, i.e. in Parfit's 'non-ontological sense'. So we can excise abstracta from our ontology.
However, the Platonist could disagree in at least one of three ways depending on how the argument is construed. First, let us suppose that all truths are abstracta. Then as soon as these truths exist, for the Platonist, they exist ontologically, but outside of space-time. Thus, strictly speaking, this thought experiment would not involve an empty ontology, since it describes there being abstracta and the Platonist holds that abstracta are ontologically committal. More importantly, if numbers are similar to truths in virtue of their abstractness, then this is not a proof that numbers exist non-ontologically. The Platonist could admit that there are numbers, but that, like the truths, they are in our ontology, but outside of space-time. So, if the truths are abstracta, then the Platonist would not have to agree that this was an empty ontology. In other words, the Platonist could object that the thought experiment is questionbegging or not correct as described.
Second, let us suppose that not all truths are abstracta. For instance, they could just be regions of reality. 15 In that case, normal spatio-temporal facts are not abstract at all, they just are the parts of the world. Then, of course, the Platonist could think that the fact that the ontology is empty just is the empty ontology. 16 So the ontology really could be empty, as Parfit claims. But it is not the case that the empty ontology just is moral or mathematical truths. The Platonist could think that there are moral and mathematical facts which are regions of reality, but then they would be part of non-spatio-temporal regions. So either the ontology is truly empty, in which case the Platonist would deny that there are mathematical abstracta, or the ontology is not truly empty (just the spatio-temporal parts) and, once again, the thought experiment is not correct as described.
However, there is another, more direct objection that the Platonist could offer which is independent of whether truths are abstracta or not. 17 As Parfit claims, and I am inclined to grant, mathematical truths are true in every world. In other words, suppose everyone is committed to there being some abstracta in every possible world (with mathematical objects being obvious candidates, and normative objects being other candidates), even though what constitutes their 'being' is under contention. Then Parfit's Empty Ontology world is incoherent for the Platonist, and not an admissible point against them. Of course, Parfit could respond that his intuition is that it is possible, which shows that Platonism is false. However, the Platonist can offer a potentially debunking explanation of this intuition that the Empty Ontology world is a possible world, even though Platonism does not allow for it.
In other words, a Platonist could offer an explanation of why it is that the Argument from Empty Ontology appears plausible or valid, as follows. When we are talking about an empty ontology, we usually imagine no spatio-temporal universe. The Platonist could agree that some existence claims about abstracta could still be true even with an empty spatio-temporal region (although in this case they would think that abstracta would still exist in the narrow, ontological sense, not in Parfit's non-ontological sense). But if we mean an entirely empty ontology such that reality has neither spatio-temporal parts nor any other parts, then it would no longer be quite as self-evident.

An argument from truth
Parfit and his Platonic interlocutors agree on the value of introducing irreducibly normative objects (abstracta) into moral theory; once we have them, we can make strong claims about the objectivity of morality, grounding its potential demandingness and its supposedly mind-independent status. Of course, it is possible to retreat to some form of naturalism, but Parfit is worried that if naturalism is true, then nothing would really matter. While I am not convinced of that claim, let us grant it to him here for the sake of argument and proceed as if naturalism is a non-starter. That leaves us with the Non-Metaphysical Cognitivist and the Metaphysical Cognitivist positions, which I introduce below. 18 Given the arguments in the previous sections, which show that Parfit has failed to demonstrate the superiority of his Non-Metaphysical Cognitivism over Metaphysical Cognitivism, are there positive considerations that also lead him towards accepting the more ontologically committal position? In this section, I argue that there are. Basically, Parfit's claims about truth and his strong normative commitments are difficult to reconcile with any theory of truth and push him towards the strong correspondence theory he wishes to avoid (745f). While I lack the space to be exhaustive here, I can indicate how some commonly accepted theories of truth fare with regard to Parfit's metaethical commitments and the difficulties he will have in trying to adopt them.
Parfit is clear that accepting the truth of claims about concreta imply that they must be introduced into our ontology: We are Cognitivists about some kind of claim if we believe that such claims can be, in a strong sense, true. Many such claims have metaphysical or ontological implications. In trying to decide whether these claims are true, we must answer some questions about what exists, in an ontological sense. That is true, for example, of claims about concrete entities, such as rocks, stars, philosophers and bluebell woods. And it may be true of all claims about the natural properties of what exists in the spatio-temporal world. When we believe that claims can be in a strong sense true, we are Metaphysical Cognitivists about such truths. (479, his emphases) In order to accept that existence claims or just ordinary claims with referring terms about concreta are true, we need to answer ontological questions about those concreta. The truth of these claims depends on the existence of the objects that they refer to.
But, according to Parfit, the same is not true of some claims about abstracta, since he is a Non-Metaphysical Cognitivist about them: There are some claims that are, in the strongest sense, true, but these truths have no positive ontological implications . . . When such claims assert that there are certain things, or that these things exist, these claims do not imply that these things exist in some ontological sense. (479) My argument draws on the tension between these two statements. Consider Parfit's commitment: truths about abstracta and concreta are both 'in the strongest sense' true. This first indicates that the appropriate theory of truth should be singular. Consider the possibility that truth could be pluralistic. 19 While this is probably not consistent with Parfit's own views -after all, he adverts to truth in the strongest sense 20 -it is a position which one could hold which might appear to vindicate his views (I will argue it would not). In this context, the primary metaethical concern is that, if normative truths are not in any way part of reality, then it is difficult to imagine that they could satisfy the conditions that Parfit desires, such as mind-independence and objectivity. 21 However, here are a few further considerations which count against truth pluralism. First, truth pluralism will make truth ambiguous. As the 'Quine-Sainsbury objection' holds, differences in domains do not automatically motivate truth pluralism. It could instead motivate an examination of the differences between the concreta and abstracta themselves (Quine 1960;Sainsbury 1996). Second, there is the issue of claims which have mixed domains, ranging from atomic sentences (Tappolet 1997) to molecular sentences. In short, if truth is plural, how come we can use these sentences to instantiate standard valid argumentative forms? On truth pluralism, such arguments would require conflation of the types of truth involved. Finally, pluralism about truth is difficult to square with the usual assumption that truth is a norm for belief (for recent discussion, see Chan 2013). If truth is plural, then this threatens to dilute the norm, or to rob it of substance (Engel 2013). There are responses to these claims that the pluralist can offer, but I take these considerations to render the position unattractive. Furthermore, even if Parfit bites these bullets and adopts truth pluralism, it still must be explained which form of truth is applicable in the case of abstracta.
This commitment to truth's 'strongest sense' also suggests that Parfit cannot accept theories of truth which we might think of as broadly procedural. On such theories, truth depends on prior commitments. It is easy to see why he cannot. As soon as truth is dependent on prior commitments, the necessity and mindindependence of truth -both of which Parfit prizes -would be threatened. Two dominant forms of such procedural theories are pragmatism and coherentism about truth. We can gloss these theories as follows: pragmatists believe that truth is that which it is expedient or instrumentally valuable to believe (cf. James 1907, 34) while coherentists believe that truth is that which coheres with some other set of claims, usually sets or subsets of antecedentally held beliefs. Both types of theories would render moral claims relativist (either to the circumstantially instrumental value of accepting or to the appropriate sets of beliefs), which is an implication Parfit is at pains to reject throughout On What Matters. 22 Furthermore, such theories of truth are intuitively not 'strong' senses of true, at least if we assume that strength requires independence from the instrumental value of accepting a claim or from other beliefs one antecedentally holds. 23 Finally, accepting such theories would be antithetical to the independence of truths about abstracta adverted to in the Argument from Empty Ontology (cf. Section 5). If normative truths were relative to the value of accepting them or to other sets of beliefs, then the Argument from Empty Ontology -which is meant to secure truths about abstracta across possible worlds -would instead undermine those truths. An empty ontology lacks anything to ground instrumental value for accepting a given normative truth or a set of antecedentally held beliefs with which a given normative truth could cohere. Another way of making the point is that if normative truths are necessary truths, it will be hard to accept truths which have relative truthconditions. For these reasons, we should reject these theories of truth about normative claims, or at least Parfit should reject them.
Another popular set of theories of truth Parfit could turn to are theories of truth we call deflationary. On such theories, the truth of a proposition is nothing above that proposition (in slogan and schematic form, for any sentence S, 'S' is true if and only if S). 24 I think that such theories are also not true 'in the strongest sense'. If truth adds little or nothing to a claim, this intuitively suggests truth is weak, not strong, or at least that there are stronger theories available. However, as Suikkanen (2017) has pointed out, there is a more important difficulty for Parfit here. 25 Accepting deflationary theories of truth leave Parfit with a dilemma that reduces his ability to separate his metaethical position from others.
Suikkanen's dilemma for Parfit is whether or not to align a deflationary theory of (normative) truth with a deflationary theory of (normative) facts. 26 A deflationary theory of facts holds that these facts would not be a genuine part of reality whereas an inflationary theory holds that they would be in some form. The idea here is that, given the maturity of certain metaethical positions, it has become more difficult to distinguish different metaethical theories from one another and that deflationism about truth makes this even more challenging for Parfit because he lacks a tool that can be used to distinguish substantive commitments. Suppose, for the first horn of the dilemma, that Parfit were to combine a deflationary theory of truth with a deflationary theory of facts. If there were no claims about the ontological status of normative facts, then the Non-Metaphysical Cognitivist would not be able to distinguish themselves from the Metaphysical Cognitivist -both would hold that normative claims are true and both would hold that normative facts are deflated. The Non-Metaphysical Cognitivist could not say that the Metaphysical Cognitivist is adding extra facts because there would be no extra ontological commitments that the Metaphysical Cognitivist would have over and above those of the Non-Metaphysical Cognitivist or, more specifically, not any that could be discussed in these doubly deflationary terms. Since Parfit wishes to carve this Non-Metaphysical from the Metaphysical position in the metaethical space, he cannot accept this implication.
The other horn of the dilemma is to adopt deflationism about truth but an inflated theory of facts. On this view, truth would add nothing to the normative claims, but facts would require some kind of ontological commitment. However, given Parfit's claims that there are no such ontological commitments, there would be no normative facts. Note that this contrasts with Metaphysical Cognitivists, who hold that there would be such facts. However, Parfit's commitments would lead to adopting a form of normative error theory. 27 An error theory is a metaethical position whereby there are no moral or moral facts in reality, although we take moral claims to be states which are beliefs (and not desire-like). So while accepting deflationism about truth means that truth could still be predicated of normative claims, there would be no normative facts. In short, it would be possible to endorse normative claims, and since truth is (accepted to be) deflationary, it would be correct to endorse the truth of normative claims. However, they would not comport with any normative facts in reality, collapsing the position into an error theory. I take it that Parfit would wish to deny this position, since avoiding normative nihilism is a major motivation for him and error theory seems to be much closer to nihilism than he would wish to be. The upshot is that deflationism about truth would either collapse the view that Parfit is attempting to carve out, or would lead to the commitments of a theory he wishes to avoid, namely, error theory.
This discussion is meant to show that Parfit cannot accept theories of truth which are procedural, in the sense of dependent on prior commitments. Nor can he adopt theories of truth which are deflationary. Although I lack the space to be truly exhaustive here, the other broad set of theories of truth are inflationary. 28 The most influential such theory is the correspondence theories of truth. Correspondence theories hold that there is some relation ('correspondence') between (parts of) reality and claims such that when the correspondence holds, the claims are true. Parfit explicitly denies this theory of truth, giving it the name 'alethic realism' (745). On the positive side, it would of course vindicate his Metaphysical Cognitivism about concreta. On the negative side, it would be similarly inflationary for abstracta. It would saddle him with all the ontological commitments he wishes to avoid.
So it also would be difficult for Parfit to accept inflationary theories. However, I think that some type of inflationary theory of truth is still best for Parfit if he wants to maintain the objectivity and robustness that abstracta provide him. 29 In contrast, if he accepts a procedural theory of truth, then the implicit references to agents or believers would render the theory too relativistic and contingent for Parfit. A deflationary theory of truth would make it difficult to distinguish his views from other metaethical theories. Of course, adopting an inflationary theory is a result that Parfit explicitly wants to resist. However, I think it is the cost that a theory which generates things which really matter -in the very strong sense Parfit wants -must pay.

On why ontology matters
Parfit's ethical and metaethical project is built on the importance of reasons, which are truths that he claims have special, irreducibly normative propertiesnamely, the property of being reasons. This strong commitment to irreducibly normative properties puts dialectical pressure on Parfit to admit them into reality, for instance, as theoretical posits.
Of course, if reasons exist in reality, then they are quite different from other objects that exist. Many have worried about this kind of existence (Blackburn 2017;Lenman 2009;Mackie 1977), but Parfit holds that, although they exist in the 'wide sense', they do not exist in an 'ontological sense'. This, he believes, allows him to meet the dialectical pressure but still maintain an ontologically cost-free metaethics. This matters for the central claims in metaethics because, if my arguments are successful, there remain reasons of parsimony to prefer naturalist and nominalist metaethics over the kinds of non-naturalism that Parfit and others favour. This is especially the case if the only type of truth which vindicates Parfit's claims is inflationary.
One way to object is to adopt the arguments of Quine (1960) that existence claims are univocal, but for the sake of argument I have granted to Parfit that 'existence' has these different senses. The problem is that merely having access to different senses does not make the problem go away; senses can be introduced that make the problem recur.
The metaethical compatibility that Gibbard and Railton find their views have with Parfit is motivated by his cost-free claims (Gibbard 2017;Parfit 2017a;Railton 2017). Thus, it behoves us to examine the justification for these claims, especially given that Parfit's combination of a strong cognitivism with a costfree ontology is quite a new innovation. Considering the potential for this position is a fruitful way of determining whether we should reconsider the metaethical space that we had before Parfit's important contributions.
Notes and private correspondence, holding that the worldly sources of normativity are entirely natural and that this is what is relevant for ontology. 6. For instance, Quine (1960) and Sainsbury (1996) object that we could address different ontological considerations by appealing to the differing ways in which abstracta and concreta come to exist as opposed to positing different senses of 'exist'. 7. Although I use the term 'Platonism' following Parfit, Platonists may or may not be followers of Plato himself; in this context, they are meant merely to hold a particular metaphysical position about the ontological acceptance of abstracta. 8. Oddly, his statement of his view compares things that exist concretely (concreta) with truths about abstracta (like mathematical and logical entities) instead of with the abstracta themselves. It is accurate that truths about such abstract objects are themselves abstract, but his passage still makes for an unnecessarily confusing juxtaposition. I take this confusion to be not of fundamental importance, so references in this essay to truths about abstracta and abstracta themselves are not distinguished. 9. My granting Parfit the 'Plural Sense View' is a substantial admission. As Olson (forthcoming) points out, it is not clear what to make of his wide non-ontological sense of 'exist' and, furthermore, it's not properly motivated. It is not properly motivated because Pafit could make sense of his puzzling claims about possible objects (721ff) by allowing that possible objects exist, but that they do not actually exist while retaining a 'Single Sense View'. However, I grant Parfit this substantial Plural Sense View for the sake of argument. 10. This is very curious terminology, since the necessary truths about abstracta must also be actually true. This follows from their necessity (under the assumption of Reflexivity, which Parfit accepts). So 'actuality' is not what distinguishes his narrow senses. I suppose that the 'narrow actualist sense' is meant to be contrasted with an ontologically lesser 'narrow possibilist sense' but Parfit nowhere mentions such a sense. 11. I am inclined to believe that Parfit's writing that they exist 'at some time' in space and time is accidental redundancy. 12. Indeed, we can go further and see that some of his claims appear to commit him to their existence, as I discuss in Section 6. 13. Although the claim is not actually about fundamentality, but instead it is supposed to be that space and time are not metaphysically exhaustive of reality. 14. Of course, it could be tempting to read Parfit's claim as a claim not about headaches, but about headache-reports, but this strengthens Parfit's case: if we tend to look at this statement as elliptical or incomplete in some way, that is because it is very obviously not truth-apt so we are trying to read it charitably. 15. A view of this sort is defended by, for instance, Hornsby (1997). 16. Here, we can think of the 'part' of the empty ontology as not a proper part, but the whole. 17. Thanks to an anonymous reviewer for suggesting this line of argumentation. 18. Here we are also granting, for the sake of argument, that we want to avoid adopting both error theories and non-cognitivist positions. For Parfit's breakdown of the metaethical conceptual space, which I am also granting him, see Parfit (2011, 263). Also, in Parfit (2017a), some of the terms for metaethical positions are slightly different from Parfit (2011); in particular, "Metaphysical Cognitivism" is replaced with 'Metaphysical Non-Naturalism' and 'Non-Metaphysical Cognitivism' is replaced with 'Non-Realist Cognitivism'. Yet another term in the literature for similar metaethical positions is 'Quietist Non-Naturalism'. I use and prefer Parfit's original nomenclature, but one can substitute one's own preferred terms throughout without affecting any of my claims. 19. A full examination of this topic is beyond the scope of this essay. However, an excellent summary of the current state of play about truth pluralism can be found in Pedersen and Wright (2013), and I do discuss some reasons to resist the view in the following. 20. It is logically possible that both Metaphysical Cognitivism and Non-Metaphysical Cognitivism are about truth in the strongest sense, but that is because there are distinct, equally strongest, senses of truth! It is unclear what kind of scale would be able to compare strengths of truth, but any plausible scale would make inflationary theories of truth (roughly, theories that require ontological commitment for truth) stronger than deflationary theories (roughly, theories that do not require ontological commitment), so the problem for Parfit recurs: if truth is inflationary for concreta, then it must be inflationary for abstracta. However, he is denying this. 21. Here, I am agreeing with Parfit that the quasi-realism espoused inter alia by Blackburn (2017) does not generate the kind of mind-independence and objectivity that Parfit takes to be desiderata. 22. One possible retort on behalf of the coherentist is that the coherentist makes claims cohere with only maximal sets of beliefs, but it is hard to see how sets of moral claims would be fixed in this manner (for instance, it might be maximally coherent that deontic statuses are inverted such that all right actions are wrong). Thanks to Preston Werner for pushing this point. 23. We need not assume that correspondence is the correct theory in order to recognize that, if it were true, it would be more demanding. 24. Theories of truth in this broad family include minimalism about truth, expressivism, prosententialism and disquotationalism. Many deflationists think that the schema is not universally true, since there are problematic instances of S which generate paradoxes. We need not concern ourselves with these complications here. 25. I thank an anonymous reviewer for pointing me to this helpful reference. 26. Some of the argumentation here is related to the influential (Dreier 2004). 27. Suikkanen (2017 more specifically identifies the resultant view as a conservationist version of error theory. 28. For an example of a theory of truth which does not fall under these three categories, Suikkanen (2017) thinks that Parfit will be forced to adopt primitivism about truth, on which truth is a predicate for which no theory will be forthcoming. I agree with Suikkanen that this is very difficult for Parfit to accept, since acceptance of this would commit him to a sui generis notion of truth which is, at the very least, a cost for the theory. However, I disagree with Suikkanen that this is the option Parfit would want to adopt. Parfit's motivations suggest a vindication of the robustness of abstracta. Stipulating that truth applies in these contexts is not really a vindication if truth is a primitive. It certainly is insufficient to ground the agreement that Gibbard and Railton have made with Parfit. When Parfit writes that these truths have no ontological implications, he cannot defend or explain this claim under truth primitivism. He can merely repeat it. To this the Platonist can respond that this position is even more mysterious than the (wholly intelligible, though surprising) ontological claims that she makes. Since Parfit thinks that making ontological committal not a 'Clear Question' is a problem, an even more serious charge could be levelled against him as a primitivist.
29. It is more grist for my mill that (Enoch 2011) has an independent argument for the moral realist being committed to inflationism about truths involving abstracta. His argument is that just as we accept scientific posits into our ontology, we should accept moral abstracta into our ontology since they can do similar explanatory work.