2. Negative Entities Enjoy Being by Courtesy

In his work, The Fragmentation of Being, McDaniel introduces the concept of ontological pluralism. At the heart of this theory lies the idea that the concept of being is not applied uniformly to all existing entities. Ontological pluralism asserts the existence of diverse modes of being, alongside a multitude of entities. This view stands in contrast to the prevailing notion in contemporary literature — known as “ontological monism” — that upholds the univocity of being, yielding that all ontological distinctions arise solely from their natures rather than the manner of their existence.Footnote ² While the debate over whether ontological pluralism surpasses ontological monism is beyond the scope of this article, our focus here is solely on addressing the enigma of negative beings within the framework of ontological pluralism.

McDaniel’s articulation of ontological pluralism suggests that there are various modes of beings corresponding to different types of entities. For instance, while our ontology may encompass both concrete objects like tables and abstract entities like numbers, McDaniel argues that these concrete and abstract entities do not share the same mode of existence. In contrast to ontological monism, which posits a single unrestricted quantifier in the language of first-order logic to encompass all existing items, ontological pluralism advocates for the introduction of multiple quantifiers. Each quantifier represents a distinct mode of existence for entities.Footnote ³ To put it more precisely, in this view, or at least in a version of it, there are various modes of being and each mode is represented by a restricted quantifier that is purported to be semantically primitive and metaphysically more natural than the unrestricted quantifier.Footnote ⁴ Hence, according to McDaniel, ontologese (the language of ontology) only includes primitive restricted quantifiers. There is no absolutely unrestricted quantifier accepted in his view as a primitive and natural quantifier. Indeed, he does not eliminate an absolute unrestricted quantifier; rather, he believes that an absolutely unrestricted quantifier should be regarded as a derivative and non-primitive quantifier (McDaniel, Reference McDaniel2017, pp. 25–33).

With this understanding of ontological pluralism in mind, let’s delve into the central inquiry of this article. As previously noted, we cannot escape the acknowledgement of the existence of negative entities, or at least some of them; however, we are inclined to perceive these entities as metaphysically derivative, dependent, or non-fundamental. McDaniel contends that his ontological pluralism provides a framework to elucidate these intuitions. According to him, it is logically coherent to posit the existence of different modes of being. Therefore, asserting the existence of negative entities is not extravagant; however, they do not possess the same mode of existence as positive entities. Instead, the reality attributed to negative entities is somewhat attenuated or less robust compared to positive entities. The pertinent question then arises: What mode of being do negative entities embody? McDaniel posits that these entities are beings by courtesy.

Being by courtesy, also called “almost nothingness,” is a derivative form of being defined in relation to more fundamental modes of being. The term “existence” in ordinary language typically refers to the generic sense of existence. Let’s assume that this generic sense of existence is fully represented by the unrestricted quantifier “∃” in first-order logic. As previously mentioned, this unrestricted quantifier is considered derivative and non-fundamental. Instead, the ideal metaphysical language comprises restricted quantifiers. For the sake of simplicity, let’s posit that, metaphysically speaking, there exist only two fundamental modes of being: one ranges over concrete objects and the other ranges over abstract entities. These modes of being are captured by two natural restricted quantifiers: “∃_m” for concrete fundamental entities and “∃_a” for abstract entities delineated in our most refined metaphysical theories.

Since “∃” is defined as an unrestricted quantifier, its function is to encompass everything that exists, regardless of its nature. Therefore, it is accurate to assert that “∃” covers the items quantified by both “∃_m” and “∃_a.” However, the domain of “∃” — as an unrestricted quantifier – is broader than the combined domain of “∃_m” and “∃_a.” Consequently, it is also true to state that “∃” encompasses items that are quantified over by neither “∃_m” nor “∃_a.” The domains of “∃_m” and “∃_a” comprise entities that possess fundamental modes of being. In contrast, the domain of “∃” includes a broader range of items, some of which do not enjoy a fundamental mode of being. Entities that fall solely within the domain of “∃” exhibit a derivative and non-fundamental mode of being, referred to as “being by courtesy.” To put it more precisely, being by courtesy “∃_b” can be formulated as follows:

McDaniel posits that negative entities are beings by courtesy. He contends that his version of ontological pluralism, or at least the interpretation outlined above, aligns with our intuitive understanding of the ontological status of negative entities. According to McDaniel, negative entities exist because beings by courtesy can genuinely be said to exist — they are encompassed within the scope of the generic unrestricted quantifier. Furthermore, McDaniel argues that considering negative entities as beings by courtesy allows us to maintain the notion that they possess a genuinely non-fundamental or derivative mode of existence that is attenuated. In other words, entities that are beings by courtesy truly exist — they belong to the domain of the generic unrestricted quantifier. However, they do not fall within the scope of expressions denoted by perfectly natural quantifiers.

According to McDaniel, there exist fundamental restricted quantifiers responsible for encompassing fully real fundamental entities. Additionally, there is an attenuated sense of being that applies to items considered derivative and non-fundamental. Based upon this distinction, McDaniel’s solution is purported to fulfil the intuitions surrounding the ontological status of negative entities. These entities are beings by courtesy, explaining why they are perceived as less real than their bearers and hosts, which are concrete material objects. In the following section, we delve into this point more precisely to ascertain whether McDaniel’s solution adequately and effectively meets the desiderata regarding the ontological status of negative entities.

3. A Challenge for Being by Courtesy

Before proceeding, it’s important to clarify a key implication of McDaniel’s theory. According to his perspective, if an entity does not fall within the domain of any perfectly natural restricted quantifier, it is categorized as being by courtesy. Therefore, McDaniel extends the classification of entities enjoying being by courtesy beyond just negative entities: Everything that lacks a fundamental mode of existence is metaphysically placed in the category of being by courtesy. Consequently, entities such as mind-dependent entities — those that depend on the existence of minds for their own existence and properties —, mere possibilia — entities that exist as possibilities rather than actual objects —, fictional entities like Sherlock Holmes, social constructs like money and race, artifacts like jackets and tables, and numerous other derivative entities whose existence may not align with the categories of fundamental restricted quantifiers all fall under the classification of being by courtesy.

So, it appears that, according to McDaniel, existing entities either possess a fundamental mode of existence or they exhibit a diminished form of being referred to as “being by courtesy.” Therefore, from a metaphysical standpoint, only fundamental entities experience a complete sense of existence; everything not encompassed by a fundamental restricted quantifier merely partakes in being by courtesy. Now it seems evident that there are items that exist at a fundamental level, and there are entities that are non-fundamental (beings by courtesy); if an entity cannot be classified in either of these two categories, it is merely considered as a non-existent item.

This classification implies a form of ontological permissivism,Footnote ⁵ wherein questions concerning the existence of items become trivial.Footnote ⁶ Determining whether something exists holds little metaphysical significance; rather, being fundamental/non-fundamental warrants serious consideration from a metaphysical standpoint. McDaniel admits ontological permissivism (McDaniel, Reference McDaniel2017, p. 163 footnote 62, and p. 164 footnote 63). In his view, except for contradictory concepts like round-squares or truly non-existent entities such as phlogiston — too remote and bizarre to fall within the domain of the generic existential quantifier — everything else possesses a sense of being, either fundamental or non-fundamental (i.e., being by courtesy). Consequently, in McDaniel’s view, everything encompassed by the generic unrestricted existential quantifier — items such as properties, meanings, numbers, fictional objects, minds, qualia, mereological composites, mere possibilia, etc. — possesses a mode of being. If any of these entities are considered fundamental according to our best metaphysical theory, then they experience a complete sense of being; otherwise, they are categorized as being by courtesy.

Ontological permissivism might be viewed as a benign consequence of McDaniel’s formulation of ontological pluralism. However, we believe that this consequence, when combined with the concept of being by courtesy, leads to counter-intuitive consequences that undermine the efficacy of applying McDaniel’s view to the problem of negative entities. As a result, McDaniel’s solution fails to address the aforementioned desiderata concerning negative beings outlined in Section 1.

To proceed, let’s consider, for the sake of argument, that our best metaphysical theory excludes mereological composite material objects. Consequently, no natural and fundamental restricted quantifier encompasses mereological composite objects. According to McDaniel’s view, such items enjoy being by courtesy. Additionally, we have previously established that negative items such as holes are also beings by courtesy. Herein lies a problem: both holes and their material hosts, which are composite objects, fall within the same category of being. However, McDaniel’s theory and the notion of being by courtesy aim to satisfy the intuition that holes, for example, are less real than their hosts. The issue arises because this intuition is only upheld when a specific metaphysical theory is assumed, one in which composite items are deemed metaphysically fundamental.

This issue presents a significant challenge for McDaniel’s theory. While his ontological pluralism is designed to remain neutral regarding which entities exist fundamentally, addressing the problem of negative entities may require favouring a metaphysical theory that considers mereological composites as fundamental. The problem lies in the fact that the distinction outlined in McDaniel’s theory alone fails to adequately address this crucial difference. The concern is that if items categorized as being by courtesy are not ontologically equivalent, ontological permissivism aligned with the concept of being by courtesy — which sharply distinguishes fundamental from non-fundamental modes of being — would result in the consequence that items enjoying being by courtesy have the same ontological status. However, intuition suggests that negative beings should still be regarded as distinct from non-fundamental positive beings.

One solution to address this problem is to introduce a new mode of being specifically tailored to negative entities, thereby distinguishing them from positive ones. However, this solution appears ad hoc. Arbitrarily adding a new mode of being would not fully resolve the issue. Furthermore, introducing a new mode of being exclusively for negative entities at the non-fundamental level does not alleviate the concern. Consider the example of holes in a block of Swiss cheese. These holes metaphysically depend on their host, i.e., the Swiss cheese. Even if they possess different modes of being at the non-fundamental levels, we still need to acknowledge that the former is less fundamental than the latter. The claim that a dependent and its dependee are metaphysically equal and equivalent proves unsatisfactory, especially when we require an ontological mechanism to distinguish the hierarchy at the non-fundamental levels.

However, a more promising solution is readily available. To capture the intuition and overcome the difficulties mentioned in the last paragraphs, we may turn to the notion of “degrees of being,” as articulated in the seventh chapter of McDaniel’s book. In this chapter, McDaniel proposes a fresh approach to formulating ontological pluralism and the notion of the equivocality of being, suggesting that being itself admits of degrees. To elucidate the concept of degrees of being, McDaniel employs the following analogy:

With this formulation, we can coherently assert that reality (being) is multi-layered. Certain layers of reality are more fundamental than others, and degrees of fundamentality are defined in terms of degrees of being. At the most fundamental level, we find fundamental entities that exist in the fullest sense of being. However, the level of an item’s fundamentality corresponds to its degree of being. An entity that is more fundamental exists to a greater degree than one that is less fundamental, and so forth. Items situated in a lower class of fundamentality are not as real as those in a higher class. In other words, existing items cannot be ontologically equivalent.

The notion of “degrees of being,” as opposed to the notion of “modes of being,” provides a framework to address the objections mentioned above. If being admits of degrees, then the concept of fundamentality can also be defined in terms of these degrees of being. Consequently, items are not strictly categorized as either fundamental or non-fundamental. Instead, we can coherently maintain that an entity is both fundamental and non-fundamental, as the fundamentality of an item is proportionate to its level of reality. An entity is more fundamental than entities that are less real than it, while simultaneously being less fundamental than entities that are more real than it. With this perspective, we can address the objections as follows: In this framework, negative entities and their bearers/hosts do not necessarily belong to the same ontological categories. Rather, they occupy different levels of reality, even if they are both derivative and non-fundamental relative to the most fundamental entities. Thus, holes are less fundamental than their hosts, and their hosts can be less fundamental than entities that enjoy a fundamental level of being, and so forth. As a result, one can effectively address the desiderata outlined at the outset of the article. Within this framework, negative beings are indeed real; however, their reality differs from that of positive ones, particularly their hosts.

As we observe, by utilizing the concept of degrees of being, the aforementioned challenges can be effectively addressed. However, in the subsequent section, we contend that if we employ the notion of “degrees of being” to resolve the issue of negative entities, there is no longer a necessity to retain the notion of “being by courtesy.” Consequently, no entity, including a negative item — contrary to McDaniel’s assertion — is subject to being by courtesy. In other words, the notion of being by courtesy cannot be coherently defined within a framework where being admits of degrees. Why?

The rationale behind our claim is that within the framework of “modes of being,” we can readily delineate a clear distinction between fundamental and non-fundamental modes of being. Our metaphysical categories consist of various, almost distinct modes of being, with existing items falling within the domain of each of these categories. As elucidated earlier, some of these categories are fundamental (those represented by primitive restricted quantifiers), while there also exists a non-fundamental category known as “being by courtesy,” reserved for items not encompassed in ontologese. Therefore, to define the notion of being by courtesy, it is imperative to maintain the sharp differentiation between fundamental and non-fundamental categories and subsequently classify all non-fundamental entities as being by courtesy.

In the framework of degrees of being, in contrast, drawing such a sharp boundary becomes problematic because the concept of fundamentality itself admits of degrees. Within this perspective, reality can be envisioned as an ordered hierarchy composed of numerous layers, each constituting a category with its own level of existence. Existing items, depending on their degrees of existence, are distributed across these ordered categories.Footnote ⁷

Within this multi-layered hierarchical framework of reality, each layer encompasses entities that possess a certain degree of being. Attempting to define a category as being by courtesy within this context leads to the challenge of the cut-off point problem. In this hierarchical structure, categories are ordered based on their level of being or fundamentality. At the lowest level, the most fundamental entities enjoy the fullest degree of reality. As we move further away from these fundamental entities, the level of fundamentality becomes increasingly diminished and attenuated.

The cut-off point problem arises when determining how far down the ordering we can descend to establish a clear delineation between categories that are metaphysically significant and those that are not (those relegated to being by courtesy). Because it is arbitrary to pinpoint this cut-off point, defining being by courtesy becomes elusive. Consequently, it becomes nonsensical to assert that certain entities enjoy being by courtesy. A potential consequence of this perspective is that everything (in the absolute sense of being a “thing”) possesses some degree of metaphysical importance. In this view, the role of a metaphysical theory is to describe the varying levels of metaphysical reality across these hierarchical layers.

4. Objection and Reply

Objection: One approach to address the aforementioned challenges is to argue for the existence of varying levels of fundamentality or naturalness, as well as levels of non-fundamentality or non-naturalness. According to this perspective, not all fundamental entities possess the same degree of fundamentality. For instance, let’s consider the possibility of strong ontological emergence, as proposed by Jessica M. Wilson (Reference Wilson2021), which suggests the existence of entities that are both fundamental and dependent, as discussed by Elizabeth Barnes (Reference Barnes2012).Footnote ⁸ In such cases, a strongly emergent entity remains fundamental, even while being dependent on its parts. However, because it is dependent, it may not be as fundamental as its constituent parts. Thus, it is reasonable to argue that there are degrees of fundamentality, with some entities being more fundamental than others.

Similarly, one can extend this idea to non-fundamental entities, positing that there are different levels of non-fundamentality. By considering the possibility of complexity layering at the non-fundamental level, we can overcome the problem raised earlier regarding the parity of entities in the category of being by courtesy. For example, let’s assume that both a composite object like Swiss cheese and its holes are considered non-fundamental in one’s ontology. According to McDaniel’s definition of being by courtesy, both Swiss cheese and its holes enjoy being by courtesy; however, they are not ontologically equivalent, as the host is ontologically prior to its holes. Therefore, by delineating different ontological layers among non-fundamental entities, we can maintain our intuitions about the priority of the host over the holes without abandoning the concept of “being by courtesy.”

It’s worth highlighting that the notion supporting this line of objection finds resonance in McDaniel’s own works. According to McDaniel, while degrees of being hold primacy in definition, this concept can be articulated in terms of degrees of fundamentality or degrees of naturalness, as they are essentially notational variants of each other. He explains:

As discussed in the previous section, defining the notion of being by courtesy requires maintaining a sharp distinction between fundamental and non-fundamental categories, categorizing all non-fundamentals as being by courtesy. McDaniel’s response to this is that the notion of being by courtesy is not precluded by the notion of degrees of being; these two metaphysical frameworks are consistent, and one can accept both simultaneously. It’s possible to uphold a sharp distinction between fundamental and non-fundamental entities while acknowledging that both categories encompass various levels of being. Thus, assuming that all derivative and non-fundamental entities are equal is erroneous. One can treat the notion of degrees of being as primitive, as advocated in McDaniel’s Reference McDaniel2017 Chapter 7, and still maintain that fundamentality remains a sharp concept within that framework; being itself varies in degrees. This approach allows for different degrees of being while still delineating a clear line between entities that are fundamental and those that are not. This distinction enables McDaniel to argue that although beings by courtesy are uniformly non-fundamental, it doesn’t imply that they all belong to the same degree of being. Hence, contrary to the argument presented in this article, one can still assert that negative beings enjoy being by courtesy even within the framework of degrees of being.

Reply: We concur with the objection that allowing for varying degrees at both the fundamental and non-fundamental levels might offer a potential solution to the problem. However, in the subsequent paragraphs, we contend that this solution relies on an assumption that, if accepted, would compromise the simplicity and intelligibility of one’s formulation of ontological pluralism. Therefore, we first articulate what this assumption is, and then we argue why accepting this assumption (i.) imposes arbitrary conditions, and (ii.) endangers one’s ideological parsimony.

Given that degrees of fundamentality, degrees of naturalness, and degrees of beings are notational variants of each other, the assumption is that there is a sharp cut-off point between fundamental degrees of beings and non-fundamental ones. Let’s call it “FC” and define it as follows:

If FC is true, then the objection holds, and it would suggest that all levels of non-fundamentality enjoy being by courtesy. To illustrate, let’s assume four different degrees of being: A, B, C, and D, arranged in such a way that each is more fundamental (>) than the other, i.e., A > B > C > D. Embracing the notion of degrees of being, as advocated by McDaniel, allows for defining levels of fundamentality based on degrees of being. With this concept, one can assert that A is more fundamental than B, B is more fundamental than C, and so forth, as they each possess different degrees of being. Now, let’s consider the scenario where one wishes to maintain that A and B are fundamental, while C and D enjoy being by courtesy. Here, one must introduce a sui generis concept of fundamentality by FC that can delineate between entities that are truly fundamental (that is, fundamental in the new sense) and those that are truly non-fundamental (i.e., being by courtesy). A and B represent different fundamental levels, demarcated by factor FC, while C and D represent different non-fundamental levels. Thus, C and D are considered to enjoy being by courtesy.

Without FC, being by courtesy and other modes of being are indistinguishable, even if one is prepared to admit the degrees of being. FC allows for the demarcation between truly fundamental and truly non-fundamental entities. Indeed, FC’s concept of fundamentality is sui generis; it cannot be reduced to degrees of fundamentality defined in terms of degrees of being. If FC were defined solely in terms of degrees of being, it would fail to effectively distinguish between A and B as fundamental and B and C as non-fundamental. Therefore, aligning degrees of being with FC enables one to assert that entities at the level of C and D enjoy being by courtesy. Thus, the concept of being by courtesy is essentially captured by FC rather than by degrees of being alone. The adoption of FC, however, poses significant challenges.

The first problem concerning FC is what is often called the “cut-off point problem.” Assuming degrees of being allows us to define fundamentality at different levels. However, if one argues that some of these levels are truly fundamental in a new sense of “fundamentality,” while the rest possess being by courtesy, the question arises: Where exactly is the cut-off point for this demarcation? By what criteria can we draw a clear line in the hierarchy of beings, asserting that levels below this line are truly fundamental, while the upper levels merely possess being by courtesy? How far down the ordering should we go? Common sense intuitions and scientific theories might help us rank degrees of being or fundamentality, but they fall short in providing criteria for distinguishing truly fundamental levels from those that are not. Given the FC framework, such a cut-off point must exist, yet we lack the criteria to delineate it. As we argued earlier in this article, there is no reasonable answer to this problem. Any cut-off point is arbitrary and ad hoc. Consequently, the objection fails because it rests on a false assumption. While appealing to the degrees of being and FC can legitimize the notion of being by courtesy, it does so at the expense of assuming a problematic (if not false) assumption: FC. For the sake of argument, let us suppose there was a cut-off point between truly fundamental and truly non-fundamental.

The more significant problem is determining the role FC could play in resolving our original puzzle about negative beings. Recall that the enigma lies in the fact that, on one hand, negative entities are real, while on the other hand, they are not as real as positive ones. Continuing the previous example, let C represent the degree of being enjoyed by my jacket, which contains a hole that enjoys the degree of being D. Both the jacket and the hole have some degree of being and are thus real to some extent, and the hole enjoys a lesser degree of being, D, compared to the jacket, C. This framework is sufficient to account for our intuitions and requirements regarding negative entities. Now, suppose we introduce FC. This leads to the conclusion that both my jacket and the hole are beings by courtesy, i.e., truly non-fundamental. However, this additional assumption does not contribute to explaining our original enigma. All that we need to resolve the problem is already provided by assuming the degrees of being. Thus, introducing FC as a sui generis form of fundamentality is theoretically redundant and unnecessary. Appealing to FC is a strategy that endangers ideological parsimony. Ontological pluralists who adhere to the notion of being by courtesy must endorse both degrees of being and FC. However, FC plays no role in explaining the ontological status of negative beings. In conclusion, accepting FC leads to unnecessary ideological commitments.

In sum, we have demonstrated that embracing degrees of being alone can satisfy our intuitions about the ontological hierarchy of reality. In this framework, negative beings naturally occupy a level of reality less fundamental than their hosts. Therefore, the thesis of degrees of being alone suffices to capture this intuition, rendering the notion of being by courtesy, entailed by FC, an ad hoc strategy that imposes unnecessary ideological commitments.