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Consider the following quality space: It seems like this quality space is the space of all possible greys. Moreover, it seems intelligible why this quality space exhausts all possible greys. The source of the intelligibility seems to be that there is an underlying unity to the space of possible greys, where one can intelligibly see how all the possible greys can be generated by continuous variation across a certain dimension. Here is a speculative hypothesis about the space of all possible qualities: the explanation for why the space of all possible qualities is ultimately intelligible is similar in kind to the explanation for why the space of all possible greys is ultimately intelligible. Namely, the space of all possible qualities has a certain kind of unity to it. The relevant notion of “unity” is hard to pin down, but at a minimum it can be understood in terms of a certain kind of connectedness: for any two possible qualities, there is a path through the space of possible qualities that connects any one quality to any other (just as there is a path through the space of possible greys that connects any grey-quality to any other). Let’s call this The Unity Hypothesis. In order to make the Unity Hypothesis more precise, we would need to take a stand on certain controversial structural questions about the space of possible qualities. For example, a natural sufficient condition for the Unity Hypothesis is that the relevant space of possible qualities P is “path-connected”, in the topological sense that for any two qualities q1 and q2 there is a continuous 8 function f: [0,1] ® P that connects q1 and q2 (i.e. f(0) = q1 and f(0) = q2).20 However, given minimal assumptions, this would imply that P is in certain ways structurally similar to the real numbers (e.g. the cardinality of P would have to be at least as great as the cardinality of the real numbers).21 This would be a controversial commitment.22 An alternative (epistemic) possibility is that P is “discrete” in the sense that the integers are discrete: it is not the case that for any two qualities there is a third quality “between” the first two (just as there is no integer between 1 and 2).23 If P was discrete in this way, then P could be represented by a graph, a mathematical structure consisting of a set of “vertices” together with a set of “edges” between certain vertices. In order to represent P, the vertices in such a graph would represent possible qualities, and an edge between two vertices would represent that the two vertices are qualitatively “adjacent” to one another. For example, 1 and 2 are adjacent in the integers, but 1 and 3 are not adjacent in the integers. If the space of possible greys was discrete, then two grey qualities q1 and q2 would be qualitatively adjacent to one another just in case q1 is either minimally darker or minimally lighter than q2 (where q1 is “minimally lighter/darker” than q2 if and only if q1 is lighter/darker than q2, but no other quality q3 is both (i) lighter/darker than q2 and (ii) darker/lighter than q1). If we grant ourselves a notion of qualitative adjacency24, then we can say that an alternative sufficient condition for the Unity Hypothesis is that P is representable by a connected graph, which is a graph where any two vertices can be connected by a path of edges starting at the first vertex and ending at the second vertex. In what follows, I will remain neutral on how exactly the Unity Hypothesis should be made precise, since our informal characterization of the Unity Hypothesis will be sufficient for our purposes.25 Why believe that the Unity Hypothesis is the only way for the space of possible qualities to be intelligible? I don’t have any decisive reason to offer. For all I know, there might be some totally different way in which the space of possible qualities might be rendered intelligible. However, positing this kind of unity in the space of possible qualities, by analogy to the space of possible greys, is the only way I can see how the space of possible qualities might be rendered intelligible. 20 Here, “[0,1]” refers to the set of all real numbers greater than or equal to 0 and less than or equal to 1. 21 Any path-connected topological space that (i) has more than one element and (ii) is “Hausdorff” has a cardinality at least as large as the continuum. For an introduction to these topological notions, see Munkres (2013). 22 See Builes and Wilson (2022) for skepticism about the possibility of there being continuum-many things. However, such a view might be able to interpret the space of possible qualities as “indefinitely extensible” (just like it interprets the space of possible real numbers as indefinitely extensible). 23 See Lee (MS) for further clarification and discussion about whether consciousness is continuous or discrete. 24 One natural way to precisify the notion of qualitative adjacency is that two qualities are qualitatively adjacent if and only if they minimally differ with respect to one dimension of quality space, but they are otherwise identical with respect to every other dimension of quality space. 25 Another epistemic possibility is that P might be structured similarly to the rational numbers, in the sense that, although it is “infinitely divisible” (for any two qualities q1 and q2, there is a quality q3 “between” q1 and q2), it is nevertheless only countably infinite. In such a case, one could impose a slightly different definition of the standard topological notion of path-connectedness. If we let [0,1]* be the space of rational numbers between 0 and 1, then another sufficient condition for the Unity Hypothesis might be that P is path-connected, in the sense that for any two qualities q1 and q2 there is a continuous function f: [0,1] ® P such that f(0) = q1 and f(1) = q2. 9 More specifically, if the space of all possible qualities consisted of multiple “disjoint” quality spaces, which were fundamentally different in kind and could not be seen to be connected with one other (like the case of mass and electric charge), then I don’t see how there could be an intelligible explanation for why those exact disjoint quality spaces would be the only possible ones. The only way for there to be an explanation for this, it seems to me, is if those quality spaces could somehow be “generated” by some underlying mechanism (such as continuous variation across a dimension in the case of the greys), but such an explanation doesn’t seem to be applicable if such quality spaces are fundamentally different in kind.26 Of course, one could easily define spaces of possibility that do not satisfy the Unity Hypothesis. For example, the space of possible properties that are determinates of either mass or electric charge is clearly not unified in the relevant sense. In this kind of “disjunctive” case, we can straightforwardly analyze the property of “being a determinate of mass or electric charge” into the properties of “being a determinate of mass” and “being a determinate of electric charge”, and we can intelligibly see how there is a unified space of properties corresponding to both disjuncts, which results in a disunified space of properties for the overall disjunctive property. Perhaps the best way to resist the Unity Hypothesis is to try to argue that the notion of a quality is also a disjunctive notion that can be analyzed into multiple unified components in this way, but it’s difficult to see how one could motivate a (non-arbitrary) disjunctive analysis of the notion of a quality. If we are willing to grant the Unity Hypothesis, then premise 3 can be supported in a more convincing way. The idea is that, if there were fundamentally different kinds of possible nonphenomenal qualities, then the space of possible qualities would be disunified, and if the space of possible qualities were disunified, then it could not be rendered intelligible. For example, if there were exactly seventeen disjoint different kinds of quality spaces, there could be no explanation why there were exactly those seventeen, rather than some other number.27 26 One might instead posit that there are an infinite number of disjoint quality spaces, in order to avoid any arbitrariness that comes with specific finite numbers (e.g. seventeen disjoint quality spaces). However, the cardinality of disjoint quality spaces is not the issue. Even if there were infinitely many disjoint quality spaces, we could still ask why there couldn’t be an extra disjoint quality space that we were missing, even though such an extra quality space would not affect the overall cardinality of quality spaces. Moreover, there is no “maximal” infinite cardinality: for every infinite cardinality, there is a larger one. So, there would still be arbitrariness in specifying the exact cardinality of the number of disjoint quality spaces. To get around these problems, one might hypothesize that the number of disjoint quality spaces is indefinitely extensible, in the sense that, no matter how many fundamentally different kinds of qualities that there could have been, there could always have been more (e.g. see Uzquiano (2015) for different ways to make the notion of “indefinite extensibility” precise). This would avoid the worry that there could always be an additional kind of quality, since there is no definite totality of “all possible qualities” in the first place. However, the only reason for thinking that sets are indefinitely extensible is that there is a formal procedure that can be used to generate a new set given any plurality of sets (e.g. one could consider the set of all sets in that plurality), but there doesn’t seem to be any kind of formal “procedure” that could generate a fundamentally new kind of quality from a plurality of other kinds of qualities. 27 One might worry that positing seventeen kinds of quality spaces is just as arbitrary as positing one quality space: why one rather than seventeen? But the number of quality spaces isn’t what’s important. What’s important is that the 10 Why accept the assumption that the space of possible qualities would be disunified if it contained both phenomenal and non-phenomenal qualities? Because of the motivations behind our initial assumption that consciousness cannot be reduced. The reason for thinking that experiential phenomena cannot be reduced to wholly non-experiential phenomena is captured by Strawson’s (2006) intuition that “The experiential/non-experiential divide, assuming that it exists at all, is the most fundamental divide in nature” (17-18). If one thought that experiential/non-experiential distinction was not a fundamental divide, then the motivation for non-reductionism about consciousness would evaporate. If experiential phenomena were fundamentally unified and continuous with wholly non-experiential phenomena, then it would be natural to think that phenomenal experience is reducible for the very same reasons that other kinds of phenomena, such as life, are reducible. There is no “fundamental divide” between the living and the non-living (e.g. viruses), so we should not be non-reductionists about life. Similarly, if there is no fundamental divide between the experiential and the non-experiential, then we shouldn’t be non-reductionists about consciousness. So, we now have the argument fully in view. In order for the space of possible qualities to be intelligible (i.e. in order for it not to lead to brute necessities), it must be unified. But adding both phenomenal and non-phenomenal qualities to the space of qualities would be disunified, because there is a “fundamental divide” between the experiential and non-experiential (motivated by the thought that experience cannot be reduced to non-experience). This kind of argument raises an immediate objection, so I’ll close this section by addressing this objection. The objection is that it is not at all clear whether the space of all possible phenomenal qualities is itself unified: visual experiences seem fairly different in kind than (say) auditory experiences. However, if the space of all phenomenal qualities is not unified, then identifying the space of possible qualities with the space of possible phenomenal qualities would not result in a unified space either. I have four main responses to this worry. My first response is to try to emphasize the continuity of conscious experience by appealing to particular examples. For example, gustatory-experiences seem to seamlessly combine with olfactory-experiences when eating food: eating food without a sense of smell is remarkably different than eating food with a sense of smell. Affective experience can seamlessly combine with various kinds of perceptual experience, such as by experiencing a foul-smelling odor, a screeching loud sound, an extremely spicy taste, or an unpleasantly rough space of possible qualities satisfies the Unity Hypothesis: a space needs to be unified in order to be intelligibly “generated” by some underlying mechanism (such as continuous variation along certain dimensions like the grey case), and a consequence (rather than a presupposition) of The Unity Hypothesis is that there aren’t multiple disjoint quality spaces that are fundamentally different in kind. 11 and abrasive texture.28 Cognitive phenomenology seems at least closely related to various kinds of sensory phenomenology, to the extent that some philosophers believe that cognitive phenomenology can be fully reduced to sensory phenomenology.29 Furthermore, there are at least sixty different known kinds of “synesthesia”, where certain sensory experiences of one modality become associated with sensory experiences of a different modality.30 Perhaps in some of these cases, sensory experiences of different modalities can be seen to be connected in ways that those of us without synesthesia cannot fully appreciate. More generally, ordinary human experience is very limited, as those who have taken various kinds of mind-altering substances can attest to. So we should be very cautious in making the inference that different kinds of experiences cannot be connected with one another just because we cannot imagine how they might be connected. My second response is to appeal to certain very general views about conscious experience that suggest that conscious experiences might be more connected than we might initially think. For example, according to “holistic” views about the structure of conscious experience, the most basic kinds of conscious experiences are total experiential states at a given time, so that at any given time, the various visual, auditory, gustatory, olfactory, cognitive, affective, etc. kinds of experiences that one is having should be thought of as mere aspects of a total experience that integrates all of these kinds of experiences into a unified whole.31 On this holistic view, it easier to see how total states of consciousness of various different modalities might be continuously connected to other total states of consciousness of various modalities. For example, on the assumption that our own total conscious states evolve continuously through time, we can continuously connect any total conscious state you have at one time (e.g. dancing at a rock concert) to any other total conscious state you have that same day (e.g. having a relaxing massage) by tracing the continuous trajectory of how your total conscious experience evolves throughout that day. Lastly, one might worry that the space of possible phenomenal qualities does not satisfy the Unity Hypothesis on the grounds that radically different kinds of experience have nothing in common, but some philosophers have argued that all experiences do have a particular phenomenal aspect in common: namely a distinctive kind of for-me-ness that is supposed to capture the essentially subjective or perspectival character of all experience.32 My third response is that the Unity Hypothesis only applies to fundamental phenomenal qualities, and it is not at all clear that the ordinary phenomenal properties that we are familiar with are 28 For more on how affective experience combines with various kinds of perceptual experience, see Fulkerson (2020) and De Vignemont (2023). 29 For a survey of debates about the nature of cognitive phenomenology (including whether cognitive phenomenology might reduce to sensory phenomenology), see Smithies (2013). 30 For an overview of synesthesia, see Banissy, Jonas, and Cohen Kadosh (2014). 31 For more on the distinction between “holistic” and “atomistic” approaches to conscious experience, see Bayne and Chalmers (2003), Bayne (2010), and Lee (2014). 32 See Kriegel and Zahavi (2015). To take another example, it has also been argued that various sensory experiences of different modalities all have a certain spatial character in common (e.g. see Aasen (2018) and Wilson (forthcoming)). 12 fundamental. For example, according to certain “constitutive” versions of panpsychism and idealism, the macroscopic phenomenal properties we are familiar with are non-fundamental properties that are grounded in the phenomenal properties had by fundamental entities (e.g. particles or the universe as a whole). It may be that our ordinary macroscopic phenomenal properties seem to be fairly disunified, even if the fundamental phenomenal properties that ground them are ultimately unified.33 My fourth and final response to this worry is simply to modus tollens. The space of all possible qualities must be intelligible, and if it is to be intelligible then it must be unified, and so if phenomenal qualities are included in the space of possible qualities, then the space of phenomenal qualities must be unified.34 It might be prima facie difficult to see how the space of phenomenal qualities can be unified, but we all have reason to think that it must somehow be if we are to avoid brute necessities. 5. The First Argument: Potential Counterexamples I have so far argued that if some possible qualities are phenomenal qualities, then we should think that all possible qualities are phenomenal qualities, on the grounds that the space of possible qualities must exhibit a certain kind of unity in order to avoid brute necessities. However, in response to this fairly abstract argument, one might simply point to certain alleged counterexamples of possible non-phenomenal qualities. The job of this section is to respond to two potential kinds of counterexamples. The first kind of counterexample appeals to properties found in science.