By Magnus Vinding. First published in March 2022.
It appears to be a common intuition that no amount of mild discomfort can be worse than extreme suffering (i.e. that extreme suffering is lexically worse than mild discomfort). Yet this view is often considered implausible due to continuum arguments. Such arguments go roughly like the following: For any duration of any state of suffering, there is a slightly less intense state of suffering that would be worse if extended for a sufficiently long duration. Therefore, the argument goes, by continually lowering the intensity and increasing the duration of suffering, we will eventually end up with a large amount of mild discomfort that is indeed worse than the initial state of suffering in the sequence, no matter how intense that initial state may be.
The aim of this essay is to present a number of views that entail value lexicality between mild discomfort and extreme suffering, and which reject the argument outlined above in different ways. My overall point is that continuum arguments are much less compelling than they are often taken to be, and that it is reasonable to challenge standard assumptions that beg the question against lexical views.
A widely accepted lexical view: Lexicality between things that matter and things that don’t
When discussing lexical views, it may be helpful to start by considering a form of lexicality that is endorsed by many views, and which is so trivial that it can be easy to overlook that it is in fact an instance of value lexicality.
One way to describe this common form of lexicality is with reference to purely hedonistic axiologies. Standard formulations of these axiologies entail that there is a lexical difference between the value of a hedonically neutral state and a slightly disagreeable state of consciousness, meaning that no amount of hedonically neutral states — including states that involve (non-hedonic) preference violations — will be intrinsically worse than a single state of consciousness that is slightly hedonically disagreeable.
Indeed, a wide range of axiologies imply value lexicality between entities that are assigned a neutral value and entities that are assigned a negative value, regardless of how slight the negative value may be. (Though axiologies often differ strongly as to what should be regarded as having neutral versus non-neutral value, meaning that different axiologies commonly entail value lexicality between each others’ purported bads, as hinted above with the case of non-hedonic preference violations.)
This trivial example of value lexicality serves to highlight two points. First, it shows that value lexicality is not some strange and alien feature that virtually no axiological view endorses, but instead a feature that is entailed by many views, at least in some form.
Second, the example highlights an important point about value lexicality, which is that lexicality can be both abrupt and gradual in nature. That is, the step from neutral to non-neutral value may be gradual in that a bad state of consciousness might be bad to just a tiny degree, while still being lexically worse than the slightly less bad state that is a perfectly neutral state. And such gradual yet abrupt lexicality is not only theoretically possible, but also quite plausible and widely endorsed, at least in the case of neutral versus slightly non-neutral states or value entities.
Abrupt but gradual lexical views
One possible reply to the continuum argument against value lexicality between unbearable suffering and mild discomfort is to argue that an abrupt but gradual threshold likewise exists between mildly bad and intensely bad states.
For example, Justin Klocksiem defends an absolute lexical threshold between “discomfort” and “genuine pain”, and argues that such a threshold is plausible both in phenomenological terms and because it helps avoid a number of implausible conclusions in value theory (Klocksiem, 2016). In Klocksiem’s view, the step from discomfort to genuine pain is an abrupt one (in evaluative terms), but it is gradual in that the intensity of genuine pain still increases in a gradual manner.
One may defend several absolute thresholds of this kind between different types of experiential states. Thus, besides Klocksiem’s threshold between “discomfort” and “genuine pain” — and in addition to the widely endorsed threshold between “neutrality” and “discomfort” — one may further defend an abrupt but gradual lexical threshold between, say, “genuine pain” and “unbearable suffering”. And perhaps additional thresholds beyond that.
In terms of geometric visualization, one may think of the crossing of each lexical threshold as a tiny step in the direction of a new dimension of experiential disvalue, akin to the step from an “origo state” of perfect neutrality toward the mildest of discomfort. (Such lexically distinct dimensions could, for instance, correspond to the activation of different circuits of aversive experience, or to different kinds or combinations of painful emotions.)
An argument in favor of additional such thresholds, beyond the threshold between neutrality and discomfort, is that it seems a priori implausible that all experiences — even when they are mediated by different neural circuits — must necessarily be ordered along a single uniform axis.
Moreover, in phenomenological and a posteriori terms, one may argue that mild discomfort and unbearable suffering are even more dissimilar in their experiential character than are states of neutrality and discomfort, and hence that it is at least as plausible that mild discomfort and unbearable suffering likewise occupy lexically distinct dimensions of experience. (Though this argument is also compatible with non-abrupt lexical views, which we will explore shortly.)
Disanalogous forms of lexicality?
One might object that the abrupt forms of lexicality outlined in the previous section are fundamentally different from the lexicality between “things that matter and things that don’t”. After all, in the latter case, we are talking about a difference between states that are perfectly neutral versus states that are not, whereas the forms of lexicality explored in the previous section involve lexicality between states that both (or all) entail some disvalue.
However, the difference between these cases is less significant than our standard unidimensional conceptions of disvalue might suggest. After all, on the views outlined in the previous section, the abrupt difference between lexically distinct states of disvalue is also a zero-to-one difference in an important sense. For example, to take a simple toy model, a way to think about abrupt but gradual lexicality could be that discomfort is mediated by activity in neural circuit C1, while genuine pain is mediated by activity in C2, and the lexicality between them would then occur when we go from merely having activity in C1 to having some activity in C2 as well. There is a similar “nothing-to-something” step in a new dimension. (Again, the views outlined in the previous section are not predicated on any particular claim about neural circuits or the like, but the broader point about seeing lexical thresholds as representing a step into a new dimension of disvalue does apply to all of these views.)
Non-abrupt lexical views
In contrast to the views explored in the previous section, there are lexical views that entail no abrupt thresholds. Several such non-abrupt lexical views have been proposed, two broad examples of which are outlined below.
Diminishing marginal disvalue of bads
One view that has been suggested is to assign diminishing marginal disvalue to instances of the same bad such that the total disvalue converges to a certain limit. This would mean that a large number of identical bads never get to be worse than a single instance of a sufficiently severe bad (see e.g. Carlson, 2000; Rabinowicz, 2003).
An argument against these views might be that it seems implausible and ad hoc to say that the disvalue of adding a given bad should depend on how many similar bads already exist. Yet a possible reply, or version of these views, could hold that the overall disvalue only diminishes in comparison to worse bads, where one may argue that diminishing marginal value is not implausible.
Specifically, one may argue that an additional bad should always add the same amount of disvalue as long as we are comparing the same kind of bad, whereas such linear addition becomes implausible when we compare bads of a different kind, such as suffering of different intensities. For example, one could reasonably argue that adding more instances of mild pain — while bad — is not bad in the same way as is increasing the intensity of pain, which arguably represents an altogether different parameter of badness (Leighton, forthcoming, “The map and the territory”). One can thus turn the objection above on its head and argue that it is more ad hoc and unwarranted to claim that the disvalue of many instances of the same pain must add up linearly in the context of inter-intensity comparisons.
A way to still assign unique and impartial quantities of disvalue to outcomes on these views might thus be to distinguish different kinds of badness, namely “instance badness”, “intensity badness”, and the more complete “instance + intensity badness” (cf. Leighton, forthcoming). Thus, speaking only in terms of “instance badness”, disvalue may plausibly increase linearly as more instances of the same bad are added. Yet in terms of the combined metric of “instance + intensity badness”, the added disvalue of the same bad may coherently be diminishing because we are implicitly comparing it to more intense states of suffering (even if these are merely potential states). Again, in value comparisons across different intensities of suffering, one could argue that this addition scheme, although not perfect, is at least more plausible than is a scheme of linear addition that renders many bearable discomforts worse than unbearable torment. (After all, the latter scheme is not plausible by default.)
Rejecting real numbers and strict “better-or-worse” answers
An alternative and in my view more plausible view is to reject that disvalue is best represented with real numbers, and to further reject that bads with non-identical disvalue must be either strictly better or strictly worse than one another. Instead, one may allow differences in disvalue to be vague or imprecise (cf. Qizilbash, 2005), or allow different bads to have a certain degree of worseness relative to each other, where this degree might assume values between 0 to 1 (cf. Knutsson, 2021).
These degrees can also be extended to lexicality itself. For instance, one may hold that lexicality between two different bads is plausible, or true, to the degree 0.3, rather than insisting that the plausibility or truth degree of lexicality must be exactly 0 or 1 (cf. Knutsson, 2021).
Note that these degrees can express either a subjective degree of plausibility that one assigns to lexicality between the bads in question (i.e. the degree to which one subjectively endorses lexicality), or an objective truth degree of lexicality between the bads. The points I make below apply equally to both interpretations, which are equivalent at the purely formal level (cf. Knutsson, 2021, “Introduction”). (I likewise use the terms “truth degree” and “degree of plausibility” equivalently below, without taking a stand on the interpretation issue.)
The views described above allow for more flexible and refined views, and they can entail lexicality between bads without any abrupt thresholds. For example, one may hold that it is plausible to degree 0.7 that some state of suffering, S0, is worse than some slightly less intense state of suffering, S1, and further hold that it is plausible to degree 0.01 that S0 is lexically worse than S1. And one may then similarly consider it plausible to degree 0.01 that S1 is lexically worse than a still less intense state of suffering, S2, which may in turn have the same relation to S3, and so on, all the way up to, say, S100.
The combined truth degree of lexicality across such a sequence can obviously be construed in myriad ways. A simple toy model might be to say that the truth degree of lexicality is additive throughout the sequence, such that, for instance, S0 is lexically worse than S5 to degree 0.05, while it is lexically worse than S10 to degree 0.10, etc.
An alternative view would be to say that the truth degree should increase by a certain factor — perhaps a factor of 10. In that case, one could hold that the truth degree of lexicality between S0 and S100 is 1 (the upper limit), while also holding that the truth degree of lexicality between any two adjacent states of suffering in this sequence is only 1/(10^100). (And if we were to introduce intermediate states of suffering between S0 and S1, the truth degree of lexicality between them could be smaller still, such that it converges to 0 as we approach exactly the same state of suffering.)
Thus, in concrete terms, these views can coherently endorse a complete value lexicality between states of mild discomfort and unbearable suffering, while not endorsing it between highly similar states of suffering.
There may be various reasons to opt for views that allow for such degrees of plausibility. One reason might simply be that there is little justification for not allowing degrees of plausibility or truth. In the absence of any positive justification for a black-or-white picture of better or worse, it seems natural to reject such a restrictive view in favor of a more nuanced range of possible judgments.
A more substantive reason to favor graded evaluations might be that they can feel more apt and precise in real-life attempts to compare similar states of suffering. In particular, it seems likely that people who experience different states of suffering directly would, at least in some cases, find it more accurate to rate the relative badness of these states in terms of degrees rather than in strictly binary terms — and they might even prefer to use a range of degrees (cf. Mayerfeld, 1999, p. 29; Parfit, 2016, p. 113).
Another substantive reason is that some philosophers have defended views that entail that the suffering of the worst-off consciousness-moment always has lexical priority compared to less intense states of suffering (Mendola, 1990; Ryder, 2001, pp. 28-29). These views essentially entail an abrupt lexical threshold at each gradual worsening of suffering with truth degree 1. One can reasonably argue that this truth degree is much too high. Yet conversely, given that sensible people have defended this view, and given that it can appear to have at least some degree of plausibility to say that the maximum sufferer deserves overriding priority, one can likewise argue that a truth degree of strictly 0 seems too low, and that a non-zero truth degree such as 0.01 or 1/(10^100) would be more plausible.
Representing disvalue with real numbers: An unexamined assumption?
The discussion above raises important questions concerning how to best represent disvalue. It is commonly assumed (e.g. among utilitarians) that it is plausible to represent disvalue with real numbers. Yet it seems to me that this assumption is often made without much justification, and without acknowledging that there are reasonable alternatives.
In particular, the assumption that we can represent disvalue with real numbers gives rise to many counterintuitive implications, and it seems that much time is spent grappling with those implications, while comparatively little time is spent questioning the initial assumption that gives rise to these issues.
After all, certain frameworks will rule out value lexicality from the outset. For instance, if we assume that the disvalue of any aversive state can be represented with a negative real number, and further assume that total disvalue should increase linearly as we add more such states (also in inter-intensity comparisons), it follows trivially that sufficiently many states of mild discomfort can be added up to be worse than any state of extreme suffering. But what is not trivial is whether this set of starting assumptions is plausible to begin with.
In this respect, it is worth being aware of potential biases due to certain ways of thinking that have become second nature to us. We are, after all, very much used to thinking in terms of real numbers and standard addition, which is obviously valid in many (other) contexts. One person with 100 dollars does indeed have as much money as 100 people who each have 1 dollar. But suffering that is rated as having an intensity of 100 on an ordinal scale of pain intensity does not similarly represent a sum of 100 mild-intensity suffering stacked on top of each other (as a purely descriptive matter), and hence it is not obvious whether the disvalue of many mild states of suffering can legitimately be summed up in this way either, as an evaluative matter (Leighton, forthcoming, “The map and the territory”).
Therefore, even if we think that it seems plausible to represent disvalue with real numbers, it seems worth at least being open to the possibility that other views might ultimately be more plausible — not least given that our familiar ways of thinking may bias us toward the use of real numbers and toward prematurely dismissing less familiar alternatives, akin to how strong familiarity with a particular numeral system can make it seem like the obviously “right one”.
It would be a shame if we allowed certain ingrained conceptual frameworks to covertly dictate our views of what matters and what is most worth prioritizing.
Acknowledgments
For their feedback on this post, I am grateful to Teo Ajantaival, Tobias Baumann, Anthony DiGiovanni, Michael St. Jules, Simon Knutsson, and Winston Oswald-Drummond.
References
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Klocksiem, J. (2016). How to Accept the Transitivity of Better Than. Philosophical Studies, 173(5), pp. 1309-1334.
Knutsson, S. (2021). Many-valued logic and sequence arguments in value theory. Synthese, 199, pp. 10793-10825.
Leighton, J. (Forthcoming). The Tango of Ethics.
Mayerfeld, J. (1999). Suffering and Moral Responsibility. Oxford University Press.
Mendola, J. (1990). An Ordinal Modification of Classical Utilitarianism. Erkenntnis, 33(1), pp. 73-88.
Parfit, D. (2016). Can We Avoid the Repugnant Conclusion? Theoria, 82(2), pp. 110-127.
Rabinowicz, W. (2003). Ryberg’s Doubts About Higher and Lower Pleasures: Put to Rest? Ethical Theory and Moral Practice, 6(2), pp. 231-237.
Ryder, R. (2001). Painism: A Modern Morality. Open Gate Press.
Qizilbash, M. (2005). Transitivity and Vagueness. Economics and Philosophy, 21(1), pp. 109-131.