1. Introduction
In his article, The Mirror Account of Hope and Fear, Carl-Johan Palmqvist aims to resurrect a tradition in the philosophy of discussing hope and fearFootnote 1 in concert with one another (Palmqvist, Reference Palmqvist2023). He observes that in contemporary discussion of hope, the mental state is usually treated in isolation—although, as Palmqvist notes, there are some exceptions (Day, Reference Day1970, Reference Day1998; Stockdale, Reference Stockdale2019; Vazard, Reference Vazard2024).
Palmqvist starts by arguing for a variation on the “standard account’ of hope (Day, Reference Day1969; Downie, Reference Downie1963). His account treats hope and fear as “mirrored’ propositional attitudesFootnote 2 that differ from each other only in respect of their opposed conative elements. Hope and fear, he claims, are similar in that they are comprised of two mental states: (i) a belief in the possibility of an uncertain outcome p and (ii) a conative attitude toward p. They differ, it is claimed, in that the conative attitude of hope is the desire that p—where desire is construed as seeing that p is good—and the corresponding, or mirrored, conative attitude constituting fear is aversion toward p, where p is seen by the agent as badFootnote 3.
With these characterizations in hand, Palmqvist approaches what he calls the co-variation thesis (CVT). The main characterization of CVT given by Palmqvist is somewhat opaque:
Co-variation thesis: In every situation where hope is possible, so is fear, and in every situation where fear is possible, so is hope. (Palmqvist, Reference Palmqvist2023, 210)
He elaborates, however, positing that:
hope and fear tend to appear in tandem, so that when we hope that p we typically also fear that –p, or at least we are in a position where such fear is possible.Footnote 4 (Palmqvist, Reference Palmqvist2023, 210)
CVT, in various forms, seems to have been held by several philosophers, including Spinoza and Hume, all of which could be interpreted as having distinct understandings of the nature of the relationship between hopes and fears. Some of these views are stronger (Seneca, Reference Seneca1969, 38; Spinoza, Reference Spinoza2004, 78), and others are weaker (Aquinas, Reference Aquinas1967, 1585; Hume, Reference Hume1969, 490).
Palmqvist argues that CVT is not true as a matter of psychological necessity, but that it does hold in standard cases. Thus, he contends that there are non-standard cases where it does not hold. Hopes and fears, Palmqvist claims, will standardly manifest together; such that if I hope that p, I will be inclined to fear that ¬p. We can see this as a “weak’ version of CVT and contrast it with a “strong’ version which would state that it is a matter of psychological necessity that if I hope that p, I fear that ¬p.
In support of the weak claim that hopes and fears do not always co-vary, Palmqvist gives an example where the two states seem to come apart. He invites us to imagine Armand, who is agnostic about whether the universe is theistic or naturalistic in origin, and does not seem to mind which is true. He hopes, however, that theism is true—although he thinks it is the least probable option. Here it appears that although Armand hopes that theism is true, he does not have the “opposite’ fear that naturalism is true, even though these are the only two possible options he can envisage. This, it is concluded, appears to be a case of hope without a corresponding fear; Armand hopes that p but does not fear ¬p. In further support, Palmqvist posits that someone interrogated by two police officers—one good cop and one bad cop—might fear being questioned by both and hope for neither. Showing, again, he claims, that fears and hopes do not always co-vary.
The cases given by Palmqvist have intuitive plausibility, thus providing a reason to be skeptical of strong CVT. However, I want to draw attention to a subtle, but vital, methodological issue present in his analysis. I’ll first proceed to diagnose this shortcoming and then I’ll propose an alternative method which ultimately, I’ll argue, strengthens Palmqvist’s argument against strong CVT, but also allows us to see that weak CVT can be construed in two ways, one more plausible than the other. Thus, we will have made progress in discussing the relation between hope and fear by revealing more theoretical options.
2. Propositional Attitudes and Negation
In order to show the methodological issue in Palmqvist’s analysis, I’ll take a case that seems to give support for CVT and analyze it using his method. We will see in doing this that the method employed is problematic in not accurately representing the divergent propositional content of hopes and fears, which has the effect of making the case for strong CVT appear more plausible and Palmqvist’s argument against it less plausible. I will then suggest an alternative approach that is more accurate in its representation of propositional content and which, when applied, strengthens Palmqvist’s case against strong CVT. The following case is adjusted from that of Armand above:
Jon loves the thought that the universe is of divine genesis (theism) and utterly hates the idea that the universe could be of natural origin (naturalism), but he’s uncertain about their truth and believes that either could possibly be the case. Jon hopes that theism is true and fears that naturalism is true.
Now, following the method and notation used by Palmqvist, we assign the proposition [theism is true] the placeholder “p’ and, the proposition that [naturalism is true]Footnote 5 “¬p’. Hence, Jon hopes that p and fears ¬p.
Using this notation, CVT can be cast as the claim that if S hopes for p, then S has a corresponding fear that ¬p. We must be extremely careful here, however. The propositional content of ¬p must just be the negation of p i.e. [it is not the case that p]. Going back to the case of Jon, then, let us ask the following: if [theism is true] is the propositional content of p, should we represent the content [naturalism is true] as ¬p? Surely not. If the content of Jon’s fear is ¬p, and p is [theism is true], then the content of Jon’s fear must be [it is not the case that theism is true]. Thus, it would be preferable to have another placeholder, say q, to represent the distinct proposition [naturalism is true]—where p and q are collectively exhaustive and mutually exclusive outcomes. This is necessary, as the semantic content in the two propositions is distinct, containing divergent concepts; that is THEISM and NATURALISM. Thus, although, as mutually exclusive and collectively exhaustive outcomes, they logically preclude each other’s truth, the propositional content of p [theism is true] is not simply the negation of p—i.e. [it is not the case that theism is true]—but is the distinct proposition [naturalism is true]. The important conceptual difference of this adjusted notation can be seen if we consider the conjunction of the two propositions:
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(i) S hopes that p ∧ q (adjusted notation)
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(ii) S hopes that p ∧¬p (Palmqvist’s notation)
(i) seems logically possible and (ii) appears contradictory. Thus, in addition to being more accurate in representing divergent content, the adjusted notation allows us to see more easily that it is plausible to hope for two “opposite’ outcomes; that is, we might not necessarily hope for one and fear the other, but could hope for both—showing this is Palmqvist’s aim, of course. But this seems much less plausible when we represent, and thus conceptualize, competing outcomes as p and ¬p.
Imagine a coin toss as another example. Heads (H) and tails (T) are mutually exclusive and collectively exhaustive outcomes; thus, the one’s obtaining precludes the other’s obtaining. In some sense, it would be right to represent H as p and T as ¬p; if we were simply concerned with the outcomes of the coin toss. We are concerned here, however, to analyze agents’ mental states and their propositional content. Hence, if the content of varied propositions is divergent, this must be shown in our analysis. It follows that if p is [it is the case that heads], then ¬p would be [it is not the case that heads], so to represent the proposition [it is the case that tails] we should use q.
So, we can see that the propositional content of hoping that q is not equivalent to that of hoping that ¬p; even though the propositions relate to the same states of affairs and report the same facts. We might remember Frege’s puzzle here: The referent of two expressions might be identical, but the semantic content can diverge; as with Batman and Bruce Wayne, for example, which both pick out the same person but differ semantically (Frege, Reference Frege1948). Thus, what I want to stress is that we cannot simply help ourselves to the conclusion that the content of the proposition ¬p, in the coin toss case for example, is [it is the case that tails], or anything other than simply [it is not the case that heads]. Using the distinct placeholder q will go some way to protecting against this.
In considering cases with multiple outcomes, we see that using the notation suggested starts to pay dividends. Imagine, for instance, that we roll a dice to win a sum of money. The money won is equal to the value of the number rolled; so if I roll 1, I win $1, if I roll 2, I get $2, and so on up to a maximum of $6. Suppose I hope for 6, as it’s the highest sum. Let us call this p. In some sense, then, 1, 2, 3, 4, and 5 can all be correctly counted as ¬p, but this analysis is not informative and, as is obvious, the propositions [it is the case that 2], [it is the case that 3], etc. all have distinct propositional content. Hence, each proposition will be represented in one’s mind distinctly, will have a different associated attitude, and will have a distinct state of affairs as its extension. To ensure an accurate and informative analysis, then, we must follow a convention of using distinct placeholders for alternative propositions; if we represent 6 as p then we should represent 1, 2, 3, 4, and 5 as q, r, s, t, and u, respectively.
3. Reconstruing CVT
With this notation in hand, we can see that weak CVT can be formulated in two ways. The first is as follows:
Weak Basal CVT: For every hope p, there is a potential corresponding fear ¬p; a fear that the hoped-for outcome will not manifest.
This means that for every hope an agent forms, they are disposed to form a corresponding fear whose propositional content is the negation of that hope’s content: that is, one will be inclined to fear that what one hopes for will fail to materialize. This version of CVT does not commit us to forming fears which have divergent content to our hopes, but only holds that we fear not getting what we hope for. The problem here, however, is that, if this is true, this fear appears to be an unfocussed and basic or “basal’Footnote 6 fear, not a fear directed at a specific alternative outcome. For it is a kind of fear that, as we can see from the dice roll example, will, in a blanket manner, cover all possible outcomes that preclude p, and it does so by being non-specified. Hence, the truth of this thesis does not license the claim, for example, that if I hope for 6 when I roll the dice, that I fear 1, I fear 2, or I fear any of the other specific outcomes because the fear that ¬p is not equivalent to the fear that q, r, or s.
If one wants to make the claim that when I hope for 6, I fear 1, or that when Armand hopes that theism is true, he fears that naturalism is true, one must commit to the second formulation of weak CVT:
Weak Non-Basal CVT: For every hope p, there is a potential corresponding set of fears q, r, s, t etc. each of which relates to a possible, alternative outcome that precludes p.
As seen in the dice game example, if this is true, an agent will, upon hoping for 6, be disposed to fear all or some of the alternative outcomes 5, 4, 3, 2, and 1. This means being inclined to form distinct propositional attitudes, all with divergent content, simply in virtue of forming one specific hope. Such a claim necessitates a substantial argument. It seems unlikely, in light of the cases discussed here, for we can imagine someone hoping for 6 but being inclined to see that 5 is also good and hoping for that too, just, perhaps, less intensely. Or even, as Palmqvist notes, having a neutral attitude toward it (Palmqvist, Reference Palmqvist2023). There seems to be nothing intrinsically negative about 5, which would be needed—at least on the mirror theory—for it to count as a fear. It is simply not as good as 6.
Importantly, in precisifying our method we have been able to see that there are competing versions of CVT which differ not just in respect to how strong or weak they claim the link between hopes and fears to be (necessary or contingent) but also in respect to the specificity of their propositional content (basal or non-basal).
We can now ask two questions: (1) How plausible are the basal and non-basal versions of weak CVT? and (2) to which version is Palmqvist committed? With regards to (1), both versions, in being weak and thus not committing us to form fears as a matter of psychological necessity, are, in light of counter-examples, more plausible than strong CVT. However, the basal version of weak CVT, appears more plausible than the non-basal version, insofar as it commits us to a much weaker claim. We are not, on weak basal CVT, committed to forming a variety of fears about alternative outcomes which all have distinct propositional content—which is what non-basal weak CVT holds. Only a single fear toward the negated content of the hope—the fear that our hope will not manifest—is posited. This is more parsimonious and prima facie psychologically more plausible than non-basal weak CVT. However, we might wonder, on this thesis, whether what we have called a basal fear, fear that -p, is really a fear. In cases such as the dice roll, if fear is characterized as being averse to the outcome, which is what Palmqvist posits, “fear’ that ¬p will not necessarily count as a fear because it will cover all outcomes that preclude the agent’s hope, and these, as we have seen from examples above, might plausibly include outcomes to which we are not averse.
Thus, the plausibility of each of the weak versions of CVT will also turn on how fear and hope are characterized. There are implications, then, for the wider philosophy of hope. Insofar as there is intuitive plausibility that some version of CVT is true, accounts of the nature of hope itself might find further support to the extent that they allow for this possibility.
Now, to the question of which version Palmquist is committed. The way he states his view, using the notation of p for hope and ¬p for fear, at first appears to show a commitment to weak basal CVT. However, we can see when we recast Palmqvist’s claim in the revised notation that he is better interpreted as espousing weak non-basal CVT, as he understands the propositional content of fears to be distinct to—not simply a negation of—the content of one’s hopes (Palmqvist, Reference Palmqvist2023), and that we are, according to his mirror account, averse to the outcome which their propositional content picks out. As mentioned above, there is a prima facie argument that Palmqvist’s view is psychologically implausible in committing us to hold that upon forming a hope, we also are disposed (though not necessarily) to forming fears with divergent propositional content. Indeed, such a view needs a robust argument, vis a vis the non-basal alternative, and the plausibility of such an argument is going to turn upon how hopes and fears are defined as mental states.
4. Concluding Remarks
In sum, I have argued that, although Palmqvist’s skepticism of CVT is warranted, in order to make progress on this issue, the method of analysis needs to be refined. I have suggested employing a notation that allows us to more accurately represent the divergent semantic content of various propositional attitudes. The treatment outlined has the virtues of providing a more accurate representation of the divergent contents of hopes and fears and allowing us to see that the weak co-variation thesis can be formulated in two ways, one of which is weaker than the other (basal and non-basal). The first posits only that the co-variant fears associated with hopes are unspecific fears about the hoped-for outcome failing to manifest. The second posits, more strongly, that when an agent hopes, multiple specific fears about alternative outcomes, containing distinct propositional content, are formed. Both versions of CVT, however, stumble on counter-examples if they are posited as a psychological necessity, as there are plausible cases of hoping without fearing. Of course, much more needs to be said about this issue, but refining our method of analysis is, I submit, a prerequisite.
Competing interests
The author declares none.
Justin J Bartlett is a philosopher at Srinakharinwirot University, Bangkok. He is currently conducting research in the areas of Metaethics, Philosophy of Mind, and Philosophy of Hope.
