3.1. Simplification by Disposition

Principles such as BTL_D and CTL_D might be taken to suggest that reasoning simplification needs to be explained in dispositionalist terms. More precisely, one might think that the following explanation of reasoning simplification is correct:

According to simplification by disposition, reasoning simplification entails being disposed to treat the target p as true. One might worry that this is too strong though: if we take the disposition to treat p as true as a sufficient condition for reasoning simplification, we can get to the claim that belief simplifies reasoning via BTL_D and hypothetical syllogism. This, however, does not quite give what doxastic dualists want: if the disposition to treat p as true is only sufficient for reasoning simplification, nothing rules out the possibility that what simplifies S's reasoning at the p-stage is not S's holding α towards p but is rather some other cognitive (possibly sub-personal) mechanism. So, dualists could no longer argue for the existence of belief on abductive grounds, namely by claiming that belief exists because it's the only type of mentalia that would best explain reasoning simplification. This shows that doxastic dualists would need something like simplification by disposition if they wanted to defend the idea that it is S's disposition to treat p as true that explains reasoning simplification.Footnote ³

simplification by disposition, however, should be rejected. Consider the following scenario: S believes that not-p, wilfully accepts that p at the p-stage of their reasoning and, as a consequence, not-p gets ruled out at that stage. By “acceptance” I here refer to the attitude of taking p as true which is under S's voluntary control, akin to a sort of decision of taking p as true in their reasoning irrespective of their confidence in p's truth.Footnote ⁴ If BTL_D holds, S is disposed to treat not-p as true in their reasoning. If S's acceptance that p in such a scenario simplifies reasoning, then S's disposition to treat p as true in their reasoning doesn't explain reasoning simplification: given BTL_D, S is in fact disposed to treat not-p as true (and therefore, S is disposed to treat p as false) in such a reasoning. An analogous objection to simplification by disposition can be mounted if we focus on CTL_D and suppose that S accepts p while having a high credence in not-p. This shows that simplification by disposition can't explain reasoning simplification in such type of scenario. I now consider some replies on behalf of simplification by disposition and argue that they all fail.

One might say that S cannot simplify their reasoning at the p-stage by accepting p, ruling out not-p while, at the same time, having a belief that not-p. Stated as it is, this reaction is unwarranted. The voluntary attitude of acceptance has already been included in the list of reasoning simplifying by doxastic dualists,Footnote ⁵ and there's nothing in the very natures of acceptance and belief that makes it impossible for S's reasoning at the p-stage to be simplified when S willingly accepts p at that stage and believes not-p. To see why, note that what matters for reasoning simplification is not that not-p gets eliminated from S's doxastic life altogether, but rather that not-p is eliminated only from the reasoning S is currently performing. This is precisely what acceptance is for: to accept that p is to decide that p is true for the sake of proceeding with a certain reasoning independently of whether or not one believes that p (see e.g. Cohen Reference Cohen1992: 20). The lack of dependence relations between an acceptance that p and a belief that p ensures that one can accept that p even though one believes that not-p. Thus, an acceptance that p can simplify reasoning at the p-stage by ruling out not-p in the scenario we are considering.

One can insist that simplification by disposition was never intended to range over cognitive attitudes other than belief and credences in the first place. So, constructing objections to simplification by disposition which involve attitudes other than belief and credences, such as acceptance, is an illicit move. I disagree: drawing conclusions about whether or not credences simplify reasoning by relying on a mistaken explanation of reasoning simplification amounts to bad theorising. Theoretical responsibility dictates that we first give a plausible account of clear cases of reasoning simplification and then move on to assess which attitudes we have reason to regard as reasoning simplifying.

The supporter of simplification by disposition might try to give a direct argument for the claim that acceptance doesn't simplify reasoning. Suppose that Marie is a lawyer and doesn't have any sufficient evidence that her client is innocent. Nonetheless, Marie wilfully accepts that they are for professional reasons. In such a case, Marie treats it as true that her client is innocent in the legal context, but it's unclear that the possibility that they are guilty has ever been ruled out. Even if Marie is acting as if her client were innocent, she might simultaneously doubt that they really are, entertaining the possibilities in which they are guilty. Now, it would be implausible to say that Marie hasn't accepted that her client is innocent on account of her lingering doubts. After all, accepting a proposition is something that you can do in the absence of sufficient evidence for it, and is therefore compatible with some room for doubt. It would thus seem that there's a sense in which Marie's acceptance of her client's innocence hasn't really simplified her reasoning: when it comes to whether she is really innocent and Marie engages in reasoning aimed at figuring out what the actual world is like, let's call this actual reasoning, acceptance might well fall short of playing the (alleged) simplifying role. On these grounds, the supporter of simplification by disposition might say that the view has to be assessed by taking into account actual reasoning only, and that in such a type of reasoning only belief is reasoning simplifying.Footnote ⁶

For the sake of argument, let's concede to the supporter of simplification by disposition the focus on actual reasoning. The first thing to note is that Marie's case won't help us assess whether or not acceptance simplifies actual reasoning. Insofar as Marie accepts that her client is innocent in a legal context, we've already restricted our focus to what we can call legal reasoning, whose aim is not to figure things out but rather to reach a verdict on the grounds of the admissible evidence. Insofar as she engages in legal reasoning, Marie treats the proposition that her client is innocent as true. But from this it doesn't follow that Marie is disposed to treat the proposition that her client is innocent as true also in actual reasoning.

This suggests that if we concede that simplification by disposition ranges over actual reasoning only, then counterexamples to this account of reasoning simplification have to be cases in which one engages in actual reasoning to establish whether p is the case, believes that not-p and accepts that p exactly for the purpose of figuring out whether p is the case. Cases like this exist: suppose, for instance, that one is reasoning about whether a certain formula p is a tautology of first-order logic. One believes that it is not and in order to come up with conclusive reasons in favour of this view, decides to take p as true for the sake of running a reductio ad absurdum type of argument. This shows that restricting the kinds of reasoning simplification by disposition ranges over won't make counterexamples go away.

One might wonder whether it is the relevant kind of disposition we associate with acceptance that needs to be restricted. Acceptance is often assumed to be context-dependent (see Cohen Reference Cohen1992), and so one might say that when one accepts that p one is disposed to treat p as true across a sufficiently wide range of contexts.Footnote ⁷ This surely marks a contrast between acceptance and belief, as belief isn't context-dependent. But it's unclear that this saves simplification by disposition from the counterexample I've raised. The context-sensitivity of acceptance can at most motivate the thought that there can be cases in which one accepts that p but is not disposed to treat p as true since one is not in the relevant range of contexts. In such cases, one's acceptance that p isn't reasoning simplifying according to simplification by disposition. However, the counterexample I'm offering should not be read that way. The counterexample brings out the existence of cases in which one accepts that p in one of the relevant contexts wherein one is also disposed to treat p as true while, at the same time, believing that not-p. Suppose, for instance, that Marie accepts that her client is innocent (while reasoning in a legal context) but believes that they are not. Plausibly, this is one of the contexts in which such an acceptance comes with a disposition to treat the proposition that the client is innocent as true. This shows that there can be cases in which one accepts that p, believes that not-p, and one's acceptance that p comes with the relevant disposition of treating p as true in one's reasoning. So, the context-sensitivity of acceptance cannot make simplification by disposition immune to counterexamples.

Finally, the supporter of simplification by disposition might concede that an acceptance that p is reasoning simplifying and try to explain this by saying that if S accepts p, they are disposed to treat p as true in their reasoning. In the scenario at issue, however, this means that S is disposed to treat p both as true and as false in their reasoning. Thus, a simple appeal to the target disposition would still leave unexplained why S's reasoning gets simplified by ruling out not-p, as opposed to p.

The preceding discussion shows that simplification by disposition isn't equipped to explain all cases of reasoning simplification.

3.2. Simplification by Representation

The alternative account I propose is:

To start unpacking simplification by representation, let us focus on the claim that “an attitude α represents-as-true p” and distinguish between what α represents and how α represents what it does.Footnote ⁸ When α represents-as-true p, p's truth is not what α represents, for α represents p only, but it is how α represents p. To put the same point differently, p's truth is not part of the content that α represents but is rather part of the mode whereby α represents p. There are various candidate modes whereby p is represented-as-true (call them “cognitive modes”): acceptance, belief, (propositional) imagination, supposition, assumption are plausible candidates. I suggest telling cognitive modes apart from one another by appealing to the existence of different relations that S bears to a mental representation whose content is p. Such relations differ from one another since their respective regulatory mechanisms, namely the cognitive mechanisms that are responsible for the formation, retention and revision of the target attitude, are geared towards different functions.Footnote ⁹ For instance, it is commonplace to say that the function of belief in our cognitive architecture is to be true. We can cash out this idea as follows:

The function of an acceptance that p, by contrast, is to enable the accepter to decide that p is true and act upon that decision in reasoning for whatever purposes they might have in the circumstances they are in. We can cash out this idea as follows:

To give yet another example, let us focus on the type of propositional imagination that has often been associated with modal thought, fiction and pretence. Imagination has been linked to our take on what would have happened had things been different (see Williamson Reference Williamson2000; Ichikawa and Jarvis Reference Ichikawa and Jarvis2012): the thought here is that imagination stands to counterfactual scenarios like belief stands to the actual world. In his seminal 1990 book, Kendall Walton writes (Reference Walton1990: 41): “Imagining aims at the fictional as belief aims at the true. What is true is to be believed; what is fictional is to be imagined.” Authors such as Currie (Reference Currie1990), Stock (Reference Stock2017) and García-Carpintero (Reference García-Carpintero2019), following Walton's lead, have expanded on the thought that a propositional imagining that p is a bona fide representation of p as being the case in the fictional, as opposed to the metaphysical, world. So, in analogy with belief function and acceptance function, we have:

Note that some authors (see e.g. Stock Reference Stock2017; García-Carpintero Reference García-Carpintero2019) claim that the imagination that is necessary for engagement with fiction is a species of the more general genus I have here described. I can be neutral on these matters, but nothing prevents us from acknowledging the existence of a distinctive enough type of imagination – what Stock (Reference Stock2017) calls f-imagining – whose function is to represent-as-true its content for the sake of getting p's truth-value in the fictional (as opposed to the more general “counterfactual”) world right. Analogous stories can be told about supposition, assumption, and other cognitive modes of representing-as-true a propositional content.

Having sketched an account of how a cognitive attitude represents-as-true its content, we can now articulate simplification by representation's pattern of explanation of reasoning simplification.

The schematic idea is this: when S's attitude α towards p represents-as-true p and S deploys α at the p-stage of their reasoning, only p is put before S's mind at that stage. This ensures that the possibility that not-p doesn't appear before S's mind at the p-stage of their reasoning, thereby reducing the complexity of S's reasoning at that stage. The idea of a proposition being put before one's mind is metaphorical, but what I concretely mean is this: in the tennis match example, S is reasoning about how likely it is that it'll rain during an upcoming tennis match. At a certain stage of that reasoning, right before performing the addition of all the relevant credences as per the total probability theorem, S rules out the possibility that the match will take place in LA and only the proposition that the match won't take place in LA is taken under consideration for the relevant computational operation, something which greatly simplifies the reasoning problem at hand.

One might say that this idea of considering a certain proposition for the specific reasoning task one is performing restricts reasoning simplification to cases of active reasoning, namely the kind of reasoning we perform deliberately while somewhat consciously going through every option and performing the relevant reasoning steps. And yet, reasoning can also take a more passive shape in which there is a certain transition from certain premise attitudes to a certain premise conclusion which automatically and unconsciously reached.Footnote ¹⁰ Now, it might be hard to think of the reasoning involving in the tennis match case as a purely passive, that is, largely unconscious and automatic, reasoning. It seems that, given the kind of complexity involved in the reasoning, S is indeed going through each option, actively making the calculations. However, I think that we can accommodate the idea of a proposition's being ruled-out even within more passive forms of reasoning: in such cases, the proposition simply plays no role in the transition from a certain premise to a certain conclusion. In the tennis match case, the proposition that it will rain in LA plays no role in S's – let us assume – unconscious and automatic reasoning about the likelihood of rain during the upcoming tennis match: that proposition simply is not part of the premises of S's probabilistic reasoning.

The schema just offered will be instantiated differently depending on the cognitive mode we focus on. Focusing on belief, when S's belief that p represents-as-true p and S deploys at the p-stage their reasoning, only p is put before S's mind (at the p-stage) as being the case in a metaphysically actual world and not-p is ruled out by such a world. When S accepts p and deploys it at the p-stage of their reasoning, S doesn't rule out not-p from the metaphysically actual world. Rather, when S accepts that p, only p is put before S's mind as being the case in what we may call S's volitionally actual world, where the volitionally actual world is the world that is the case according to S's will for the purpose of the reasoning they are conducting.Footnote ¹¹

Belief and acceptance are attitudes we deploy in practical and theoretical reasoning about the actual world, which I've dubbed “actual reasoning”. The foregoing, then, articulates simplification by representation's pattern of explanation of practical and theoretical actual reasoning simplification. However, cognitive studies on modal reasoning and engagement with fiction and pretence suggest that we use and exploit our imagination to reason counterfactually and fictionally. Imagination is similar to belief as far as their inferential potentials are concerned: it has been argued that when one engages in counterfactual reasoning, namely reasoning of the form “If I φ-ed, then x would ψ”, one imagines the antecedent and the upshot is an expectation about what would happen if the world were as imagined (see Williamson Reference Williamson2000; Currie and Ravenscroft Reference Currie and Ravenscroft2002; Ichikawa and Jarvis Reference Ichikawa and Jarvis2012; Sinhababu Reference Sinhababu2013). If so, when S imagines that p at the p-stage of their counterfactual reasoning, only p is put before S's mind (at the p-stage) as being the case in the possible world considered as counterfactual and not-p is ruled out by such world. This is how, according to simplification by representation, counterfactual reasoning gets simplified by propositional imagination. Assuming, with Currie (Reference Currie1990), Walton (Reference Walton1990), Stock (Reference Stock2017) and García-Carpintero (Reference García-Carpintero2019), that propositional imagination is necessary to engage in fiction, let us say that when S imagines that p at the p-stage of their fictional reasoning, only p is put before S's mind (at the p-stage) as being the case in the fictionally actual world and not-p is ruled out by such a world, where the fictionally actual world is the world that is the case according to the fictional project S is undertaking while, for instance, reading a certain novel. This is how, according to simplification by representation, propositional imagination can simplify fictional reasoning.

This completes my presentation of simplification by representation. Let us turn to assessing its merits.

Let us begin with Staffel's tennis match case: simplification by representation can account for it by saying that S's belief that the match won't take place in LA is reasoning simplifying since such a proposition is represented-as-true for the sake of getting its truth-value right and this cognitive mode doesn't leave open that the match will take place in LA. Focus now on the case that spells trouble for simplification by disposition, namely the scenario in which S believes that not-p, accepts that p and simplifies their reasoning at the p-stage by ruling out not-p. As I read the case, S deploys or activates their acceptance that p in reasoning, whereas they don't deploy or activate their belief that not-p. If S doesn't deploy their belief that not-p in their reasoning, that attitude doesn't represent-as-true not-p in S's reasoning. So, the fact that S's belief that not-p rules out the possibility that p doesn't contradict the fact that S's acceptance that p represents-as-true p in S's reasoning and can therefore be reasoning simplifying. This, to my mind, shows that simplification by representation is superior to simplification by disposition.

At this stage, one might worry that the two views are just notational variants of the same idea.Footnote ¹² I don't think they are though. Combining simplification by disposition with CTL_D entails that credences are reasoning simplifying attitudes, whereas combining simplification by representation with CTL_D doesn't. This is a distinction that will make a crucial difference as to the question of whether credences are reasoning simplifying attitudes. I will come back to this below.

To keep assessing simplification by representation, I now want to consider two alleged data that are meant to spell trouble for the idea that belief, once understood in a standard fashion, is reasoning simplifying. These data are presented in Dinges (Reference Dinges2021). My aim is to argue that such data can be explained in a simplification by representation-friendly way. The first alleged datum is that we often simplify reasoning by ruling out a proposition's falsity on the basis of purely statistical evidence. Dinges maintains that (Reference Dinges2021: 202) “[belief] is often assumed to be something like the inner version of assertion” and goes on to claim that in the tennis match case we would not assert that the match doesn't take place in LA. If Dinges is right then either belief is not intimately linked to assertion or it is not the attitude we deploy when we simplify reasoning on purely statistical grounds.

The dilemma, however, rests on a revisionary take on the significance of purely statistical evidence cases for assertion: what is standardly acknowledged in the literature is that it seems inappropriate to assert the content of a belief in cases of purely statistical evidence and not that we don't or wouldn't assert propositions in such cases: in lottery situations, for instance, it's not surprising to hear people asserting “My ticket is a loser” by reflecting on the very high probability that their ticket is a loser. It'll take a little philosophical effort to explain why there's something off with that assertion.Footnote ¹³ The fact that it is somehow inappropriate to assert propositions in such cases would at most show that it is also somehow inappropriate to believe them (I say “at most” since this would require making the disputed assumption that assertion and belief are governed by the same norm.) This verdict in no way speaks in favour of the dilemma presented by Dinges though: from the fact that it is inappropriate to assert and believe p in certain circumstances it doesn't follow that we don't or wouldn't assert or believe p in those circumstances. simplification by representation is therefore left unscathed.Footnote ¹⁴

One might reformulate the previous point in normative terms and say that it's appropriate to rule out not-p on the basis of merely statistical evidence, whereas it's not appropriate to assert p on such grounds. This leads us to the interesting question of what norms, if any, govern reasoning simplification, and whether those norms align to norms of assertion and belief. Addressing this question in depth is beyond the scope of this paper, but the following point seems to me correct: reasoning simplification appears to be permitted in cases where ignoring a negligible possibility helps us spare time and cognitive resources. So, while there can definitely be cases in which we hold a very high credence in p on the grounds of merely statistical evidence, what ensures the permissibility of ruling out not-p is not the statistical support in favour of p's truth but rather the cognitive benefits that reasoning simplification would bring about in such a case. This, to my mind, suggests that while assertion and belief are typically governed by epistemic norms, reasoning simplification might be subject to practical norms that would explain the appropriateness of ruling out not-p in spite of the fact that one holds p on the basis of merely statistical evidence.

The second alleged datum is that reasoning simplification is sensitive to stakes. Dinges (Reference Dinges2021: 203) offers the following case:

Dinges claims that we wouldn't rule out the proposition that it won't rain and that this shows that reasoning simplification is sensitive to stakes: when the stakes regarding S's belief that p are higher than a certain threshold, then it's intuitively plausible to maintain that we don't simplify our reasoning at the p-stage by ruling out the possibility that not-p, or so Dinges contends.

We are not compelled to accept this reading of the rain case though, for there's an alternative reading of it which is compatible with simplification by representation. The alternative reading has it that the intuitive datum elicited by the rain case is that I should not simplify my reasoning by ruling out the possibility that it will not rain since, given the high-stake scenario I'm in, I don't know that it will not rain. To substantiate further the alternative reading, we might appeal both the existence of epistemic norms governing practical reasoning and the idea that practical factors affect such norms. Suppose that if I'm reasoning about how to go to my wedding in Palo Alto, I should treat the proposition that it won't rain as a reason to act in such-and-such a way only if I know that it won't rain.Footnote ¹⁵ If we further assume that practical factors like stakes affect knowledge,Footnote ¹⁶ then it's plausible to say I don't know that it won't rain in Palo Alto. This shows that I should not treat the proposition that it won't rain in Palo Alto as a premise in my practical reasoning and, therefore, that it's inappropriate for me to not consider the possibility that it'll rain in Palo Alto in framing my decision problem. So, the lesson we can draw from the rain case is that it is inappropriate or irrational to simplify our reasoning because the stakes are so high that we should consider even the crazily improbable options. simplification by representation is fully compatible with this lesson.