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Counterfactual definiteness

Sat, 12 Sep 2026 15:46:44 +0000

A peculiar question that has divided philosophers since the Middle Ages (and possibly earlier) concerns the status of Conditional Excluded Middle. CEM says that for any propositions A and C, either C would be the case if A were the case, or ¬C would be the case if A were the case. Some accept CEM as valid, others reject it. In the last few decades, the CEM supporters have been gaining ground, especially in the field of semantics. See, for example, "Williams 2010, "Moss 2013, "Mandelkern 2018, "Shaffer and Beebe 2019, "Cariani and Goldstein 2020, "Marty, Romoli, and Santorio 2020, and "Ramotowska et al. 2025.

I belong to the other camp: I believe that CEM is invalid. My reasons aren't particularly original; they are essentially the ones given in "Jeffrey 1977, 193, "Hájek 2009, 217, "Joyce 1999, 172f., "Lewis 1981, 331, and "Bennett 2003, 191, among others.

Most supporters of CEM don't seem to understand these reasons.

A principle is invalid if it has at least one counterexample. The opponents of CEM that I've cited think that the principle is false in certain cases involving indeterministic chance events: if a certain type of chance process A has both C and ¬C as possible outcomes, and A doesn't occur, then neither C would have occurred nor ¬C would have occurred if A had occurred.

The usual toy example is (1):

(1)If this fair coin had been flipped, it would have landed heads/tails.

But – here's the misunderstanding: our claim is not that statements like (1) are false. Our claim is that they are false on the assumption that the antecedent describes a particular kind of physical process. Whether any processes of this kind exist in worlds like ours is an open question. Bohmian mechanics, for example, implies that there are none.

I want to tear my hair out when I read papers like "Marty, Romoli, and Santorio 2020 and "Ramotowska et al. 2025 in which ordinary people are asked to make truth-value judgements about sentences like (1). That's not what our dispute is about! The anti-CEM hypothesis is that CEM fails in a particular class of cases. What needs to be checked is how people are disposed to talk about these cases, not about ordinary coin flips.

To appreciate the point about chance, you have to know a bit of physics.

Suppose we prepare two electrons in an entangled state, sending one to Alice and the other to Bob. Alice has a measuring device with which she can measure the spin of her electron along one of two axes, depending on the setting of a switch. Bob also has such a device for his electron, with axes that are different from Alice's. Alice and Bob both choose an axis, measure, and register the outcome ("up" or "down").

Suppose this process is repeated many times, with Alice and Bob choosing different axes at different times. Quantum mechanics predicts that the recorded measurements will display certain statistical correlations, which have been verified experimentally.

Now assume that there's always an answer to what would have happened if Alice or Bob (or both) had chosen different axes. For example, we can ask whether, on a particular run, Alice would have obtained the same result if Bob had chosen a different axis. Intuitively, the answer is "yes". We can assume that Alice and Bob are really far apart, so that there's no causal connection between Bob's choice and Alice's measurement. So (2) seems plausible.

(2)Alice's measurement would have been the same if Bob had chosen a different axis.

But this assumption of counterfactual locality, together with the assumption of counterfactual definiteness (that there is always an answer to what would have been measured if Alice and Bob had chosen such-and-such axes), contradicts the verified predictions of quantum mechanics. This is a version of "Bell's theorem.

(Obviously, deriving the contradiction requires a little more precision. The derivation also requires a further "no conspiracy" assumption that is widely, but not universally accepted.)

So the friend of CEM has to deny (2). More precisely, they have to say that as the experiment is repeated over and over, there is an increasingly precise number of runs (around 41%) in which Alice's measurement would have been different if Bob had chosen a different axis. They have to posit a mysterious counterfactual dependence between spacelike-separated events.

Bohmian mechanics endorses this dependence, and suggests a mechanism of how it might come about. But most physicists think the mechanism doesn't work. They reject the dependence. So they deny the other ingredient in the derivation of the contradiction: counterfactual definiteness. On this view, it is neither true that Alice would have measured "up" nor that she would have measured "down" (or anything else) if she had chosen a different axis. There is "no fact of the matter" about what outcome she would have obtained.

To me, this looks like a reasonable response. The Wikipedia page on "counterfactual definiteness even suggests that the failure of counterfactual definiteness is implied by various interpretations of quantum mechanics. I don't think that's quite correct. But the important point is that physicists who have supported these interpretations have explicitly rejected counterfactual definiteness.

If CEM were valid, rejecting counterfactual definiteness would not even be an option. All these physicists – and all the philosophers I've cited above – would misunderstand their own language, promoting theories that are analytically false.

Worse, if CEM were valid, the grammar of English, together with findings from physics, would force us to believe in mysterious patterns of counterfactual dependence between spacelike-separated events. This is giving way too much power to grammar.

I've assumed that supporters of CEM would have to endorse the "counterfactual definiteness" that figures in Bell's theorem. Perhaps this could be denied. Some friends of CEM admit that there may be "no fact of the matter" about what would have happened if a certain antecedent had been true. "Stalnaker 1980 is the classic source. On Stalnaker's account, counterfactuals are evaluated relative to a selection function f, but the context of utterance often doesn't supply a unique f. For a counterfactual to be true in a context ("supertrue"), it has to be true relative to all selection functions f that are compatible with the context.

But does this help? It's not enough to somehow vindicate the judgements that there's "no fact of the matter". We need to get around the trouble raised by Bell's theorem. As far as I can see, counterfactual definiteness remains true relative to each selection function f. Granting the other ingredients of Bell's theorem, and holding fixed f, we can still derive violations of counterfactual locality: we can derive that in a certain number of runs, Alice's measurement would have been different if Bob had chosen a different axis. So this comes out supertrue.

Bennett, Jonathan. 2003. A Philosophical Guide to Conditionals. New York: Oxford University Press.

Cariani, Fabrizio, and Simon Goldstein. 2020. “Conditional Heresies.” Philosophy and Phenomenological Research 101 (2): 251–82. "https://doi.org/10.1111/phpr.12565.

Hájek, Alan. 2009. “Fifteen Arguments Against Hypothetical Frequentism.” Erkenntnis 70 (2): 211–35.

Jeffrey, Richard C. 1977. “Mises Redux.” In Basic Problems in Methodology and Linguistics: Part Three of the Proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada-1975, 213–22. Springer.

Joyce, James. 1999. The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.

Lewis, David. 1981. “Causal Decision Theory.” Australasian Journal of Philosophy 59: 5–30.

Mandelkern, Matthew. 2018. “Talking About Worlds.” Philosophical Perspectives 32 (1): 298–325. "https://doi.org/10.1111/phpe.12112.

Marty, Paul, Jacopo Romoli, and Paolo Santorio. 2020. “Counterfactuals and Undefinedness: Homogeneity Vs Supervaluations,” 21.

Moss, Sarah. 2013. “Subjunctive Credences and Semantic Humility.” Philosophy and Phenomenological Research 87 (2): 251–78.

Ramotowska, Sonia, Paul Marty, Jacopo Romoli, and Paolo Santorio. 2025. “Counterfactuals and Quantificational Force: Experimental Evidence for Selectional Semantics.” Semantics and Pragmatics 18: 6:1–43. "https://doi.org/10.3765/sp.18.6.

Shaffer, Michael J., and James Beebe. 2019. “Folk Judgments about Conditional Excluded Middle.” In Advances in Experimental Philosophy of Logic and Mathematics, edited by Andrew Aberdein and Matthew Inglis, 251–76. Bloomsbury Academic.

Stalnaker, Robert. 1980. “A Defense of Conditional Excluded Middle.” In Ifs, edited by William Harper, Robert C. Stalnaker, and Glenn Pearce, 87–104. Reidel.

Williams, J. Robert G. 2010. “Defending Conditional Excluded Middle.” Noûs 44 (4): 650–68. "https://doi.org/10.1111/j.1468-0068.2010.00766.x.

Are credences beliefs about probability?

Sat, 29 Aug 2026 09:46:41 +0000

There's a lively literature on how graded beliefs (credences) relate to ungraded beliefs. Some hold that ungraded beliefs are reducible to credences, others that credences are reducible to ungraded beliefs; yet others hold that both are real and irreducible to one another. I find this debate confusing. By which of course I mean: confused. I'll try to explain why. I'll also comment on one particular proposal, that credences are beliefs about probability; an interestingly new version of this has just been defended in "Buchanan and Dogramaci 2026.

First, why I find the debate confusing. Imagine a parallel debate about desire. Desires patently vary in strength: we desire some things more than others. In decision theory, an agent's desires are represented by a utility (or "desirability") function that assigns numbers to propositions; the higher the number, the stronger the desire. Now imagine someone asks how these graded desires relate to ungraded desires: are graded desires reducible to ungraded ones, or the other way round?

I hope it's clear why this would be confused. There are no ungraded desires! Every desire has a (comparative) strength; the utility function represents this strength.

We might still ask how the ungraded concept (or word) 'desire' relates to the graded concept of a utility function. In particular, can we analyse simple desire reports in terms of the subject's utility function? If so how? These are good questions. (They are explored, for example, in "Phillips-Brown 2021 and "Blumberg and Hawthorne 2022.)

You might say that the case of belief is importantly different: while desires vary in strength, beliefs do not. But is that true? It seems false to me. Surely it can't be taken for granted.

So we shouldn't assume that there is any such thing as ungraded belief. What we have is an ungraded concept (or word) 'belief'. We may ask how this concept relates to the concept of credence. Can we analyse belief reports in terms of the subject's credence function, or the other way round?

So that's a meaningful question. "Buchanan and Dogramaci 2026 suggest that credence reports can indeed be analysed in terms of (ungraded) belief reports. Their proposal follows an earlier proposal in "Moon and Jackson 2020, according to which 'S gives credence x to p' means 'S believes that the evidential probability of p conditional on S's evidence equals x'. To avoid some counterintuitive consequences of this proposal, Buchanan and Dogramaci suggest that we shouldn't fix the evidence to be the subject's evidence at the relevant time. We shouldn't fix the evidence at all. According to Buchanan and Dogramaci, 'S gives credence x to p' means 'S believes that the probability of p is x', where 'the probability of p is x' expresses an "assessment-sensitive proposition" (in the sense of "MacFarlane 2014) whose truth-value varies not just from world to world, but from point of assessment to point of assessment. More precisely, what matters about points of assessment is the evidence available at them. Formally, 'p has probability x' is true relative to a world w and evidence E iff the evidential probability (at w) of p conditional on E is x.

This may look strange at first, but the basic idea is well-known in the semantics of epistemic modals. Consider 'might'. Whether something might be the case depends on the available information; this information parameter can be shifted by operators. Thus 'S believes that might p' expresses (roughly) that p is compatible with S's information (not: with the speaker's information). To formalise this, we have to make the truth-value of 'might p' sensitive to a (shiftable) information parameter. (Assessment-sensitive accounts add that when the parameter isn't shifted, it is generally fixed by the context of assessment, rather than the context of speech.) Since 'probably' is also an epistemic modal, it is natural to extend this treatment to 'the probability of p is x'.

But let's return to that information parameter. Buchanan and Dogramaci suggest that the information parameter can be identified with an evidence proposition: 'the probability of p is x' is true relative to E (and a world w) iff the evidential probability (at w) of p conditional on E equals x. (Whether evidential probability is world-relative is an interesting question that we don't need to get into.) For the project of analysing credence statements, this leads to a fatal problem.

The Bayesian concept of credence is supposed to measure an agent's comparative confidence, showing up, for example, in betting behaviour and other choices. How this quantity relates to evidential probability is an open question on which the founding fathers of Bayesianism were divided. Carnap (and arguably Laplace) thought there is a connection: ideally, an agent's credence in p should equal the extent to which p is supported by their evidence. Ramsey, de Finetti, Savage and Jeffrey disagreed. But even for Carnap, the link between credence and evidential probability is normative. No Bayesian ever thought that it is analytic. But that's what the proposals in "Moon and Jackson 2020 and "Buchanan and Dogramaci 2026 would entail.

We can bring out this problem by thinking of cases that put pressure on the normative link between credence and probability. In "Schwarz 2025, I describe scenarios in which, I claim, a rational agent should give high credence to some proposition p even though they know that the proposition has low evidential probability (conditional on their evidence). It doesn't matter if I'm right. What matters is that the position I'm defending is intelligible. We can imagine an agent whose credence in p is high (as revealed by their verbal and non-verbal behaviour: they accept bets on p, they say that they're confident in p, etc.), but who also judges that p has low evidential probability (conditional on their evidence and any other relevant evidence). If there was an analytic connection between credence and beliefs about evidential probability, this kind of scenario would be unintelligible.

There's a lesson here for the semantics of epistemic modals. In the scenarios I describe, the agent might well say 'probably p'. So the information parameter relative to which epistemic modals like 'probably' are evaluated can't be identified with an evidence proposition. It has to be represented by a full probability measure (or a set of such measures). This is, in fact, a fairly standard assumption in the semantics of epistemic modals. (See, for example, "Yalcin 2007 or "Stalnaker 2014.)

With this change, we can rescue the proposal in "Buchanan and Dogramaci 2026. Recall that, according to B&D, 'p has probability x' is true or false relative to (a world and) an evidence proposition: 'p has probability x' is true relative to E iff the evidential probability of p given E is x. Let's drop the reference to evidence and evidential probability. We can say that 'p has probability x' is true relative to a probability measure iff that measure assigns x to p.

So the following version of B&D's proposal survives the problem I've raised: 'S gives credence x to p' means 'S believes that the probability of p is x', where 'the probability of p is x' is true relative to a probability measure iff that measure assigns x to p.

I have some quibbles about the suggested equivalence, but I'm willing to grant it for the sake of the argument. So we can translate credence reports into belief-about-probability reports. But have we thereby reduced the concept of credence to an ungraded concept of belief?

Buchanan and Dogramaci assume that we have. They assume that the reduction of credence to belief succeeds as long as we can translate credence talk into belief talk. But what if the relevant belief talk can only be understood in terms of credence?

I've granted that 'S gives credence x to p' is equivalent to 'S believes that the probability of p is x'. But what is it to believe that the probability of p is x? What kind of state is this? It's not an ordinary belief. Ordinary beliefs represent the world as being one way or another. This one doesn't. What if the state we attribute with 'S believes that the probability of p is x' can only be understood with the concept of credence?

I have two more complaints.

Remember that 'credence' has a well-established use in decision theory and Bayesian epistemology. The question is whether we can analyse this concept in terms of ungraded belief. A positive answer would lead to a strange view.

Ungraded beliefs play no role in Bayesian decision theory. What an agent should do is a matter of their credences and utilities. If these credences are a sub-class of beliefs (namely, beliefs about probability), we get a picture on which only these beliefs (beliefs about probability) figure in the explanation of rational behaviour; beliefs that are not about probability are idle wheels in an agent's cognitive architecture. This looks unappealing. But if we give other ungraded beliefs a role in decision theory, we have to rework decision theory; the beliefs-about-probability won't play the standard decision-theoretic role of credence. That is, the concept of credence that will be reduced to that of belief won't be the concept we find in standard decision theory.

My last complaint. Credence functions assign numbers to propositions, but what they represent – an agent's credal state – isn't essentially numerical. That we measure credal states with numbers between 0 and 1 is obviously a matter of convention. We could just as well use numbers from 0 to 100. We could also use a non-probabilistic representation; for many purposes, log-probabilities (or negative log-probabilities) are actually more convenient than probabilities. In any case, all these numerical representations measure something that isn't intrinsically numerical. What is that something?

An attractive idea is that credence functions measure comparative confidence (much as utility functions measure comparative desire). This approach is nicely defended in another new paper, "Bowen 2026. Here we take as given a relation of "more confident than". If this relation satisfies certain formal constraints, it is representable by a unique probability measure, which we call the agent's 'credence'. Personally, I think we need to say more about what "more confident than" means, ultimately bringing in dispositions to act. But never mind those details. The point is that this whole idea makes no sense if credences are beliefs about probability. The theory of measurement explains how certain qualitative, relational facts can be represented by numerical functions. It doesn't explain how such facts could be represented by ungraded beliefs about a numerical function.

So no, credences are not beliefs about probability.

Blumberg, Kyle, and John Hawthorne. 2022. “Desire.” Philosophers’ Imprint 22 (0). "https://doi.org/10.3998/phimp.2116.

Bowen, Miriam Khodadadeh. 2026. “What Are Degrees of Belief? A Defence of Comparativism.” Synthese 208 (3): 107. "https://doi.org/10.1007/s11229-026-05731-6.

Buchanan, Ray, and Sinan Dogramaci. 2026. “Belief About Probability.” Journal of Philosophy, forthcoming.

MacFarlane, John Gordon. 2014. Assessment Sensitivity: Relative Truth and Its Applications. Oxford University Press.

Moon, Andrew, and Elizabeth Jackson. 2020. “Credence: A Belief-First Approach.” Canadian Journal of Philosophy 50 (5): 652–69. "https://doi.org/10.1017/can.2020.9.

Phillips-Brown, Milo. 2021. “What Does Decision Theory Have to Do with Wanting?” Mind 130 (518): 413–37. "https://doi.org/10.1093/mind/fzaa057.

Schwarz, Wolfgang. 2025. “Dynamic Rationality and Disproportionate Belief.” Philosophers’ Imprint 25: 1–17.

Stalnaker, Robert. 2014. Context. Oxford: Oxford University Press.

Yalcin, Seth. 2007. “Epistemic Modals.” Mind 116 (464): 983–1026.

Neg-raising through question-raising?

Wed, 26 Aug 2026 11:33:40 +0000

"Neg-raising" occurs when a negation that appears to have wide scope (over some operator) is interpreted as having narrow scope. For example, (1) conveys not only the absence of a belief that pizza is available (as one might expect), but also the presence of a belief that pizza is unavailable.

(1)I don't think there's any pizza.

There is a large literature on this phenomenon, with many competing explanations. Foolishly, I've tried to contribute to this literature with a "new proposal.

My proposal is that neg-raising is an instance of a more general phenomenon whereby negative utterances are interpreted as conveying positive information. (2), for example, tends to convey not only that Jack didn't sing Hey Jude, but also that Jack sang something else – especially if Hey Jude has intonational focus.

(2)Jack didn't sing Hey Jude.

The effect in (2) is somewhat less well-studied, but one can find some promising conjectures. For example, "Rooth 1996, 293–95, "Beaver and Clark 2008, 45–49, and "Simons et al. 2010, 318 suggest that it arises because (2) is taken to address the question ("qud") what did Jack sing?, which presupposes that there's something that Jack sang. This pragmatic presupposition, combined with the literal meaning of (2), entails that Jack sang something other than Hey Jude.

Suppose this is the correct account of (2). Can it be extended to (1)? Arguably, yes. The idea is that (1) is taken to address the question what I think about the availability of pizza. The question presupposes that I have an opinion on this issue: either I think that pizza is available or that it is not. This presupposition, combined with the literal meaning of (1), entails that I think that pizza is unavailable.

If this explanation is on the right track, the neg-raising interpretation of ¬φ(p) as φ(¬p) arises iff ¬φ(p) is assumed to address a question of the form "which p is such that φ(p)?", in which φ is held fixed and the complement p is varied. Can we test this? My sense is that theories of discourse structure in the tradition of "Roberts 1996, "Rooth 1996, and "Beaver and Clark 2008 don't allow us to directly inspect the addressed question, but one can find good indirect evidence.

For example, focus marking gives a strong hint: focussed constituents generally aren't held fixed in the addressed question. On the proposed account, the neg-raising effect should therefore depend on whether the relevant predicate (e.g., "think") is focussed. This prediction seems correct.

We would also expect that comparatively weak and inconspicuous predicates are more likely to trigger neg-raising than strong and conspicuous predicates. For example, (3) doesn't convey that Jack sang a song other than Hey Jude because the unusual predicate (although more or less equivalent to "sing") draws attention to itself: the speaker plausibly wants to elaborate on how Jack moved his lips; this is varied in the qud.

(3)Jack didn't move his lips in a way that could be recognized as singing Hey Jude.

By the same reasoning, we can explain why (4) doesn't trigger neg-raising: when a speaker uses "100% sure", they want to elaborate on the strength of their belief, which is varied in the qud.

(4)I'm not 100% sure that there is pizza.

So the proposal looks promising. Fleshing it out requires some care. For example, one might assume that the question addressed by (5) is what I think we'll have for dinner: pizza or pasta or curry or …

(5)I don't think we'll have pizza for dinner.

But then (5) would convey that there's a specific dish other than pizza that I think we'll have for dinner, which it doesn't.

It's also not entirely clear how the proposal deals with quantified cases like (6).

(6)Nobody thinks we'll have pizza for dinner.

In both cases, though, there are plausible solutions, as I explain in my paper. I also suggest that my proposal has a good chance of explaining the limited cyclicity of neg-raising and the licensing of certain negative polarity items that much of the linguistics literature has focussed on.

But I'm not a linguist, and I'm not sure how these details should be worked out.

That's why I was foolish to embark on this project. I've submitted my manuscript to Semantics & Pragmatics and (in a heavily revised form) to Meaning; the response has been polite, but uniformly negative. Linguists want to see a concrete mechanism, not a hand-wavy story. All I have is a hand-wavy story. The story still seems plausible to me. I hope one day somebody will pick it up.

Beaver, David I., and Brady Z. Clark. 2008. Sense and Sensitivity: How Focus Determines Meaning. John Wiley & Sons.

Roberts, Craige. 1996. “Information Structure in Discourse: Toward a Unified Theory of Formal Pragmatics.” Ohio State University Working Papers in Linguistics 49: 91–136.

Rooth, Mats. 1996. “Focus.” In The Handbook of Contemporary Semantic Theory, edited by Shalom Lappin. Oxford: Blackwell.

Simons, Mandy, Judith Tonhauser, David Beaver, and Craige Roberts. 2010. “What Projects and Why.” Semantics and Linguistic Theory, 309–27. "https://doi.org/10.3765/salt.v20i0.2584.

Moral fictionalism, cooperation, and motivation

Tue, 18 Aug 2026 13:16:33 +0000

"Gerritsen 2023 raises a good worry about revolutionary moral fictionalism, as advocated in "Joyce 2001.

The (revolutionary moral) fictionalist says that our naive moral practice rests on the mistaken assumption that there are mind-independent moral facts. There are no such facts. But this doesn't mean that we should stop caring about morality. It is in our personal interest, according to the fictionalist, to adopt a fiction of morality and continue talking and acting much like before.

Gerritsen points out that there is no good reason to think that the moral fiction that best serves our personal interest would resemble our pre-revolutionary moral beliefs. In particular, it is hard to see how giving moral status to non-human animals or future generations could promote our personal interests.

This seems right. And the problem goes deeper.

Joyce asks what moral fiction we (as group) should adopt, to promote our personal interests. Gerritsen grants that this is the right question. But it isn't.

Compare a Prisoner's Dilemma – one-shot, with purely selfish players. The collective choice that would be best for the group of both players would, obviously, be cooperation. In the original scenario, this means keeping silent and getting a mild prison sentence. That would yield the best total (and average) utility for the two players. But it doesn't follow that each player, individually, should cooperate. In a Prisoner's Dilemma, each player does better by defecting.

So we have to distinguish between the collective action that would best promote the interests of everyone (in some group) and the individual action that would best promote the interest of a given individual (in the group).

The choices we actually face are individual choices. I can't decide what moral fiction you will adopt. I can only decide what I will do. So the practically relevant question isn't what moral fiction we should adopt, but what moral fiction I should adopt, and maybe also what moral fiction I should publicly support, if I have reason to think that this may influence the choice of others.

But if we ask what moral fiction best serves my personal interests (when adopted by me), it's not just non-human animals and future generations that seem to drop out of the picture. Other people in my community share the same fate. The moral fiction that best serves my interests is one according to which I am the ultimate location of moral value: something is good iff it serves me.

If that's right, revolutionary moral fictionalism is even more revolutionary than Gerritsen suggests. It would call for a dramatic change to the content of our moral attitudes.

Not only that. The resulting change would make us all worse off. Morality requires caring about others. The Prisoner's Dilemma illustrates that a community in which people care about each other often fares better than a community in which everyone only cares about themselves. It's better for everyone if there are norms against cheating, free-riding and promise-breaking, even though everyone would be better off if they alone broke those norms.

One might respond that this is only a theoretical problem. Some have argued that in ordinary interactions, cooperative behaviour happens to be in our personal interest – for example, because non-cooperative dispositions are detectable or would be remembered. I don't buy this.

One might also respond that a non-selfish moral fiction is somehow easier to adopt and live by than a selfish moral fiction – perhaps because advocating for a selfish moral fiction is against our interest and it's cognitively hard to live by one fiction while advocating for a different fiction. I don't buy that either.

There's a better response, but it points to a deeper problem with fictionalism.

The better response is that it's not the business of fictionalism to prescribe what we should desire. The fictionalist recommendation is that we should adopt whatever fiction best furthers our desires, whatever these may be. And our desires aren't just selfish. I care about other people, and animals, and future people. I desire that they do well and aren't subject to wanton cruelty. The moral fiction that best furthers these desires won't be selfish; it may well attribute moral value to the well-being of others.

(This would also help with Gerritsen's worry.)

But wait. We need to know why I care about other creatures. After all, I believe that they have moral value. Perhaps my desire for their well-being is grounded in this belief, which the fictionalist wants me to drop (and replace by a fictionalist quasi-belief). If so, we can't hold that desire fixed: it rests on a mistake.

So, do my cooperative desires rest on my moral beliefs? This is a vexed question. The question is especially difficult for the fictionalist, as they are committed to the following two claims.

Moral beliefs are genuine beliefs with a peculiar subject matter. They aren't desire-like attitudes in disguise. This distinguishes fictionalism from expressivism.
Moral beliefs motivate: they affect our desire-like states. Otherwise nothing would be lost (practically speaking) if we simply drop our moral beliefs.

The simplest way to make sense of these claims is to assume that we all have an innate and unchangeable desire to bring about whatever is "morally good", where moral goodness is a peculiar unobservable (and "non-natural") property.

One can imagine agents like this. They resemble people with a deep desire that God's commands are obeyed, whatever these might be: if they believe that God commands fasting on Fridays, they fast and get outraged at anyone who doesn't; if they come to believe that God actually requires eating pretzels on Fridays, they eat pretzels and chastise anyone who doesn't. Agents like this would be "moral fetishists", as described in "Smith 1994.

Most of us aren't moral fetishists. Our moral beliefs are more intimately entangled with our desires and reactive attitudes. When I watch a movie about factory farming, I want this practice to be stopped, but not because I think that it lacks a peculiar non-natural property whose presence I desire.

The fictionalist needs an account of how our desires can be divided into those that rest on our (mistaken) moral beliefs and those that don't. I don't see how this can be done.

Gerritsen, Eline. 2023. “The Second Revolution of Moral Fictionalism.” Ergo an Open Access Journal of Philosophy 9 (0). "https://doi.org/10.3998/ergo.2276.

Joyce, Richard. 2001. The Myth of Morality. Cambridge University Press.

Smith, Michael. 1994. The Moral Problem. Oxford: Blackwell.

Logical omniscience: beyond fragmentation and impossible worlds

Fri, 31 Jul 2026 13:38:25 +0000

Standard Bayesianism assumes that agents are "logically omniscient": they assign credence 1 to all necessary truths. This seems wrong.

But we need to be clear about the data (as Stalnaker has emphasized, for example in "1991 and "1999). It's not a datum that we don't give credence 1 to all necessary truths. "Credence" is a theoretical term. The data that cast doubt on logical omniscience are things like this:

I utter "I don't know the 12th digit of pi".
I utter "I'm more confident that the 12th digit of pi is greater than 3 than that it's smaller".
I complain that the cashier gave me the wrong change when in fact I miscounted.
I make a stupid move in a chess game.

The attitude reports may seem decisive: if "I don't know the 12th digit of pi" is true, then surely any theory according to which I know (or I'm sure about) the 12th digit of pi is false!

But that's too quick. The mechanics of attitude reports is complicated and misleading. In particular, attitude reports can be metalinguistic. (See "Mates 1950.) I might say, "I don't know if it's warmer than 50 degrees Fahrenheit", even though I'm walking around in a T-shirt. What I'm unsure about isn't really the temperature: I'm confident that it's more than 10 degrees Celsius (=50 degrees Fahrenheit). What I'm unsure about are the conventions for the Fahrenheit scale; I don't know what temperature is picked out by "50 degrees Fahrenheit".

Let p be the hypothesis about the world that's expressed by "it's warmer than 50 degrees Fahrenheit". The same hypothesis is expressed by "it's warmer than 10 degrees Celsius". I know that this hypothesis is true. But I don't know that it's expressed by "it's warmer than 50 degrees Fahrenheit". And oddly, I can express this by saying "I don't know that it's warmer than 50 degrees Fahrenheit".

Some apparent failures of logical omniscience can be explained away in this fashion. If I don't know what "dodecahedron" means, I might say "I don't know if a dodecahedron has 12 faces", even though it's a necessary truth that a dodecahedron has 12 faces. My apparent ignorance of a necessary truth is really ignorance of a contingent truth about words.

But this isn't the whole story. Many apparent failures of logical omniscience have a different character. These are the hard cases. They all have the puzzling feature that there's a sense in which I actually know the necessary truths of which I'm ignorant.

A maths example. An integer is divisible by 3 iff the sum of its decimal digits is divisible by 3. I recently explained why this is true to my 10-year-old daughter, starting with an arbitrary two-digit integer, ab: We know that this means a*10 + b. And a*10 = a*9 + a. So ab = a*9 + (a + b). Obviously, a*9 is always divisible by 3. So if we divide a*9 + (a + b) by 3, we get the same remainder as if we just divide a+b.

Nowhere in this explanation did I give her any genuinely new information, and not just because what I said is necessarily true. Even re-interpreted metalinguistically, my daughter already knew everything I told her. At no point could she have said "oh, I didn't know that". My explanation only helped her make explicit what she knew all along.

A chess example might be clearer, because there's no need to invoke the metalinguistic reinterpretation.

I'm a poor chess player. Suppose I make a move that allows my opponent to checkmate me in two moves. I didn't see that coming: I didn't know that if I make this move, I can be checkmated in two moves. But why not? You could have explained to me: "If you make this move, your opponent can move their bishop here; then you have to do either A or B; in the first case, they can checkmate you by doing X; in the second case, they can checkmate you by doing Y." None of this would be news to me. I certainly knew that they could move their bishop to the relevant place. And so on. Your explanation helps me see what I knew all along.

Intuitively, it's clear what's going on in cases like these. The subject has all the required information. But they haven't "put it together"; they haven't converted it into the form that's needed to act on it, verbally or nonverbally.

To understand this kind of failure, we need a model of how agents store and retrieve information, and how this affects their choices. That's the heart of the problem of logical (non-)omniscience. Discussions of the problem often ignore it.

Many authors rest content with modelling the surface data. They try to come up with formal revisions of Bayesianism that allow assigning nontrivial probabilities to necessary truths, perhaps by allowing for "impossible worlds". I don't find this terribly helpful. When I didn't realize that my chess move leads to an easy checkmate, did I assign positive credence to an impossible situation in which my move was safe? What kind of situation would this be? Is it a situation where my opponent can't move their bishop? Or where that isn't a threat to which I have to respond with A or B? And so on. No answer looks plausible. And no answer reflects that fact that my problem is one of access, not ignorance.

Fragmentation models of logical nonomniscience, going back to "Lewis 1982, look more promising. These models are inspired by the idea that the subject in a hard case of logical nonomniscience fails to "put together" all the information they have. The information is stored in different "fragments" of their cognitive system. But that's still a crude simplification. In a typical example, the subject is perfectly able to put together two or three of the relevant facts, and to act on the result, but they fail to put together seven or eight pieces of information. The fragmentation models I know of don't account for that.

In general, the problem isn't just about combining pieces of information. It's about retrieving information that's needed in a specific format from a database that stores swaths of information in a variety of formats. This may fail for all sorts of reasons. Conversion between formats may be too hard. The relevant part of the database may be poorly indexed. Or whatever.

One challenge here is to find a good level of abstraction. Standard Bayesianism assumes that everything is instantly accessible. A more realistic model would drop this assumption, ideally without committing to details about the agent's cognitive architecture. (We shouldn't assume, for example, that information is stored in sentential form.)

It's not obvious if this challenge can be met. Sometimes tricky data can be accommodated by tweaking our models. But sometimes the data reflect "lower-level" facts that have no simple, systematic characterisation at the level we've interested in.

Lewis, David. 1982. “Logic for Equivocators.” Noûs 16: 431–41.

Mates, Benson. 1950. “Synonymity.” University of California Publications in Philosophy 25: 201–26.

Stalnaker, Robert. 1991. “The Problem of Logical Omniscience, I.” Synthese 89 (3): 425–40. "https://doi.org/10.1007/BF00413506.

Stalnaker, Robert. 1999. “The Problem of Logical Omniscience II.” In Context and Content, 255–73. Oxford: Oxford University Press.