Is It Okay for Nihilists to Doublethink?

Edison Yi
21 min readApr 10, 2021

Abstract:

In the novel 1984, ‘doublethink’ refers to the simultaneous possession of two contradictory beliefs. In this essay, I argue that given certain patterns of credences, a kind of doublethink is expected and rationally permissible. Specifically, I argue that some nihilists can be expected to retain their substantive moral beliefs and that doing so is rationally permissible. This is possible because belief is question-sensitive. As Holguín (2020) argues, we always believe things relative to questions. Such a question-sensitive account is desirable because it can account for the rational permissibility of certain sets of seemingly contradictory beliefs. A question-sensitive account of belief can predict and allow doublethink by incorporating two features of questions. Modelled as partitions, different questions partition the same possibilities in different ways. Departing from Holguín’s account, I argue that questions properly ignore certain possibilities, restricting the set of admissible answers. I will show that, given these principles, nihilists can have substantive normative beliefs as long as their credence satisfy certain requirements. Life after nihilism need not be bleak.

1. Introduction

Nihilism is the view that nothing matters. More precisely, it is the view that nothing has value, and there is no reason to do, want, or feel anything (Kahane, 2017). This entails the view that all evaluative propositions are false. What will happen if you come to believe in nihilism? A tempting view says that if I believe that all evaluative propositions are false, I will lose my belief in any evaluative proposition[1]. After all, unless people failed to notice the incompatibility of their beliefs, they typically seem to try to resolve inconsistent beliefs by dropping at least one of them. This, according to Kahane (2017), means that nihilism has scary consequences. If I start believing that nothing has value, then I will likely stop believing that anything has value, and I will thereby stop caring about everything.

I will argue that, contrary to Kahane’s assumption, we often expect people to have beliefs that are prima facie contradictory. In particular, it is not unusual for us to have beliefs of the form P and have some other belief that implies ¬P. Additionally, we don’t ordinarily consider this rationally impermissible. Applying this general observation to nihilism, I will draw the descriptive conclusion that 1) for nihilists with sets of credences that fulfill certain conditions, we should expect them to believe that nihilism is true and continue to believe in ordinary evaluative propositions such as ‘torturing penguins is wrong’. Further, I will argue that 2) believing in nihilism while possessing substantive evaluative belief is rationally permissible given certain sets of credences. In short, people doublethink, and that’s okay. To argue for this, I will appeal to a highly plausible question-sensitive account of belief (Holguín 2020), which posits that belief is a three-place relation between a subject, a proposition, and a question. According to this account, ‘Belief’ will denote different attitudes depending on the questions supplied by the context. The belief that is rational and expected for someone to have relative to a question is determined by her credences.

The notion of credence, or degrees of belief, is easily neglected in discussing what happens after we come to believe in something. But it is a critical mistake. I can be more or less confident in a belief. How confident I am in nihilism surely influences what happens after I come to believe in nihilism. It is also plausible that it should influence what patterns of belief revision are rationally permissible for me.

Section 2 of the essay introduces the question-sensitive account of belief developed by Holguín (2020). Section 3 applies the account to unconfident nihilists whose credence in nihilism falls short of 50% and shows that they are counterexamples to the tempting view that if you come to believe in nihilism, you will lose all of your evaluative beliefs. Section 4 introduces an amendment to Holguín’s account which allows questions to properly ignore certain possibilities. It continues to show that, given these amendments, any nihilist whose credence in nihilism is under 100%, even if the credence was 99.9%, can still, in principle, be expected to believe in evaluative propositions that directly contradict nihilism. Moreover, it is rationally permissible for them to hold these beliefs.

2. Belief is Question-Sensitive

On Holguín’s (2020) view, thinking that p is a relation between an agent S, a proposition p, and a question Q. To think that p is to guess that p is the answer to the question at hand, and that to think that p rationally is for one’s guess to that question to be (in a certain sense) non-arbitrary. I will follow Holguín in treating the meanings of questions as partitions, where a partition is a set of mutually exclusive and exhaustive propositions. So thinking is always relative to a partition Q.

As Holguín (2020) and Rothschild (2019) argued, there is good evidence that thinking is just believing. That is to say, ‘think’ and ‘believe’ semantically express the same attitude. Why think this? Because if they expressed different attitudes, then there should be cases where thinking and believing comes apart. Yet, it is very difficult, if not impossible, to think of such cases. For example, it is difficult to recover coherent readings of the following sentences:

a. I believe Covid-19 will cause a recession, but I don’t think that it will cause a recession.

b. Adrian thinks that Wang will like the present, but he doesn’t believe that Wang will like it.

c. Kate thinks that Mac can cook, but MaryAnn believes that Mac can cook.

In contrast, we can easily find coherent sentences where ‘believe’ comes apart with ‘is sure’. For example:

d. I believe Covid-19 will cause a recession, but I am not sure that it will cause a recession.

If we deny thinking is believing, we need an explanation for why (a) through © sound incoherent. Lacking such an explanation, we have strong evidence that thinking is believing. In the rest of the essay, I will assume that thinking is believing, and that Holguín’s account is true for belief as well as thinking just as he claims. If it turns out that thinking isn’t believing and that something akin to Holguín’s view is true for the former but not the latter, I think my arguments, properly rephrased in terms of ‘thinking’, will still have shown that it can be rationally permissible and expected to think that nihilism is true while also thinking that many positive evaluative claims are true.

To see why Holguín’s view is attractive, we will start by observing that belief is extremely weak (Hawthorne et al, 2016). One can rationally believe p despite the probability that p being arbitrarily close to zero given one’s evidence. Consider the following case:

Suppose there is a lottery with 100 tickets. You know that Amia has purchased 45 tickets, and the rest of the tickets are evenly distributed among 55 people. Question: Who do you think will win the lottery?

It would be completely reasonable for you to answer ‘I believe Amia will win the lottery’. You know that Amia is 45 times more likely to win the lottery than anyone else. Of course, it is also reasonable to say ‘I am not sure’. But the rationally permissibility of suspending belief doesn’t rule out the rational permissibility of believing that Amia will win the lottery.

This kind of case can be generalized such that Amia’s probability of winning is arbitrarily close to 0. There may be a lottery of 1 trillion tickets where Amia has 10 billion tickets and the rest of the tickets are evenly distributed among 990 billion people. In response to the question ‘who do you think will win?’, the answer ‘I think Amia will win’ seems unproblematic, despite Amia only having a 1% probability of winning.

Seeing that belief is extremely weak helps us resolve the initial incredulous reaction to the claim that we can believe p while believing something that implies ¬p. Many people have the intuition that believing a proposition entails having a credence of over 50% in it (which the extremely weak account of belief denies). If this is so, then believing p while believing something that implies ¬p necessarily involves having an inconsistent set of credences. But since belief is extremely weak, this is not the case. A virtue of Holguín’s view is that it explains why belief is extremely weak[2].

Before we spell out Holguín’s view in more detail, it is helpful to put the following case on the table:

Election: Suppose you are concerned with the 2020 US presidential election. Your respective credences for Trump, Sanders, and Biden winning are 40%, 35%, and 25%. These credences are well supported by your evidence. It follows that your respective credences for Trump winning and losing are 40% and 60%.

On your way to work, a stranger asks you: Who do you think will win?

A perfectly respectable answer is: I believe Trump will win.

During lunch break, your colleague asks you: Do you think Trump will win?

A perfectly respectable answer is: No, I believe one of the other candidates will win.

These answers seem perfectly felicitous. They sound like belief-reports that could be true without the person making them having to be irrational. In either conversation, it doesn’t seem reasonable to accuse you of falsely reporting beliefs that you don’t have. Nor does it seem fair to accuse you of being irrational in making either response since your reported beliefs seem to have a reasonable basis in your credences.

How could it be that you are permitted to have seemingly contradictory beliefs? If we take your reports at face value, you believe that Trump will win. However, prima facie, it seems that if you believe that a Democrat will win, then you don’t believe that Trump will win. But it can’t be the case that you simultaneously believe that Trump will win and don’t believe that Trump will win! That’s an outright contradiction. As Holguín shows, a good way to explain away this contradiction is by positing that belief is question-sensitive. Let Trump, Sanders, and Biden be the propositions that Trump, Sanders, and Biden will win the 2020 election respectively. In the first context, the relevant question (partition) is {Trump, Sanders, Biden}, where your credence for Trump is highest. In the second context, the relevant question is {Trump, ¬Trump}, where your credence for ¬Trump is highest. Under Holguín’s account, instead of you making contradictory reports of the same belief relation, you are reporting two distinct belief relations, belief{Trump, Sanders, Biden} and belief{Trump, ¬Trump}. You believe{Trump, Sanders, Biden} that Trump will win, and you don’t believe{Trump, ¬Trump} that Trump will win. There is no contradiction.

To explain why it seems permissible for you to believe{Trump, Sanders, Biden} that Trump will win, and believe{Trump, ¬Trump} that Trump won’t win, Holguín posits the following normative constraint for what you are rationally permitted to believe:

NORMATIVE BEST GUESS: An agent S is rationally permitted to believeQ that p just in case: the conjunction of all the evidence available to S and S’s best guess to the question Q? entails p.

For our purposes, a best guess can be defined as a proposition in the partition for which your credence is no lower than any other proposition in the partition[3]. In the first context, since the question supplied by the context is {Trump, Sanders, Biden} and your best guess to this question is Trump, it is rationally permitted for you to believe Trump, explaining why your reported belief didn’t seem objectionable. In contrast, Sanders and Biden are not your best guess in the first context, neither is Trump in the second context, which explains why the corresponding assertions wouldn’t felicitous.

On some views, such as Holguín’s (2020), one’s beliefs don’t supervene on one’s credence. What one believes is a matter of choice, while the person’s credence merely determines what is rationally permissible for one to believe. In virtue of this element of choice, people won’t always conform to normative best guess. Nonetheless, we can make a descriptive observation:

DESCRIPTIVE BEST GUESS: An agent S normally believesQ that p if and only if: the conjunction of all the evidence available to S and S’s best guess to the question Q? entails p.

This seems highly plausible. If we know that Tim’s respective credences for Trump, Sanders, and Biden winning are like yours and Tim is asked the aforementioned questions, we expect him to give the answers that are rationally permissible according to normative best guess, as a matter of empirical knowledge. If Tim were to give different answers, you would likely be justified to draw the conclusion that you got his credences wrong. This seems to be because humans are by and large rational in these matters. Of course, there are irrational people and even rational people don’t always conform to normative best guess, but my claim is only that we expect descriptive best guess to be true in general.

Call the phenomenon of having a beliefQ1 that p relative to a question where p implies q and a beliefQ2 that ¬q relative to a different question doublethink. It follows from descriptive best guess that it is normal to doublethink when there exists a partition Q? with at least three member propositions which includes p and S’ credence in p is no lower than any other member proposition but lower than 50%.

3. Doublethink for Weak Nihilists

Now we can return to nihilism. One implication of descriptive best guess follows straight away. One can believe in nihilism relative to one question but believe evaluative propositions relative to another question. Take the following case:

Weak nihilism: Consider George, who has credences 40%, 35%, and 25% for nihilism, moral realism, and moral non-cognitivism respectively. George also thinks that even if moral non-cognitivism is true, there are still true and false moral claims (Blackburn 1984, 1998). When it comes to penguins, George has overwhelmingly strong evidence that if moral realism or moral non-cognitivism is true (or if nihilism is false), then it is wrong to torture penguins. What does George believe?

If nihilism, moral realism, and Blackburn’s brand of moral non-cognitivism aren’t mutually exclusive, then suppose our agent assigns a credence of 0% to any alternative view. So we can have the following two questions (partitions): {nihilism, moral realism, moral non-cognitivism} and {nihilism, ¬nihilism}. In plain English:

Question 1: Which meta-ethical theory do you think is true?

Question 2: Do you think that nihilism is true?

This case is analogous to the 2020 election case. The most relevant partition for question one seems to be {nihilism, moral realism, moral non-cognitivism } and the most relevant partition for question 2 seems to be {nihilism, ¬nihilism}. Descriptive best guess predicts that George will believe{nihilism, moral realism, moral non-cognitivism } that nihilism is true and therefore nothing matters, but believe{nihilism, ¬nihilism} that nihilism is false and therefore it is not the case that nothing matters. Further, since we expect George to believe{nihilism, ¬nihilism} that nihilism is false, and George’s total evidence in conjunction with his best guess to {nihilism, ¬nihilism} entails that torturing penguins is wrong by hypothesis, we also expect him to believe{nihilism, ¬nihilism} that torturing penguins is wrong.

We now have a counterexample to the tempting view that if I believe in nihilism, I will lose my belief in any given evaluative proposition. Note the plausibility of this counterexample doesn’t need rely exclusively on the truth of Holguín’s question-sensitive account of belief. We find it plausible that there can be doublethink in the election case. People who think that we doublethink in the election case but not the nihilism case owes us an explanation of why these two cases are disanalogous. What Holguín’s view does is it gives us an account that explains and vindicates our intuitions about these cases.

The reader may wonder at this point whether we should just abandon talk of beliefs? If we only talk of credences, couldn’t we avoid this confusing situation where people may simultaneously believe that p and ¬p? Alas, no, because as I mentioned previously, your beliefs aren’t always determined by your credences. Contrast the following case.

If you were asked to bet on the winner of the 2020 election, assuming the aforementioned credences, you will likely bet on Trump. This seems true because you believe that Trump will win. However, another person, call him Tom, could quite plausibly share your credence but believe that Sanders will win due to wishful thinking. Tom likelihood of betting on Sanders will likely be higher than yours. This is explained by differences between Tom and Sam’s beliefs, but not differences between their credences. Under Holguín’s account of beliefs, what one believes is, quite literally, a choice. It may be reasonable to expect people to believe what is, in fact, their best guess most of the time. But in cases where people fail to be rational, one can believe something that he doesn’t have the highest credence in. Crucially, in these cases, we expect one’s beliefs, not credences, to drive one’s actions. Because of this closer covariance with behaviour, it is important to not just abandon ‘belief’ in favour of ‘credence’.

4. Doublethink for Serious Nihilists

However, there is a serious objection that one can make on behalf of Kahane. I’ve only shown that we can doublethink about nihilism given highly artificial sets of credences. In particular, for a person to doublethink about nihilism, it seems required that she has a credence of less than 50% in nihilism. But real life nihilists don’t have such credences. For one thing, if asked whether nihilism is true, many nihilists would happily say yes! Since the relevant partition here seems to be {nihilism, ¬nihilism}, it would follow from descriptive best guess that these nihilists have a credence of over 50% in nihilism. Call these nihilists serious nihilists.

I think we can still doublethink about p even if our credence in p is over 50%. However, to show this, we need to add an amendment to Holguín’s account.

4.1 Possibilities Properly Ignored

We need to allow the restriction of the set of possible worlds that are partitioned. Again, we are treating questions as partitions, where a partition is a set of mutually exclusive and exhaustive propositions. We will also treat a proposition as a set of possible worlds. Holguín treats questions as partitions of logical space. For every partition, the union of all member propositions includes all logically possible worlds, and the best guess is the member proposition in which you have the highest credence. However, it is not clear why we should partition over logical space, and there are reasons to think that the set of possible worlds over which questions partition should sometimes be restricted. We often ignore certain possibilities when we answer or ask questions due to the context we are in. The best guess to a question must be a possibility that is not properly ignored in the context. Once we have updated our account of rational belief to allow for proper ignorance, it can be shown that the possibility of nihilism can be ignored even when your credence in it is over 50%. If this is right, then you can still believe that torturing penguins is wrong relative to some questions because the possibility of nihilism is properly ignored relative to these questions.

To see how context changes admissible answers to a question, consider:

Primary: Suppose I think it is somewhat likely that no one will win an outright majority in the 2020 Democratic Primary. My credence for no one winning is 40%, and my credence of Biden and Sanders winning a majority are 35% and 25% respectively.

Conversation:

Friend: Do you think someone will win a majority?

(a) Yes, I believe someone will win a majority.

Friend: Who do you think will win a majority?

(b) I believe Biden will win a majority.

?? © I believe no one will win a majority.

In this conversation, (b) seems appropriate but not © because the second question seems to presuppose that someone will win a majority, and I can’t object to this presupposition because, in asserting (a), I have already expressed a belief in the presupposition. So, when answering the second question, the possibility of no one winning a majority is properly ignored. If the second question were partitioning the logical space, my best guess would be that no one will win a majority. But clearly, in the context of the conversation, the appropriate response to the second question names either Biden or Sanders, even if my credence for no one winning a majority is higher than that of either candidate winning.

Since it is rationally permissible for me to answer ‘I believe Biden will win a majority’ in response to question (2) even when I have a higher credence no one winning a majority, normative best guess and descriptive best guess are false if conjoined with the claim that propositions in a partition must mutually exhaust all logically possibilities. Instead, we should adopt normative best guess and descriptive best guess in conjunction with the claim that propositions in a partition must mutually exhaust all possibilities that are not properly ignored by the question. To elaborate a bit more, for a question to ignore p is to restrict the set of possible worlds to a subset of ¬p. A partition ignores a possibility p if and only if the set of possible worlds denoted by the disjunction of all propositions in the partition is a subset of ¬p. In the example, Ignoring the possibility of no one winning is just to restrict the possible worlds we are considering to those where someone wins. Thus, the partition becomes {Sanders, Biden}. Since my best guess relative to this partition is Biden, we can explain why (b) is felicitous.

4.2 What to Ignore

If there are contexts in which nihilism is properly ignored for the serious nihilist relative to some question, then we have a way for even serious nihilists to believe evaluative propositions. To see whether there are such contexts, let’s first look at the ways in which contexts can rule out possibilities. It may, for example, do so with contextual presuppositions, as shown by the previous example with the Democratic Primary. When answering the second question, the possibility of no one winning a majority m is properly ignored in virtue of the fact that I have already expressed my belief in ¬m, or my belief that someone will win a majority, in the same conversation. This seems to be how contexts work in general. If in a context c, a subject s has expressed a belief in some proposition p, then s cannot answer ¬p to subsequent questions in the same context. In effect, the possibility of ¬p is properly ignored for all subsequent questions in the same context. Assuming that if I believe p, then there will always be contexts in which I can express that belief (after which ¬p can be properly ignored), we can formulate the general principle:

PRESUPPOSITION OF BELIEFS: if I believe P relative to some question x, then there are contexts in which my belief in ¬P is properly ignored relative to some question y.

4.3 Nihilism Properly Ignored

According to presupposition of beliefs, if we can show that even serious nihilists may believe ¬nihilism relative to some question, then this entails that there may be contexts where serious nihilists can properly ignore nihilism relative to some question and therefore hold substantive normative beliefs. Take the question: is it bad to torture penguins? An exhaustive partition is:

Q1 = {Torturing penguins is bad, torturing penguins is good, torturing penguins has zero value, torturing penguins is beyond good or bad (nihilism)}

If nihilism is properly ignored, the question becomes:

Q2 = {Torturing penguins is bad, torturing penguins is good, torturing penguins has zero value}

Relative to this question, even a serious nihilist would likely have the highest credence in torturing penguins being bad. Therefore, he can be expected to believe that torturing penguins is bad relative to this question, and it would be rationally permissible for him to have this belief.

How is it possible for serious nihilists to believe in ¬nihilism? It is possible because one’s credence in nihilism can be subdivided. Consider again the election case. Your credences for a Democrat and a Republican winning are 60% and 40% respectively. You believe that a republican will win relative to the partition {a democrat wins, a Republican wins}. Yet, there are two ways a democrat can win. Worlds in which a democrat wins can be subdivided into ones where Sanders and Biden win. You believe that a republican will win relative to the subdivided partition {Biden wins, Sanders wins, a Republican wins}.

A similar story might be true for nihilism. There are many ways in which nihilism may turn out to be true. As Kahane (2007) himself noted, an error theoretical argument being sound and valid is only one way in which nihilism might be true. What we need is to show that serious nihilists can have credences in multiple mutually exclusive ways in which nihilism can be true such that their credence in each is less than their credence in ¬nihilism (as illustrated in diagram 1).

Nihilistic possibility 1

20%

Nihilistic possibility 2

20%

Nihilistic possibility 3

20%

¬Nihilism

40%

Diagram 1: A set of credences such that someone can be both a serous nihilist and believe ¬nihilism relative to some questions

Moral error theoretical arguments are one way through which one can be convinced of nihilism. Error theorists argue that there are no moral values. If for something to matter is just for it to have moral value, then error theory entails that nothing matters. Error theory is often understood to involve a conceptual claim and an ontological claim (Isserow 2018). Conceptual claims from distinct error theoretical arguments are often true in different sets of words. For example, Olson (2014) claims that moral discourse is committed to irreducibly normative facts that favour certain actions and there are no such facts. Joyce (2001) claims that moral discourse is committed to the existence of categorical reasons and there is no such reason. Philosophers in the free will debate often claim that morality requires the existence of moral responsibility (Wolf 1981; Campbell 1957; Stace 1952). If moral responsibility requires free will and there is no free will, then there are no moral values. In addition, one may think that moral properties are necessarily non-natural properties, but moral non-natural properties don’t exist. Possible alternative conceptual claims that a nihilist can have credence in are boundless. You may have some credence in morality being conceptually committed to the existence of God while also having some credence in it being committed to the possibility of consensus of rational agents in ideal conditions. Indeed, a nihilist may have some credence in each of these claims. But these conceptual claims do not have to be true in exactly the same sets of worlds: categorical reasons need not be irreducibly normative; moral discourse may be committed to categorical reasons but not free will in some worlds.

Additionally, the same conceptual claim can be coupled with many mutually incompatible ontological claims to reach the error theoretic conclusion. Take the conceptual claim that morality requires the existence of non-natural properties. Given this claim, error theory would be true in worlds where only physical properties exist but also worlds where only physical and mathematical properties exist. You may have some credence in both possibilities.

If a nihilist has some credence in each of these error theoretical arguments, his credences may just be subdivisible enough to allow a belief in ¬nihilism relative to some question. Then, given presupposition of beliefs, there are questions that can properly ignore nihilism relative to which nihilists can believe that torturing penguins is bad. I suspect many nihilists will think that in worlds where nihilism is false, it’s bad to torture penguins.

5. Conclusion

I have tried to show that, given Holguín’s question-sensitive account of belief with an amendment that allows the restriction of the possibility space partitioned by questions, some nihilists can be expected to hold substantive evaluative beliefs and be rational in doing so. In the election case, we expect people with the given credences to think that no republican will win relative to some question but think that Trump will win relative to a distinct question. We also think it is rationally permissible to hold these beliefs. My claims for nihilists are analogous. We should expect nihilists with certain sets of credences to affirm nihilism relative to some questions but express substantive evaluative beliefs in other contexts. There is nothing rationally impermissible or inconsistent about this. Similar arguments to those given in this essay could also be given for moral error theory, epistemic error theory, and other views that deny the truth of a general class of propositions. Contrary to what we might have thought, doublethink is more widespread and rational than it may seem. Contrary to Kahane (2017)’s claim, nihilists are not in danger of losing all of their evaluative beliefs.

Mackie (1977) famously thought that first and second order ethical questions are orthogonal to each other. But this claim seemed really strange. If you believed that all moral propositions were false, how could you still hold first-order moral views? How could you continue to reason about first-order moral problems? If my arguments in this essay are successful, then we have a way of explaining how first and second order ethical questions can be orthogonal in a sense. First-order moral questions sometimes properly ignore some second-order possibilities such as nihilism or error theory. When an error theorist ponders moral questions, she is deliberating about what to believe relative to questions that presuppose non-nihilism. At the same time, we can explain the strangeness of Mackie’s claim. The strangeness originates from a conflation between belief and certainty (or one what one may call full belief). Under my account, if you were certain that all moral propositions were false, you would indeed likely drop your first-order moral views. Belief, however, is much messier than certainty.

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[1] More specifically, you will lose any positive, non-trivial evaluative belief.

[2] In addition, it also explains why belief is non-monotonic and closed under entailment while giving us an explanation of why counterexamples to closure are intuitively appealing.

[3] This is a simplification, as this definition only covers complete answers. A more complete definition of ‘best guess’ should also cover the rational permissibility of believing in partial answers to questions.

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Edison Yi

This blog contains a collection of satires, notes, and essays on philosophy, economics, etc. I’m a master’s student in Philosophy at Oxford.