# On the Probabilistic Problem for A Single-Meaning Account of ‘Ought’

A central distinction in “Thoughts About Oughts” (Episode 60) is that between epistemic and deontic uses of ‘ought.’ As a quick review, here’s an example of an epistemic use of ‘ought.’ Imagine that you open the window in the morning, feel a strong breeze and suffocating humidity, and see a massive, dark wall of clouds on the horizon. You declare to your roommate:

(Ep) It ought to rain today.

And for an example of a deontic use of ought: Imagine that you have a final exam tomorrow, which you need to pass in order to graduate. You’ve been invited to catch up with some friends at the bar. Your roommate, ever loyal, reminds you:

(Dn) You ought to stay in and rest tonight.

In (Ep), you’re expressing an expectation about how the world will be in the future, given what you know now (the current weather conditions, and what sort of weather tends to follow such conditions). In (Dn), your roommate is suggesting what the proper course of action is for you, given what your goals are.

These ought-statements seem to be doing quite different things: the epistemic use is concerned with how the world will be, given how things are now; the deontic use is concerned with what one should do, in order to achieve some goal. How should we understand the relationship between these uses of ‘ought?’ Cariani suggests in the episode that we should see ‘ought’ as sharing a single meaning in each case, accounting for the difference between the epistemic and deontic cases contextually: ‘ought’ has the same meaning in (Ep) and (Dn), the differences we sense have to do with other semantic (and perhaps non-semantic) factors surrounding the occurrence of ‘ought.’

Cariani, however, offers a couple of problems for the single-meaning view. One of these has to do with probability: when we recast what (Ep) and (Dn) using probabilistic language instead of ‘ought,’ we encounter two very different types of claims. But if the probabilistic analogues of (Ep) and (Dn) are expressing distinct things, and we arrive at these analogues by giving a rough analysis of ‘ought’ in each case (by substituting probabilistic language for ‘ought’ in each statement), this seems to suggest that ‘ought’ means something different in each case, against the single-meaning view. Here, I’d like to flesh out a bit more the ways in which the probabilistic analogues of (Ep) and (Dn) differ.

Let’s start with (Ep). As Cariani suggests, we might phrase the probabilistic analogue of (Ep) like this:

(ProbEp): It will probably rain today.

(Ep) and (ProbEp) seem to be closely related, because both make a prediction about how the weather will turn out in the future. This prediction is qualified by facts about the current weather conditions (humidity, strong wind, dark clouds on the horizon), and some general facts about weather patterns (rain tends to follow high humidity, strong wind, and dark clouds on the horizon). A slightly more rigorous formulation of (ProbEp) might go: Given the current weather conditions and general facts about weather patterns, it will probably rain today.

Let’s imagine that you tell your roommate (ProbEp) because she is trying to decide if she should bring an umbrella to work today. So the relevant possible outcomes are: 1. It rains today; 2. It does not rain today. We might model your reasoning in this way: you first assign a probability to each relevant possible outcome, given the current conditions—let’s say you assign a probability of .7 (70%) to ‘It rains today,’ and .3 (30%) to ‘It does not rain today.’ You then assert that the outcome with the greatest probability, ‘It rains today,’ is most likely to occur. In effect, when you assert (ProbEp), you’re asserting that a particular outcome (rain) is the most likely of a set of relevant possible outcomes, given current conditions.

Now let’s look at (Dn). If we were to recast (Dn) in the same way as (Ep), we would say something like: ‘You will probably stay in and rest tonight.’ But this clearly doesn’t capture your roommate’s meaning—she isn’t predicting an outcome, she’s informing you of what course of action you should undertake. To better capture (Dn) with probabilistic language, we might instead say:

(ProbDn): It is most likely that you will pass the exam if you stay in and rest tonight.

This seems to better capture your roommate’s meaning: she’s taking a particular outcome as fixed (your passing the exam), and making a claim about what course of action from a set of relevant possible courses of action is most likely to bring about this outcome. We might model her reasoning in this way: she assigns a probability to a fixed outcome (passing the exam) for each of a set of actions (staying in and resting, going out to the bar with friends). Let’s say she assigns a probability of .9 (90%) to your passing the test if you stay in, and a probability of .5 (50%) to your passing the test if you go to the bar. (ProbDn) expresses the conclusion of her assessment, that the course of action most likely to bring about the desired outcome is your staying in and resting tonight.

One way of capturing the difference between (ProbEp) and (ProbDn), and thereby the apparent difference between the meaning of ‘ought’ in (Ep) and (Dn), is by contrasting the reasoning processes modeled in each case. In the case of (ProbEp), we’re holding fixed a set of conditions, and assessing the probability of a set of outcomes given those conditions, in order to determine which outcome is more likely. In the case of (ProbDn), we’re holding fixed a particular outcome, and assessing the probability of that specific outcome over various conditions (your possible courses of action). In reasoning to (ProbEp), we’re varying the outcomes; in reasoning to (ProbDn), we’re varying the conditions.

Here’s a schematic illustration. In the reasoning process for (ProbEp), you are effectively assigning probabilities like this:

Pr(R|W)= .7

Pr(~R|W)= .3

Where ‘R’ stands for ‘It rains today,’ ‘W’ stands for the facts about the current weather conditions and general facts about weather patters, and ‘~’ for ‘not.’ We’d read the first line as: “The probability that it rains today given the current weather conditions and general facts about weather patterns is .7.” We’d read the second line as: “The probability that it does not rain today given the current weather conditions and general facts about weather patterns is .3.” Notice that what changes between the first and second lines is on the left-hand side of ‘|,’ the symbol for ‘given’—the outcome given certain conditions.

In the reasoning process for (ProbDn), your roommate is effectively assigning probabilities like this:

Pr(E|S)= .9

Pr(E|F)= .5

Where ‘E’ stands for ‘you pass the exam,’ ‘S’ stands for ‘you stay in and rest,’ and ‘F’ stands for ‘you go out to the bar with friends.’ Here, what changes between the first and second lines is to the right of ‘|’—the conditions under which we’re assessing the probability of an outcome. The outcome itself stays fixed, unlike in the reasoning process for (ProbEp).

The core difference between (ProbEp) and (ProbDn), then, can be cast in terms of what’s held fixed and what’s varied in the reasoning processes behind the statements: the outcomes are varied in the case of (ProbEp), while the conditions are held fixed; the conditions are varied in the case of (ProbDn), while the outcome is held fixed.

We can crystalize this difference through one of its consequences. In the reasoning process behind (ProbEp), it was no coincidence that the probabilities assigned to the possible outcomes added up to 1 (.7 for ‘It rains today,’ .3 for ‘It does not rain today’). These outcomes collectively exhausted logical space: it must either rain today or not, so the probability of ‘it will rain today or it will not rain today’ is 1. In general, when determining which of a set of possible outcomes is most likely, the sum of the probabilities assigned to each outcome will add up to 1, because the possible outcomes will collectively exhaust all the possibilities. (Though one of the outcomes may be a ‘catch-all’ like ‘something that I’m not currently considering happens.’)

In contrast, the probabilities assigned to each course of action in the reasoning process behind (ProbDn) do not add up to 1 (.9 for ‘passing the test if you stay in and rest,’ .5 for ‘passing the test if you go out to the bar with friends’). This was no coincidence, either. The statement: ‘you pass the exam after staying in and resting or you pass the exam after going out to the bar with friends’ does not exhaust logical space in the way ‘it rains today or it does not rain today’ does. (While we can say that it must either rain today or not rain today, we cannot say that you must either pass the exam if you stay in and rest or pass the exam if you go out to the bar with friends.) Assessing the probability of a set of possible outcomes given fixed conditions must yield a set of probabilities that add up to 1; assessing the probability of a fixed outcome over various conditions need not do so.

We’ve done some work to flesh out Cariani’s problem for the single-meaning account of epistemic and deontic ‘ought’s by showing how a probabilistic analysis of each use of ‘ought’ yields a different sort of claim. How might the proponent of the single-meaning account respond? Here are three general strategies:

1. Deny that the probabilistic analyses above adequately capture the meaning of ‘ought’ in the epistemic and deontic cases: while (ProbDn) and (ProbEp) say different things, we were mistaken to take these as analyses of ‘ought’ in (Dn) and (Ep), respectively.
2. Accept the analogy between (Ep) and (Dn) on the one hand, and (ProbEp) and (ProbDn) on the other, but try to explain the difference made explicit in the contrast in the case between (ProbEp) and (ProbDn) is really a contextual difference in the case of (Ep) and (Dn).
3. Bite the bullet, accept that epistemic and deontic uses of ‘ought’ have different meanings, but try to preserve our intuition that they are instances of the same word by showing how the epistemic and deontic uses are intimately related (unlike, say, the use of ‘bank’ to refer to the financial institution and the use of ‘bank’ to refer to the land alongside a river or stream).

Do you have thoughts for how to elaborate any of these three strategies, or an alternative response to the problem? Do you have any questions about the exposition of the problem? Comments and questions are welcome in the section below.

Phil Yaure

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