1. A limited norm

When considering Schiffer’s objection to the knowledge norm for action, Alexander Jackson (Reference Jackson2012) responds as follows (where ‘AKP’ is a variant of the knowledge norm KN):

AKP states “Treat the proposition that p as a reason for acting only if you know that p" (Jackson Reference Jackson2012, 354). Central to Jackson’s point is the claim that treating a proposition as a reason for action is closely linked to having a full belief. The observation Jackson makes is now very straightforward. In Schiffer’s case, the agent does not fully believe that it will rain. Rather, she merely has a 0.4 credence that it will rain. But if treating something as a reason for action requires fully believing the proposition in question, then the agent in Schiffer’s case does not treat the proposition that it will rain as a reason for action. There is then no counterexample to the knowledge norm. A counterexample of the desired kind would require a case in which the agent appropriately treats a proposition as a reason for action without knowing it. What we would have instead is a case in which the agent does not know the proposition and does not treat it as a reason for action.

On Jackson’s resolution, the knowledge norm for action is closely connected to, and possibly even derivable from, the knowledge norm for full belief (more on this in section 3). On this latter norm, one should fully believe a proposition p only if one knows p. It is instructive to note that there is no similar problem of uncertainty regarding the knowledge norm for full belief (Jackson Reference Jackson2012, 357). It is clear that credences (aka partial beliefs) are outside the scope of the knowledge norm for full belief. It would be a nonstarter to suggest that one should have a credence of 0.4 that it will rain only if one knows that it will rain. In a similar vein, one should hold, according to Jackson (Reference Jackson2012), that acting on uncertain propositions is outside of the scope of the knowledge norm for practical reasoning.

Crucial to Jackson’s point is the claim that treating a proposition as a reason for action requires full belief. But one may wonder what we are then doing when we decide to take an umbrella based on a 0.4 credence that it will rain. It still seems that our epistemic stance toward the proposition that it will rain is treated as counting in favor of taking an umbrella. So, at least prima facie, there seems to be a sense in which the proposition is treated as a reason for action.

I think there is an interesting ambiguity to be considered here. This ambiguity comes out very clearly in the variant of the knowledge norm for practical reasoning I wish to focus on in this paper. The phrase “relying on a proposition in one’s practical reasoning” can be understood in a narrow sense where it is meant to express fully relying on a proposition. If we make this reading explicit, we arrive at the following norm:

When one fully relies on a proposition, one treats the proposition as a fact. When treated as a fact (or as true), an agent evaluates her alternatives, as Ross and Schroeder (Reference Ross and Schroeder2014, 264) put it, “by the same procedure by which she would evaluate them conditional on p.” In other words, one does not reckon in one’s practical reasoning with the possibility that the relevant proposition might be false.

In contrast, one can, it seems, merely partially rely on a proposition in one’s reasoning. When one does so, one does not treat the proposition as a fact. In other words, one does reckon in one’s practical reasoning with the possibility that it might be false.

We could, of course, ask whether partial reliance is also governed by knowledge:

However, it seems clear that Schiffer’s case is a counterexample to this norm. In Schiffer’s case, it is plausible that the agent partially (but not fully) relies on the proposition that it will rain. And it is clear that the agent does not know that it will rain. So KNP is clearly false. Note, though, that this does not affect KNF, for in Schiffer’s case the agent does not fully rely on the proposition in question.

In what follows, I shall try to develop an account of partial reliance. On this account, partial reliance is a sui generis mental act. Some existing solutions to the problem of uncertainty can be seen as trying to account for partial reliance in terms of full reliance on a “partial” proposition, that is a proposition about chances (Hawthorne and Stanley Reference Hawthorne and Stanley2008) or possibilities (Weisberg Reference Weisberg2013), or a proposition which itself consists of probability spaces (Moss Reference Moss2018). Instead, the account I wish to develop qualifies the attitude rather than the content.

2. Partial reliance

In this section, I explain what an account of graded reliance is intended to deliver. I start with a brief explication of the notion of reliance. I will then describe the problem of coming up with a norm governing partial reliance.

According to Williamson (Reference Williamson2000, 99), relying on a proposition p is to use p as a premise in practical reasoning. Following Williamson, I shall therefore construe reliance as a mental act. On this construal, when one relies on p, one assigns p a certain role in an episode of practical reasoning. An act-sense of reliance contrasts with a state-sense of reliance as proposed by Facundo Alonso (Reference Alonso2014, 165). According to Alonso, reliance is a mental state similar in kind to a belief state. As I see it, these differences are largely terminological, for a state-sense of reliance seems to be derivable from an act-sense. One may say that one relies in the state-sense iff one is willing to rely in the act-sense under appropriate circumstances (see also section 3). On this way of setting things up, the state-sense of reliance relates to the act-sense similar to how a disposition relates to its manifestation. As a matter of fact, the state-sense of reliance may simply describe a disposition to rely in the act-sense of reliance under certain conditions.Footnote ⁹

The philosopher’s concept of relying on a proposition in one’s reasoning does not seem to be deeply rooted in natural language. Nevertheless, sentences such as “I relied on the information provided by the Guardian” or “The court relied on the fact that the defendant had access to the building” seem to express something which comes at least close to it. To the extent that the everyday concept of reliance informs the philosophical notion, it is interesting to observe that the everyday concept is gradable. One can say things like “I relied more on the information provided by the Guardian than on the information provided by the Sun.” In this case, what is expressed seems to be that the propositions communicated by the Guardian are treated by me as a better basis for further decision-making and reasoning than the propositions published in the Sun.

However, comparative talk about reliance can also trace the strength of reasons rather than their epistemic standing. For example, a statement to the effect that in a circumstantial case the court relied more on the fact that the defendant had blood on her hands than on the fact that she had motive can naturally be interpreted as saying that the court took the blood on her hands to be a stronger reason for conviction than the fact that she had motive. This can be so even when the two facts have the same epistemic standing from the standpoint of the court.

In the light of this flexibility, developing a concept of partial reliance is in my eyes best seen as a project of explication in the sense of Rudolf Carnap ([1950] Reference Carnap1962, chap. 1): one takes a concept used in natural language but shapes it further based on theoretical considerations. With respect to the notion of partial reliance, I shall therefore assume that it has some basis in natural language without presupposing that there is a perfect match. In particular, I shall ignore that ‘reliance’ in natural language sometimes traces the strength of reasons rather than their epistemic standing.

With this in mind, what can we say about full and partial reliance? Let us take the somewhat easier part of this question first. To fully rely on a proposition p in one’s practical reasoning can plausibly be taken to ignore ¬p-possibilities for the purposes of solving a decision problem. For instance, if I rely fully on the proposition that my lottery ticket lost, then I might decide to throw it away (cf. Hawthorne and Stanley Reference Hawthorne and Stanley2008, 572). I would not throw it away if I still reckoned with the possibility that it might have won. Full reliance thus requires a kind of practical certainty that the proposition in question is true.Footnote ¹⁰ Proponents of a knowledge norm think that knowledge provides the relevant standard for being practically certain. For instance, Brian Weatherson (Reference Weatherson, Brown and Gerken2012) argues that a possibility can be legitimately excluded from one’s decision-making iff one knows that it is not actual.Footnote ¹¹

The somewhat harder task is to say what it means to partially rely on a proposition in one’s reasoning. In contrast to full reliance, partial reliance on a proposition p means to take p into account while solving one’s decision problem without ignoring ¬p-possibilities.Footnote ¹² Since reliance is gradable, one can partially rely on p to a low, an intermediate, or a high degree. Relying on p to a high degree can plausibly be understood as putting a lot of weight on p in one’s decision-making while putting little weight on ¬p. Relying on p to an intermediate degree would mean putting roughly equal weight on p and on ¬p. And relying on p to a low degree would mean to putting little weight on p and a lot of weight on ¬p. Footnote ¹³

To illustrate, consider again the lottery example. Given the high likelihood of one’s ticket having lost, one would give this proposition a lot of weight in one’s reasoning. Assuming, however, that one is not certain, one will also put some weight on the proposition’s negation, albeit very little. This latter fact is responsible for why one’s reliance on holding a losing ticket still counts as partial. Once one’s reliance is partial, one will typically not decide to throw the lottery ticket away, for this response typically requires that one can fully rely on not holding a winner.

The present idea moves the proposal close to one part of Weisberg’s account. He writes:

Weisberg goes on to suggest that weighing reasons can be understood along the lines of expected value calculation. An expected value is, after all, a weighted average of one’s utilities, where the weights are supplied by one’s credences.

One difference between the present account and Weisberg’s is that Weisberg takes the relevant reason to be a proposition about what is possible, i.e., that it may rain. Such modal reasons are then to be given different weight in one’s reasoning. On the model I wish to develop, one partially relies on whatever is the embedded proposition. That is, one would partially rely on the proposition that it will rain and give this proposition different weight in one’s reasoning. Of course, one could also (fully) rely on the proposition that it may rain, but that would not be an essential ingredient of the account I favor. Note that the analogy with expected value calculation is more direct on the present proposal. For what is given different weight in the calculation of expected value is not a modal proposition of the form ‘may (p)’ but rather the embedded proposition p, to which the corresponding credence attaches.

Before moving forward, let me pause and consider a possible objection.Footnote ¹⁴ Could it be that what I classify as degrees of reliance merely reflects a context-relativity of reliance? For instance, Alonso (Reference Alonso2014, 177–78) suggests that one may be prepared to rely on a proposition in one context but not in another (see also Alonso Reference Alonso2016). The example Alonso presents is one in which an agent is prepared to rely on a rope holding her weight when deciding to climb a small rock but not when deciding to climb a big rock. In this example, the agent has some reasonable doubts about the rope’s strength, which is why relying on it in climbing the big rock would mean risking her life, at least from the agent’s own perspective.Footnote ¹⁵ Once such a context-relativity is granted, one could say that partial reliance occurs when one is disposed to rely on the proposition in question only in some but not all relevant contexts. One may go on to propose that one is disposed to rely on one proposition p more than on another proposition q iff for the set of contexts in which both propositions are relevant the set in which one is disposed to rely on q is a proper subset of the set of contexts in which one is prepared to rely on p. Footnote ¹⁶

Although I agree that this way of construing reliance would give us some kind of gradability, it would still leave a certain type of gradability unaccounted for. The problem is that there can be intra-contextual differences concerning reliance. In other words, there can be single contexts with only one decision problem to solve in which I rely on one proposition more than another. Following up on the example above, I may only partially rely on the proposition that the rope will hold my weight when deciding whether to climb the big rock, but I may simultaneously fully rely on the proposition that the rock has at least a certain altitude (which grounds my concerns about what I stand to lose should I fall). These difference would show, for instance, by my assigning different probabilities to the respective propositions when calculating the expected value of potential actions. Thus, it seems there can be differences in reliance even in a single context which are not plausibly described in terms of context-relativity. (I continue discussing the rope example on in section 3.)

With a notion of partial reliance in place, we can ask whether it is norm governed in any way. Very roughly, finding a norm which governs partial reliance would amount to solving the following equation for ‘ϕ’:

To give an example of what might solve this equation, let us go back to how Schiffer (Reference Schiffer2007, 189) introduces the problem of uncertainty for the knowledge norm. Next to his critical remarks, there is the positive suggestion that agents rely on a “justified partial belief” in decisions under uncertainty. This suggests to consider the following norm: it is appropriate to partially rely on p in one’s practical reasoning iff one has a justified partial belief in p. There will be more to say on a norm for partial reliance. For the time being, it suffices to see how one may use PN? as a schema to search for a norm governing partial reliance. The next section discusses how one may simplify this search.

3. Reliance and belief

I think progress can be made regarding our main question by clarifying the relation between full reliance and full belief on the one hand and partial reliance and partial belief on the other.

There seems to be a tight connection between belief and practical reasoning: “Intuitively, one believes p outright when one is willing to use p as a premise in practical reasoning” (Williamson Reference Williamson2000, 99). If we want to be sensitive to the distinction between full and partial reliance, we may capture the proposed relation between full belief and reliance as follows:

For present purposes, there is no need to decide whether this principle can serve as a definition of belief or whether it merely describes something closer to the functional role of belief for practical reasoning.Footnote ¹⁷

With BP in place, it suggests itself to consider the mirror image of BP for partial belief:

On this proposal, to have a partial belief would mean to be willing to rely on p to some extent in one’s practical reasoning. It would mean to put some weight on p in one’s practical deliberation that is proportional to the degree to which one believes p. If we avail ourselves of a more fine-grained notion of credences and degrees of reliance, then we may put a more fine-grained principle in place of PP:

To have a certain credence in p, on this view, is to be prepared to put a corresponding weight on p in one’s practical reasoning.

On a reliance-based account of credence and belief as presented so far, there is a continuity between credences and full belief which mirrors a corresponding continuity between partial reliance and full reliance. As higher credences go with higher degrees of reliance and full belief goes with full reliance, full belief is a kind of practical certainty which implies credence 1. It bears emphasizing that on this picture credence 1 is merely a kind of practical certainty that can be present even when something like Cartesian certainty—certainty beyond any kind of doubt—is absent.Footnote ¹⁸

The two principles BP and PP do not express any kind of norm. Rather, they are metaphysical hypotheses about full and partial belief. For our present project of finding a norm for partial reliance, they can nonetheless provide some helpful clues. We already touched upon the knowledge norm for full belief (Bird Reference Bird2007; Engel Reference Engel2004; Smithies Reference Smithies2012; and Williamson Reference Williamson2000, Reference Williamson, Preyer and Peter2005b):

This norm is often cast as a mere conditional (“Believe p only if you know p”). But on the assumption that knowledge implies belief, which I shall make for the purposes of this paper (but see Radford Reference Radford1966 and Myers-Schulz and Schwitzgebel Reference Myers-Schulz and Schwitzgebel2013), there is no harm in stating the norm as a biconditional.

One can see this norm for belief as being grounded in the corresponding norm for full reliance. If it is, first, appropriate to fully rely on p in one’s practical reasoning iff one knows p and, second, belief is grounded in being willing to fully rely on p, then it seems to follow, or at least it is strongly suggested, that one should believe p iff one knows p. Footnote ¹⁹ In other words, BN holds because of KNF: knowledge is the norm for full belief because knowledge is the norm for full reliance and full reliance is what grounds full belief.

As a working hypothesis, one may consider the exact same relationship for partial reliance and credence. One would hypothesize that there is a certain state which governs partial reliance and partial belief alike. This would establish an equivalence between the conditions under which relying on p is normatively proper and the conditions under which having a corresponding credence in p is normatively proper:

In the light of this equivalence thesis, we can make our life somewhat easier by searching for a norm on partial belief. As I think we have a better intuitive grip on the conditions under which one should form a certain credence, this promises to be progress.

Before moving on, let me comment on one general aspect of the norm for partial reliance I am searching for. The knowledge norm on full reliance associates full reliance with a purely epistemic state, knowledge (at least to the extent that knowledge itself is not influenced by pragmatic factors). In a similar vein, the hypothesized norm for partial reliance associates partial reliance with a purely epistemic state, namely with normatively proper credences (at least to the extent that credences themselves are not influenced by pragmatic factors). This general aspects runs against more pragmatic construals of reliance. For instance, Alonso (Reference Alonso2014, Reference Alonso2016) takes reliance to be partly governed by pragmatic factors. Thus, to continue with an example mentioned earlier, one may rely on a rope being strong enough to hold one’s weight when deciding to climb a small rock but not when deciding to climb a big rock. As reliance can come with various risks, a less than perfectly justified proposition may be sufficiently justified to be relied upon in a low-stakes context while being insufficiently qualified to perform this role in a high-stakes context.

On the notion of reliance I am after, I would describe the situation somewhat differently. If one only has a certain credence that the rope will hold one’s weight, one can still partially rely on this proposition in one’s decision-making. As a result, one may decide to climb the small rock because the associated risks are low and one will enjoy doing so (climbing may, in the situation at hand, have maximal expected value). However, even though one can partially rely on this proposition, this does not mean that one should be inclined to climb the big rock, too. As climbing the big rock has an extremely negative possible outcome, the expected value of not climbing may be higher than the expected value of climbing. For this reason, partial reliance can explain the difference in the decisions one should make without being influenced by pragmatic factors.

Nevertheless, I think there is a well-entrenched notion which is pragmatically influenced in much the same way Alonso construes reliance: the notion of acceptance. Footnote ²⁰ In a given situation, we may treat certain propositions as if we fully believed them because in this way we can simplify our reasoning and save time and energy. One may even vary the example above to yield a situation in which I do not want to think too hard and too long about the matter of climbing the small rock. For this reason, I decide to accept that the rope will hold my weight and quickly reason to the conclusion that I may use it to climb the rock. Let me say that I think the phenomenon of acceptance is a real one. But it is not the phenomenon I am trying to capture in terms of full and partial reliance.

4. Toward unification

The previous section explained that the conditions for proper partial reliance can be expected to be the same as the conditions for proper partial belief. This parallels a similar relation between full reliance and full belief: the conditions for proper full reliance are the same as the conditions for proper full belief. If this proposal is correct, then we can get a grip on proper partial reliance by facilitating our understanding of proper credence.

As it stands, the picture developed so far is open to the objection that it is bifurcated in a potentially worrisome way. On the one hand, there is full reliance, which is, just like full belief, governed by knowledge. On the other hand, there is partial reliance, which is governed by whatever governs proper credence. Is there anything that ties the two norms together?

There are, it seems to me, two dimensions along which one would like to unify the picture. The first dimension concerns the content of the two norms. If full belief is governed by knowledge, credence should be governed by conditions which stand to credence in a way sufficiently similar to how knowledge stands to full belief. If this can be secured, then the two norms would be unified by making a claim of broadly the same kind. But there is also a second dimension of possible comparison. This dimension concerns the structure of how the two norms are related. Ideally, one would like to show that there is a well-balanced division of labor between the two norms without the possibility of conflict.

Let me start by admitting that giving a fully developed account of the nature of normatively proper credences is beyond the scope of the present paper. Fortunately, there is already a rich literature on justified credence and probabilistic knowledge one can draw from. For example, Moss (Reference Moss2018, chaps. 5.6–5.7) argues that, on her conception of probabilistic knowledge, credences can have almost any of the properties typically ascribed to knowledge, including safety or sensitivity. More recently, Beddor and Goldstein (Reference Beddor and Goldstein2021) develop a more detailed conception of safety for probabilistic knowledge (in a framework of information-sensitive semantics).

Moss as well as Beddor and Goldstein are concerned with probabilistic knowledge of the form ‘S knows that probably p.’ Nevertheless, it seems possible to adapt certain aspects of their proposals. To a first approximation, one could then say that a credence is safe iff in all nearby worlds w in which the credence is formed in the same (or a sufficiently similar) way, it matches (or is sufficiently close to) the epistemic probability for the agent at w. Footnote ²¹ In this way, safe credences would be credences which aptly track the epistemic probabilities without involving a certain element of luck.Footnote ²² Of course, this can only be a first approximation to a full account, but it may suffice to indicate that there does not seem to be a principled hurdle to extend the notion of safety (or sensitivity) to credences without adopting probabilistic contents.

There is also no question that credences can be reliable as the works by Dunn (Reference Dunn2015), Pettigrew (Reference Pettigrew2021) and Tang (Reference Tang2016) indicate. Konek (Reference Konek2016) develops an account of proper credence based on cognitive skill, drawing on virtue-theoretic approaches to knowledge. Although far from being conclusive, this is further evidence that for any property potentially characterizing the nature of knowledge beyond true belief, credences can have a similar property. If so, then proper credences could be described in terms of conditions similar to the conditions required by knowledge, whatever those ultimately turn out to be. As far as their content is concerned, this would unify the norms on full belief and credence.

To guard against a possible misunderstanding, let me make explicit that assuming that there are conditions which stand to credence as knowledge stands to full belief does not require credence to be apt for having just any property knowledge might have. There are differences between full belief and credence which are likely to be reflected in differences in whatever normative conditions govern these attitudes. This point is relevant for assessing the fact that knowledge implies truth. It seems very clear that the truth of p is not a standard of correctness for a credence in p. A high credence in p is not incorrect just because p happens to be false (Tang Reference Tang2016, 65). If one possesses misleading evidence, it rather seems correct to assign p a high credence even if p is, as a matter of fact, false. The reason for this seems to be that the function of credences is to gauge indecisive evidence. Consequently, credences between zero and one do not take a stance on the truth or falsity of p: when challenged by the falsity of p, it is always appropriate to respond that one did not commit to the truth of p because one assigned the negation of p a positive credence as well (Ross and Schroeder Reference Ross and Schroeder2014, 276).Footnote ²³

Let us now turn to the structural question. Can we ensure that the norms for proper full and partial reliance cohere with each other?

To address this question, recall that full reliance has been characterized as requiring practical certainty. Knowledge in turn is supposed to be the normative standard for practical certainty. Therefore, practical certainty is, on this view, proper iff one has knowledge.

The norms for full and partial reliance make contact when partial reliance converges to full reliance and (practical) credences to (practical) certainty. In order to avoid conflict, a norm for proper credence must secure that one should be certain of a proposition p iff one knows p.

I think this requirement can be satisfied if we assume that the standard for proper credences is a probability which comes from conditionalizing on what one knows. Conditional on what one knows, one’s knowledge will be certain. And conversely, everything made certain by what one knows is something one will at least be in a position to know.Footnote ²⁴ Thus, if one requires that the standard for proper credences is partly set by a probability conditional on what one knows, the structure of the two norms would be set up in such a way that they do not conflict where they make contact.

A residual issue is what kind of probability is involved in setting the standard for proper credence. This question is not yet settled by assuming that these are probabilities conditional on what one knows as virtually any kind of probability could in principle be conditionalized on what one knows. It is, I think, very plausible to assume that a certain kind of epistemic probability is involved in the standard for proper credence. A proper credence in p, formed by an agent A at a time t, would at least have to match the epistemic probability of p conditional on what the agent knows.Footnote ²⁵

Taking proper credences to go with epistemic probabilities conditional on what one knows moves the proposal fairly close to the one offered by Hawthorne and Stanley (Reference Hawthorne and Stanley2008). Recall that for Hawthorne and Stanley, one deals adequately with uncertainty in practical deliberation when one possesses knowledge about the corresponding evidential probabilities. The difference is that for Hawthorne and Stanley (Reference Hawthorne and Stanley2008), one has to form an epistemic attitude about epistemic probabilities (at least on one of the proposals they consider; see fn. 7), while on the present suggestion one merely has to form an epistemic attitude in accordance with the epistemic probabilities.Footnote ²⁶

On the picture developed in this paper, one can just as well partially rely on a proposition as one can fully rely on it in one’s decision-making. Full reliance is governed by proper full belief, which was assumed to be knowledge. In a similar way, partial reliance is governed by proper credence. Steps toward unifying this picture can be taken in two directions. I proposed that one should think of proper credence in this context as being characterized by conditions which stand to partial belief as knowledge stands to full belief. Moreover, conflict between these norms can be avoided if one assumes that knowledge is the standard for practical certainty, while the credences relevant for practical deliberation are governed by epistemic probabilities conditional on what one knows.

5. Concluding remarks

Let us take stock. On the present proposal, knowledge governs full reliance, while proper credence governs partial reliance. An account along these lines enables one to take Schiffer’s example at face value. Agents can and oftentimes should rely on uncertain information. When they do, they do not have to know the proposition in question. However, just as there is a normative constraint on full reliance, so there is a normative constraint on partial reliance.

This picture will not be attractive to everyone. But it should be attractive to friends of a knowledge norm for full belief who also favor a nonreductive account of credences. On the latter kind of account, credences are not to be reduced to full beliefs about probabilities and have ordinary propositions as their content. Hence, the question of when one should have a certain credence does not reduce to the question of when one should have a certain full belief. Moreover, credences would be expected to play a role in decision-making which does not reduce to the role of full beliefs. If one shares these views, a norm on partial reliance and credences which is similar to the knowledge norm on full reliance and full belief should be attractive.

The present account is tailored to cashing out knowledge norms for practical reasoning in terms of reliance. There are similar norms in which the notion of a reason takes center stage. For instance, Hawthorne and Stanley (Reference Hawthorne and Stanley2008) hold that one should treat a proposition p as a reason for action only if one knows p. Can the present account be adapted to reason-based norms as well? As far as I can see, a positive answer to this question is possible, although I must leave the details for another occasion. Just as one can fully or partially rely on a proposition, it seems possible to adopt a qualified attitude toward potential reasons. One can fully or partially possess a reason depending on whether one possesses knowledge or merely has a (warranted) high credence. Thus, one may propose that one should treat a proposition p as a full reason for action only if one knows p. But one may treat a proposition p as a partial reason when one only has a (warranted) high credence.

Let me close with a few remarks on how the present picture sheds light on the potential tension between the knowledge norm for practical reasoning and classical decision theory in terms of expected value maximization. To better conceptualize this issue, let us distinguish a formal from a material understanding of decision theory. On a formal conception, decision theory would just make a very minimal claim: for some agent-dependent probability function p and some agent-dependent utility function u, the action one should choose is an action which has maximal expected value relative to p and u. As it stands, a formal conception merely says something about the structure of the choices one should make. A material conception, on the other hand, adds to a formal conception constraints beyond the mere formal structure, for example, constraints on the probability function and the utility function to be used in one’s calculation of expected value.

As far as I can see, knowledge norms do not speak strongly on the formal aspect of decision theory. As far as the norms on full/partial reliance and full/partial belief are concerned, various decision rules could in principle be adopted (for more on this, see Weisberg Reference Weisberg2013). The knowledge norms just tell us to what degree one should rely on a certain proposition in one’s practical reasoning. They do not tell us how to decide in the light of certain full or partial information. Therefore, these norms are fully compatible with expected value maximization (but they are also compatible with alternative decision rules). The original knowledge norm for practical reasoning is only in tension with expected value maximization if the norm is supposed to govern not only practical reasoning with full beliefs but also practical reasoning with uncertain premises (this seems to be Schiffer’s [2007] point). Once it is granted that practical reasoning can involve one’s credences, it is perfectly coherent to assume that the right conclusion to draw from uncertain premises is to choose an action with maximal expected utility.

So, let us suppose for the moment that expected value maximization provides the right answer to the form a decision theory should take. Let us further suppose that the norms on full belief and partial belief proposed so far are on the right track. What follows for the material aspect of decision theory?

It is at this point, I think, where the present picture no longer stays neutral. In my view, the norms on full and partial belief are best seen as providing an answer to material questions of good decision-making. The norm on partial belief suggests that a certain credence should enter the calculation of expected value only if it is "knowledge-like.” Thus, this norm results in a substantial normative constraint on the probabilities entering the calculation of expected value. The knowledge norm on full belief can be seen as a limiting case of this construal. As it describes what one can fully rely upon in one’s practical reasoning, it allows to rule out those possibilities which are incompatible with one’s knowledge. That is, compatibility with one’s knowledge would be the entry condition for a possibility to be considered in one’s decision-making. A view like this has been advocated by Weatherson (Reference Weatherson, Brown and Gerken2012). According to Weatherson, knowledge answers the question of which possibilities should enter one’s decision matrix in the first place. The probabilities in one’s calculation of expected value would then range over those possibilities compatible with one’s knowledge.

The picture just sketched is in deep disagreement with radically subjective Bayesianism. According to this view, there are hardly any material constraints going beyond a merely formal constraint on one’s decision-making. As long as one’s probabilities and utilities are coherent, one would not violate any norm of proper decision-making when choosing an action which maximizes expected value. The picture developed in this paper opposes the radically subjective Bayesian by demanding substantial normative constraints on which probabilities to use when deciding what to do.