This competition entry has been selected for publication by the Forum team.

1. Introductory Remarks

Giovanni’s Challenge of Unawareness purports to establish that no justification is available, for agents like us, for any impartial and altruistic preference of one action (or intervention) over another. Giovanni designates a central component of his challenge as the Normative Premise.

(For a summation of Giovanni’s challenge in its entirety, see Appendix 1.)

I contend that Giovanni’s Normative Premise is unmotivated. The main contribution of this entry is an effort to demonstrate this contention. A secondary contribution is to recommend a strategy for demonstrating that Giovanni’s Normative Premise is false—and also for demonstrating that agents like us can have impartial and altruistic preferences for some actions over others.

I proceed as follows. I begin by arguing that Giovanni’s Normative Premise is normative twice over—and, more specifically, that its content embeds both epistemic normativity and moral normativity. Next, I argue that the normative content of Giovanni’s Normative Premise is at least partially unmotivated—and, more specifically, that the Normative Premise’s morally normative content is unmotivated. I then infer that Giovanni’s Normative Premise is unmotivated. After considering some objections, I motivate a recommendation for further inquiry into what it means for a preference (or preference comparison) to be impartial. For the sake of avoiding unnecessary diversions from this plan, I relegate various supplemental discussions to appendices. 

2. The Normativity of the Normative Premise

In this section, I am going to argue that Giovanni’s Normative Premise is normative twice over—that the content of the premise embeds both epistemic normativity and moral normativity. To do this, I need to get a bit more precise about just what the Normative Premise says. And to be more precise, I need to clarify the meaning of some technical terms. 

2.1 Clarifying Terms

For an agent S and actions A, B, say that S c-prefers A to B if and only if: 

• S prefers A to B;
• the reason for S preferring A to B is a comparison between A and B; and
• the comparison between A and B is an impartial and altruistic comparison of the possible consequences of A and B. 

This follows Giovanni’s definition of c-preference in “Cluelessness: Summary of the argument, why it matters, and counterarguments.”

Say that an epistemically ideal agent is an agent free from epistemic obstacles. Epistemic obstacles include, in part, biases, tendencies to make fallacious inferences, non-responsiveness to evidence, memory limits, and limited attention span. (This is a provisional clarification, offered for the sake of gesturing toward the relevant notion. Nothing that follows depends upon the precise meaning.)

Say that the expected value of an action is a measure of the amount of overall goodness that action is expected to produce, relative to all possible consequences. For arbitrary action A with countably many possible consequences a₁, …, a_n such that each possible consequence a_i has its respective probability p_i of obtaining, the standard measure for the expected value of A is given as the sum of the products a_ip_i. If the consequences and probabilities are precise numbers, the expected value is precise. If the consequences or probabilities are, instead, intervals of numbers, the expected value is imprecise.

2.2. On Being Normative Twice Over

The clarifications of technical terminology afford a more precise statement of Giovanni’s Normative Premise. I posit that the following interpretation is apt.

(For an argument justifying the aptness of this interpretation, see Appendix 2.)

I maintain that the Normative Premise—or, at least, my interpretation thereof—is normative twice over. What I mean is this: the Normative Premise embeds both epistemically normative content and morally normative content. The epistemic normativity is, I think, obvious. The moral normativity is less obvious. I’ll unmask it in two steps. First, I’ll isolate the epistemically normative content from the remaining content. Then I’ll argue that the remaining content is morally normative. 

2.3. Isolating the Epistemic Normativity

The Normative Premise embeds content that is epistemically normative because it imposes a constraint for having justified c-preferences and justification is epistemically normative. To isolate the epistemically normative content of the Normative Premise, consider the following proof. (The premises are prefixed with “NP” to indicate their relevance to the Normative Premise.)

The first premise (= NP1) unpacks what it means to have justification. It gives the epistemically normative content of the Normative Premise. The second premise (= NP2) is definitional, derived from the meaning of c-prefer. So if the Normative Premise also embeds morally normative content, that content must be in the third premise (= NP3). I claim that it is.                                

2.4. Revealing the Moral Normativity

To reveal the moral normativity of Giovanni’s Normative Premise, I need to analyze the premise that I claim embeds this normativity (= NP3). I’ll do so by constructing an informal proof for the premise. Since the premise is a conditional and its antecedent mentions impartial and altruistic comparisons, I’ll develop the construction by unpacking what it means for a comparison to be impartial and altruistic.

The first premise unpacks what it means for a comparison of possible consequences to be altruistic. The second unpacks what it means for a comparison of possible consequences to be impartial. The third derives from the standard measure for calculating expected values.

Here's how the proof works. The first two premises jointly entail that impartial and altruistic comparisons about doing more good are comparisons with respect to all possible consequences. The third premise connects this to the notion of expected values: it entails that impartial and altruistic comparisons about doing more good are thereby comparisons of expected value.

 I take the proof to show that some content of Giovanni’s Normative Premise is (implicitly) morally normative. This moral normativity is hidden, in part, in the idea of an altruistic comparison (in NP3-1). Altruistic comparisons are comparisons about what “does more good,” and these comparisons are morally normative because the intended notion of doing more good is morally normative. The moral normativity is also hidden in the idea of an impartial comparison (= NP3-2). This idea gives guidance to for what it means to “do more good.” The guidance appears as a constraint on what impartiality requires of altruistic comparisons. It appears here because that constraint says what it takes to do more good: "does more good" is in the antecedent of the premise about impartiality.

(Perhaps worth noting is that in “The challenge of unawareness for impartial altruist action guidance: Introduction,” Giovanni glosses the notion of an impartial perspective as “one that gives moral weight to all consequences, no matter how distant.” For Giovanni, “impartiality entails that we account for all moral patients, and all the most significant impacts we could have on them.” This aligns with the second premise (= NP3-2) of the argument from this section.) 

3. Evaluating the Moral Normativity

In the prior section, I isolated the moral normativity embedded in Giovanni’s Normative Premise: it is hidden in the notion of an altruistic comparison (= NP3-1) as well as in the guidance given to this notion by the further notion of impartiality (= NP3-2). In this section, I am going to argue that the embedded moral normativity is unmotivated. Before doing this, however, I’ll offer some brief remarks on how my concern differs from some more standard concerns with Giovanni’s Normative Premise.       

3.1. Clarifying the Concern

My concern is that the guidance given for the morally normative content of Giovanni’s Normative Premise is unmotivated. This concern pertains to the notion of impartiality, and in particular to the following interpretation of that notion:

Because this interpretation says, in effect, that impartial comparisons require comparing all possible consequences, designate it as Modal Completeness (for ease of reference).

 My concern is that Modal Completeness—the interpretation of what it means for a comparison to be impartial—is unmotivated. My concern is not that that Modal Completeness is false (although I suspect it is.) For the sake of preemptively clarifying what my concern is, consider some competing concerns about Modal Completeness.

First, my concern is neutral regarding the plausibility of “near-termism.” Near-termism recommends “bracketing” possible consequences that we don’t know about in favor of “near-term” consequences. If near-termism is correct, Modal Completeness is false: impartial comparison about which actions do more good does not require comparing all possible consequences because some of these consequences are not near-term. My concern is that regardless of whether near-termism is true, Modal Completeness is unmotivated.

Second, my concern is neutral about whether distant positive and negative consequences somehow balance or “cancel out.” If long-term possible consequences cancel out, Modal Completeness is false: impartial comparison about which actions do more good does not require comparing all possible consequences because balancing among long-term consequences obviates the need to compare them. My concern is that regardless of whether distant positive and negative consequences cancel out, Modal Completeness is unmotivated.

Third, my concern is neutral about whether the moral efficacy of actions diminishes with time. J.J.C. Smart, in “An Outline of a System of Utilitarianism” (1973), motivates the idea of diminishing efficacy with a metaphor.

Smart’s metaphor, if apt, entails that Modal Completeness is false: if the good that actions do diminishes with time, then actions make no difference to the goodness of their distant (or distant enough) possible consequences; and if this is so, impartial comparison about which actions do more good does not require comparing all possible consequences of those actions. My concern is that regardless of whether the moral efficacy of any action diminishes with time, Modal Completeness is unmotivated.      

3.2. Justifying the Concern

Having clarified my concern with Modal Completeness, I now turn to justifying the concern. My argument, in brief, is that there are alternative, independently motivated interpretations for what it means for a comparison to be impartial, some of these interpretations undermine the Normative Premise, and so affirming Modal Completeness rather than one of its competitors is unmotivated. I’ll consider, in sequence, three such interpretations.

One alternative to Modal Completeness derives from a judicial standard for impartiality. The relevant standard is given in Canon 2 of the Model Code of Judicial Conduct from the American Bar Association. The standard specifies that impartiality is a matter of being competent, diligent, and free from bias, prejudice, or undue external influence. Applied to comparisons of which actions do more good, the standard yields an alternative to Modal Completeness, as follows:

Unlike Modal Completeness, Judicial Impartiality does not require that impartial comparisons are comparisons of all possible consequences. It requires only competence, diligence, lack of bias, and so on for any comparison of possible consequences, regardless of how narrow or broad the set of compared consequences happens to be.

A second alternative to Modal Completeness derives from Richard Bradley's "Impartial Evaluations under Ambiguity" (2022). Bradley proposes an impartiality constraint for a social betterness relation. The relation rank orders distributions of well-being (or goodness) among individuals over sets of possible states of the world. His impartiality constraint, labeled Outcome Anonymity, states, in effect, that if X(s) is a distribution of well-being among individuals for one state of the world and σX(s) is a distribution of well-being that permutes the individuals from X(s)—or reshuffles the well-being assigned by X(s) to specific individuals—then neither of X(s), σX(s) is preferable to the other. Applied to comparisons of which actions do more good, the standard yields an alternative to Modal Completeness, as follows:

Outcome Anonymity does not require that impartial comparisons are comparisons of all possible consequences. It requires only that every comparison of possible consequences, regardless of scope, be invariant across certain permutations.

A third alternative to Modal Completeness derives from Bolker-Jeffrey Expected Utility Theory. This theory includes a so-called Impartiality Axiom. For any X, Y, Z from a given set ℒ of possible consequences (or propositional representations thereof), the axiom states that if X, Y, Z are pairwise contrary, if X and Y are indifferent (neither is preferable to the other), and if X is indifferent to Z and X-or-Z is indifferent to Y-or-Z, then for any possible consequence W in ℒ such that W is contrary to each of X and Y, X-or-W is indifferent to Y-or-W. Applied to comparisons of which actions do more good, the Bolker-Jeffrey Impartiality Axiom yields an alternative to Modal Completeness, as follows:

Bolker-Jeffrey Impartiality requires that comparisons over a given set of possible consequences satisfy the Bolker-Jeffrey Impartiality Axiom. Because this set need not include all possible consequences, Bolker-Jeffrey Impartiality does not require that impartial comparisons are comparisons of all possible consequences.

The preceding considerations demonstrate that there are (at least) three alternatives to Modal Completeness. Each alternative is independently motivated. No alternative entails Modal Completeness. Because Modal Completeness is a more stringent constraint for impartial comparisons, and because Giovanni's Challenge of Unawareness does not motivate the greater aptness of Modal Completeness, the alternatives demonstrate that Modal Completeness is unmotivated. Given the result, from the preceding section, that Modal Completeness specifies (in part) the morally normative content of the Normative Premise, I conclude that the Normative Premise inherits this lack of motivation: the Normative Premise is also unmotivated. 

4. Addressing Objections

In this section, I address several objections. The objections concede that Modal Completeness specifies (in part) the morally normative content of the Normative Premise. The first denies that Modal Completeness is unmotivated. The others deny that the requirement to compare all possible consequences derives from an interpretation of what it means for a comparison to be impartial. 

4.1. Avoiding Arbitrariness

The first objection concedes that there are competitors to Modal Completeness. It denies that the existence of these alternatives demonstrates that Modal Completeness is unmotivated. The objection itself consists of two core contentions. The first is that impartial comparisons must be non-arbitrary. The second is that comparisons of possible consequences are arbitrary if they do not consider all possible consequences. The objection is that there is good motivation for both contentions. The first seems to be a corollary to Judicial Impartiality because arbitrary comparisons are subject to bias and other undue external influences. The second derives from the empirical fact that agents like us seem to lack any principled reason for restricting comparisons to some possible consequences but not others—and so any such restriction is arbitrary.

My response to the first objection is that it is insufficient. There are at least four viable interpretations for what it means for comparisons to be impartial. Even if Modal Completeness and Judicial Impartiality require non-arbitrariness of impartial comparisons, at least one alternative—namely, Bolker-Jeffrey Impartiality—does not. Bolker-Jeffrey Impartiality requires that comparisons over a given set of possible consequences satisfy the Bolker-Jeffrey Impartiality Axiom. It imposes no constraint on what this given set might be. Hence, it does not require that the set be selected in a non-arbitrary manner. Because Bolker-Jeffrey Impartiality does not require non-arbitrariness of impartial comparisons, there is no good reason to prefer an alternative that does. Hence, even if there is some motivation for supposing that impartial comparisons should not be arbitrary, that motivation is incomplete and, for this reason, insufficient.

By way of supplementing this response, I also take issue with the contention that unprincipled restrictions are arbitrary ones. Just as impartial comparisons need not be non-arbitrary ones, non-arbitrary restrictions need not be principled ones. By way of motivation, consider the difference between two kinds of monarchy. Suppose that both vest authority to make laws entirely in the monarch. Suppose that the absolute kind also vests authority to change laws entirely in the monarch, while the constitutional kind imposes constitutional restrictions on such changes. Because the law in both kinds of monarchy arises by fiat of the monarch, the law in both is unprincipled. Constitutional restrictions make law in the constitutional monarchy predictable. The absence of such restrictions makes law in the absolute monarchy unpredictable.

The law in the constitutional monarchy is less arbitrary than law in the absolute monarchy. Moreover, lest all law be arbitrary merely by virtue of having some human origin, there is a sense in which law in the constitutional monarchy is not arbitrary at all. For if having some human origin does not make law arbitrary, and if the only difference between law in the two kinds of monarchy is predictability, being unprincipled does not make law arbitrary. So, too, I claim, with comparisons of possible consequences. Even if there is no principled reason to restrict the range of possible consequences subject to comparison, an unprincipled restriction need not be arbitrary. If range restrictions are akin to laws, they are not arbitrary so long as they are predictable. There are, moreover, predictable ways to set such restrictions—for example, by restricting the range of possible consequences to consequences that might occur within a certain time span, or to those made salient by some structured analytic technique, or to those that make it rational to have a preference among them. (John Broome, in Weighing Goods (1991), proposes a restriction of this last sort.)

4.2. Defining C-Preferences

A second objection is technical. The core of the objection is that the notion of c-preferring, by definition, requires that comparisons among actions are comparisons of all the possible consequences of those actions. For the sake of developing this objection, recall that S is said to c-prefer A to B if and only if: 

• S prefers A to B;
• the reason for S preferring A to B is a comparison between A and B; and
• the comparison between A and B is an impartial and altruistic comparison of the possible consequences of A and B.

The core of the second objection is that the final clause in this definition implicitly quantifies over all possible consequences. If so, it follows that Modal Completeness is true as a trivial corollary to the definition of c-preferring.

         My response to the second objection is that it merely shifts the motivation burden. Define a notion of c*-preferring that does not require, as a matter of definition, comparisons across all possible consequences. If the second objection succeeds, the Challenge of Unawareness concerns lack of justification for c-preferences but not for c*-preferences. But the challenge gives no motivation for why justification for c-preferences is more desirable than justification for c*-preferences. My contention is that this motivation needs to come from some reason for preferring Modal Completeness to alternative interpretations of what impartial comparisons require. But even if this contention is incorrect, the motivation needs to come from somewhere. Hence, even if the objection is correct, it merely shifts the motivational burden.

4.3. The Meaning of Altruism

A third objection focuses on the meaning of altruism rather than the meaning of c-preferring. The core of the objection is that the notion of altruistic comparison—or, more specifically, the notion of what it means to compare actions with respect to the good each does—itself requires comparisons of all the possible consequences of those actions. James Lenman, in “Cluelessness and Consequences” (2000), seems to endorse the core of this objection. Lenman focuses on a kind of altruistic consequentialism whereby each person should favor actions (or policies) “with a view to the goodness of overall consequences.” He stipulates that, by ‘consequences’, he means “all the consequences.” Given this stipulation, it follows that even if impartiality alone does not require impartial comparisons of possible consequences to span all possible consequences, impartiality together with altruism does.

         My response to the third objection is that it also merely shifts the motivational burden. To be altruistic is to be concerned for the good of others. But it is no requirement of altruism that this concern extend to all others—much less to all possible others. Perhaps those with concern for the good of more others are more altruistic than those with more limited concern. But having concern for those who belong to some a community, and lacking concern for those outside the community, is altruistic at least to some extent. So the notion of altruistic comparison does not, by itself, require comparisons of all possible consequences. Imposing this requirement by stipulation merely shifts the motivational burden.

4.4. Consequentialism

A fourth objection is a natural counter-reply to the preceding response—and also, in a sense, an extension of the first objection. The core of the objection is that there is good motivation for supposing that impartial and altruistic comparisons of actions, with respect to the good they do, require comparisons across all possible consequences of those actions. This is because the requirement is a direct corollary to Standard Consequentialism. Standard Consequentialism maintains that the moral status of actions is a matter of their overall consequences, and it imposes no restriction on the consequences that matter. If the consequences that matter are unrestricted, it follows that Standard Consequentialism itself requires comparisons across all possible consequences of those actions. Hence, the objection goes, far from being unmotivated, Modal Completeness is well-motivated by Standard Consequentialism.

         My response to this objection is that Standard Consequentialism is standard in name only. In “The Definition of Consequentialism” (2022), Oscar Horta and colleagues survey specialists on consequentialism about four putatively necessary conditions for consequentialism. The four conditions are (roughly):

• Outcome Dependence: whether something is right or wrong depends completely on the outcomes that (may) occur.
• Value Dependence: whether something is right or wrong depends completely on the goodness or badness of the outcomes that (may) occur.
• Maximization: whether something is right or wrong depends completely on whether certain things are (or may be) maximized.
• Agent Neutrality: whatever makes something right or wrong must do so independently of the viewpoint of any particular agent.

Of these conditions, only Maximization is relevant. Because maximizing something about outcomes requires comparisons across all possible consequences, Maximization entails Modal Completeness. But Horta and colleagues find that roughly 87% of their respondents (28 of 34) affirm that Maximization is not a requirement of consequentialism. For example, Satisficing Consequentialism maintains that rightness and wrongness depend only on whether outcomes are good enough; and since good enough can be a function of only some possible consequences, Satisficing Consequentialism does not entail Modal Completeness. So too, presumably, for certain other alternatives to so-called Standard Consequentialism. Hence, even if Standard Consequentialism motivates Modal Completeness, that motivation is incomplete and, for this reason, insufficient.

4. A Way Forward

Before proceeding, perhaps it is helpful to have a brief summation of the main thread.

• I posited a specific interpretation of Giovanni's Normative Premise.
  • Section 1 gives the original version of the premise.
  • Section 2.1 clarifies technical terms in the posited interpretation.
  • Section 2.2 gives the interpretation itself.
• I argued that the Normative Premise embeds content that is both epistemically normative and morally normative.
  • Section 2.3 gives the argument about epistemic normativity.
  • Section 2.4 gives the argument about moral normativity.
• I argued that the morally normative content of the Normative Premise is unmotivated.
  • Section 3.1 differentiates the argument from some other, more common objections.
  • Section 3.2 gives the argument.
  • The gist of the argument is that there are alternative morally normative contents, and the specific content embedded in the Normative Premise is unmotivated.
• I inferred that the lack of motivation for the morally normative content of the Normative Premise renders the Normative Premise itself unmotivated.
  • Section 3.2 gives the argument.
  • Section 4 responds to objections.

In this section, for the sake of not being entirely negative, I propose a way forward.

I contend that the success of Giovanni's Challenge of Unawareness depends, at least in part, on whether there is good motivation for the morally normativity embedded in his Normative Premise (= Modal Completeness). By the same token, motivating some alternative morally normative content affords a strategy for avoiding Giovanni's challenge. Suppose, for the sake of illustrating this strategy, that there is good motivation for endorsing Judicial Impartiality. Suppose, in other words, that impartial comparisons need to be competent, diligent, and free from bias, prejudice, or undue external influence. Then avoiding Giovanni's Challenge of Unawareness is a matter of demonstrating that agents like us are in a position to make comparisons that meet the standard for Judicial Impartiality. (Referring to the appendices, Judicial Impartiality gives a revised version of the Normative Premise, and the relevant demonstration would establish that a revised version of the Empirical Premise is false.)

The specifics of the preceding strategy for avoiding Giovanni's challenge depend upon which alternative standard for impartial comparisons is apt for c-preferences. Perhaps Judicial Impartiality is too weak for the intended notion of impartial (and altruistic) comparison. Perhaps Bolker-Jeffrey Impartiality is apt for ­c-preferences and yet, by virtue of some independent requirement on the relevant set of possible consequences, entails Modal Completeness. Resolving these issues requires inquiry that is independent of concerns about balancing among long-term possible consequences or diminishing moral efficacy of actions (among others). For this reason, I recommend more careful inquiry into the demands of impartial and altruistic comparisons of actions. How might such an inquiry unfold? By way of concluding, I offer a preliminary sketch for one possible answer.

I imagine the inquiry as taking guidance from the Intelligence Community (IC) and building upon structured techniques, from the IC, for intelligence analysis. These techniques cover five phases: planning, or determining a knowledge base and gaps therein; collection, or gathering necessary information, either from the knowledge base or through additional inquiry; processing, or compiling information; analysis; and production, revising the analysis for coherence and relevance. For comparing actions with respect to the good they (might) do, there are fairly reliable procedures for collection, processing, analysis, and production. The planning phase requires determining what information is available about possible consequences, and then identifying relevant gaps in that information. Differentiating relevant gaps from irrelevant ones is where inquiry into the demands of impartial and altruistic comparison is relevant.

Because intelligence analysis is relevant to forecasting, it faces its own challenge of unawareness. The IIC resolves this challenge through a set of standards for analytic objectivity and sound intelligence tradecraft. It codifies these standards as Intelligence Community Directive (ICD) 203. ICD 203 directs analysts to consider alternative actions. For forecasting, this means considering possible consequences as well. But ICD 203 does not require analysts to consider all possible alternatives or all possible consequences thereof. Instead, it requires them to distinguish reliable information from assumptions and judgments, and to express and explain significant uncertainties associated with their analysis. These requirements, in effect, operationalize the demand for impartial and objective analysis.

Forecasting in intelligence analysis differs from the kind of forecasting relevant to doing the most good because the former comes with imposed parameters—for duration, scope, and so on—that the latter does not. Even so, the IC is a resource for how to go about operationalizing impartiality in the context of forecasting. Moreover, unlike weather forecasting, intelligence forecasting is often high-stakes, and it has much closer relevance to budget and resource allocation decisions. Since the IC at least sometimes manages to make non-arbitrary forecasts and offer justified recommendations for some pursuing courses of action rather than others, perhaps there is some wisdom in IC practice and procedure that indicates why Giovanni’s Normative Premise is false and what an appropriate alternative to it might be.

Appendix 1: Giovanni’s Challenge of Unawareness

Giovanni’s Challenge of Unawareness is an argument that consists of three key claims.

The conclusion of Giovanni’s argument is the claim that no justification is available, for agents like us, for any impartial-altruistic preference of one action (or intervention) over another. I borrow the language for these claims from "Announcing: Cluelessness Critiques Competition." There's similar language from Giovanni at "Cluelessness: Summary of the argument, why it matters, and counterarguments."

Appendix 2: Interpreting the Normative Premise

The inferential relations among the key claims in Giovanni's Challenge of Unawareness are not entirely clear. The intended relations seem to have the form: 

         P1.   If φ, then ψ.

         P2.   If χ then not-ψ.

         P3.   χ.

        C.     not-φ.

where φ = “some impartial-altruistic preference for action A over action B is justified,” ψ has something to do with expected value comparisons, and χ concerns how coarse-grained our understanding of consequences happens to be.

I offer a more precise reconstruction of Giovanni’s Challenge of Unawareness. The reconstruction invokes several technical terms that are clarified in the main body. It also invokes an additional term.

Say that the grain of understanding for the possible consequences of an action is the level of detail available for understanding those consequences. If the level of detail is highly specific, the grain of understanding is fine. If the level of detail is rather general, the grain of understanding is coarse.

Given the proffered clarifications for various technical terms, consider the following reconstruction for Giovanni’s Challenge of Unawareness.

I offer two reasons for accepting the premises in the reconstruction as apt interpretations for Giovanni’s key contentions.

First, the reconstruction for Giovanni’s Challenge of Unawareness is formally valid. It instantiates the exact pattern of reasoning given at the beginning of this appendix.

Second, the conceptual premise (= R2) from the reconstruction admits to a proof that seems to be entirely analytic.

The first premise (= R2-1) derives from a seemingly analytic (inverse) correlation between grain of understanding and level of precision. The second premise (= R2-2) derives from a seemingly analytic requirement that justification disallows a certain degree of arbitrariness. 

References

Broome, John. 1991. Weighing Goods. Blackwell.

Bradley, Richard. 2022. Impartial Evaluations under Ambiguity. Ethics 132.2.

Horta, Oscar, Gary David O’Brien, and Dayron Teran. 2022. The Definition of Consequentialism: A Survey. Utilitas 34.4.

Lenman, James. 2000. Cluelessness and Consequences. Philosophy & Public Affairs 29.4.

Smart, J.J.C. 1973. An Outline of a System of Utilitarianism. In J.J.C. Smart and Bernard Williams, eds., Utilitarianism: For & Against. Cambridge University Press.