In A Theory of Justice (1999 ed., pg. 24), Rawls says:

The nature of the decision made by the ideal legislator is not, therefore, materially different from that of an entrepreneur deciding how to maximize his profit by producing this or that commodity, or that of a consumer deciding how to maximize his satisfaction by the purchase of this or that collection of goods. In each case there is a single person [emphasis added] whose system of desires determines the best allocation of limited means. ... [This view means] conflating all persons into one ... [and] does not take seriously the distinction between persons.

This reminds me of Hannah Arendt's preoccupation with human plurality. At any rate, Rawls' foil here by his definitions was utilitarianism, which can be abstracted over as consequentialism and then aggregationism. The mathematical sense of "aggregating" seems like assimilating quantification over multiple things to quantifying over a singleton for a set that contains those things (e.g. {{a, b}} is a singleton over a pair). Accordingly, would a deontic logic informed by Rawlsian/Arendtian considerations work better (make more sense/be more faithful to those considerations) if it used plural quantifiers?

  • the article you link to definitely seems plausible. "Why, then, would we ever aggregate? The reason is that we are affected by behavior that has general effects, especially unintended side effects, on all sorts of people among whom we ourselves are often to be found.". i'm a but confused why you cite rawls' ideal legislator though: wouldn't their laws have no "unintended side effects"?
    – user64448
    Commented Jan 26, 2023 at 6:06
  • oh right you were citing that paper in a counter intuitive way. it seems arguable that rawls has no need for aggregation. but anyway doesn't the quote you cite claim that the legislator is not one person; wouldn't aggregation be about the number of people harmed / beneficiaries? glossing the two does not seem "individualistic", but what do i know
    – user64448
    Commented Jan 26, 2023 at 7:01
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    @vqlk Rawls mentions an interpretation of Bentham which has the Benthamite ethos less as an abstract construct and more as a practical heuristic for dealing with large populations in a democratic context. So Rawls allows that there is an aggregationist motive that doesn't involve an implicit metaphysical conflation of distinct persons. I'll look for the exact passage to see how Rawls evaluates the Benthamite in this context. Commented Jan 26, 2023 at 9:09
  • oik cool, sorry for the hurried misreading^2. in reality, if we couldn't quantify how all people are bad, we'd be stuck. or at least, infinitely exploitable hah
    – user64448
    Commented Jan 26, 2023 at 9:14
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    @vqlk AToJ, pg. 285: "[Maine] suggests that... they are simply a working rule of legislation, and this is how Bentham regarded them. ... The [pragmatic] necessity to neglect differences between persons, even very real ones, leads to the maxim to count all equally, and to the similarity and marginality postulates." But so Rawls concludes instead that aggregationism is to be avoided because those postulates (of choice theory) trespass upon other "formal constraints of the concept of right" (most importantly, the public-knowledge constraint, since utilitarian calculations can be too complex). Commented Jan 26, 2023 at 10:05

2 Answers 2


I don't think the use of plural quantifiers makes any real difference. The issue you are addressing is that some theories of ethics require us to aggregate individual desires or preferences, and there are many different ways to do this. What Rawls is objecting to is the idea that when making a moral or legal decision, a person might ignore the differences between individuals and assume that all individuals can be considered as a single undifferentiated whole.

A moral theory that avoids this trap will still need to speak of collections of people in some way. Treating people in a morally equitable fashion would hardly be feasible if we were not allowed to generalise at all. Even the golden rule speaks of 'others' in an undifferentiated way.

Plural quantification provides a way to express the logic of collections of things. In particular, it allows us to use first order logic in cases where we would otherwise require set theory or second order logic. It allows us to distinguish between what is collectively true and what is distributively true. Plural quantification also allows us to translate sentences involving second order quantification over monadic predicates into first order logic.

But the motivation behind plural quantification is mostly one of logical and ontological parsimony. If we follow Quine's criterion of existence as that which we quantify over, then it is nice not to quantify over properties and sets if we can avoid it. We can speak instead of pluralities of things by expressing that plurality within the mechanics of quantification itself.

As far as the application of quantification to a deontic logic is concerned, it really doesn't matter whether you use plural quantification, or help yourself to set theory or second order quantifiers. You will face plenty of difficulties without worrying about ontological commitment.

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    This answer seems sufficient, but before accepting it I would like to mention moral particularism as a possible counterexample to the requirement of generalization in ethics. It's not a counterexample available to Rawls on account of his "formal constraints on the concept of right," though; I'm not sure about Arendt, on the other hand. Still, for Rawls, it might be nice to not have to quantify over sets, if set theory is metaphysically contentious (but he only mentions the possibility of deep ethical math in passing). Commented Jan 26, 2023 at 1:59
  • Offhand, Arendt seems much more moral-particularist than Rawls, in part by being more particularist about metaphysics, maybe (Rawls talks of general properties while noting that it is hard to parse such talk on various levels). At least, her characterization of totalitarianism as a "logically obsessive" political mindset seems to express or reflect some suspicions about generalization in normative discourse. Commented Jan 26, 2023 at 2:04
  • IDT particularism would be opposed to aggregation per se @KristianBerry all it means is we lack principles. i.e. Dancy is trying to show that we can make the right decision without principles: without any generality whatsoever how would we reason to "the right answer". look for example of particularist moral reasoning (i've not read any his books). that may help
    – user64448
    Commented Jan 26, 2023 at 6:09
  • dancy relies on "prototypical properties": "the prototypical properties that are typical of a bird—for instance, its capability of flying, its having feathers, and its having wings, et cetera. With regard to the atypical cases, such as those of penguins and baby birds, we can rightly categorize them as birds because they have enough of those prototypical properties that are typical of a bird". aren't these "rules"? @KristianBerry which is to miss the point that he's not a consequentialist (whether or not these conflict)
    – user64448
    Commented Jan 26, 2023 at 6:44
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    @vqlk good catch! I don't know too much about how particularism has been adapted to theories on other levels of meta-/normative ethics so this is a solid resource. Commented Jan 26, 2023 at 9:12

∀ x and ∃ x

are singular quantifiers: all lying is wrong; this lying is wrong. I take if you are asking whether "some lying is wrong" suffices to capture moral knowledge about lying. Whether or not it's in the spirit of Rawls:

  1. Aggregation is not sufficient for universality. I can know that I should not - supposing it will mostly just harm everyone involved - lie, even if I exclude some people (some lies) from consideration.

  2. Aggregation is not necessary for universality. I can know that "all lying is wrong" and - I would think - that harming anyone counts, without worrying about aggregating the consequences of my lying (whether or not I should aggregate if I am a consequentialist).

Rejecting aggregation is probably a useful way of looking at consequentialism, specifically limiting some of its more unhelpful / less intuitive "consequences". Killing someone to harvest their organs would harm them greatly, and if you cannot "sum" the good it would do to the donor recipients, then the argument for it can't really get started. I can see why a liberal would find that appealing.

  • that was kinda ugly, but probably true ha
    – user64448
    Commented Jan 26, 2023 at 7:35
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    Rawls discusses aggregationism (not by name) in connection with axiology more than deontology. He's objecting to the idea that agent-relative goods can be agent-neutralized and then summed together in some kind of "mass noun" way that is then converted into a count noun over "the" good. But he does discuss whether axiology is prior to deontology or not, and if so, how either is prior, so there should be a transition to your considerations. Commented Jan 26, 2023 at 10:09
  • i can see why that would be problematic @KristianBerry for him. worth thinking about
    – user64448
    Commented Jan 26, 2023 at 10:15

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