A.

In debates over rights, as much as, or perhaps more than, in any philosophical debate, it is important to see the forest for the trees. At the level of the forest, rivaling theories of rights attempt to descry the core structural features of one of the most important concepts in our normative landscape. Interest theorists, for whom rights function to protect the right-holder's interests, will theorists, for whom rights function to protect the right-holder's control over another's duty, and others have all attempted to gain supremacy in articulating what it is to hold a right. Descending into the trees, it might be considered an adequacy constraint on a theory of rights—barring special pleading for adoption of a revisionary approach—that its test for right-holding delivers results chiming sufficiently with our intuitions. Our focus here will be on the primary such test for a prominent version of the interest theory. We shall descend far into the trees, but when we emerge we will have a sharpened view of the forest. It turns out that interrogation and articulation of this test for right-holding just is interrogation and articulation of the interest theory itself.

As noted, according to interest theorists (ITs)Footnote ¹ of rights, or right-holding, rights function to protect the right-holder's interests. True. But this leaves a lot unsaid. Most saliently for our purposes, it is certainly not the case that every agent who stands to benefit from performance of a duty under a contract or norm gets to be a right-holder. For a theory to allow this to be the case—to allow for a vast explosion of right-holders—would be tantamount to a reductio thereof. To take a third-party beneficiary example, explored in more detail later in the paper, suppose that X has contracted with Y for the payment of several thousand dollars by Y to Z. Suppose further that Z plans to spend all of her newly obtained money on some furniture from W's shop. And, to extend the example, W may be planning on using those proceeds at V's grocery store, and so on, ad infinitum. Not all these agents can be right-holders here. But where and how to draw the line?

It's worth noting that our motivating third-party beneficiary example is a fairly quotidian legal scenario. We might contrast it with questions about whether, for example, animals and dead people can be IT right-holders. Fascinating and philosophically important as these latter questions may be, there is a sense in which they are more marginal than a core case like our motivating legal example. Our descent into the trees of IT is, again, providing a sharpened view of the forest itself.

So the challenge for ITs is to respect the core of the interest theory while in a principled manner delimiting the set of right-holders. The foremost explicit attempt to do this has involved invocation of Bentham's test (BT).Footnote ² Predictably, invocation of this test has come under attack, with the ultimate aim of casting doubt on the tenability of IT itself. My purpose in this paper is to render BT as clearly and accurately as possible—something not always done by its foremost advocate. Doing so will get us involved in issues of modality—ultimately, that is, in rendering BT's logical form. The upshot of all this is that a core attack on BT falls away, and, to that extent, IT remains standing as a promising theory of rights.

At the risk of special pleading, it may be worth emphasizing just what is at stake here (particularly given that the reader is asked to work quite hard at points, on seemingly small details concerning the formulation of BT). What is at stake is the very tenability of (Kramer's) IT itself.Footnote ³ As I will come to show, it is not that BT is some bolt-on to the core of IT, wheeled out to fire-fight in emergency cases. BT is rather the core of IT. If BT fails, IT fails.

B.

Our ultimate aim, then, is to provide a definitive formulation of BT, and consequently to roll out how the definitive formulation is invulnerable to a core attack that has been levied against it. Before getting there, though, some background and build-up work (of independent interest) is necessary. The specific plan, then, is, sequentially (and, largely, chronologically) as follows: (1) To do some broad brush stage-setting, setting up some operative “analyses” of rights and of the issue itself at a very general level. Here the origins of our third-party beneficiary example are canvassed and an immediate shortcoming of extant formulations of IT is flagged. (2) To look closely at HLA Hart's original (Reference Hart1982) discussion of BT.Footnote ⁴ It is important to go nearer to the historical origins of BT in order to understand its contemporary evolution. It will turn out that things are not quite as they seem—or, at any rate, as they seemed to Matthew Kramer in his subsequent (Reference Kramer, Kramer, Simmonds and Steiner1998) discussion of Hart on BT.Footnote ⁵ The extent to which Hart's BT has been improved upon is at best unclear. (3) To investigate some issues arising from Kramer's initial (Reference Kramer, Kramer, Simmonds and Steiner1998) presentation of BT.Footnote ⁶ A key issue that arises is that correct application of BT involves detriments lying at the hands of the duty-bearer, and this segues into some key attacks on BT. In a nutshell, detriments simpliciter are not enough to activate BT: the source of the detriment must be the duty-bearer. (4) To introduce Gopal Sreenivasan's (Reference Sreenivasan2005) two key attacks on BT (and correspondingly IT),Footnote ⁷ with a focus on one such attack involving the possibility of waiver of the duty in question, and to briefly outline Kramer's highly complex (Reference Kramer and Steiner2007) response to this attack.Footnote ⁸ The worry is that the response is not only highly complex, but also unnecessarily hostage to some philosophical fortunes. (5) To drill into Kramer's canonical (Reference Kramer2010) formulation of BT.Footnote ⁹ At this point we shall attempt—our ultimate modal task—to render BT's logical form as the best means of responding to Sreenivasan. This response is simple and hostage to no philosophical fortunes. (6) Finally, to roll out, by means of confrontation with Sreenivasan's latest example, how this correct understanding of BT's logical form renders it invulnerable to one of Sreenivasan's (Reference Sreenivasan2005, Reference Sreenivasan and McBride2017) core attacks on it.Footnote ¹⁰ Moreover, as noted, by contrast with Kramer (Reference Kramer and Steiner2007),Footnote ¹¹ this defense of BT is simple, unfussy, and comprehensive.

C.

A biographical remark. At a workshop I hosted on rights in Singapore in 2015, Kramer, the hardiest contemporary proponent of IT, orally disclosed (in a rare moment of compromise) that, were he not an IT, he would be a hybrid theorist (HT), with the foremost hybrid account being Sreenivasan's (Reference Sreenivasan2005).Footnote ¹² To use philosophers’ parlance, the closest possible world in which Kramer isn't an IT is a world in which he's an HT.Footnote ¹³

The same point applies to me. But in reverse. I have recently (Reference Kramer and McBride2017, ms) gone in print defending my own hybrid theory of (claim-)rights.Footnote ¹⁴ While it owes a lot to Sreenivasan's HT, it is my own hybrid account called the tracking theory. I'm, naturally, attracted to it, and I look forward to hearing objections to it, and hopefully deflecting them. But it may—just may—be that the tracking theory is ultimately unsuccessful. And it's fair to say, were I not to be a tracking theorist (given that I think the tracking theory is the best type of hybrid theory), I may well switch allegiance to IT. It's likely that the closest possible world in which I'm not a tracking theorist is a world in which I'm an IT.Footnote ¹⁵ So, at a general level we've seen that what is at stake in this paper is BT, and the corresponding tenability of IT itself (which is predicated on BT). At a more personal level, though, preserving the tenability of IT serves to keep open a fallback position for me.

A.

As with many issues in contemporary analytic jurisprudence, the story can be traced back (at least) to HLA Hart (Reference Hart1955):

Y's mother is a third-party beneficiary (3PB) under this norm. Now for Hart, a will theorist (WT), for whom the function of rights is to protect the right-holder's control over a duty, Y, and not Y's mother, possesses a right in this scenario: Y has, whereas Y's mother does not have, control over X's duty—in the sense of power to demand/waive its performance. And, according to Hart, IT is unable to account for Y's having a right, and falsely decrees that Y's mother has a right, in this scenario. Be this as it may, though Hart does not extend matters under this scenario to other agents who may benefit from X's performance of his duty (e.g., alternative caregivers who would have to step in should X not perform, friends of Y's mother who will enjoy her increased vitality as a result of the care, etc.), the implication is clear. For virtually all duties, many agents will stand to benefit from performance of the relevant duty. But it is an adequacy constraint on any theory of rights that not all such agents get to be right-holders. We can think of this delimitation challenge on a theory of rights most generally as the 3PB-objection. Insofar as IT identifies having a right with such a benefit, the foregoing adequacy constraint will not be met. An explosion of rights ensues.

B.

With the dialectic so configured, the IT response should be obvious: viz reject the identification of having a right with being a person benefiting from the performance of a duty as a component of IT. It is only such an identification that leads to an IT explosion of rights. And indeed such a rejection is present in the foremost contemporary IT formulation, as advanced by Kramer (Reference Kramer and McBride2017):

(The second thesis distinctive of IT, for Kramer, is that control over the relevant duty is neither necessary nor sufficient for right-holding for IT. By contrast, said control is necessary and sufficient for WT, meaning WT does not face a delimitation challenge in any problematic sense. Leaving aside the slight oddity of including a negative condition like this in the analysis of IT, it is not germane for present purposes.) Now straightforwardly, this formulation, (IT-1), does not identify being a person benefiting from the performance of a duty with being a right-holder: such a status is only a necessary, and not also a sufficient, condition on being a right-holder. As such, this formulation of IT avoids mandating an explosion of rights.

But IT achieves this at a cost of incompleteness. What (IT-1) leaves us with is not a theory of rights, in that such a theory must offer an analysis of rights (where an analysis would offer a set of necessary and sufficient conditions for right-holding). Of course, Kramer is aware of this, at least implicitly. And while (IT-1) does not mandate an explosion of right-holders, for all it says it leaves open such a possibility. Otherwise put, without augmentation by a sufficient condition to close the loop, IT is incomplete as a full-blown theory of rights, and is open to charges of rights explosion. And in a sense to be made clear presently, Bentham's test—BT—provides that augmentation (for Kramer).

A.

Again, our story can be traced back (at least) to Hart (Reference Hart1982).Footnote ¹⁸ It is often said, disparagingly and sometimes truly, of contemporary general jurisprudents that they get their Austin through Hart. And it is opined that truth gets distorted thereby. It might be said, analogously here, that contemporary rights theorists get their Hart's Bentham's test through Kramer. And, again analogously, it is opined that truth gets distorted thereby. Of course, were we to go right to the source, we would go straight to Bentham himself. But time is limited, and we make some advance by paying detailed attention to Hart himself on BT, before getting to Kramer on Hart on BT. In what follows I engage in interpretation—perhaps better, constructive interpretation—of Hart. My principal aim is less to pinpoint what Hart was actually thinking, or had in mind, and more simply to carve out a position definitively Hartian in spirit.

B.

Here, then, is Hart (Reference Hart1982) himself on BT:

By way of preliminaries, Hart gets to this passage (and its focus on laws) through consideration of, and an attempt to elucidate, Bentham's somewhat murky distinction between assignable and unassignable individuals. And one central use of the distinction, for Bentham, is to explain “public rights,” which, for him, resolve into rights held by unassignable individuals. The rough idea behind the assignable individuals / unassignable individuals distinction is clear: the former are, in some sense, picked out by the relevant norm as beneficiaries (paradigm: a quotidian two-party contract), whereas the latter are not (paradigm: tax laws). But the fact that criminal law anti-murder norms exist, for Bentham, to benefit (and confer rights upon) assignable individuals presents something of a mystery: individuals protected by such norms are not mentioned in the norm, either by name or (definite) description. So more must be said about the foregoing picked out relation. And that more lies in the passage above, and in BT.

C.

As a conduit to making several remarks on Hart on BT (always with one eye on Kramer on Hart on BT), let us extract from the above quotation, and put on display, Hart's pithiest statement of BT:

Now insofar as our quarry is something approaching an analysis of assignable right-holders, (H-BT*) is hopelessly circular: its right-hand side (the analysans) invokes the very thing to be explained (the analysandum).Footnote ²¹ Indeed, in the first sentence of our excerpted passage above ((H-BT*) is extracted from the second), Hart implicitly seems to recognize this by putting “assignable” in quotes and attempting to gesture at explaining “assignable” in other terms.

Given all this, we make progress, I think, by grasping the nettle Hart never quite grasped, and reformulating things thus:

So (H-BT) is just (H-BT*), but without “assignable” in its right-hand side. We have thereby shorn (H-BT*) of its vicious circularity.Footnote ²² A good thing. But is (H-BT) workable? I think so. We can roll it out (check for yourselves) with respect to our foregoing cases: in a quotidian two-party contract the test is straightforwardly met, and in tax laws it equally straightforwardly is not. Happily (for Bentham), the test is also met in criminal law anti-murder norms.

It follows, then, with (H-BT), that we have a non-circular, and workable, analysis of assignable right-holders. This last italic is worth emphasizing: for Bentham, BT is not a test for right-holding generally; a separate test must be wheeled out to account for unassignable right-holders, that is, for “public rights.” The mechanics of such a test are not germane for present purposes, but, anticipating matters somewhat, it should be noted that Kramer's BT is a test for right-holding generally. That is to say, Kramer puts BT to work to account for, for example, public rights that citizens pay their taxes. And, of course, it is no criticism of Kramer that he puts BT to a use different from Bentham's. Indeed, insofar as Kramer's use of BT is more comprehensive and simple, that is a count in favor of Kramer.Footnote ²³

D.

Now, with Hart on BT on the table, let us drill into our two key, and related, points for present purposes (i.e., always with one eye on Kramer). Let us explain our first point by way of consideration of criminal law anti-murder norms. This point will seem banal and humdrum at first blush. But it paves the way to a deeper understanding of BT and its genealogy. Palpably, an anti-murder norm provides protection to multiple individuals—all the members of the polity (and others besides). And such a norm, for Bentham, protects assignable individuals—gives assignable rights—by dint of meeting BT. So what is clear is that norms with multiple modes of protection—that is, norms providing protection to multiple individuals—can confer assignable rights for Bentham. This is to say, Adam, Ben, and all the other members of the polity are assignable individuals benefiting in the requisite way from (and so being conferred rights by) their jurisdiction's anti-murder norm. But, it is of course not the case that to establish its breach any particular individual—Adam, Ben, anyone else—must be shown to have suffered an individual detriment. That is, for none of Adam, Ben, or anyone else, taken severally or individually, is it necessary that they suffer a detriment for there to be breach of the anti-murder norm (and thus for them to be assignable right-holders). All that is required is that this be so for an individual—some member of the (ever fluctuating) polity.

A different way of making much the same point is as follows. (H-BT) is fundamentally a test with respect to general categories of individuals: specifically, the category of assignable right-holders. It is assuredly not a test for directly picking out individual right-holders. That is to say, (H-BT) is assuredly not of this form:

Were something in the ballpark of (H-BT**) the relevant test, it would fail—as Bentham wished—to classify any of Adam, Ben, etc. as (assignable) right-holders under their jurisdiction's anti-murder norm. And this is all important, if banal and humdrum thus far. But it will shed its banality and humdrumness shortly.

E.

Now to our second, and related, final point on Hart on BT. According to (H-BT), the test for an assignable right-holder (i.e., (H-BT)'s right-hand side), is:

On the face of it, what we have here is some form of necessary condition on the relevant norm's breach. But, we've already seen, for any specified candidate assignable right-holder, such as Adam, Ben, etc., under the anti-murder norm, it is not that their own detriment is necessary for breach. Just one of their detriments. All just to say that any cognate Hartian version of BT, piggybacking on (H-BT), typed throughout at the level of individual right-holders, would take the form of specifying necessary elements, not for breach tout court (as (H-BT**) mistakenly does), but rather of sufficient sets for breach. To pick on Adam, a right-holder under the anti-murder norm: detriment to Adam is not necessary for breach (detriment to Ben, etc., will do just fine), but detriment to Adam can form part of a necessary element of a sufficient set for breach.Footnote ²⁵

Such a Hartian version of BT would be specifying so-called NESS conditions on breach (with the NESS conditions constituting the right-hand side of a biconditional for individual right-holding). In sum, while (H-BT), on the face of it, specifies a necessity test, to leave matters there would be to obscure: modified, to test for individual right-holders, it would enshrine a NESS test.Footnote ²⁶

(Here is a closing remark, drawing on the italicized portion of (H-BT RHS) above, though I am not sure how much to make of it. We may be able to approach the point obliquely, by considering an epistemological stance held by, for example, Timothy Williamson.Footnote ²⁷ For Williamson, as for nearly every epistemologist, knowledge entails truth. One can't know something unless it's true. One can't know falsehoods. Truth is a necessary condition on knowledge. So much is uncontroversial. But at this point a split occurs between Williamsonians and the rest.Footnote ²⁸ For the rest, this necessary condition—truth—can be combined with additional conditions—justification, belief, plus others—to specify severally necessary and jointly sufficient conditions on knowledge. And a lot of the challenge, for the rest, lies in precisifying what else must be added to a justified true belief to constitute knowledge. By contrast, for Williamson, this necessary condition—truth—cannot be combined with others to specify severally necessary and jointly sufficient conditions on knowledge. Knowledge is basic, and not built up—constructed—out of other, admittedly necessary, conditions, such as truth and belief. All just to say, Williamson would likely not, whereas the rest might, baldly assert that: to establish that a proposition is known one must show that proposition to be true. It is not strictly that a Williamsonian would think this false, but rather that it carries the pragmatic implicature that a way of “establishing” that a proposition is known is to “show” that the proposition has several necessary and jointly sufficient properties. It carries a pragmatic implicature, that is, that if you show that a proposition has these specified properties, that is sufficient to establish it as knowledge. Williamson would be much more liable to simply assert (alongside the rest): for a proposition to be known it must be true. And this assertion does not carry the foregoing pragmatic implicature. The point is tentative, but I think it may carry over to any cognate Hartian version of BT, piggybacking on (H-BT), typed throughout at the level of individual right-holders. One possible reason for such a version of BT's epistemic nature—“establish,” “must be shown”—is for it to carry the cognate foregoing pragmatic implicature, viz: that it specifies necessary elements, not for breach tout court, but of sufficient sets for breach.)

A.

In this section, I want to make two main points about Kramer on (Hart on) BT. I then conclude by applying Kramer's first stab at BT to the key test case. Its failure is instructive.

Here, then, is Kramer's (Reference Kramer, Kramer, Simmonds and Steiner1998) first stab at BT:

Now, as a prolegomenon to our two main points in this section, let's make three quick remarks, of descending importance, on (K-BT 1998), picking up on points already made. First, and most importantly, it is a test typed throughout at the level of individual right-holders. More accurately, it's focused on particulars rather than on types or universals. The particulars can, though don't have to, be individuals; they can be collective entities also. Second, it is a test for right-holding simpliciter. That is, Kramer wields it to account for rights held by the “public,” as well as those held by private persons. Third, no reference is made to the intentions of the relevant lawmakers. (K-BT 1998) is pitched at a high level of abstraction or generality. As such, it abstains from committing on how the norm in question should be interpreted—something that may, but need not, involve the intentions of the relevant lawmakers. Put differently, while it presupposes some method of interpretation of the relevant legal materials, it does not itself determine which. In this respect, then, (K-BT 1998) abstains from committing on matters of interpretation (and of evaluation, in a sense to be explained shortly). Each of these three features is in contrast with Bentham. And we shall explore each of these features further shortly. Now, though, to our two main points.

B.

First, (K-BT 1998), by contrast with (IT-1), is an analysis of right-holding. It specifies, that is, necessary and sufficient conditions for right-holding. It, and not (IT-1), is the true core of IT. With (K-BT 1998), and only with it, we have a true interest theory of right-holding. Interestingly, Kramer (Reference Kramer and McBride2017)Footnote ³⁰ appears to deny this (in response to a challenge from Leif Wenar (Reference Wenar and Kramer2008)Footnote ³¹ to specify IT necessary and sufficient conditions for right-holding):

I find this passage's reasoning a bit odd, insofar as it is offering a reason to deny offering an IT analysis of rights (in the face of the evidence). Again, a detour to epistemology might be helpful (though the point generalizes, and one could use many philosophical, indeed jurisprudential, analyses to make the same point). A key challenge many epistemologists tackle is offering an analysis of knowledge. Here is one possible such analysis: knowledge just is safe, true, belief.Footnote ³⁴ In fact, this is an analysis I've flirted with. But that is beside the point. The point is that each of these three putative constituents of knowledge are themselves in need of further analysis. And that is to say that, for anyone offering the above analysis, a full specification of knowledge would have to draw upon a theory, or account, of safety, truth, and belief. But, so what? This is a common feature of philosophical analyses. Why should this—how could this—preclude the above analysis, or constitute an objection to offering it? One can offer the above analysis, and then choose the degree to which one wants to provide a full specification of knowledge. The less one says about the putative constituents of knowledge, the less commitments one's theory of knowledge has, but, correspondingly, the less full one's specification of knowledge is. And in itself, this needn't be a bad thing, overall: the pros of fewer hostages to fortune may outweigh the cons of full specification. And, mutatis mutandis, the same holds the more one says: more commitments, the more full a specification, etc.

I trust the carry-over to the realm of rights theorizing is clear. (K-BT 1998) is a biconditional stating necessary and sufficient conditions for IT for right-holding—the analysandum. Its right-hand side—the analysans—contains the term “duty,” so a full IT specification of right-holding would give a theory, or an account, of that term (and a less full one would not). This is all true and fairly humdrum. There is nothing here to deny the palpable fact that (K-BT 1998) is the core of IT. It, and not (IT-1), is IT's analysis of right-holding.

Despite what (2017)-Kramer says,Footnote ³⁵ this is a good thing for Kramer and IT. As Kramer sets things up, one could be forgiven for thinking the picture seems roughly as follows. (IT-1) (alongside the negative condition (IT-2), which I would dispense with) is the core of IT: it is necessary for right-holding that the right protects the right-holders’ interests. And Bentham's test—at this point, (K-BT 1998)—would be wheeled out to deal with certain tricky cases on the periphery. But this would be a horribly piecemeal picture: For example, what would make a case apt for treatment by Bentham's test? In fact, and happily, the situation is precisely the reverse of this picture. (K-BT 1998) is the core of IT (dealing with all cases), with (IT-1) coming in, at the periphery, to supplement (K-BT 1998). (K-BT 1998)'s right-hand side talks of “benefit” to the putative right-holder, and (IT-1) elaborates on precisely how we are to understand “benefit”—a matter of evaluation—within the context of IT. A much less piecemeal picture. This is all to say, (IT-1) augments (K-BT 1998), and not the converse.

C.

Second, then, let us note the manner in which Kramer (Reference Kramer, Kramer, Simmonds and Steiner1998) took his formulation ((K-BT 1998)) to be a betterment of—an advance on—Hart's ((H-BT)):

It is helpful here to think of S and T as separate agents, such that the two instances of legal protection are accorded to distinct individuals. Kramer's point here is effectively that, intuitively and clearly, both S and T are right-holders under this norm. But any form of BT that, when attempting to descry individual right-holders, asks what detriment is necessary (simpliciter) for breach will classify neither S nor T as right-holders. It's a classic overdetermination problem: detriment to either will do the trick. And Kramer claims that Hart's BT is of just such a form. For that reason, Kramer deems it necessary to switch to a sufficiency formulation, according to which both S and T are classed as right-holders: for both S and T, taken severally, the relevant detriment is sufficient for breach.

Our previous discussion (in Sections III.D–Footnote III.E) of Hart's BT with respect to criminal law anti-murder norms paves the way to dismissing this reason of Kramer's to consider his formulation of BT an improvement on Hart's. Hart's BT is not specified at the level of individual right-holders. Were one to craft a cognate version specified at that level, it would only be the following that would render it vulnerable to this objection of Kramer's:

But we've seen that we have no reason to craft things thus. Indeed—though I forbore from doing so, as it is not contained in Hart—any Hartian version of BT specified at the level of individual right-holders will detail necessary elements, not for breach tout court, but rather of sufficient sets for breach. It will detail, that is, NESS conditions on breach (whether explicitly or implicitly).Footnote ³⁸ And for both S and T, taken severally, the relevant detriment will constitute NESS conditions for breach. Kramer's scenario involving norm N thus provides no reason to move beyond Hart—in the sense of it constituting some kind of counterexample to him.

D.

Finally, then, let us apply (K-BT 1998) (reproduced) to Kramer's (Reference Kramer, Kramer, Simmonds and Steiner1998) key test 3PB-style case:

Now let us quickly deal with X and Z as right-holders, enabling us to then focus on W. It is not that X and Z are wholly uncontroversial cases—Sreenivasan (Reference Sreenivasan2005, Reference Sreenivasan and McBride2017) has quibbled with Kramer's account of their status as right-holdersFootnote ⁴⁰—just that they are not our present chief concern. So, Y's—the duty-bearer's—reneging on the promise constituting the contract is a detriment to X's status as a moral agent that is sufficient to establish breach of the contract.Footnote ⁴¹ And that same reneging is an even more straightforward and prosaic detriment to Z to the tune of several thousand dollars, which is likewise sufficient to establish breach of the contract. So far, so (relatively) straightforward.

Things get more interesting, for present purposes, when we look at what Kramer (Reference Kramer, Kramer, Simmonds and Steiner1998) says in applying (K-BT 1998) to the case of W:

But this is confused. The reasoning is as follows. W's detriment of no sales is not sufficient for breach by Y: compatibly with said lack of sales, Y may have fulfilled the terms of the contract. It may be, that is, that Z got the money from Y but simply changed her mind concerning the purchases from W's shop. All true. But irrelevant to applying (K-BT 1998) to the case of W. (And it seems to me that this confused reasoning is repeated by Kramer (Reference Kramer and Steiner2007), mutatis mutandis.Footnote ⁴³) And descrying its irrelevance will prove illuminating in understanding BT, and in particular in our ultimate aim of rendering BT invulnerable to a core attack from Sreenivasan. The core behind the confusion in this passage from Kramer is that it neglects the fact that, in order to truly apply BT, we need a detriment “at the hands of” the duty-bearer.Footnote ⁴⁴ Let me explain.

To check for fulfilment or otherwise of BT, we need to consider scenarios in which the detriment in question is at the hands of the duty-bearer—so much is clear from (the right-hand side of) (K-BT 1998) itself, and Kramer's extradefinitional remarks on it. But this is precisely what Kramer has failed to do in the foregoing excerpted passage. Kramer's explanation of why W fails BT in fact precisely relies upon the fact that detriment undergone by W need not be at the hands of the duty-bearer, Y. It may rather, that is, be exclusively at the hands of Z. So Kramer's reasoning in applying (K-BT 1998) to W is off target. An application that was on point would run as follows: we need to identify a detriment to W at the hands of the duty-bearer, Y. So we commence by pondering a case in which (i) Y reneges on the promise constituting the contract, resulting in a detriment to Z to the tune of several thousand dollars, and we then imagine (ii) Z (as a consequence) failing to (use that money to) make purchases at W's store.Footnote ⁴⁵ Facts (i) and (ii) combined clearly do suffice to establish breach of contract. As such, and contrary to Kramer's inclinations, a straightforward application of (K-BT 1998) results in W passing BT and being classed a right-holder.

E.

So something is still not quite right with (K-BT 1998). Now, it must be conceded here that, as we shall see shortly, Kramer (Reference Kramer2010) has undertaken several “refinements” to BT.Footnote ⁴⁶ Importantly, though, on occasion Kramer advertises these refinements not as substantive shifts, but rather as efforts to tease out what was really there all along. Two points, of ascending importance, are in order. First, given all the above, it is, we shall see, palpably clear that Kramer's (Reference Kramer2010) formulation marks a substantive shift from—an improvement over—his (Reference Kramer, Kramer, Simmonds and Steiner1998) formulation. This should be noted. But—and this leads us to our more important second point—without more this would just be point-scoring. Second, then, the importance of dwelling on this (Reference Kramer, Kramer, Simmonds and Steiner1998) misstep of Kramer's (and not simply fast-forwarding straight to his (Reference Kramer2010) formulation) lies in its nature and origins. Kramer's putative explanation of why W fails BT involved a detriment to W not lying at the hands of the duty-bearer, but to apply the test properly the detriment must lie at the duty-bearer's hands. It turns out that this very neglect is at the heart of the strand of opposition to BT deriving from Sreenivasan, and to which we shall now turn. So stopping to note Kramer's neglect here is instructive (and not mere point-scoring).

A.

In the course of outlining his own hybrid theory (HT) of (claim-)rights, Sreenivasan (Reference Sreenivasan2005) has marshaled two forceful criticisms of Kramer's BT (and thus of Kramer's IT).Footnote ⁴⁷ Our focus, from here on in, is on just one of these criticisms, but we ought to mention the other briefly en passant. In brief, and transposing matters to our current example,Footnote ⁴⁸ Sreenivasan asks: what about Z's grandmother,Footnote ⁴⁹ who has an interest in seeing her grandchildren receive benefits? Sreenivasan says it is hard to see how any version of BT classifying X as a right-holder can avoid also so classifying Z's grandmother. And—the flip side—how any version excluding Z's grandmother as a right-holder can avoid also excluding X. Either way: counterintuitive upshots.

In response to all this, Kramer (Reference Kramer and Steiner2007) invokes a distinction between vicarious (e.g., Z's grandmother's) and non-vicarious (e.g., X's) interests, with only the latter category of interests getting to count for the purposes of BT, and so for the purposes of being a right-holder.Footnote ⁵⁰ Now Kramer (Reference Kramer and Steiner2007) says some things to flesh out this distinction,Footnote ⁵¹ but Sreenivasan has recently (Reference Kramer and McBride2017) forcefully put pressure on Kramer's distinction and employment thereof.Footnote ⁵² This debate, however, and its resolution, is not our present concern. Suffice it to say, though, insofar as BT is to be successfully employed by ITs, it does appear that some distinction along the lines of Kramer's must be invoked.Footnote ⁵³

(At the 2015 workshop itself in Singapore, I challenged Kramer to attempt to offer necessary and sufficient conditions for—an analysis of—vicarious interests,Footnote ⁵⁴ something he has yet to attempt. In line with previous remarks, any such conditions may themselves require analysis, and interpretation in application. That is to say, they need not—likely would not—provide any kind of algorithm for vicarious interests. Still, it seems like Kramer needs to make such an attempt, and he appeared to accept my challenge. So let us await news from Kramer on this front.)

B.

This brings us, then, to Sreenivasan's (Reference Sreenivasan2005, Reference Sreenivasan and McBride2017) second criticism of Kramer's BT, on which we shall focus:

So, the objection is clear enough. Because of the (mere) possibility of waiver by X, the palpably modal dimension to BT isn't, according to Sreenivasan met: for neither Z (as Kramer wants it), nor X (as Kramer wants it, and as any theory of rights reliant on BT must have it) is their detriment sufficient to establish—does it entail—breach. The foregoing detriments don't guarantee breach due to the possibility of waiver.

Sreenivasan's most recent (Reference Sreenivasan and McBride2017) recapitulation is helpful:

C.

In response to Sreenivasan's original (Reference Sreenivasan2005) presentation of this criticism, Kramer (Reference Kramer and Steiner2007) introduces a further set of distinctions and refinements to his BT.Footnote ⁵⁸ I agree with Sreenivasan that the invocation of these distinctions and refinements is mistaken. Where I differ is in the moral I draw from it. While Sreenivasan takes his second criticism to have succeeded, I simply think Kramer has taken the wrong path in responding to it. We ought, very briefly, to review Kramer's response.

Daniel Dennett's Philosophical Lexicon has the following entry:

The worry is that Kramer's BT, has been—becomes—(overly) chisholmed. We already have the (seemingly necessary) vicarious/non-vicarious distinction to handle Sreenivasan's first criticism. We now get, in responding to Sreenivasan's second criticism, the following as well. First, we get a distinction between, on the one hand, duties where time for ascription and performance can be distinguished (e.g., a contract to deliver goods on a specific date), and on the other hand, those where it cannot (e.g., the duty not to assault). Second, we get a refinement of his BT involving time indices, and a commitment to a theory concerning the truth conditions of future contingents, both of which he then invokes to deal simply with duties like the contractual duty above.Footnote ⁶⁰ For Kramer (Reference Kramer and Steiner2007), Sreenivasan's second criticism only applies to such duties.Footnote ⁶¹

Now, at a general level, we have yet more distinctions and refinements, and we ought to be wary of making them unless absolutely necessary. And more specifically, we ought, I think, to be suspicious of any theory of right-holding that has to make a substantive commitment on the much vexed, and highly controversial, issue of truth conditions of future contingents. Something just smells badly wrong about that: Why should IT be hostage to fortune to a substantive resolution of this interminable debate in metaphysics/philosophy of language?Footnote ⁶² Finally, as Sreenivasan (Reference Sreenivasan and McBride2017) has recently pointed out,Footnote ⁶³ with the help of a new example, it is simply not the case (as Kramer claims) that his second criticism only applies to duties like the contractual duty above.Footnote ⁶⁴ And we'll return to Sreenivasan's novel example in the final section of this paper.

To take stock, then, here is the state of play. After some stage-setting, and investigation into Hart's formulation of BT, we turned to Kramer on BT—initially (K-BT 1998), which we looked at in the previous section. We noted that Kramer's claims to have bettered, or remedied, Hart on BT were off target. And we also, inter alia, noted that something was amiss with Kramer's application of (K-BT 1998), with the promise that pinpointing Kramer's error here would prove instructive. We have just now—in this section—set out Sreenivasan's two criticisms of (in the first instance) (K-BT 1998), and seen Kramer's efforts to respond thereto. Kramer has clearly taken a wrong turn when it comes to Sreenivasan's second criticism. And the final two sections of this paper will correct that wrong turn. In the next section, we drill into Kramer's canonical formulation of BT (which we will label (K-BT 2010)). At this point we will render BT's logical form, which is the key to discerning the (by this point, familiar) error in Sreenivasan's second criticism. In the final section, we will roll out the optimum formulation of BT, and show how it is unthreatened by Sreenivasan's latest (Reference Sreenivasan and McBride2017) example, and strictures.

A.

Here, then, is Kramer's (Reference Kramer2010) canonical formulation of BT:

I am hopeful that Kramer would not object to me cleaning up, and streamlining, his canonical BT thus:

So formulated, it is clear we are dealing here with necessary and sufficient conditions for right-holding—that is, with an IT analysis of right-holding.

Before getting to the key points I want to make in this section, a few side comments, piggybacking on issues already broached. First, immediately after presenting (K-BT 2010), Kramer flags that “‘undergoing of a detriment’ should really be ‘undergoing of some development that is typically detrimental for a human being.’” This is helpful in bringing out a point made above: contrary to what might be thought, it is BT that is the core of IT, with Kramer's (IT-1)Footnote ⁶⁷ serving to augment, and amplify, some of the terms of BT. Second, as Kramer correctly notes (and indeed noted in (Reference Kramer, Kramer, Simmonds and Steiner1998)), whatever the correct interpretation of sufficiency here, it will not be logical sufficiency. It will be something weaker. Third, the shift from (K-BT 1998) to (K-BT 2010) marks a shift from the epistemic (“sufficient to establish”) to the ontological (“sufficient to constitute”). And Kramer sees this as an improvement (proclaiming that he was operating with the epistemic form in (Reference Kramer, Kramer, Simmonds and Steiner1998) simply to engage with Hart). Be this as it may, we have already noted a (helpful) pragmatic implicature conveyed by any Hartian formulation of BT, piggybacking on (H-BT), typed throughout at the level of individual right-holders: viz to convey that with the test we are in the realm of NESS conditions on breach. (Of course, any such Hartian formulation could make its status as a NESS test express rather than implied. And, as we shall see, once (K-BT 2010) is fully decomposed, its status as a NESS condition is express rather than implied.)

B.

Let us, then, roll out (K-BT 2010) with our operative example. To roll it out, we need to understand “minimal sufficiency,” a term contained therein:

And in other words still, a test involving minimal sufficiency is a form—a special type—of NESS test.

With all the pieces on the table, then, here is (K-BT 2010) in action:

And so Z, but not W, has a right by (K-BT 2010). Fine. But things have changed since (K-BT 1998); moreover we are, in a sense, right back to Hart.

Let me take these points in turn. First, Kramer (Reference Kramer2010) avers:

With respect, insofar as elucidation (as it clearly does) involves application of BT, it just isn't clear that this is so. The explanation for why W isn't a right-holder is fundamentally different as we move from application of (K-BT 1998) to application of (K-BT 2010). In (K-BT 1998), we saw, Kramer concluded that W wasn't a right-holder, on account of W's detriment being compatible with X's having performed under the contract: W's detriment is not, in a straightforward sense, sufficient simpliciter for breach. By contrast, here, with respect to (K-BT 2010), we've just seen that the explanation is not that, but rather the fact that the set of Y's not paying Z and (consequently) Z's not patronizing W's store is not minimally sufficient, due to the “redundancy” of W's detriment (at the hands of Y) in explaining breach.

So, a change. And in itself this needn't be grounds for criticism. But it should be explicitly and unequivocally noted that there has been a substantive change. And, moreover, a change for the better: the (1998) application revealed an important misstep. Identifying that misstep is critical for understanding our subsequent analysis of Sreenivasan's critique of BT: it is a misstep repeated by Sreenivasan. The root of the misstep is in neglecting the fact that in any application of BT we must consider detriments to the candidate right-holder “at the hands of” the duty-bearer.Footnote ⁷¹ And the bottom line is that Kramer's application of (K-BT 1998) doesn't (while his application of (K-BT 2010) does) do this. The very point of Kramer's application of (K-BT 1998) was that the duty-bearer needn't have reneged on his promise.

Second, then, it must simply be noted that the canonical test we are left with—(K-BT 2010)—need not be, despite what Kramer advertises, in any conflict with Hart (or, indeed, Bentham). I have already argued that we best construed Hart on BT as having a somewhat different focus from Kramer. But, I attempted to show that any cognate version of (H-BT), focused throughout, a la Kramer, on pinpointing individual right-holders, would take the form of a NESS test. And Kramer's (K-BT 2010) is simply a special kind of NESS test: it's a NESS test, every element of which is necessary, and focused on constitutive conditions for right-holding. We are, in a sense, not too far from where we started.Footnote ⁷²

C.

We are about to be in a position to answer Sreenivasan's (second) critique of BT. As a prolegomenon to that we need to be explicit about BT's—here, Kramer's canonical (K-BT 2010)'s—logical form. Recall it:

Now let the abbreviation and initials “Det D-B” = (there is at least one set of facts,Footnote ⁷³ none of which is redundant, which includes the undergoing of a) detriment (by Q) at the hands of the duty-bearer(, R). And let “Breach” = breach of the norm. Moreover, let “□” = the necessity operator (prescinding from any interpretation thereof), and “>” = material implication, or the material conditional, i.e., if, then. (See the Appendix for the truth table for material implication. Those unfamiliar with symbolic logic should consult it now.)

(With this in hand, a quick detour to the meteorological domain will be instructive. Consider someone uttering: “Rain entails clouds.” There would seem to be two ways to disambiguate this, admittedly odd, utterance, viz:

• (1) If it's raining, then necessarily it's cloudy.

• (2) Necessarily: if it's raining, then it's cloudy.

Plausibly (1) is false. If it's raining in the actual world, yet some worlds made accessible by the necessity operator aren't cloudy (likely the non-raining worlds, but we don't need to check), (1) is false. (1), as with (2), thus asks us to look also at non-raining worlds to assess the necessity claim. This is not strictly a logical point. So if raininess was a really modally robust fact, in the sense that it only became false in extremely remote worlds, and if the operative notion of necessity were weak enough, then maybe we wouldn't hit non-raining worlds in evaluating (1). But plausibly this isn't so here. And my thought is, following Sreenivasan, in the realm of BT and his cases, we must consider waiver worlds: they're made salient by the examples.

Yet (2) may well be true. To evaluate (2), we check for whether, in worlds made accessible by the necessity operator, the material conditional “if it's raining, then it's cloudy” is true. Such worlds will either be raining worlds or non-raining worlds. Insofar as every raining world is a cloudy world, this is enough for (2)'s truth, as the non-raining worlds will deliver the vacuous truth of the foregoing material conditional, regardless of whether they're cloudy worlds or not.

Our meteorological detour has, I hope, served a number of purposes. First, to introduce in natural language a simple example highlighting the scope-distinction point that I wish to drill into with respect to BT. Second, as noted, the semantics of (1) and (2) here seem to mirror the semantics of BT when it comes to Sreenivasan's examples: just as non-raining worlds are salient here, so too waiver worlds are salient in assessing Sreenivasan's cases.)

Now there are two possible interpretations of (K-BT 2010) that arise, viz:

We can note that in neither formulation do we need to make time indices explicit. Of course, we will evaluate each at a time, but that needn't feature in their formulations. The basic claim is that each of (LF1) and (LF2) can be read in English as (K-BT 2010). Try it.

A way of thinking of this is as follows. The “minimal” component of “minimal sufficiency” has been folded into Det D-B's non-redundancy criterion. It remains, then, to accommodate “sufficiency” into the logical form of (K-BT 2010). Palpably, it must be something more—something stronger—than bare material implication: viz Det D-B > Breach.Footnote ⁷⁴ This is to say, the right-hand side of (K-BT 2010) is not satisfied—as it would be were it simply bare material implication—in a circumstance in which there was the relevant detriment, and there was breach of the norm, but these two facts obtained purely by chance.Footnote ⁷⁵ (Because our running example precisely doesn't involve these two facts obtaining by chance, to see a “chance” case we need a different example: suppose R has a duty to pay S $100. And suppose R fails to pay S $100. Suppose finally R punches Q. Q has here undergone a detriment at the hands of the duty-bearer, R. And R has breached his duty to S. Were the relevant notion of “sufficiency” in BT bare material implication, BT would preposterously classify Q a right-holder under the $100-norm. As a bare material implication, the non-redundancy criterion that had been folded into Det D-B when interpreting “minimal sufficiency” is no longer present: bare material implications don't trade in notions of (non)redundancy. So it is no problem for my example that Q's detriment is redundant. In fact, that is its very point.) Rights don't come so cheap.

Clearly, then, we need something stronger to capture (K-BT 2010)'s sense of “sufficiency.” We need, that is, to account for some form of entailment between the relevant detriment and breach of the norm. And my point here is that there are two ways of capturing this, expressible by means of the two locations of the necessity operator in (LF1) and (LF2). This is a modal scope distinction, with (LF1) expressing narrow, and (LF2) expressing wide, scope of the necessity operator.Footnote ⁷⁶ Now scope distinctions are commonplace in philosophy, but rather than say more about them in the abstract, let us tease out the foregoing distinction by way of applying matters to Sreenivasan's criticism of BT. The basic point can be stated pithily, if somewhat gnomically, at the outset: Sreenivasan's criticism only works against the wrong logical form of BT; against the right logical form of BT, it is inert.

D.

We do well to recapitulate Sreenivasan's most recent (Reference Sreenivasan and McBride2017) recapitulation of his (Reference Sreenivasan2005) criticism:

We can now call this the “might have waived” (MHW) objection. Indeed, this recapitulation enables us to bring out two things. First, this criticism of BT, though originally aimed at the multiple- (i.e., more than two-)party example that has been running throughout this paper,Footnote ⁷⁹ can also be aimed at a simple two-party case: the duty Sreenivasan is commenting on is a duty of Y's (the promisor) to provide money to Z (a third party), but it could just as well be a duty of Y's to provide money directly to X (the promisee). And this all rams home the fact that BT (in whatever incarnation) is at the core of IT: it's not something to be wheeled out, in an ad hoc manner, simply to handle multiple-party cases. Second, one must, plainly, read in certain background facts, such as the fact that the contract has not been waived by the parties, in order to get minimally sufficient conditions for breach. The important point, though, as I make clear later, is that this is not—cannot be—the interest theorist holding fixed, by diktat, the existence of the duty across all accessible possible worlds; it's merely positing its existence in the actual case and affirming that its absence counterfactually means there can be no breach of contract.

So we noted that each of (LF1) and (LF2) were the two possible interpretations of (K-BT 2010). Without more, (K-BT 2010) itself doesn't distinguish between them. A way of seeing the right (and wrong) interpretation of (K-BT 2010) is to run Sreenivasan's MHW objection against (K-BT 2010). MHW works—indeed works straightforwardly—against the narrow scope (of the modal operator, necessity) reading:

Here is why. Sreenivasan begins with the platitude that in the circumstance in which X waives Y's duty to pay Z, and in which Y resultantly fails to—doesn't—pay Z, Z's detriment is not (minimally) sufficient for breach of the norm: there is no breach, because there is no (longer any) norm. You can't breach what doesn't exist. Fine. But Sreenivasan's extension of this platitude is problematic.Footnote ⁸¹

Sreenivasan describes the waiver case as “the special” case. But he then says that Z's detriment isn't sufficient for breach even in the non-special case of no-waiver. In such a case, we have Z's detriment, and we have breach. Now if the right-hand side of (K-BT 2010) were simply bare material implication—viz Det D-B > Breach—then such a set of facts alone would be “sufficient” for breach. But Sreenivasan is here getting traction out of the fact that the relevant notion of sufficiency in BT cannot be as weak as this: were it this weak, the test would be met when detriment and breach obtained, but obtained purely by chance (as in our parenthetical “punching” example, above). Explosion of right-holders. So we need something stronger than bare material implication. We need to inject a modal dimension to BT. All true. But the problem is that Sreenivasan (implicitly) injects the wrong modal dimension. He injects, if you like, the modal operator in the wrong vein.

Sreenivasan's MHW objection works—importantly, only works—when the modal operator, necessity, is added with narrow scope, a la:

Supposing BT were read as (LF1), Sreenivasan is basically saying (keeping our focus on Z): start with the non-special, ex hypothesi actual, case of no-waiver. If Y non-performs, there is detriment at his hands to Z. And there is breach of the norm. This ex hypothesi actual set of facts, of course, doesn't falsify the right-hand side (i.e., Det D-B > □ Breach). But, by the same token, it alone doesn't establish its truth. Given the necessity operator's—□'s—position, to establish the right-hand side's truth we'd have to establish that in all relevant possible worlds—all those made accessible by the necessity operator—there is breach of the norm. But Sreenivasan is correct that in at least some of these possible worlds, X will have exercised a power of waiver, and there will be no breach of norm resulting from Y's non-performance in such worlds. Result: the right-hand side of (LF1) is falsified, and so there is no right for Z (contrary to Kramer's wishes).

A different way of seeing this result is as follows: we start, in the actual world, with detriment at the hands of a duty-bearer. In this sense, it is true that BT presupposes a duty-bearer, but (unproblematically) only in the actual world, and not, as we shall come to see, across all counterfactual worlds.Footnote ⁸² But to test for whether the right-hand side of (LF1) is true (or not), we have to fan out to check whether there is breach of the relevant norm at all accessible possible worlds, in some of which there has been exercise of waiver. On this way of putting the point, when we are evaluating the conditional (Det D-B > □ Breach), constituting the right-hand side of (LF1), once we establish the truth of Det D-B in the actual world, we are done with respect to the truth of the conditional's antecedent (though not with respect to its consequent).Footnote ⁸³

E.

So were (LF1) the logical form of BT, Sreenivasan's criticism would work; were it (LF2) (with the modal operator taking wide scope), I want to come to show, it doesn't work. As I said, each of (LF1) and (LF2) is left open by Kramer's (K-BT 2010), so this means any advocate of BT (e.g., Kramer) should explicitly opt for (LF2). Recall it:

Happily, for ITs, Sreenivasan's criticism evaporates on this reading of BT. Here's why. Again, we start, with our running example, in the actual world, with detriment at the hands of a duty-bearer. And there is breach of the norm. Fine. Sreenivasan's MHW point is then raised: he notes that we need more than this to satisfy the right-hand side of BT, and, in particular calls our attention to the fact that the duty might have been waived, such that there is no breach.

But (LF2) preserves a (required) role for the necessity operator in BT, while avoiding this MHW criticism. In essence, the wide scope of the necessity operator in (LF2) basically means that the bare material conditional—viz (Det D-B > Breach)—must be true in all accessible possible worlds. And it is. As before, BT presupposes a duty-bearer in the actual world, and we've seen there is breach when Z suffers a detriment at the hands of the duty-bearer, Y. So the bare material conditional is true in the actual world.

But now in considering the MHW criticism we still fan out across possible worlds (as with (LF1)), but not in exactly the same fashion. By contrast with (LF1), when we are evaluating: □ (Det D-B > Breach), constituting the right-hand side of (LF2), once we establish the truth of Det D-B in the actual world, we are not done with respect to the truth of the conditional (Det D-B > Breach)'s antecedent. Given the placement of the necessity operator, we must fan out to check whether the material conditional (Det D-B > Breach) is true in all accessible possible worlds. And the point will be that in some of those worlds—the worlds in which a waiver is exercised—Det D-B will be false.

The point is, as we fan out from the actual world in which (ex hypothesi) no power of waiver is exercised, accessible worlds will either be those in which that power is exercised, or those in which it isn't. Those, like the actual world (ex hypothesi), in which power of waiver isn't exercised, will have the same result as we already noted: (Det D-B > Breach) comes out true. The important point is what happens in the accessible worlds where power of waiver is exercised. In such worlds, the following is, of necessity, the case: the material conditional (Det D-B > Breach) comes out vacuously true. (A material conditional is vacuously true just in case its antecedent is false, regardless of the truth value of its consequent.)

The key to clinching this important last point is astonishingly simple. Worlds in which X waives Y's duty are worlds in which there can be no detriment to Z at the hands of the duty-bearer (regardless of what Y actually does),Footnote ⁸⁴ because Y is no longer a duty-bearer, because there is no longer a duty.Footnote ⁸⁵ Put differently, in such circumstances, there is no such detriment, since there is no longer an operative promise. Given all this, there are no accessible worlds in which the material conditional (Det D-B > Breach) is false. Which is to say: □ (Det D-B > Breach) is true. Which is to say, Z has a right under the correct logical form of BT, viz (LF2).

In sum, the MHW criticism founders against the correct logical form of BT, viz (LF2). In our running example, □ (Det D-B > Breach) is true. The material conditional in question—viz (Det D-B > Breach)—is either (non-vacuously) true or vacuously true (and never false). Now this line of reasoning is, to my mind, unimpeachable.Footnote ⁸⁶ The upshot is that BT (and in its canonical formulation (K-BT 2010)) is undented by Sreenivasan's MHW objection. Moreover, BT is undented in a simple, unfussy, and comprehensive manner: Kramer's response to the MHW objection involved complex refinements and modifications, whereas mine simply involves getting clear on—bringing out into the open—BT's logical form, viz (LF2).

Nonetheless, in the final (substantive) section, I'll roll out matters with respect to Sreenivasan's last word on the MHW criticism. Doing so will only serve to bolster the key moves I've made within this section.

A.

Sreenivasan's (Reference Sreenivasan and McBride2017) latest example introduces an explicitly temporal dimension to proceedings (where Muhammad and Joe are both (let us say professional) boxers):

So the basic point is that Joe is clearly a right-holder (after the bell, i.e., outside the round), but BT, according to Sreenivasan, cannot deliver this result. We have here another variant of his MHW objection. The major advance, or innovation, of this case is its explicit temporal dimension. Be all this as it may, (LF2)—the correct logical form of BT—can handle it. Recall:

And recall also: we do not need to make time indices explicit in (LF2). Of course, we will evaluate (LF2)—check for right-holding—at a time, but that needn't feature in (LF2)'s formulation. The basic point is that (LF2)'s modal structure can readily accommodate the temporal dimension of Sreenivasan's (Reference Sreenivasan and McBride2017) example.

B.

Before rolling out (LF2) with respect to this case, it's worth considering the two (putatively, exhaustive) options Sreenivasan gives to a defender of BT (i.e., Kramer). It will turn out that the path I take is close, but instructively not identical, to one of these options. First, then, Sreenivasan suggests “inserting a further clause into Kramer's test [BT], explicitly excluding the possibility that someone has waived the duty in question (for the interval in question).”Footnote ⁸⁸ Now Sreenivasan questions the “consistency” of such a further clause with IT. And it is important to stress that what is being countenanced here is not a clause merely excluding waiver itself (we've already noted that a, what I take to be agreed upon, presupposed background fact is indeed the existence of a duty), but a clause excluding the very possibility of waiver. Quite apart from any matters of consistency, however, I would counsel against any (further) ad hoc bolt-on to IT: even if it is consistent with IT, there is a much more elegant and simple solution at hand.

Sreenivasan's second option is close(r), but not quite on the money. This is to claim that BT has an “unarticulated presuppositional structure” of no-waiver, with that presupposition not being satisfied, and the test thus not applying, to Joe's “being stung” during the round.Footnote ⁸⁹ And Sreenivasan hints that Kramer (Reference Kramer and Steiner2007)Footnote ⁹⁰ comes close to this tack. Now Sreenivasan's comments here on problems for IT taking this second option are somewhat murky. Let me, then, try to do better on Sreenivasan's behalf: if such a presupposition were genuinely unarticulated, then any version of IT reliant on BT would be undermined. But we can see that such a presupposition—in particular, a presupposition of no-waiver in the actual (though not in all accessible possible) world(s)—is fully articulate in BT. Part of the issue, or confusion, here lies in the strength of the relevant presupposition. Kramer (Reference Kramer and Steiner2007) notes:

And Kramer follows this passage by saying that Sreenivasan would probably not disagree with this. I agree with Kramer on this. So there is a bit of mystery going on here. I think the mystery can be dispelled by seeing the strength of the presupposition that Sreenivasan (mistakenly) thinks is involved in BT, and in its handling of his cases. The presupposition in question is in fact fairly weak, and fully explicit (and also made by Sreenivasan). In teasing out the presupposition, I go beyond anything said by Kramer, but I am hopeful that he will agree with me.

C.

Before applying (LF2) (the correct logical form of BT), by turn during, and outside, the round we do well to note this footnote remark from Sreenivasan (the footnote occurring alongside some highly equivocal remarks in the main text):

This gets to the nub of matters. With respect, I do fuss here. And, again with respect, such fussing is material. To say that an agent “did not perform her duty to ϕ,” in the absence of cancellation, presupposes that the agent “breached her duty to ϕ.” And to breach one's duty to ϕ straightforwardly does imply that one had a duty to ϕ. We can only say, for example, that Muhammed has breached his duty to abstain from assaulting Joe insofar as he had such a duty. This is, with respect, plain as day and indubitable. And we can helpfully contrapose the central conditional here to see that the following is also plain as day and indubitable: if one has no duty to ϕ, one cannot be said to have breached a duty to ϕ.

Now Sreenivasan says that whether such fussing is correct is “immaterial.” A way of reading this remark is that Sreenivasan is conceding that, even if my foregoing claim is right, he can still roll out his MHW objection to BT. So suppose I am right. Sreenivasan is correct to note that we are free to describe, for example, Joe's detriment at the hands of Muhammad in many ways, including “being stung”—a way that is neutral between whether we are in or out of the round. And when Muhammed “stings” Joe there is, to be sure, a physical detriment suffered by Joe regardless of whether we are in or out of the round. True. So this licenses Sreenivasan's claim in the main text that Muhammed “stinging” Joe “entails detriment” to Joe,Footnote ⁹³ but it doesn't license his footnote claim above that it (invariably) “causes the relevant detriment.”Footnote ⁹⁴ Such “stinging” only causes the relevant detriment when Muhammed is a duty-bearer: pivotal to BT is that it checks for detriment at the hands of the duty-bearer. And Muhammed is only the relevant kind of duty-bearer outside the round, not within. Failure to be attentive to this was, we noted, at the heart of Kramer's misapplication of his original BT—(K-BT 1998).

D.

Finally, then, with all this in play—in particular, having noted (in passing) that the strength of the presupposition that BT makes with respect to a duty's existence is crucial, and that we must be focused on detriment at the hands of the duty-bearer in applying BT—let us roll out matters. Here, then, is a rollout of (LF2)—the correct logical form of BT—with respect to Sreenivasan's most recent MHW case.Footnote ⁹⁵ Recall:

In Sreenivasan's case, we clearly have Joe's (and, of course, Muhammed's) right (not to be assaulted) going in and out of existence as we transition from rounds to the interim period (sitting in their corners). And (LF2) delivers this result straightforwardly.

First, then, consider the (in some respects) easier period of during the round. Thanks to Joe's waiver, Muhammed is no longer a relevant duty-bearer. Insofar as one wants to put things in terms of “presuppositions,” there is a fully articulate presupposition on the left-hand side of (LF2) that there be a duty in play (in the actual world). And this enforces matters on the right-hand side. To even get in a position to test for its truth, in the first instance, we need the actual world to be one in which there is some detriment at the hands of the duty-bearer that we can describe, and a corresponding breach.Footnote ⁹⁶ But this isn't so: even if Muhammed “stings” Joe (causing him physical setbacks), this is not a relevant detriment, as Muhammed isn't a duty-bearer (at this time).Footnote ⁹⁷ As such, without more (i.e., without the need to consider counterfactuals), (LF2) is not triggered, and a test that isn't triggered can't deliver a right. (LF2) thus can be said to deliver the result that Joe has no such right within the round.

Second, then, let's consider the somewhat harder, or more complex, period of outside the round. Joe's waiver is now, we might say, suspended.Footnote ⁹⁸ Once again, the same fully articulate “presupposition” is in play. This time, though, in the actual world, there is some detriment at the hands of the duty-bearer that we can describe, and there is a corresponding breach. In applying (LF2) this is a good—and essential—start to determining Joe's right, but it is not the end of the matter. To respect the modal force of (LF2)'s right-hand side—the necessity operator—we need to fan out into accessible possible worlds to test for the truth of the material conditional (Det D-B > Breach) therein. And as Sreenivasan notes, in some of those accessible possible worlds—the way in which (LF2) implicitly incorporates the temporal dimension of the present case—the “sting” occurs, contrary to fact, just before the bell draws the round to a close. It occurs, that is, when the waiver is back in play. This is fine, and demonstrates the weakness of the “presupposition” articulated in BT: the requirement of no-waiver is simply in the actual world. There is no sense in which the requirement extends across all accessible possible worlds. Put vernacularly, BT doesn't (in what would, if it did, be an ad hoc manner) rig modal space.Footnote ⁹⁹

So, let us fan out into modal space. Clearly in accessible possible worlds—like the actual—where we are outside the round, the preceding result will (still) obtain: (Det D-B > Breach) is true. The trickier part is those accessible possible worlds where we are inside the round. But, in a sense, we have already, in dealing with Sreenivasan's first MHW case, seen how things play out. In these worlds, (Det D-B > Breach) comes out vacuously true, and BT is thus satisfied. Such worlds in which Muhammad “stings” Joe are worlds where Muhammad is not a duty-bearer, on account of there being no existent duty (at the relevant time). It means, while there is a “sting,” there is not the relevant detriment for purposes of evaluating the material conditional (Det D-B > Breach) as either non-vacuously true/false: there is no detriment at the hands of the duty-bearer, as Muhammad is not a relevant duty-bearer.Footnote ¹⁰⁰ As before, then, in accessible possible worlds, (Det D-B > Breach) is either non-vacuously true (the actual world, and accessible possible worlds where the “sting” is outside the round) or vacuously true (accessible possible worlds where the “sting” is inside the round). (Det D-B > Breach) is never false. That is to say, □ (Det D-B > Breach) is true, and BT delivers the correct result that Joe has a right outside the round.