In Calosi and Wilson (Phil Studies 2019/2018), we argue that on many interpretations of quantum mechanics (QM), there is quantum mechanical indeterminacy (QMI), and that a determinable-based account of metaphysical indeterminacy (MI), as per Wilson 2013 and 2016, properly accommodates the full range of cases of QMI. Here we argue that this approach is superior to other treatments of QMI on offer, both realistic and deflationary, in providing the basis for an intelligible explanation of the interference patterns in (...) the double-slit experiment. We start with a brief overview of the motivations for QMI and for a determinable-based account of MI (§1). We then apply a developed 'glutty' implementation of determinable-based QMI to the superposition-based QMI present in the double-slit experiment, and positively compare the associated explanation of double-slit interference with that available on a metaphysical supervaluationist account of QMI (§2). We then present and respond to objections, due to Glick (2017) and Torza (2017), either to QMI (§3) or to our specific account of QMI (§4); in these sections we also positively compare our treatment of double-slit interference to that available on Glick's deflationary treatment of QMI. We conclude with some dialectical observations (§5). (shrink)
This paper explores quantum indeterminacy, as it is operative in the failure of value‐definiteness for quantum observables. It first addresses questions about its existence, its nature, and its relations to extant quantum interpretations. Then, it provides a critical discussions of the main accounts of quantum indeterminacy.
Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how (...) to resolve the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)
On many currently live interpretations, quantum mechanics violates the classical supposition of value definiteness, according to which the properties of a given particle or system have precise values at all times. Here we consider whether either metaphysical supervaluationist or determinable-based approaches to metaphysical indeterminacy can accommodate quantum metaphysical indeterminacy (QMI). We start by discussing the standard theoretical indicator of QMI, and distinguishing three seemingly different sources of QMI (S1). We then show that previous arguments for the conclusion that (...) metaphysical supervaluationism cannot accommodate QMI, due to Darby 2010 and Skow 2010, are unsuccessful, in leaving open several supervaluationist responses. We go on to provide more comprehensive argumentation for the negative conclusion. Here, among other results, we establish that the problems for supervaluationism extend far beyond the concern that is the focus of Darby's and Skow's discussions (according to which a supervaluationist approach is incompatible with the orthodox interpretation, in light of the Kochen-Specker theorem) to also attach to common understandings of other interpretations on which there is QMI (S2). We then argue that a determinable-based account can successfully accommodate all three varieties of QMI (S3). We close by observing the positive mutual bearing of our results on the coherence and intelligibility of both quantum mechanics and metaphysical indeterminacy (S4). (shrink)
A number of analytical philosophers have recently endorsed the view that the world itself is indeterminate in some respect. Intriguingly, ideas similar to the view are expressed by thinkers from Chinese Madhyamaka Buddhism, which may shed light on the current discussion of worldly indeterminacy. Using as a basis Chinese Madhyamaka thought, together with Jessica Wilson’s account of indeterminacy, I develop an ontological conception of indeterminacy, termed ontic indeterminacy, which centres on two complementary ideas—conclusive indeterminability and provisional (...) determinability. I show that OI is well-equipped to tackle several issues of worldly indeterminacy. My overarching aim is to present a viable and sustainable perspective on the subject of indeterminacy to enrich analytical philosophers’ insights into the intricate nature of reality. (shrink)
This paper defends the idea that there might be vagueness or indeterminacy in the world itself--as opposed to merely in our representations of the world--against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague properties and relations ; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague (...) objects ; we argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the world as a whole might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)
In this book I examine various forms of indeterminacy in the law and scrutinize (i.a. by way of game theoretical models) the conditions under which they can be strategically used. In particular, I analyze the advantages and disadvantages of indeterminacy in the wording of laws, contracts, and verdicts. Legal texts are particularly interesting insofar as they address a heterogeneous audience, are applied in a variety of unforeseeable circumstances and must, at the same time, lay down clear and unambiguous (...) standards. I argue for the claim that semantic vagueness is less relevant than commonly supposed in the debate, while other forms of indeterminacy (in particular, polysemy and standard-relativity) are underrated or altogether ignored. This misconception is, as I argue, due to a systematic confusion between semantic vagueness and these forms of indeterminacy. Once it is resolved, the value of indeterminacy can be clearly shown. (shrink)
In this article, I argue that the small-improvement argument fails since some of the comparisons involved in the argument might be indeterminate. I defend this view from two objections by Ruth Chang, namely the argument from phenomenology and the argument from perplexity. There are some other objections to the small-improvement argument that also hinge on claims about indeterminacy. John Broome argues that alleged cases of value incomparability are merely examples of indeterminacy in the betterness relation. The main premise (...) of his argument is the much-discussed collapsing principle. I offer a new counterexample to this principle and argue that Broome's defence of the principle is not cogent. On the other hand, Nicolas Espinoza argues that the small-improvement argument fails as a result of the mere possibility of evaluative indeterminacy. I argue that his objection is unsuccessful. (shrink)
Indeterminacy in its various forms has been the focus of a great deal of philosophical attention in recent years. Much of this discussion has focused on the status of vague predicates such as ‘tall’, ‘bald’, and ‘heap’. It is determinately the case that a seven-foot person is tall and that a five-foot person is not tall. However, it seems difficult to pick out any determinate height at which someone becomes tall. How best to account for this phenomenon is, of (...) course, a controversial matter. For example, some (such as Sorensen (2001) and Williamson (2002)) maintain that there is a precise height at which someone becomes tall and such apparent cases of indeterminacy merely reflects our ignorance of this fact. Others maintain that there is some genuine – and not merely epistemic – indeterminacy present is such cases and offer various accounts of how best to account for it. Supervaluationists (such as Keefe (2008)), for example, claim that the indeterminacy with respect to vague terms lies in their not having a single definite extension. Rather, each term is associated with a range of possible precise extensions or precisifications such that it is semantically unsettled which is the correct extension. One precisification of ‘tall’ might allow that anyone over five feet ten inches is tall, whereas another would only allow those over six foot to qualify; but no precisification will take someone who is five foot to be tall, and someone who is seven foot will count as tall on all precisifications. Thus – while someone who is seven foot will be determinately tall and someone who is five foot determinately not so – it will be indeterminate whether someone who stands at five foot eleven inches is tall. -/- Yet, it is important to stress that putative cases of indeterminacy are not limited to vague predicates of this kind. Philosophers have invoked indeterminacy in discussions of topics as diverse as moral responsibility (Bernstein (forthcoming)), identity over time (Williams (2014)), and the status of the future (Barnes and Cameron (2009)). In this paper, we focus on two areas where discussion of various kinds of indeterminacy has been commonplace: physics and fiction. We propose a new model for understanding indeterminacy across these domains and argue that it has some notable advantages when compared to earlier accounts. Treating physics and fiction cases univocally also indicates an interesting connection between indeterminacy in these two areas. (shrink)
You may not know me well enough to evaluate me in terms of my moral character, but I take it you believe I can be evaluated: it sounds strange to say that I am indeterminate, neither good nor bad nor intermediate. Yet I argue that the claim that most people are indeterminate is the conclusion of a sound argument—the indeterminacy paradox—with two premises: (1) most people are fragmented (they would behave deplorably in many and admirably in many other situations); (...) (2) fragmentation entails indeterminacy. I support (1) by examining psychological experiments in which most participants behave deplorably (e.g., by maltreating “prisoners” in a simulated prison) or admirably (e.g., by intervening in a simulated theft). I support (2) by arguing that, according to certain plausible conceptions, character evaluations presuppose behavioral consistency (lack of fragmentation). Possible reactions to the paradox include: (a) denying that the experiments are relevant to character; (b) upholding conceptions according to which character evaluations do not presuppose consistency; (c) granting that most people are indeterminate and explaining why it appears otherwise. I defend (c) against (a) and (b). (shrink)
The threat of ontological deflationism (the view that disagreement about what there is can be non‐substantive) is averted by appealing to realism about fundamental structure—or so tells us Ted Sider. In this paper, the notion of structural indeterminacy is introduced as a particular case of metaphysical indeterminacy; then it is argued that structural indeterminacy is not only compatible with a metaphysics of fundamental structure, but it can even safeguard it from a crucial objection; finally, it is shown (...) that, if there are instances of structural indeterminacy, a hitherto unacknowledged variety of ontological deflationism will arise. Unless structure is shown to be determinate, ontological deflationism remains a live option. Furthermore, I will consider whether structural indeterminacy could be challenged by adopting a naturalistic epistemology of structure; the question is answered in the negative on the basis of a formal result concerning theory choice. Finally, I submit a new way of articulating the epistemology of structure, which hinges on the very possibility of structural indeterminacy. (shrink)
This paper discusses and relates two puzzles for indicative conditionals: a puzzle about indeterminacy and a puzzle about triviality. Both puzzles arise because of Ramsey's Observation, which states that the probability of a conditional is equal to the conditional probability of its consequent given its antecedent. The puzzle of indeterminacy is the problem of reconciling this fact about conditionals with the fact that they seem to lack truth values at worlds where their antecedents are false. The puzzle of (...) triviality is the problem of reconciling Ramsey's Observation with various triviality proofs which establish that Ramsey's Observation cannot hold in full generality. In the paper, I argue for a solution to the indeterminacy puzzle and then apply the resulting theory to the triviality puzzle. On the theory I defend, the truth conditions of indicative conditionals are highly context dependent and such that an indicative conditional may be indeterminate in truth value at each possible world throughout some region of logical space and yet still have a nonzero probability throughout that region. (shrink)
This paper examines two puzzles of indeterminacy. The first puzzle concerns the hypothesis that there is a unified phenomenon of indeterminacy. How are we to reconcile this with the apparent diversity of reactions that indeterminacy prompts? The second puzzle focuses narrowly on borderline cases of vague predicates. How are we to account for the lack of theoretical consensus about what the proper reaction to borderline cases is? I suggest (building on work by Maudlin) that the characteristic feature (...) of indeterminacy is alethic normative silence, and use this to explain both plurality and lack of consensus. (shrink)
It has frequently been suggested that quantum mechanics may provide a genuine case of ontic vagueness or metaphysical indeterminacy. However, discussions of quantum theory in the vagueness literature are often cursory and, as I shall argue, have in some respects been misguided. Hitherto much of the debate over ontic vagueness and quantum theory has centered on the “indeterminate identity” construal of ontic vagueness, and whether the quantum phenomenon of entanglement produces particles whose identity is indeterminate. I argue that this (...) way of framing the debate is mistaken. A more thorough examination of quantum theory and the phenomenon of entanglement reveals that quantum mechanics is best interpreted as supporting what I call the “vague property” construal of ontic vagueness, where vague properties are understood in terms of determinable properties without the corresponding determinates. (shrink)
I propose a new argument showing that conscious vision sometimes depends constitutively on conscious attention. I criticise traditional arguments for this constitutive connection, on the basis that they fail adequately to dissociate evidence about visual consciousness from evidence about attention. On the same basis, I criticise Ned Block's recent counterargument that conscious vision is independent of one sort of attention (‘cognitive access'). Block appears to achieve the dissociation only because he underestimates the indeterminacy of visual consciousness. I then appeal (...) to empirical work on the interaction between visual indeterminacy and attention, to argue for the constitutive connection. (shrink)
This paper constructs a model of metaphysical indeterminacy that can accommodate a kind of ‘deep’ worldly indeterminacy that arguably arises in quantum mechanics via the Kochen-Specker theorem, and that is incompatible with prominent theories of metaphysical indeterminacy such as that in Barnes and Williams (2011). We construct a variant of Barnes and Williams's theory that avoids this problem. Our version builds on situation semantics and uses incomplete, local situations rather than possible worlds to build a model. We (...) evaluate the resulting theory and contrast it with similar alternatives, concluding that our model successfully captures deep indeterminacy. (shrink)
Barnes (2014) has argued in this journal for the following conditional: If there is any metaphysical indeterminacy, this must be at the most fundamental level of reality. To argue for this claim, Barnes relies on two principles that I shall call bivalent completeness and determinate link. According to the former, a complete description is a bivalent assignment of truth values to every sentence. The determinate link, instead, establishes that the determination relation between levels of reality preserves determinacy from one (...) level to another. In response to Barnes’ conclusion, Eva (2018) has recently pointed out that bivalent completeness is question begging. In this paper, I will first show why Eva's line of reasoning can be resisted. My aim will then be to present a stronger case against Barnes’ argument by challenging the determinate link. In the presence of metaphysical indeterminacy, the link between fundamental and derivative facts might itself be the locus of indeterminacy. I will conclude by showing that Barnes and Eva make many unwarranted assumptions regarding both indeterminacy and fundamentality. The logical space around the connection between these two notions appears to be much wider than what they seem to be aware of, or so I will argue. (shrink)
An influential theory has it that metaphysical indeterminacy occurs just when reality can be made completely precise in multiple ways. That characterization is formulated by employing the modal apparatus of ersatz possible worlds. As quantum physics taught us, reality cannot be made completely precise. I meet the challenge by providing an alternative theory which preserves the use of ersatz worlds but rejects the precisificational view of metaphysical indeterminacy. The upshot of the proposed theory is that it is metaphysically (...) indeterminate whether p just in case it is neither true nor false that p, and no terms in ‘p’ are semantically defective. In other words, metaphysical indeterminacy arises when the world cannot be adequately described by a complete set of sentences defined in a semantically nondefective language. Moreover, the present theory provides a reductive analysis of metaphysical indeterminacy, unlike its influential predecessor. Finally, I argue that any adequate logic of a language with an indeterminate subject matter is neither compositional nor bivalent. (shrink)
Moral indeterminacy can be problematic: prospectively it can give rise to deliberative anguish, and retrospectively, it can leave us in a limbo as to what attitudes it is appropriate to form with respect to past actions with indeterminate moral status. These problems give us reason to resolve ethical indeterminacy. One mechanism for doing so involves the use of our normative powers to place obligations on ourselves and to waive our claims against others. This mechanism could operate through an (...) explicit agreement, but could also operate through implicit endorsement of a social convention. However, there are important limits on when the mechanism can eliminate moral indeterminacy. (shrink)
If the world itself is metaphysically indeterminate in a specified respect, what follows? In this paper, we develop a theory of metaphysical indeterminacy answering this question.
In this paper I argue that Gareth Evans’ famous proof of the impossibility of de re indeterminate identity fails on a counterpart-theoretic interpretation of the determinacy operators. I attempt to motivate a counterpart-theoretic reading of the determinacy operators and then show that, understood counterpart-theoretically, Evans’ argument is straightforwardly invalid.
In simple action theory, when people choose between courses of action, they know what the outcome will be. When an individual is making a choice "against nature," such as switching on a light, that assumption may hold true. But in strategic interaction outcomes, indeterminacy is pervasive and often intractable. Whether one is choosing for oneself or making a choice about a policy matter, it is usually possible only to make a guess about the outcome, one based on anticipating what (...) other actors will do. In this book Russell Hardin asserts, in his characteristically clear and uncompromising prose, "Indeterminacy in contexts of strategic interaction... Is an issue that is constantly swept under the rug because it is often disruptive to pristine social theory. But the theory is fake: the indeterminacy is real."In the course of the book, Hardin thus outlines the various ways in which theorists from Hobbes to Rawls have gone wrong in denying or ignoring indeterminacy, and suggests how social theories would be enhanced--and how certain problems could be resolved effectively or successfully--if they assumed from the beginning that indeterminacy was the normal state of affairs, not the exception. Representing a bold challenge to widely held theoretical assumptions and habits of thought, Indeterminacy and Society will be debated across a range of fields including politics, law, philosophy, economics, and business management. (shrink)
In the mid-20th century, descriptive meta-ethics addressed a number of central questions, such as whether there is a necessary connection between moral judgment and motivation, whether moral reasons are absolute or relative, and whether moral judgments express attitudes or describe states of affairs. I maintain that much of this work in mid-20th century meta-ethics proceeded on an assumption that there is good reason to question. The assumption was that our ordinary discourse is uniform and determinate enough to vindicate one side (...) or the other of these meta-ethical debates. I suggest that ordinary moral discourse may be much less uniform and determinate than 20th century meta-ethics assumed. (shrink)
This article explores the notions of indeterminacy and creation in Castoriadis’ work. The notions of indeterminacy and creation are initially associated with Castoriadis’ conception of Being as Chaos contradicted with what Castoriadis calls “ensemblistic-identitary logic”. The conception of Being as Chaos is then linked with the notion of otherness analyzed as creation ex nihilo. In particular, creation ex nihilo is analyzed in the context of Castoriadis division of Being’s multiplicity into difference and otherness. I will argue that Being’s (...) multiplicity as difference refers to the “ensemblistic-identitary logic” while otherness comes up with a novel form of Being identified as ex nihilo creation. Finally, otherness is approached through Castoriadis’ conception of time whereby otherness and, consequently, time is further associated with Castoriadis’ notion of imaginary as the latter deploys in the social-historical field of mankind through the imaginary significations of society. (shrink)
For Sengzhao (374−414 CE), a leading Sanlun philosopher of Chinese Buddhism, things in the world are ontologically indeterminate in that they are devoid of any determinate form or nature. In his view, we should understand and use words provisionally, so that they are not taken to connote the determinacy of their referents. To echo the notion of ontic indeterminacy and indicate the provisionality of language, his main work, the Zhaolun, abounds in paradoxical expressions. In this essay, I offer a (...) philosophical analysis and rational reconstruction of Sengzhao’s linguistic thought, with a view to exploring the rationale for and purpose of his use of paradoxical language. (shrink)
An attractive approach to the semantic paradoxes holds that cases of semantic pathology give rise to indeterminacy. What attitude should a rational agent have toward a proposition that it takes to be indeterminate in this sense? Orthodoxy holds that rationality requires that an agent disbelieve such a proposition. I argue that a rational agent should be such that it is indeterminate whether it believes the proposition in question. For rational agents, indeterminacy in the objects of their attitudes will (...) filter up to the attitudes themselves. (shrink)
Quine's argument for indeterminacy and inscrutability equivocates about what it is for one set of truths to determine another. In addition to being unsupported, these doctrines lead Quine to reject our ordinary notions of meaning, truth, and reference in favor of certain replacement notions, including stimulus meaning, and disquotational, or Tarski, truth and reference for one's own present language. This is self-defeating. To formulate the doctrines of physicalism, underdetermination, indeterminacy, and inscrutability, one must refer to the totality of (...) true propositions about the subject matter of physics, and it's relation to all other propositions--something precluded by Quine's semantic eliminativism. (shrink)
This paper defends the idea that there might be vagueness or indeterminacy in the world itself---as opposed to merely in our representations of the world---against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague *properties and relations*; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague *objects*; (...) we argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the *world as a whole* might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)
This paper argues that several sorts of metaphysical and semantic indeterminacy afflict the causal relation. If, as it is plausible to hold, there is a relationship between causation and moral responsibility, then indeterminacy in the causal relation results in indeterminacy of moral responsibility more generally.
: Significant issues remain for understanding and evaluating the Quinean critique of the analytic/synthetic distinction. These issues are highlighted in a puzzling mismatch between the common philosophical attitude toward the critique and its broader intellectual legacy. A discussion of this mismatch sets the larger context for criticism of a recent tradition of interpretation of the critique. I argue that this tradition confuses the roles and relative importance of indeterminacy, a priority, and analyticity in the Quinean critique.
It is often assumed that there is a close connection between Quine's criticism of the analytic/synthetic distinction, in 'Two dogmas of empiricism' and onwards, and his thesis of the indeterminacy of translation, in Word and Object and onwards. Often, the claim that the distinction is unsound (in some way or other) is taken to follow from the indeterminacy thesis, and sometimes the indeterminacy thesis is supported by such a claim. However, a careful scrutiny of the indeterminacy (...) thesis as stated by Quine, and the varieties of the analytic/synthetic distinction, reveals that the two claims are mutually independent. Neither does the claim that the distinction is unsound follow from the indeterminacy thesis, nor that thesis from unsoundness claim, under any of the common interpretations of the analytic/synthetic distinction. (shrink)
In ‘Fair Infinite Lotteries’ (FIL), Wenmackers and Horsten use non-standard analysis to construct a family of nicely-behaved hyperrational-valued probability measures on sets of natural numbers. Each probability measure in FIL is determined by a free ultrafilter on the natural numbers: distinct free ultrafilters determine distinct probability measures. The authors reply to a worry about a consequent ‘arbitrariness’ by remarking, “A different choice of free ultrafilter produces a different ... probability function with the same standard part but infinitesimal differences.” They illustrate (...) this remark with the example of the sets of odd and even numbers. Depending on the ultrafilter, either each of these sets has probability 1/2, or the set of odd numbers has a probability infinitesimally higher than 1/2 and the set of even numbers infinitesimally lower. The point of the current paper is simply that the amount of indeterminacy is much greater than acknowledged in FIL: there are sets of natural numbers whose probability is far more indeterminate than that of the set of odd or the set of even numbers. (shrink)
One pressing question facing Barnes andWilliams is that of which vari- eties of metaphysical indeterminacy can be can accommodated within their framework. In what remains, I shall examine whether their framework can allow that it sometimes metaphysically indeterminate whether an object exists. I shall begin by outlining an argument, due to Theodore Sider, to the conclusion that vague existence is impossible.
A growing literature is premised on the claim that quantum mechanics provides evidence for metaphysical indeterminacy. But does it? None of the currently fashionable realist interpretations involve fundamental indeterminacy and the ‘standard interpretation’, to the extent that it can be made out, doesn't require indeterminacy either.
Derek Parfit has offered numerous arguments in an attempt to establish that identity is not what matters. Jens Johannson has recently argued that Parfit's various arguments for the claim that identity is not what matters fail to establish what Parfit takes such arguments to establish. Johannson contends that this is due in part to the invalidity of one of Parfit's key arguments, and the fact that Parfit ignores a position that is compatible with the conclusions of his successful arguments and (...) the claim that identity is in fact what matters, namely, that I survive fission as either one of the fission products or the other, but it is indeterminate which one I survive as. I aim to establish here that both of Johannson's assertions are problematic. As a corollary of this task, I hope to shed some light on the relationship between indeterminacy and fission-based arguments for the claim that identity is not what matters. (shrink)
This article examines whether Willard Van Orman Quine’s indeterminacy thesis can be sustained. The argument from above, Quine argues, can derive indeterminacy as its conclusion. I will argue that the indeterminacy claim cannot be sustained. I further argue that Quine changed the formulation of the underdetermination of theory by evidence (UTE) argument from what Duhem said to the Quine/Pierce meaning verification view, in order use the new formulation of UTE to imply indeterminacy. Given all that, we (...) see when we apply the old UTE argument we only arrive at underdetermination of theory by evidence, and that applies to all sciences, philosophy and knowledge, including philosophy of language. (shrink)
In the first part of the paper, I present a framework for the description and evaluation of teleosemantic theories of intentionality, and use it to argue that several different objections to these theories (the various indeterminacy and adequacy problems) are, in a certain precise sense, manifestations of the same underlying issue. I then use the framework to show that Millikan's biosemantics, her own recent declarations to the contrary notwithtanding, presents indeterminacy. In the second part, I develop a novel (...) teleosemantic proposal which makes progress in the treatment of this family of problems. I describe a procedure to derive a (unique) homeostatic property cluster [HPC] from facts having to do with the properties that a certain indicator relied on, in the events leading to its fixation in a certain population. This HPC is the one that should figure in the content attribution to the indicator in question. (shrink)
