Metaphysical Indeterminacy

Possibility semantics offers an elegant framework for a semantic analysis of modal logic that does not recruit fully determinate entities such as possible worlds. The present papers considers the application of possibility semantics to the modeling of the indeterminacy of the future. Interesting theoretical problems arise in connection to the addition of object-language determinacy operator. We argue that adding a two-dimensional layer to possibility semantics can help solve these problems. The resulting system assigns to the two-dimensional determinacy operator a well-known (...) logic (coinciding with the logic of universal modalities under global consequence). The paper concludes with preliminary investigations of how to integrate the system with a temporalist conception of propositions and how to compare to more established frameworks. (shrink)

This work in progress develops a systematic metaphysics from a single foundational claim: that a state of perfect indifference – one containing no contrast, no "this rather than that" – is self-refuting the moment it is posited, whether approached epistemically (what must be true for anything to be possible) or ontologically (what must be true for anything to exist). Both routes converge on a single minimal structure, provisionally termed a "minimal asymmetry," and this convergence is named the Principle of Reflexive (...) Intelligibility. A pivotal "Limit" section then delivers the argument's real conclusion, replacing the seemingly settled one reached just before it: the question of whether the epistemic structure precedes the ontological, or the two co-constitute one another, cannot be answered from within the argument, because "prior to" is itself already a determination available only inside the structure the question tries to get behind. This entails a further consequence applied reflexively to the text itself: the argument is valid but its soundness cannot be checked, since verifying soundness requires a separation between claim and ground that has not yet occurred at that level. -/- The text then turns its own critical lens onto its central term, demonstrating live, through a deliberate performative contradiction, that even a sentence explaining the limits of language ("within the condition of determinacy") is true when first read and false on reflection – a claim only intelligible once the reader has followed its "footprints to nowhere". This reader-relative, time-indexed handling of contradiction distinguishes the text from comparable historical strategies: Wittgenstein discards the ladder once climbed, Hegel dialectically supersedes the contradiction, and Derrida leaves his comparable term, différance, permanently suspended. Crucially, the text does not rest this method on an unverifiable private feeling – it is only used at one moment in the text; it grounds genuine understanding in "reach" and "closure" – the depth and spread of abstraction levels a crystallization can hold – which function as public, structurally locatable criteria rather than private sensation, meeting the standard demand that meaning be checkable by more than one observer. From this position, the argument descends into determinate categories – being, time, space, the observer, reason, ethics, language, culture, and institutions – each redefined as the same ground encountered at a different level of abstraction, before ascending through music, death, play, and the sacred. Written in dual registers of argument and phenomenological prose, the text frames this constructive descent as more philosophically productive than resting in the unfalsifiable claims typical of ungrounded metaphysical systems. You can read it via the external link. (shrink)

It has been argued that quantum mechanics provides the best case for thinking there is genuine metaphysical indeterminacy. In particular, it seems that the locations of quantum systems are indeterminate in a way that doesn’t depend on semantic or epistemic limitations. In this paper, I draw on concepts from the metaphysics of location to dispel this impression. Using quantum versions of exact and weak location introduced by Pashby (2016), I distinguish two accounts of quantum location: the spanner view and the (...) inexact location view. Each account requires the rejection of an intuitive locative principle, but I argue that neither gives rise to metaphysical indeterminacy. (shrink)

Many of the most pressing moral problems we face involve collective harms generated by large numbers of individually insignificant actions. Unlike triggering cases—where a threshold exists such that a single act could be decisive—non‐triggering cases lack any such sharp cutoff. In these cases, no individual act appears to make a difference to whether harm occurs, and it may be metaphysically indeterminate whether a given aggregate is harmful or whether a marginal contribution plays any causal role at all. I argue that (...) standard approaches to moral responsibility, which rely on difference‐making or expected outcomes, struggle to provide action‐guiding reasons in these contexts. Drawing on the security‐dependence account of causation, I argue that agents have pro tanto moral reasons to refrain from actions that make harm more secure, even when those actions neither determine outcomes nor probabilistically influence them in any straightforward sense. Doing so explains how individual actions can remain morally relevant under conditions of overdetermination and metaphysical indeterminacy. (shrink)

I investigate the hitherto unexplored hypothesis that powers may be ontically vague, and offer an account of what powers would be like in such a case. The proposed account offers an innovative characterisation of powers as forces that transform themselves into their manifestations. It builds on, but also critiques, Neil E. Williams’s (2019) recent theory of powers. I conclude by considering the general implications of my proposal for the metaphysics of causality.

These are my materials (a short precis, and replies to Alan Rhoda and Daniel Rubio) for an invited symposium on my book _The Open Future: Why Future Contingents are All False_ (OUP, 2021) in IJPR. [The commentaries from Rhoda/Rubio are available on their respective PhilPapers profiles.].

The way we answer questions about what there is crucially depends on the language and the logic in which they are framed. This entry introduces the orthodox view on how to carry out such debates, as was formulated by W. V. O. Quine, as well as a number of influential alternatives. A further issue that is explored is whether disagreement about what there is turns on mind-independent features of reality, or it is an artifact of language.

Metaphysical indeterminacy (MI) is indeterminacy originating in the nonrepresentational world. I develop a theory of MI in terms of objective chance with a number of attractive features: it provides a reductive analysis of MI; it applies at both macroscopic and microscopic scales; it demystifies the target phenomenon by employing no special‐purpose metaphysical primitives; it does not prejudge the question whether the logic of a language capable of describing an indeterminate subject matter is classical, or whether its semantics is bivalent; it (...) comes with built‐in epistemic criteria informed by a naturalistic methodology. The chancy account is compared to three salient alternatives: the Third‐Way View, which postulates the existence of indeterminate propositions; Metaphysical Supervaluationism, which takes indeterminacy to be a metaphysical primitive; and the Determinable‐Based Account, which reduces the target phenomenon to patterns of determinables and determinates. It is argued that the chancy account fares better overall when tested against two paradigmatic case studies: future indeterminacy, and quantum indeterminacy. Applications to further domains are also sketched, and a number of open problems outlined. (shrink)

This paper offers uniform, unified solutions to the three problems of material constitution, i.e., the Puzzle of the Statue and the Clay (the modal version), the Puzzle of the Ship of Theseus, and the Problem of the Many. The solutions are based on the single idea that there is much indeterminacy in the material world. The solution to the first puzzle states that there is only one object in the sculptor’s studio whose modal profile is largely indeterminate. The solution to (...) the second puzzle states that while the Original Ship survives the changes either as the Repaired Ship or as the Reassembled Ship, it is indeterminate which one. The solution to the third puzzle states that while the cat on the mat is identical with one of the many precise catlike objects on the mat, it is indeterminate which one. The metaphysical-mathematical theory behind these solutions is spelled out, according to which all propositions, properties, and relations are in reality Boolean-degreed, including the numerical identity relation, and the indeterminacy of a proposition is identified as the proposition’s involving an intermediate Boolean degree between Truth (or 1) and Falsity (or 0). (shrink)

The standard formulation of Relational Quantum Mechanics (RQM) models events through projective measurements, thereby importing idealisations that fail to capture generalized quantum measurements. We show that this limitation is not intrinsic to RQM but to the PVM framework. By identifying relational events with effects—the elements of POVMs that encode physically implemented interactions—RQM becomes fully POVM-native. Events are effect-ascriptions, and relational state updates follow the general Kraus rule, with no appeal to projectors or Hilbert-space dilations. This reformulation constitutes an initial step (...) toward dissolving the “Problem of Generic Measurements” recently raised by Calosi and Riedel [11], thereby naturally accommodating weak, noisy, and continuous measurements. We conclude our analysis by identifying at least three possible metaphysical candidates for our POVM-native formulation of RQM. (shrink)

Since its inception in 1996, Rovelli’s Relational Quantum Mechanics (RQM) has left the status of non-interacting systems notably underexplored. When discussed at all, one prevailing view has maintained that attributing properties to isolated systems within RQM is simply meaningless. However, it has become increasingly evident that without a satisfying account of non-interacting systems, RQM risks sliding toward antirealist interpretations–at least insofar as such systems are concerned. In response to this crucial challenge, two main approaches have been advanced. One is a (...) form of dispositionalism, which suggests that isolated physical systems possess only dispositional properties. The other appeals to a determinable-based account of metaphysical indeterminacy, suggesting that a non-interacting quantum system may bear a determinable property without possessing any unique determinate of that determinable at a given time. In this paper, we offer a new response to the question of what can be meaningfully said about quantum systems prior to measurement in the context of RQM. In particular, drawing on the formalism of Positive Operator-Valued Measures (POVMs), we emphasize that (1) preparation–like measurement–constitutes a physical interaction capable of assigning relational properties to a system, and that (2) POVMs are indispensable for the proper description of observables with continuous spectra. On this basis, we propose that RQM can accommodate an entity-realist interpretation of non-interacting systems by attributing to them what we term relational unsharp properties. As we will show, this theoretical move preserves the relational nucleus of RQM while enabling a physically and philosophically coherent account of non-interacting quantum systems. (shrink)

Creationism about fictional and theoretical names holds that seemingly empty names such as ‘Sherlock Holmes’ and ‘Vulcan’ refer to abstract objects created by authors and scientific theorists. This paper poses an objection to creationism: in cases of fiction writing or scientific theorising where it is indeterminate whether one succeeds or fails in referring to an object in the world, creationism renders it metaphysically indeterminate whether an abstract object is created. However, the indeterminate existence of abstract objects constitutes an untenable metaphysical (...) commitment, offering a compelling reason to reject creationism. (shrink)

This paper expounds A. G. Baumgarten’s innovative account of contingent existents. It will be shown that Baumgarten’s contribution consists in accounting for the difference between merely possible and actual beings in terms of determinacy. The resulting account is attractive: it does not require a distinct property that sets actual beings apart, and it provides a promising metaphysical backdrop for explaining thought about possibilia.

This article proposes a reading of quantum metaphysical indeterminacy from the perspective of Parsons' Nuclear Meinongianism. In doing so, we identify a fundamental incompatibility between a key feature of Parsons' theory and standard quantum mechanics. Our approach interprets quantum indeterminacy as property incompleteness. However, this move, when combined with Parsons' framework, leads to what we term the ``Incompleteness-Entails-Nonexistence Principle'' (IENP), which implausibly entails the nonexistence of quantum objects. For Meinongianism to be a suitable tool for the metaphysics of quantum mechanics, (...) this principle must be addressed. We argue for dropping the IENP and discuss the resulting metaphysical and metametaphysical consequences. (shrink)

We consider the observables describing spatiotemporal properties in the context of two of the most popular approaches to quantum gravity (QG), namely String Theory and Loop QG. In both approaches these observables are described by non-commuting operators. In analogy with recent arguments put forward in the context of non-relativistic quantum mechanics [see Calosi and Mariani (Philos. Compass 16(4):e12731, 2021) for a review], we suggest that the physical quantities corresponding to those observables may be interpreted as ontologically indeterminate—i.e., indeterminate in a (...) way that is non-epistemic and semantic-independent. This working hypothesis has not received enough attention in the current debate on QG, and yet it may prove explanatory useful in several respects. First, it provides a clear background for understanding how some features of QG are ontologically continuous to features of quantum mechanics. Second, it sets the stage for asking new interesting questions about QG, for instance concerning the status of the so-called Eigenstate-Eigenvalue link. Third, it indirectly shows how the debate on ontological indeterminacy may extend well beyond the non-relativistic case, contrary to what seems to be assumed. Fourth, and perhaps more importantly, it provides a promising alternative to the received view on QG [Wüthrich et al. (Philosophy Beyond Spacetime: Implications from Quantum Gravity, Oxford University Press, Oxford, 2021)] according to which spacetime is not fundamental. On the view we shall suggest, spacetime may be indeterminate and yet fundamental. (shrink)

Del Santo and Gisin have recently argued that classical mechanics exhibits indeterminacy and that by treating the observables of classical mechanics with real number precision we introduce hidden variables that restore determinacy. In this article we introduce the conceptual machinery required to critically evaluate these claims. We present a characterization of indeterminacy which can capture both quantum indeterminacy and the classical indeterminacy Del Santo and Gisin propose. This allows us to show that there is an important difference between the two: (...) their classical indeterminacy can be resolved with hidden variables in a manner which is not possible for quantum indeterminacy. (shrink)

ABSTRACT This article develops a phenomenological account to characterize the openness of the future. More specifically, showing that phenomenological experience is necessary to derive the belief that the future is open by adopting a realist reading of phenomenology where our experience can be used to speculate beyond the thought-world correlation postulated by Quentin Meillassoux and show that this openness is best captured as an indeterminacy of the future itself. This indeterminacy of the future is the indeterminacy of which events are (...) actualized or made to happen out of all the potential events. Here, our phenomenological experience allows us to feel what it is like to have the ability to participate in an event and make it happen. We can then generalize such ability to all other objects even inanimate ones. As a result, we have a phenomenological but non-anthropocentric account of the openness of the future. (shrink)

Smooth Infinitesimal Analysis (SIA) is a remarkable late twentieth-century theory of analysis. It is based on nilsquare infinitesimals, and does not rely on limits. SIA poses a challenge of motivating its use of intuitionistic logic beyond merely avoiding inconsistency. The classical-modal account(s) provided here attempt to do just that. The key is to treat the identity of an arbitrary nilsquare, e, in relation to 0 or any other nilsquare, as objectually vague or indeterminate—pace a famous argument of Evans [10]. Thus, (...) we interpret the necessity operator of classical modal logic as “determinateness” in truth-value, naturally understood to satisfy the modal system, S4 (the accessibility relation on worlds being reflexive and transitive). Then, appealing to the translation due to Gödel et al., and its proof-theoretic faithfulness (“mirroring theorem”), we obtain a core classical-modal interpretation of SIA. Next we observe a close connection with Kripke semantics for intuitionistic logic. However, to avoid contradicting SIA’s non-classical treatment of identity relating nilsquares, we translate “=” with a non-logical surrogate, ‘E,’ with requisite properties. We then take up the interesting challenge of adding new axioms to the core CM interpretation. Two mutually incompatible ones are considered: one being the positive stability of identity and the other being a kind of necessity of indeterminate identity (among nilsquares). Consistency of the former is immediate, but the proof of consistency of the latter is a new result. Finally, we consider moving from CM to a three-valued, semi-classical framework, SCM, based on the strong Kleene axioms. This provides a way of expressing “indeterminacy” in the semantics of the logic, arguably improving on our CM. SCM is also proof-theoretically faithful, and the extensions by either of the new axioms are consistent. (shrink)

In this paper, I examine a case for fundamental indeterminacy (FI) by Elizabeth Barnes and offer my counterarguments. Barnes' account of FI includes both the characterization of FI and why we need to accept it. I argue that her reasons for accepting FI can be challenged even when we accept her characterization of FI. Her main claim is that finding a fundamental proposition that our fundamental theory is indeterminate about (FPF) gives us a reason to accept FI in metaphysics. I (...) challenge her claim by pointing out more plausible options to address FPFs. An FPF may either indicate that the theory is nonfundamental or lead us to accept the antirealist view; there is no room for FI in either option. One may insist on accepting FI, but I argue that it is not theoretically rewarding enough. Hence, Barnes' case for FI can be contested. (shrink)

1. Jay Newhard (2021) proposes a novel solution to the Liar Paradox, which he calls the alethic indeterminacy solution. Bradley Armour-Garb (2021) raises a pair of objections to the alethic indeter...

The degreed view is an influential account in the debate on quantum value indefiniteness, linking the gradedness of quantum properties to quantum indeterminacy. This paper challenges the connection between degrees and indeterminacy by presenting an example of a graded quantum property that does not entail metaphysical indeterminacy. Through an investigation of two graded approaches to location in quantum mechanics, the paper argues that while the first account, degreed instantiation of exact location, is indeterminate, the second account, degreed quantum location, is (...) not. This indicates that indeterminacy and degrees are not inherently linked, offering a novel perspective on quantum ontology. The paper advocates adopting a graded view of quantum properties without indeterminacy, potentially leading to a paradigm shift in understanding quantum phenomena. (shrink)

Indeterminacy is metaphysical (or worldly) if it has its source in the way the world is (rather than how it is represented or known). There are two questions we could ask about indeterminacy. First: does it exist? Second: is indeterminacy derivative? I focus on the second question. Specifically, I argue that (at least some) metaphysical indeterminacy can be derivative, where this roughly means that facts about indeterminacy are metaphysically grounded in facts about what is determinate.

Many philosophers take for granted that there is a strong pre‐theoretical intuition that the future is open and that it is worth trying to make sense of that intuition in theoretical terms. In this paper, I give a characterisation of the ordinary intuition in terms of three elements: our sense of agency, the difference in normativity between memories and expectations and naïve understanding of causality. Those intuitions allow us to pin down certain desiderata that an account of openness should respect. (...) Firstly, the fact that the future is open is not merely due to our epistemic situation (the fact that we do not know what the future will bring). Secondly, openness is not merely a matter of nomological indeterminism; even if indeterminism is part of what makes the future open, it cannot be the end of the story. Thirdly, openness requires more than ‘modal flexibility’ (i.e. the fact that the future could be different from what actually will be). I provide a minimal theory of openness, which respects those desiderata and which is based on the semantic notion of unsettledness and the metaphysical notion of indeterminacy. Roughly, the future is open if future‐tensed claims concerning contingent matters are such that their truth value is presently unsettled, and they are semantically unsettled because the future is metaphysically indeterminate. I then argue that this theory is compatible with what I call the closed future view. According to the latter, there is only one way in which things will go, although, given indeterminism, it is unsettled which way it is. I then consider an objection to my compatibility claim: if the open future claim is metaphysically substantive, there should be a way to differentiate it from the closed future scenario. I consider whether a friend of openness could rely on a dynamic metaphysics of time (such as presentism, or the growing block view) in order to differentiate their position from the closed future scenario. I argue that the appeal to a dynamic universe is ineffective. (shrink)

Contrary to the popular thought, classical logic, in the deductive sense, is not tied to bivalence (i.e., 2-valuedness) in its semantics, for any many-element Boolean algebra, e.g., 4-element, 8-element, 16-element, ..., or infinite-element Boolean algebra, can be used for the semantics equally well. Classical logic with a Boolean many-valued semantics is called Boolean many-valued logic. In philosophy we encounter situations in which we want to say that there is no fact of the matter about whether certain statements are true or (...) false, such as the situations described in the Fission Problem for personal identity, the Sorites Paradox, and the Liar Paradox. In such situations, it is reasonable to give the relevant sentences neither Truth (or 1) nor Falsity (or 0) but intermediate truth values between 0 and 1. In the Boolean many-valued approach advocated in this book, we assign intermediate Boolean values to those sentences. This way, we can have not just two but many truth values at our disposal but retain classical logic as our base logic at the same time. -/- As a preliminary to the philosophical discussions given in the subsequent chapters, Chap. 1 offers short but rigorous accounts of classical logic, many-element Boolean algebras, and the Boolean many-valued semantics of classical logic. It is maintained, among other things, that classical logic is not just a set of deduction rules but rather a set of rules that include also metadeduction rules; and that the notion of logical consequence to be employed in the Boolean many-valued semantics ought to be not that of truth preservation but that of so-called bottomline preservation. (shrink)

Chapter 2 offers the Boolean many-valued solution to the Fission Problem for personal identity; and, in the process, the chapter delineates the basic ideas of the Boolean many-valued approach. Suppose that person a goes into surgery, in which his memory is transplanted to two cloned bodies of his while his original body is destroyed, and that two persons, b and c, come out of the surgery, each thinking that he is a. In this situation, it is reasonable to say that (...) while a is identical with either b or c but not both, it is indeterminate which one. A Boolean 4-valued model is given that supports this claim. Then it is shown that if a splits into not just two, but 3, 4, ..., n persons instead, the number of Boolean values necessary for the models will increase to at least 8, 16, ... 2^n, respectively. The pros and cons of using a single large Boolean algebra for a uniform treatment of all those cases is discussed. The same models are applied for a (partial) solution of the Problem of the Many, and some outstanding issues, to be resolved in the subsequent chapters, are spelled out. (shrink)

Semanticism about vagueness states that vagueness exists not in the world itself but only in our semantic representations of the world, whereas onticism acknowledges the existence of at least some vagueness in the world itself. Chapter 4, while acknowledging that the Boolean many-valued approach itself is neutral to the semanticism/onticism debate, argues for onticism and spells out an ontic theory of indeterminacy and vagueness consistent with the Boolean many-valued approach. The theory postulates Boolean degrees in propositions, properties, and relations, including (...) the numerical identity relation and the set-membership relation. Evans’s argument against vague identity is refuted. (shrink)

Chapter 5 discusses two issues involving truth, the disquotation schema, and the Boolean many-valued approach. In the Boolean many-valued approach, the (deductive) law of excluded middle is retained but the (semantic) principle of bivalence is abandoned. However, Timothy Williamson has argued against the tenability of this option, contending that excluded middle must imply bivalence. The first half of the chapter refutes Williamson’s argument by showing that truth in a Boolean many-valued semantics, i.e., the highest value of a Boolean algebra, is (...) not disquotational truth that Williamson needs in his argument. The former truth predicate is called the correspondence truth predicate and distinguished from the disquotational truth predicate. The second half of the chapter offers the Boolean 4-valued solution to the Liar Paradox, in which each ungrounded atomic sentence such as the Liar sentence is given one of the two intermediate values between truth and falsity. The disquotation schema breaks down for the ungrounded atomic sentences, and therefore the paradox is avoided. The last section concludes the entire book. (shrink)

In the (shorter) first half of Chap. 3, the Boolean many-valued solution to the Sorites Paradox is given. The (much longer) second half investigates the relation between the Boolean many-valued approach and another, popular, approach to vagueness, the precisificational approach. It is shown that the Boolean value of a sentence can be identified with the set of precisifications in which the sentence is true. A notion of logical consequence, called the reformulated bottomline preservation notion, can be introduced directly to precisificational (...) spaces; alternatively, the S4 determinacy (or ‘determinately’) operator can be introduced into the spaces with a bivalent semantics. These three approaches, i.e., the Boolean many-valued approach, the precisificational approach with the reformulated bottomline preservation notion of logical consequence, and the modal, S4 determinacy operator approach, are shown equivalent. Supervaluationism, of both global and local variety, is dismissed as employing incorrect notions of logical consequence. Another modal operator, the S5 determinacy operator, is introduced. (shrink)

This book shows that the assumption that classical logic is essentially a bivalent (i.e., 2-valued) logic, a logic of truth and falsity, is an incorrect and harmful conception. Classical logic is certainly a Boolean logic, and the smallest (non-degenerate) Boolean algebra is the 2-element Boolean algebra; however, there are numerous Boolean algebras that have more than 2 elements, such as the 4-, 8-, 16-, ..., infinite-element Boolean algebra, and they all work equally well for the semantics of classical logic. Contrary (...) to the popular thought, there is such a thing as classical (or Boolean) many-valued logic. The book applies this logic to solve such philosophical problems as the Fission Problem for personal identity, the Sorites Paradox, and the Liar Paradox. All these problems concern situations that involve indeterminacy or vagueness, situations where there seems 'no fact of the matter' that makes the relevant sentences true or false, thus requiring truth value gaps between truth and falsity. Because of that, classical logic has been thought to be an inadequate tool to deal with the problems. This book, however, offers solutions to those problems by retaining classical logic but assigning intermediate Boolean values to the relevant sentences. The book is of great value to researchers and graduate students in philosophy, especially for those who are interested in the philosophical issues surrounding indeterminacy, vagueness, and truth. (shrink)

This essay outlines a hierarchical framework of Reality that allows for degrees of Reality. I use Reality (with a capital “R”) to designate reality in a primitive, metaphysical sense. Reality, grounding, and essence are the key elements of the framework presented here. I assume that Reality must have a fundamental level and all fundamental phenomena must be Real. Moreover, I postulate that everything non-fundamental is ultimately grounded in the fundamental Real. But what about the Reality of the non-fundamental? I argue (...) that it is possible for non-fundamental phenomena to be Real, Unreal, or Semi-Real. The framework developed here accommodates these possibilities and illuminates them using the notion of essence. I argue that the essential nature of a phenomenon determines its degree of Reality. The framework does not assume that Reality must have degrees but only that it may have degrees. Its theoretical attractiveness consists in its ability to accommodate many diverse intuitions about grounding, help us better understand and classify theories about grounding, and illuminate Reality and its possible degrees. (shrink)

In ‘Alethic undecidability and alethic indeterminacy’, Jay Newhard (2020) proposes what he calls an ‘alethic indeterminacy’ approach to the semantic paradoxes. In this paper, I explore his proposed approach. What I will show is that Newhard’s response to the paradoxes cannot be sustained. If I am right about this, then this spells the end for his type of approach.

This work applies Jessica Wilson’s metaphysical indeterminacy approach, ba-sed on the determinable-determinate distinction, to ancient ontologies, focu-sing on the Cyrenaic school. It argues that this conceptual framework elucida-tes the nature of indeterminacy in Cyrenaic metaphysics, complementing and resolving tensions in Ugo Zillioli’s interpretation. The study reviews the con-temporary debate on metaphysical indeterminacy, presents Wilson’s approach and its applications, and applies it to ancient ontologies, particularly the Cyre-naic school. It discusses the conceptual and interpretative advantages of this application, contributing to a (...) deeper understanding of Cyrenaic metaphysics within the context of indeterminacy ontologies in ancient philosophy. (shrink)

There is ample divergence among students of vagueness as to what exactly should be understood by a vague object, or by ontic, or metaphysical vagueness in general. In fact, the very intelligibility of the notion of a vague object has been called into question by important philosophers in the past, indicating that the task of finding a coherent, philosophically fertile characterization of the notion is not a simple one. This article aims to contribute to this undertaking, by identifying, examining and (...) comparing some of the main proposals in the literature. It is suggested that we should try to characterize vague properties and relations independently of any particular view about vague objects, and then to formulate a criterion for vague objects in terms of indefinite instantiation of sharp properties. It is shown that this approach makes it easier to evaluate certain semantic-epistemic dismissive strategies concerning the possibility of there being vague objects. It is briefly indicated that if the objects are analysed with the theoretical and conceptual resources of quantum physics (and not of classical physics, as is ordinarily done), such dismissive strategies are seriously undermined. (shrink)

A standard approach to indeterminacy treats ‘determinately’ and ‘indeterminately’ as modal operators. Determinacy behaves like necessity; indeterminacy like contingency. This raises two questions. What is the appropriate modal system for these operators? And how should we interpret that system? Ken Akiba has developed an account of ontic indeterminacy that interprets possible worlds as worldly precisifications. He argues that this account vindicates S4 as the logic of indeterminacy. In this paper I explore one significant and surprising consequence of this view. I (...) do this in two stages. First, I prove a technical result, which I call the Infinite Indeterminacy Theorem. Roughly put, this theorem states that, at any given precisification w, either every instance of indeterminacy admits of never-ending higher-order indeterminacy, or else there's indeterminacy in an infinite amount of distinct atomic formulas. In slogan form: either all indeterminacy is infinitely ascending or else there's infinitely wide indeterminacy. Second, I unpack the metaphysical consequences of this technical result (under its intended interpretation) and assess their plausibility. I conclude that these consequences commit Akiba's theory to highly contentious – and arguably untenable – views about the metaphysics of indeterminacy and related matters. (shrink)

Orthodox quantum theory tells us that properties of quantum systems are represented by self-adjoint operators, and that two properties are incompatible just in case their respective operators do not commute. We present a puzzle for this orthodoxy, pinpointing the exact assumptions at play. Our solution to the puzzle specifically challenges the assumption that non-commuting operators represent incompatible properties. Instead, they represent incompatible levels of specification of determinates for a single determinable. This solution yields insight into the nature of so-called quantum (...) indeterminacy and demonstrates a new and fruitful application of the determinable-determinate relation in quantum theory. (shrink)

Recently, we (Synthese, 199(5–6):13247–13281, 2021) proposed Kripke-like semantics for two quantum logics of interderminacy. These logics expand the vocabulary of standard Birkhoff-von Neumann propositional quantum logic with a pair of modal operators interpreted as “it is (in)determinate that”, allowing them to express in the object language statements such as “it is indeterminate that system S is spin-up in the x-direction”, as well as statements of any logical complexity involving ascriptions of (in)determinacy. We present an axiomatization of a logic closely related (...) to one of these quantum logics of indeterminacy and prove that this axiomatization is sound and complete with respect to the Kripke-like semantics. We then prove that this logic is decidable. (shrink)

The question of whether Everettian quantum mechanics (EQM) justifies the existence of metaphysical indeterminacy has recently come to the fore. Metaphysical indeterminacy has been argued to emerge from three sources: coherent superpositions, the indefinite number of branches in the quantum multiverse and the nature of these branches. This paper reviews the evidence and concludes that those arguments don’t rely on EQM alone and rest on metaphysical auxiliary assumptions that transcend the physics of EQM. We show how EQM can be ontologically (...) interpreted without positing metaphysical indeterminacy by adopting a deflationary attitude towards branches. Two ways of developing the deflationary view are then proposed: one where branches are eliminated, and another where they are reduced to the universal quantum state. (shrink)

Theorists who advocate worldly (metaphysical or ontological) indeterminacy—the idea that the world itself is indeterminate in one or more respects—should address how we understand the signifying nature and function of language in light of worldly indeterminacy. I first attend to Sengzhao and Jizang, two leading thinkers in Chinese Sanlun Buddhism, to reconstruct a Chinese Madhyamaka notion of ontic indeterminacy. Then, I draw on the thinkers’ views to propose a provisional (non-definitive) understanding of the nature and use of language. Under this (...) understanding, an expression signifying a thing is provisional in that the expression connotes no determinate feature of the thing. (shrink)

A non-solipsist form of presentness is usually thought to require the non-relative co-presentness of space-like separated events, where this requirement further implies the non-relative simultaneity of these events. Since special relativity is thought to rule out any global, non-relative simultaneity, typical non-solipsist forms of presentness are taken to be inconsistent with special relativity. To address this problem, we re-explain the relationship between the non-solipsism of presentness and co-presentness by appealing to metaphysical indeterminacy. We propose presentness indeterminacy, the thesis that where (...) an event, p, is determinately present, any event in space-like relation to p lacks a determinate tense. We argue that for many theories of time, indeterminate co-presentness is all that the non-solipsism of presentness requires. Since there is no determinate co-presentness, the inconsistency between presentness and special relativity in these theories disappears. (shrink)

A social fact S is grounded by some plurality of grounds. And the fact that S has the grounding-conditions it does is anchored by some set of anchors. Epstein has recently suggested (2019) that the anchoring relation is a cross-world determination relation. In this paper we put forward three arguments against this view. First, we argue from the analogy between social and non-social kinds: there is no cross-world determination involved in non-social natural kinds. Secondly, we take issue with the very (...) idea of cross-world determination: no determination relation in our current metaphysical toolkit can have relata that occupy different possible worlds (in the relevant sense). Thirdly, we argue that cross-world anchoring generates an indeterminacy problem: if S holds in an anchorless world w, and there are distinct anchors (for S) holding at w1 and w2 respectively, then it is indeterminate whether S’s grounding-conditions hold in virtue of the w1-anchors or the w2-anchors. (shrink)

Is it sometimes indeterminate whether two events or variables are causally related? Can causal statements be vague? The analysis of three potential types of cases of causal indeterminacy and causal vagueness yields an affirmative answer. The claim that some cases of omission, and some cases of prevention, give rise to indeterminate causal relations depends on the premise that omissions and preventions can be causal. A second type of indeterminate causation corresponds to causal statements whose truth value is indeterminate because they (...) contain vague predicates. Such vagueness can have two sources. Only one yields indeterminate causation. Finally, there is indeterministic probabilistic causation. If “indeterministic overdetermination” is interpreted as metaphysical rather than epistemic, it is inappropriate to speak of indeterminacy. Rather, there is no fact of the matter about which of the two sources of probability raising really is the cause. It is more appropriate to say that both are contributing causes. “Indeterministic trumping” gives rise to a form of indeterminacy that belongs to the category of the open future. Once the effect has occurred, no indeterminacy remains. (shrink)

The “consequence argument”, together with the “luck objection”, which are summed up by the “standard argument against free will”, state that if our volition were dependent on physical causally indeterministic processes, our actions would lack control and, thereby, result in random behavior that would be a mere matter of luck and chance. In particular, quantum indeterminacy is supposed to be of no use in support of libertarian agent-causation theories because any volitional act interfering with the probability distributions de fining quantum (...) laws would lead to its violation. Building upon recent conjectural work questioning this assumption (Clarke 2010, Kastner 2016, Masi 2023), it is shown, with a concrete example involving quantum indeterminacy, how a hypothetical agent with access to the temporal ordering of events can pre-determine the result of a process taking place in time without modifying the probability laws defining it. This conclusion is then taken as a basis for a libertarian panpsychist interpretative model. (shrink)

One feature of language is that we are able to make mistakes in our use of language. Amongst other sorts of mistakes, we can misspeak, misspell, missign, or misunderstand. Given this, it seems that our metaphysics of words should be flexible enough to accommodate such mistakes. It has been argued that a nominalist account of words cannot accommodate the phenomenon of misspelling. I sketch a nominalist trope-bundle view of words that can.

ABSTRACT:Organismal superposition holds that the same individual both is and is not an organism, as a consequence of organismal pluralism. When coupled with the assumption that death is the cessation of an organism, this entails that there is no unique answer as to whether brain death is biological death. This essay argues that concerns about organismal pluralism and superposition do not undermine a theory of biological death, nor entail any metaphysical indeterminacy about the biological vital status of a brain-dead individual.

Recent philosophical discussions about metaphysical indeterminacy have been substantiated with the idea that quantum mechanics, one of the most successful physical theories in the history of science, provides explicit instances of worldly indefiniteness. Against this background, several philosophers underline that there are alternative formulations of quantum theory in which such indeterminacy has no room and plays no role. A typical example is Bohmian mechanics in virtue of its clear particle ontology. Contrary to these latter claims, this paper aims at showing (...) that different pilot-wave theories do in fact instantiate diverse forms of metaphysical indeterminacy. Namely, I argue that there are various questions about worldly states of affairs that cannot be determined by looking exclusively at their ontologies and dynamical laws. Moreover, it will be claimed that Bohmian mechanics generates a new form of modal indeterminacy. Finally, it will be concluded that ontological clarity and indeterminacy are not mutually exclusive, i.e., the two can coexist in the same theory. (shrink)

An increasing number of philosophers argue that indeterminacy is metaphysical (or worldly) in the sense that indeterminacy has its source in the world itself (rather than how the world is represented or known). The standard arguments for metaphysical indeterminacy are centered around the sorites paradox. In this essay, I present a novel argument for metaphysical indeterminacy. I argue that metaphysical indeterminacy follows from the existence of constitutive social construction; there is indeterminacy in the social world because there is indeterminacy in (...) how the social world is constructed. (shrink)

In his work on the open future, Patrick Todd outlines three models of how to deal with future contingents. These models must answer two questions: one metaphysical, about what facts there are in the world; one semantic, about how to deal with sentences involving ‘will.’ Model 1 has a privileged timeline. Model 2 has an actual future timeline but leaves it indeterminate which timeline that is. Model 3 has no future timeline. All three give will-sentences a modal treatement, as a (...) box over available futures. I will argue that Todd’s second model has problems and should be improved. The first is that it denies what Todd labels as the basic metaphysical intuition behind open-futurism. The second is that indeterminacy about the facts that characterize the actual timeline breaks through into indeterminate identity. I propose a fix to model 2 eliminating its actual future and resolving an issue that arises in applying the neutral semantics Todd endorses to indeterminate sentences. This improved model, I suggest, may even compare favorably to Todd’s preferred model 3. (shrink)

It has been argued that quantum mechanics forces us to accept the existence of metaphysical, mind-independent indeterminacy. In this paper, we provide an interpretation of the indeterminacy involved in the quantum phenomena in terms of a view that we call Plural Metaphysical Supervaluationism. According to it, quantum indeterminacy is captured in terms of an irreducibly plural relation between the actual world and various misrepresentations of it.