This paper argues that “free will” is vague. The argument has two steps. First, I argue that free will is a matter of degrees and, second, that there are no sharp boundaries separating free decisions and actions and non‐free ones. After presenting the argument, I focus on one significant consequence of the thesis, although others are mentioned along the way. In short, considerations of vagueness help understand the logic behind so‐called manipulation arguments, but also show why these arguments are ultimately (...) flawed. (shrink)
I defend the hypothesis that the semantic paradoxes, the paradoxes about collections, and the sorites paradoxes, are all paradoxes of reference fixing: they show that certain conventionally adopted and otherwise functional reference-fixing principles cannot provide consistent assignments of reference to certain relevant expressions in paradoxical cases. I note that the hypothesis has interesting implications concerning the idea of a unified account of the semantic, collection and sorites paradoxes, as well as about the explanation of their “recalcitrance”. I also note that (...) it does not necessarily imply that one should not expect the sometimes hoped for “unique” solution to a paradox of these kinds. (shrink)
The presentation of the “dual picture of vagueness” in my earlier work is supplemented here with a number of additional considerations. I emphasize how the picture lends itself naturally to treatments of the contribution of a typical degree adjective to propositional content and to truth conditions. A number of reasonable refinements of the picture are presented, especially concerning occasions of use of a degree adjective in which a class containing a sorites series is somehow involved in content fixing, but in (...) such a way that an extension ultimately gets fixed for the predicate. I also develop the observation that standard theories of the logical and semantic paradoxes rely on the idea that the content-fixing mechanisms for the paradoxical expressions work well in general but fail in some localized cases, and that while standard theories of the sorites paradox are clearly not based on this idea at all, the dual theory is fully based on the idea. Next, I offer a few remarks on some recent theories of vagueness and the sorites that are broadly in the spirit of the dual picture, emphasizing the aspects where the latter compares favorably against those recent theories. Finally, the question whether the dual theory is statable with truth according to the theory itself is considered in more detail than in my earlier presentation. (shrink)
This dissertation explores the prospects of postdeflationary substantive theorizing about truth. Postdeflationary theories define the concept of truth or the property of being a true truthbearer in a way that respects the deflationary desiderata of clarity, purity, and permissiveness with truth-aptness, without a necessary commitment to the core negative thesis of the deflationary approach. Postdeflationary substantive theories further acknowledge the complexity and explanatory utility of truth in understanding and defining other concepts and phenomena. The motivation for pursuing this study arises (...) from the so-called contemporary crisis of truth, where a substantive understanding of truth is subjected to widespread skepticism, critique, and even cynicism both inside and outside of philosophy in formal and mundane discourse. To better understand this crisis, particular attention is directed towards the deflationary critique of substantive theories of truth, which is a prevalent point of discussion in contemporary literature on western analytic philosophy. By exploring the limits and philosophical sustainability of deflationary critique of substantive accounts of truth, valuable insight is gained about the contemporary crisis of truth and the potential for substantive theorizing about truth in general. This dissertation composes of an introduction and four original research publications that address two connected themes: exploration of the philosophical sustainability of deflationary critique of substantive theories of truth, and exploration of the prospects for development of the now popular substantive pluralist theories of truth. These themes constitute both negative and positive aspects in relation to analyzing the prospects of postdeflationary substantive theorizing about truth. The first part of this dissertation focuses on arguing against the widespread deflationary readings of W.V.O. Quine’s truth, who is widely interpreted as a prominent and influential deflationist in both the secondary literature on his philosophy and contemporary truth-theoretic debates more broadly conceived. The first essay demonstrates that Quine’s immanent conception of truth involves commitments that are incompatible with general and theory-specific framings of the deflationary thesis. The second essay demonstrates conflicts between Quine’s views and what has in recent literature been argued as strong and moderate variants of the deflationary thesis. In conclusion, these essays demonstrate that the widespread deflationary readings of Quine’s truth are mistaken, thus removing a prominent thinker from the deflationists ranks while simultaneously casting suspicion towards the philosophical sustainability of the deflationary approach in general. The second part of this dissertation explores the prospects of postdeflationary substantive theorizing about truth by analyzing the limits and prospects for development of the increasingly popular substantive pluralist theories. The third essay explores different ways in which semantic ambiguity poses trouble for current pluralist models. The fourth essay argues that to achieve the theoretical desiderata that pluralists ask from discourse domains, the latter ought to be individuated on ontological rather than topical grounds. In conclusion, these essays demonstrate that while current pluralist models involve shortcomings, they encompass potential for development and provide a viable prospect for sustainable postdeflationary substantive theorizing about truth. (shrink)
Carter (Noûs 55(1):171–198, 2021) argued that while most simple positive numerical sentences are literally false, they can communicate true contents because relevance has a weakening effect on their literal contents. This paper presents a challenge for his account by considering entailments between the imprecise contents of numerical sentences and the imprecise contents of comparatives. I argue that while Carter's weakening mechanism can generate the imprecise contents of plain comparatives such as `A is taller than B', it cannot generate the imprecise (...) contents of comparatives that quantify the difference between their arguments, such as `A is exactly n times as tall as B'. I then propose an alternative theory on which intervals serve as both thick degrees on a scale and denotations of numerical expressions. I argue that the alternative theory can account for the imprecise contents of both forms of comparatives as well as the data that motivate Carter's theory. (shrink)
In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the (...) search for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)
This short article pairs the realms of “Mathematics”, “Philosophy”, and “Poetry”, presenting some corners of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greek heroic epic, or the consistent meter with standardized rhyme scheme and a “volta” of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion Barbu, the creator (...) of the Barbilian spaces, have written appreciated poems. We will focus here on an avant-garde movement in literature, art, philosophy, and science, called Paradoxism, founded in Romania in 1980 by a mathematician, philosopher and poet, and on the laboured writing exercises of the Oulipo group, founded in Paris in 1960 by mathematicians and poets, both of them still in act. (shrink)
This paper summarises the contributions to our Topical Collection on indeterminacy and underdetermination. The collection includes papers in ethics, metaethics, logic, metaphysics, epistemology, philosophy of science, philosophy of language and philosophy of computation.
If Amelia utters ‘Brad ate a salad in 2005’ assertorically, and she is speaking literally and sincerely, then I can infer that Amelia believes that Brad ate a salad in 2005. This paper discusses what makes this kind of inference truth-preserving. According to the baseline picture, my inference is truth-preserving because, if Amelia is a competent speaker, she believes that the sentence she uttered means that Brad ate a salad in 2005; thus, if Amelia believes that that sentence is true, (...) then she must believe that Brad ate a salad in 2005. I argue that this view is not correct; on pain of irrationality, normal speakers can’t have specific beliefs about the meaning of the sentences they utter. I propose a new account, relying on the view that epistemically responsible speakers utter sentences assertorically only if they believe all the propositions which they think those sentences might mean. (shrink)
Methodological deflationism is a policy about how we should conduct ourselves when it comes to theories of truth: in particular, a deflationary theory of truth should be taken as one’s starting point, and the notion of truth should be inflated only as necessary. This policy is motivated, in part, by the need to balance the theoretical virtue of parsimony with that of explanatory sufficiency. In this article, the case is made that the methodological deflationist is in no position to properly (...) balance those virtues—a point made evident by tracing the relationship between semantic theories and the explanatory needs of theories of truth. Furthermore, methodological deflationism threatens to unduly influence semantic theorizing and, in doing so, displays an inappropriate bias towards deflationary theories of truth. (shrink)
I argue that vagueness produces counterexamples to modus tollens. I begin by outlining cases where indicative and counterfactual conditionals seem intuitively to be determinate even when their antecedents are borderline and their consequents are determinately false. Accepting these intuitions has some revisionary implications; however, rejecting them leads to unacceptable consequences for our knowledge of conditionals. I thus take it that we should accept that our intuitions are reliable. I show it follows that modus tollens fails. I conclude by defending this (...) consequence from some objections. (shrink)
Dorothy Edgington’s work has been at the centre of a range of ongoing debates in philosophical logic, philosophy of mind and language, metaphysics, and epistemology. This work has focused, although by no means exclusively, on the overlapping areas of conditionals, probability, and paradox. In what follows, I briefly sketch some themes from these three areas relevant to Dorothy’s work, highlighting how some of Dorothy’s work and some of the contributions of this volume fit in to these debates.
Sometimes, when comparing a pair of items, it appears that neither is better than the other, nor that they are equally good, relative to a certain value that they bear. Cases of this kind have come to be referred to as superhard comparisons. What grounds superhard comparisons? On the dominant views, held by Joseph Raz and Ruth Chang, they are grounded, at least partially, in the failure of the three classic value relations—‘better than’, ‘worse than’, and ‘equally good’. On an (...) alternative view, which might be called the vagueness view, first developed by John Broome, they are grounded in vagueness about which of the classic value relations holds between the items. In this paper, I pay special attention to superhard comparisons in the context of choice and develop a novel argument against the dominant views on the basis of an account of decision-making under vagueness in ‘better than’. The upshot is that a new vagueness view emerges. (shrink)
This chapter discusses the defence of metaphysical indeterminacy by Elizabeth Barnes and Robert Williams and discusses a classical and bivalent theory of such indeterminacy. Even if metaphysical indeterminacy arguably is intelligible, Barnes and Williams argue in favour of it being so and this faces important problems. As for classical logic and bivalence, the chapter problematizes what exactly is at issue in this debate. Can reality not be adequately described using different languages, some classical and some not? Moreover, it is argued (...) that the classical and bivalent theory of Barnes and Williams does not avoid the problems that arise for rival theories. (shrink)
Miriam Schoenfield argues that moral realism and moral vagueness imply ontic vagueness. In particular, she argues that neither shifty nor rigid semantic accounts of vagueness can provide a satisfactory explanation of moral vagueness for moral realists. This paper constitutes a response. I argue that Schoenfield's argument against the shifty semantic account presupposes that moral indeterminacies can, in fact, be resolved determinately by crunching through linguistic data. I provide different reasons for rejecting this assumption. Furthermore, I argue that Schoenfield's rejection of (...) the rigid semantic account is based on a presupposition that ultimately implies the very same claim that is under dispute: the vagueness of moral predicates in imperfect languages persists in the perfect language, as well. (shrink)
‘Puzzles’, ‘word games’, ‘logical anomalies’, whatever we call them, they perplex us and challenge our familiar patterns of reasoning. One of these puzzles, among many others, originated from the mind of an ancient Megarian logician, Eubulides of Miletus, and endures to the modern day.1 Its name, ‘sorites’, can be traced to the Greek word soros, meaning ‘heap.’ The answer to whether one grain of sand ‘is a heap’ or ‘is not a heap’ seems quite simple: it is not a heap. (...) However, as we add grains to the one, at what future point does the non-heap become a heap? Our decision is fraught with uncertainty. Are the objects or the language we are using to describe them vague? In academic philosophy, the ancient Greek puzzle has gained the status of a paradox, as philosophers apply stoic and modern logic to these propositions considered to have vague predicates. The current debate has developed quite serious and wide-ranging implications, such as whether sorites issues provide adequate grounds for abandoning our standard ontology (or our understanding of what really exists), 2 and (germinating into another discipline) whether vagueness in the language of legal rules can generate disagreement as to whether there are right answers to questions of law. 3 Several unique solutions to the paradox have been proposed, yet all suffer from specific inadequacies that might, upon further reflection, disappear in the event that we endeavour to produce a synthesis. When we say that we are attempting to derive a synthesis, we seek to combine elements of two solutions for the sake of creating a new (and hopefully, though not necessarily, a better) one. The paradox of the sorites, or ‘the heap’, appeals to us because it challenges our assumption that we may categorically describe clear cases and their negations, yet fail to distinguish the borderline ones. I will demonstrate that some combinations of solutions are easy fits while others are extremely weak and awkward as attempts at resolving the paradox. Nonetheless, the process of synthesis produces three noteworthy combinations. (shrink)
Edgington has proposed a degree-theoretic account of vagueness that yields a highly elegant solution to the sorites paradox. This paper applies her account to the paradox of Theseus’ ship, which is generally classified among the paradoxes of material constitution and not as a sorites paradox.
In psychiatry there is no sharp boundary between the normal and the pathological. Although clear cases abound, it is often indeterminate whether a particular condition does or does not qualify as a mental disorder. For example, definitions of ‘subthreshold disorders’ and of the ‘prodromal stages’ of diseases are notoriously contentious. Philosophers and linguists call concepts that lack sharp boundaries, and thus admit of borderline cases, ‘vague’. This overview chapter reviews current debates about demarcation in psychiatry against the backdrop of key (...) issues within the philosophical discussion of vagueness: Are there various kinds of vagueness? Is all vagueness representational? How does vagueness relate to epistemic uncertainty? What is the value of vagueness? Given the immense social, moral, and legal importance of demarcating the normal from the pathological in psychiatry, what are the pros and cons of gradualist approaches to mental disorders, that is, of construing boundaries as matters of degree? (shrink)
This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided (...) which bear on three debated issues concerning quantification. (shrink)
Classical logic rests on the assumption that there are two mutually exclusive and jointly exhaustive truth values. This assumption has always been surrounded by philosophical controversy. Doubts have been raised about its legitimacy, and hence about the legitimacy of classical logic. Usually, the assumption is stated in the form of a general principle, namely the principle that every proposition is either true or false. Then, the philosophical controversy is often framed in terms of the question whether every proposition is either (...) true or false. The main purpose of the paper is to show that there is something wrong in this way of putting things. The point is that the common way of understanding the controversial assumption is misconceived, as it rests on a wrong picture of propositions. In the first part of the paper I outline this picture and I argue against it. In the second part I sketch a different picture of propositions and I suggest how this leads to conceive the issue of classical logic in different terms. (shrink)
Available from UMI in association with The British Library. Requires signed TDF. ;An attempt is made to find the proper response to paradoxes of the sorites-type. In PART I, a chain argument is given with 'tall' in which it seems that a false conclusion is derived by repeated steps of MPP from true premises. In particular, each of the conditional premises is derived by UE from a so-called inductive premise sustained by familiar claims that 'tall' is both vague and observational. (...) A variety of tokens is then given of what seems to be the same paradox-type; some particularly interesting examines are yielded by a common form of essentialism. In PART II, it is argued that the original paradox with 'tall' is not plausibly solved by taking borderline sentences as either true or false. The 'gap' account on which borderline sentences are neither true nor false provides no leverage in itself, nor when combined with the distinctively anti-realist theses introduced in PART III. In PART IV, the force of the paradoxes is also shown to survive the proposal that borderline sentences should be assigned one of many truth-values between true and false. The problem of interpretation is compounded by the same difficulties faced by some of the more sedate accounts considered earlier. This leaves the conclusion in PART V that our original appraisal of the chain argument with 'tall' is mistaken only in the perverse sense that it is a mistake to suppose that some mistake must have been made. From this it follows that there is a sense in which our language is inconsistent, but much of the hostility aroused by this claim is shown to dissipate once its content is explained in terms of the rule-conflict thesis. (shrink)
There are certain metaphysically interesting arguments ‘from vagueness’, for unrestricted mereological composition and for four‐dimensionalism, which involve a claim to the effect that idioms for unrestricted quantification are precise. An elaboration of Lewis’ argument for this claim, which assumes the view of vagueness as semantic indecision, is presented. It is argued that the argument also works according to other views on the nature of vagueness, which also require for an expression to be vague that there are different admissible alternatives of (...) the relevant sort, such as epistemicism, as defended by Williamson. Recent attempts to resist the argument are discussed and rejected. (shrink)
Logic, Semantics, Ontology consists of three papers concerned with ontological issues. The first, "That There Might Be Vague Objects", is a critical study of Gareth Evans's essay, "Can There be Vague Objects". The author argues that the formal argument presented in Evans's paper is valid and that a contradiction can indeed be derived from the statement that it is indeterminate whether a is b. However, the deduction theorem fails in the required logic: Hence, one can not derive the validity of (...) the statement that it is determinate whether a is b. ;One who holds the view that there are vague objects is committed to the legitimacy of those principals to which appeal is required in the proof. Hence, the view that there are vague objects is committed to the claim that no statement of the form "It is indeterminate whether a is b" can be true, but also to denying the validity of its negation. Possible motivations for such a position are sketched and its tenability is defended. ;The second paper, "Whether Structure May Be Misleading", is a critical study of Crispin Wright's Frege's Conception of Numbers as Objects, in which Wright defends Platonism, the view that there areObjects of various sorts. The author argues that Wright's view is too promiscuous, that Wright's view appears to commit us to the existence of far too may sorts of objects. The causes of this ontological extravagance are isolated, and the author suggests ways to avoid it. In the process, however, the author also argues that certain classical Reductionist arguments fail and that their failure is closely connected with the strongest motivations for Platonism. (shrink)
Fundamental problems of the uses of formal techniques and of natural and instrumental practices have been raised again and again these past two decades, in many quarters and from varying viewpoints. We have brought a number of quite basic studies of these issues together in this volume, not linked con ceptually nor by any rigorously defined problematic, but rather simply some of the most interesting and even provocative of recent research accomplish ments. Most of these papers are derived from the (...) Boston Colloquium for the Philosophy of Science during 1973-80, the two exceptions being those of Karel Berka (on scales of measurement) and A. A. Zinov'ev (on a non-tradi tional theory of quantifiers). Just how intriguing these results (or conjectures?) seem to us may be seen from some brief quotations: (1) Judson Webb: ".... the abstract machine concept has many of the appropriate kinds of properties for modelling living, reproducing, rule following, self-reflecting, accident-prone, and lucky creatures... the a priori logical results relevant to the abstract machine concept, above all Godel's, could not conceivably have turned out any better for the mechanist. " (2) M. L. Dalla Chiara: "... modal interpretation (of quantum logic) shows clearly that it possesses a logical meaning which is quite independent of quantum mechanics. " (3) Isaac Levi: (as against Peirce and Popper) "... infallibilism is con sistent with corrigibilism, and a view which respects avoidance of error is an important desideratum for science. (shrink)
Clearly, vagueness is an inevitable feature of natural language. The practice of law, which is necessarily done within the confines of language, must inevitably come to grips with the phenomenon of vagueness. What philosophers working with these concerns tend to debate about is the extent to which vagueness affects law and the role that vagueness plays therein. Roy Sorensen argues that vagueness in law is not functional and therefore to be avoided as much as possible by judges. Sorensen equates the (...) decisions that judges make about borderline cases with lying. Sorensen bases his conclusions in part upon the idea that borderline cases do admit of truth-values; it is simply the case that we do not have the means to discover these truth-values. I find that Sorensen may be too quick on the draw in accusing judges of the moral indiscretion of lying, and that judges, though perhaps acting insincerely in a truly minimal sense, are in fact not lying. (shrink)
According to a popular, plausible, but also controversial view about the nature of vagueness, vagueness is a matter of semantic indecision. I show that, even if «I» is vague and the view of vagueness as semantic indecision is correct, I could be a material composite object all the same.
This article aims to examine the import of science to the contemporary philosophical debate on ontic vagueness. It is shown, first, that our best theory on the structure of mater, quantum mechanics, clearly ascribes vague properties to objects. This point is explained by both a general theoretical analysis and by some simple examples. The advantage of these examples over that which has been hotly discussed in the literature is underlined. Secondly, it is pointed out that stronger evidence for the existence (...) of vague objects is available through a series of theoretical and experimental results in microphysics, imposing severe constraints on any theory purporting to restore sharpness in the properties of quantum objects. (shrink)