Vagueness and Indeterminacy, Misc

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)

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)

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 banal 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’ (Clarke-Doane & Hamkins (...) [2017]) 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 a ‘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 upshot is that, if Higher Order Pluralism is true, then there is no fixed metatheory from which to characterize higher order reality. (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.

Summary A. Vagueness is not definable in terms of behaviour (Section 4).

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)

Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2006 Prague Colloquium on "Reasoning about Vagueness and Uncertainty".

R. M. Sainsbury; III*—Tolerating Vagueness, Proceedings of the Aristotelian Society, Volume 89, Issue 1, 1 June 1989, Pages 33–48, https://doi.org/10.1093/arist.

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 and A. A. Zinov'ev. Just how intriguing these results seem to us may be seen from some brief quotations: 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. " M. L. Dalla Chiara: "... modal interpretation shows clearly that it possesses a logical meaning which is quite independent of quantum mechanics. " Isaac Levi: "... 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)

Can we solve the Problem of the Many, and give a general account of the indeterminacy in definite descriptions that give rise to it, by appealing to metaphysically indeterminate entities? I argue that we cannot. I identify a feature common to the relevant class of definite descriptions, and derive a contradiction from the claim that each such description is satisfied by a metaphysically indeterminate entity.

In this research work I take into account the relation of indistinguishability. This relation seems to be prima facie reflexive, symmetric and transitive; in short, an equivalence relation. However, there are some cases where the relation under consideration fails to be transitive. In this thesis I will discuss two of those cases: vagueness of gradabale adjectives and count nouns, and identity criteria involving perceptual phenomena. My research attempts to answer the following question: how is it possible to communicate and to (...) make meaningful judgments using vague terms and non-transitive identity criteria? This thesis presents an analysis of vagueness and identity criteria that shows that speakers always consider the elements which vague expressions refer to or whose names compose identity statements within a context and from a certain level of precision. I also attempt to provide a formal treatment of vague adjectives and count nouns on the one hand, and of identity criteria on the other. I employ two key concepts in both the treatments: context dependence and granularity. (shrink)

A theory of higher-order vagueness for partially-defined, context-sensitive predicates like is blue is offered. According to the theory, the predicate is determinately blue means roughly is an object o such that the claim that o is blue is a necessary consequence of the rules of the language plus the underlying non-linguistic facts in the world. Because the question of which rules count as rules of the language is itself vague, the predicate is determinately blue is both vague and partial in (...) a sense analogous (though not completely identical) to the sense in which is blue is vague and partial. However, higher-order vagueness stops there. Although the anti-extension of is determinately blue differs from that of is blue, further iterations of determinately have no semantic effect. The paper closes with a discussion of the need to posit sharp and precise lines dividing the range of potential application of a vague predicate into semantically distinct categories. It is argued that this is less of a problem for the present theory than for many others, because the categories into which the range is divided by the present theory -- like the category of counting as blue because the rules of the language offer speakers no discretion, as opposed to the category of counting as blue because speakers have invoked an absolute minimum of discretion in adjusting the contextually sensitive boundaries of the predicate -- are not those that the linguistic competence of ordinary speakers equips them to make highly accurate and reliable judgments about. (shrink)