Supervaluationism and Logical Consequence: A Third Way

It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness. This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logical consequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion.     

真理、符合与收缩论

The central claim of this essay is that many deflationary theories of truth are variants of the correspondence theory of truth. Essential to the correspondence theory of truth is the proposal that objective features of the world are the truthmakers of statements. Many advocates of deflationary theories (including F. P. Ramsay, P. F. Strawson and Paul Horwich) remain committed to this proposal. Although T-sentences (statements of the form “s is true iff p”) are presented by advocates of deflationary theories of truth as truisms or analytic truths, T-sentences are often understood as entailing commitment to the central proposal of the correspondence theory.     

Some definitions of negation leading to paraconsistent logics

In positive logic the negation of a propositionA is defined byA X whereX is some fixed proposition. A number of standard properties of negation, includingreductio ad absurdum, can then be proved, but not the law of noncontradiction so that this forms a paraconsistent logic. Various stronger paraconsistent logics are then generated by putting in particular propositions forX. These propositions range from true through contingent to false.     

Reasons why in normative explanation

Normative explanations, which specify why things have the normative features they do, are ubiquitous in normative theory and ordinary thought. But there is much less work on normative explanation than on scientific or metaphysical explanation. Skow [2016. Reasons Why. Oxford: Oxford University Press] argues that a complete answer to the question why some fact Q occurs consists in all of the reasons why Q occurs. This paper explores this theory as a case study of a general theory that promises to offer us a grip on normative explanation which is independent of particular normative theories. I first argue that the theory doesn't give an adequate account of certain enablers of reasons which are important in normative explanation. I then formulate and reject three responses on behalf of the theory. But I suggest that since theories of this general sort have the right kind of resources to illuminate how normative explanation might be similar to and different from explanations in other domains, they nonetheless merit further exploration by normative theorists.     

Yes,Virginia, there Really are Paraconsistent Logics

B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever negation symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics — the preservationist logics — are not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations — even those that emerge from dialetheic approaches — does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism.     

Modernity and Morality in Habermas's Discourse Ethics

Discourse ethics is originally conceived as a programme of philosophicaljustification of morality. This depends on the formal derivation of the moral principle (U) from non-moral principles. The moral theory is supposed to fall out of a pragmatic theory of meaning. The original programme plays a central role in Habermas's social theory: the moral theory, if true, provides good evidence for the more general theory of modernization. But neither Habermas nor his followers have succeeded in providing a formal derivation. This essay shows how and why Habermas's proposed derivation is impossible. As if aware of the lacuna, Habermas has recently suggested that (U) can be derived by 'abduction' rather than deduction. The proposal draws heavily on modernization theory; hence the only justification for (U) now available to him rests on premises drawn from that theory. The original programme of the justificationof morality has thus given way to the weaker programme of the philosophical elucidationof morality. Further, since Habermas's moral theory is no longer justified independently of modernization theory, but at least partly by it, the moral theory cannot without circularity provide evidence for the modernization theory.     

Vague Objects with Sharp Boundaries

In this article I shall consider two seemingly contradictory claims: first, the claim that everybody who thinks that there are ordinary objects has to accept that they are vague, and second, the claim that everybody has to accept the existence of sharp boundaries to ordinary objects. The purpose of this article is of course not to defend a contradiction. Indeed, there is no contradiction because the two claims do not concern the same ‘everybody’. The first claim, that all ordinary objects are vague, is a claim that stems both from common sense intuitions as well as from various types of ontologies of ordinary objects. This puts then pressure on theories of vagueness to account for the vague nature of ordinary objects – but, as we shall see, all theories of vagueness have to accept the existence of sharp thresholds. This is obvious in the case of epistemicism, and it is a well‐known defect of supervaluationism, but as we will see friends of metaphysical vagueness do have to endorse the existence of sharp thresholds in their theory as well. Consequently, there are reasons for dissatisfaction with these accounts, since they do not seem to be able to do the job we asked them to do. 1     

How Truth Behaves When There’s No Vicious Reference

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of “no vicious reference” generated both by revision theories of truth and by fixed-point theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.     

Minimally inconsistent LP

The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial.     

Vagueness as closeness

This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate ‘F’ is vague just in case for any objects a and b, if a and b are very close in respects relevant to the possession of F, then ‘Fa’ and ‘Fb’ are very close in respect of truth. The definition is extended to cover vagueness of many-place predicates, of properties and relations, and of objects. Some of the most important advantages of the definition are that it captures the intuitions which motivate the thought that vague predicates are tolerant, without leading to contradiction, and that it yields a clear understanding of the relationships between higher-order vagueness, sorites susceptibility, blurred boundaries, and borderline cases. The most notable consequence of the definition is that the correct theory of vagueness must countenance degrees of truth.     

Vagueness and Blurry Sets

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S ₁ to the effect that Bob is bald is x true, for x in [0,1], there should be a further statement S ₂ which tells us how true S ₁ is, and so on – that is, it accommodates higher-order vagueness – without resorting to the claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic – as opposed to the semantics – of vague discourse is classical. I model the extension of a vague predicate P as a blurry set, this being a function which assigns a degree of membership or degree function to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence 0.3,0.2, for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature.     

SQUEEZING AND STRETCHING: HOW VAGUENESS CAN OUTRUN BORDERLINENESS

The paper develops a critical dialectic with respect to the nowadays dominant approach in the theory of vagueness, an approach whose main tenet is that it is in the nature of the vagueness of an expression to present borderline cases of application, conceived of as enjoying some kind of distinctive normative status. Borderlineness is used to explain the basic phenomena of vagueness, such as, for example, our ignorance of the location of cut-offs in a soritical series. Every particular theory of vagueness exemplifying the approach makes use, in the vague object language, of a definiteness operator which, however substantially interpreted, unavoidably inherits the vagueness of the expressions on which it operates ('higher-order vagueness'). It is first argued that finite soritical series force a surprising collapse result concerning a particular set of expressions involving the definiteness operator. It is then shown that, under two highly plausible assumptions about higher-order vagueness (the existence of 'absolutely definitely' positive and negative cases and the 'radical' character of higher-order vagueness itself), the collapse result implies the inadequacy of the dominant approach as a theory of vagueness, as its main tenet can be, at best, not absolutely definitely true.     

Higher-Order Sorites Paradox

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions (such as ‘borderline’ and ‘definitely’) introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ^ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox.     

Epistemicism,Distribution, and the Argument from Vagueness

This paper consists of two parts. The first concerns the logic of vagueness. The second concerns a prominent debate in metaphysics. One of the most widely accepted principles governing the ‘definitely’ operator is the principle of Distribution: if ‘p’ and ‘if p then q’ are both definite, then so is ‘q’. I argue however, that epistemicists about vagueness (at least those who take a broadly Williamsonian line) should reject this principle. The discussion also helps to shed light on the elusive question of what, on this framework, it takes for a sentence to be borderline or definite. In the second part of the paper, I apply this result to a prominent debate in metaphysics. One of the most influential arguments in favour of Universalism about composition is the Lewis‐Sider argument from vagueness. An interesting question, however, is whether epistemicists have any particular reasons to resist the argument. I show that there is no obvious reason why epistemicists should resist the argument but there is a non‐obvious one: the rejection of Distribution argued for in the first part of the paper provides epistemicists with a unique way of resisting the argument from vagueness.     

Foundational beliefs and the structure of justification

I argue that our justification for beliefs about the external physical world need not be constituted by any justified beliefs about perceptual experiences. In this way our justification for beliefs about the physical world may be nondoxastic and this differentiates my proposal from traditional foundationalist theories such as those defended by Laurence BonJour, Richard Fumerton, and Timothy McGrew. On the other hand, it differs from certain non-traditional foundationalist theories such as that defended by James Pryor according to which perceptual experience is sufficient to justify beliefs about the external world. I propose that justification for propositions describing our perceptual experiences partially constitutes any justification we may possess for beliefs concerning the external world. In this way, our justification for beliefs about the physical world may only be inferential since it is grounded in any justification we have for at least one other proposition. This theory occupies an intermediate position between the two aforementioned foundationalist accounts, which allows it to sidestep problems that confront each of them.     

DO FALLIBILIST ACCOUNTS OF THE GROWTH OF KNOWLEDGE UNDERESTIMATE AND ENDANGER SCIENCE?

All fallibilist theories may appear to be defective, because they allegedly underestimate the security of at least some scientific knowledge and thereby leave science less defensible than it otherwise might be. When they call all scientific knowledge conjectural they may seem at first blush to underestimate the superiority of science vis a vis pseudo‐science. Fallibilists apparently fail to account for the fact that science turns theory into facts, because even “facts” are held only provisionally. This impression is false: the relatively secure establishment of facts can be accounted for with a fallibilist view. After theories have been honed through sharp criticism, there is often no reason to doubt some aspects of them. These aspects are what we regard to be factual knowledge, even though these facts are also provisionally accepted as such. We then explain the newly won factual knowledge with deeper theories, which often correct our factual knowledge in spite of its apparent security. Theories of justification add nothing useful to the fallibilists' observation that science finds the best theories because it has the highest standards of criticism. Fallibilist theories today give the best account and defence of science. We may abandon the quest for some kind of assurance that goes beyond the determination that some theory can answer all known objections to it and take up more interesting problems, such as how we can find new objections and how criticism may be improved and made institutionally secure. ¹ 1 I am grateful to Joseph Agassi and an anonymous referee of this journal for comments on an earlier draft of this essay.
     

Does Vagueness Exclude Knowledge?

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken.     

Making it Implicit: Brandom on Rule Following

In Making it Explicit , Brandom aims to articulate an account of conceptual content that accommodates its normativity—a requirement on theories of content that Brandom traces to Wittgenstein's rule following considerations. It is widely held that the normativity requirement cannot be met, or at least not with ease, because theories of content face an intractable dilemma. Brandom proposes to evade the dilemma by adopting a middle road—one that uses normative vocabulary, but treats norms as implicit in practices. I argue that this proposal fails to evade the dilemma, as Brandom himself understands it. Despite his use of normative vocabulary, Brandom's theory fares no better than the reductionist theories he criticises. I consider some responses that Brandom might make to my charges, and finally conclude that his proposal founders on his own criteria.     

Commensurability, incommensurability, and cumulativity in scientific knowledge

Until the middle of the present century it was a commonly accepted opinion that theory change in science was the expression of cumulative progress consisting in the acquisition of new truths and the elimination of old errors. Logical empiricists developed this idea through a deductive model, saying that a theory T superseding a theory T must be able logically to explain whatever T explained and something more as well. Popper too shared this model, but stressed that T explains the old known facts in its own new way. The further pursual of this line quickly led to the thesis of the non-comparability or incommensurability of theories: if T and T are different, then the very concepts which have the same denomination in both actually have different meanings; in such a way any sentence whatever has different meanings in T and in T and cannot serve to compare them. owing to this, the deductive model was abandoned as a tool for understanding theory change and scientific progress, and other models were proposed by people such as Lakatos, Kuhn, Feyerabend, Sneed and Stegmüller. The common feature of all these new positions may be seen in the claim that no possibility exists of interpreting theory change in terms of the cumulative acquisition of truth. It seems to us that the older and the newer positions are one-sided, and, in order to eliminate their respective shortcomings, we propose to interpret theory change in a new way.The starting point consists in recognizing that every scientific discipline singles out its specific domain of objects by selecting a few specific predicates for its discourse. Some of these predicates must be operational (that is, directly bound to testing operations) and they determine the objects of the theory concerned. In the case of a transition from T to T, we must consider whether or not the operational predicates remain unchanged, in the sense of being still related to the same operations. If they do not change in their relation to operations, then T and T are comparable (and may sometimes appear as compatible, sometimes as incompatible). If the operational predicates are not all identical in T and T, the two theories show a rather high degree of incommensurability, and this happens because they do not refer to the same objects. Theory change means in this case change of objects. But now we can see that even incommensurability is compatible with progress conceived as the accumulation of truth. Indeed, T and T remain true about their respective objects (T does not disprove T), and the global amount of truth acquired is increased.In other words, scientific progress does not consist in a purely logical relationship between theories, and moreover it is not linear. Yet it exists and may even be interpreted as an accumulation of truth, provided we do not forget that every scientific theory is true only about its own specific objects.It may be pointed out that the solution advocated here relies upon a limitation of the theory-ladeness of scientific concepts, which involves a reconsideration of their semantic status and a new approach to the question of theoretical concepts. First of all, the feature of being theoretical is attributed to a concept not absolutely, but relatively, yet in a sense different from Sneeds's: indeed every theory is basically characterized by its operational concepts, and the non-operational are said to be theoretical, this distinction clearly depending on every particular theory. For the operational concepts it happens that their mean-     

Truth in the Tractatus

My paper takes issue both with the standard view that the Tractatus contains a correspondence theory and with recent suggestions that it features a deflationary or semantic theory. Standard correspondence interpretations are mistaken, because they treat the isomorphism between a sentence and what it depicts as a sufficient condition of truth rather than of sense. The semantic/deflationary interpretation ignores passages that suggest some kind of correspondence theory. The official theory of truth in the Tractatus is an obtainment theory – a sentence is true iff the state of affairs it depicts obtains. This theory differs from deflationary theories in that it involves an ontology of states of affairs/facts; and it can be transformed into a type of correspondence theory: a sentence is true iff it corresponds to, i.e. depicts an obtaining state of affairs (fact). Admittedly, unlike correspondence theories as commonly portrayed, this account does not involve a genuinely truth-making relation. It features a relation of correspondence, yet it is that of depicting, between a meaningful sentence and its sense – a possible state of affairs. What makes for truth is not that relation, but the obtaining of the depicted state of affairs. This does not disqualify the Tractatus from holding a correspondence theory, however, since the correspondence theories of Moore and Russell are committed to a similar position. Alternatively, the obtainment theory can be seen as a synthesis of correspondence, semantic and deflationary approaches. It does justice to the idea that what is true depends solely on what is the case, and it combines a semantic explanation of the relation between a sentence and what it says with a deflationary account of the agreement between what the sentence says and what obtains or is the case if it is true