It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...) Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (shrink)

Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...) either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties. (shrink)

Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for postulating (...) this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (shrink)

Although the Evans argument against vague identity has been much discussed, proposah for blocking it have not so far satisfied general conditions which any solution ought to meet. Moreover, the relation between ontically vague identity and ontic vagueness more generally has not yet been satisfactorily addressed. I advocate a way of resisting the Evans argument which satisfies the conditions. To show how this approach can vindicate particular cases of ontically vague identity, I develop a framework for describing ontic vagueness in (...) general in terms of multiple actualities. This provides aprìncipled approach to ontically vague identity which is unaffected by the Evans argument. (shrink)

In this paper I present a new argument against vague identity — one that is more fundamental than existing arguments — and I also try to explain why we find the idea of vague identity puzzling, in a way that will dispel the puzzlement. In brief, my argument is this: to make clear sense of something, one must at least model it set-theoretically; but due to the special place of identity in set-theoretic models, any vague relation that one does model (...) set-theoretically will not be identity, for real identity will already be there, built into the background of the model, and perfectly precise. (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.

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard (...) classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

The supporter of vague objects has been long challenged by the following ‘Argument from Identity’: 1) if there are vague objects, then there is ontically indeterminate identity; 2) there is no ontically indeterminate identity; therefore, 3) there are no vague objects. Some supporters of vague objects have argued that 1) is false. Noonan (Analysis 68: 174–176, 2008) grants that 1) does not hold in general, but claims that ontically indeterminate identity is indeed implied by the assumption that there are vague (...) objects of a certain special kind (i.e. vague objects*). One can therefore formulate a ‘New Argument from Identity’: 1′) if there are vague objects*, then there is ontically indeterminate identity; 2) there is no ontically indeterminate identity; therefore, 3′) there are no vague objects*. Noonan’s strategy is to argue that premiss 1′) is inescapable, and, as a consequence, that Evans’s alleged defence of 2) is a real challenge for any supporter of vague objects. I object that a supporter of vague objects who grants the validity of Evans’s argument allegedly in favour of 2) should reject premiss 1′). The threat of the New Argument from Identity is thus avoided. (shrink)

One well-known objection to supersubstantivalism is that it is inconsistent with the contingency of location. This paper presents a new objection to supersubstantivalism: it is inconsistent with the vagueness of location. Though contingency and vagueness are formally similar, there are important philosophical differences between the two. As a result, the objection from vague location will be structurally different than the objection from contingent location. The paper explores these differences and then defends the argument that supersubstantivalism is inconsistent with the plausible (...) thesis that it is vague where I am located. (shrink)

A reply to two responses to an earlier paper, "A Liar Paradox".

This essay argues that deflationism is incompatible with the phenomenon of referential indeterminacy. This puts the deflationist in the difficult position of having to deny the possibility of what otherwise seems like a manifest and theoretically important phenomenon. Section 1 provides background on deflationism. Section 2 considers an intuitive argument by Stephen Leeds to the effect that deflationism precludes RI; the essay argues that this argument does not succeed. The rest of the essay presents its own, distinct argument for the (...) incompatibility of deflationism and RI. Section 3 argues that direct RI—RI that is not simply a derivative of some other, nonreferential instance of indeterminacy—is strictly incompatible with deflationism. Section 4 considers a couple of different ways the deflationist might try to achieve indirect RI—via indeterminate identity and indeterminate synonymy—and argues that each is unsatisfactory. (shrink)

I will here present a number of problems concerning the idea that there is ontological vagueness, and the related claim that appeal to this idea can help solve some vagueness-related problems. A theme underlying the discussion will be the distinction between vagueness specifically and indeterminacy more generally (and, relatedly, the distinction between ontological vagueness and ontological indeterminacy). Even if the world is somehow ontologically indeterminate it by no means follows that it is, properly speaking, ontologically vague.1..

Philosophy and Phenomenological Research, EarlyView.

This unique anthology of new, contributed essays offers a range of perspectives on various aspects of ontic vagueness. It seeks to answer core questions pertaining to onticism, the view that vagueness exists in the world itself. The questions to be addressed include whether vague objects must have vague identity, and whether ontic vagueness has a distinctive logic, one that is not shared by semantic or epistemic vagueness. The essays in this volume explain the motivations behind onticism, such as the plausibility (...) of mereological vagueness and indeterminacy in quantum mechanics and they offer various arguments both for and against ontic vagueness; onticism is also compared with other, competing theories of vagueness such as semanticism, the view that vagueness exists only in our linguistic representation of the world. Gareth Evans’s influential paper of 1978, “Can There Be Vague Objects?” gave a simple but cogent argument against the coherence of ontic vagueness. Onticism was subsequently dismissed by many. However, in recent years, researchers have become aware of the logical gaps in Evans’s argument and this has triggered a new wave of interest in onticism. Onticism is now widely regarded as at least a coherent view. Reflecting this growing consensus, the present anthology for the first time puts together essays that are focused on onticism and its various facets and it fills in the lacuna in the literature on vagueness, a much-discussed subject in contemporary philosophy. (shrink)

In "Counting and Indeterminate Identity", N. Ángel Pinillos develops an argument that there can be no cases of `Split Indeterminate Identity'. Such a case would be one in which it was indeterminate whether a=b and indeterminate whether a=c, but determinately true that b≠c. The interest of the argument lies, in part, in the fact that it appears to appeal to none of the controversial claims to which similar arguments due to Gareth Evans and Nathan Salmon appeal. I argue for two (...) counter-claims. First, the formal argument fails to establish its conclusion, for essentially the same reason Evans's and Salmon's arguments fail to establish their conclusions. Second, the phenomena in which Pinillos is interested, which concern the cardinalities of sets of vague objects, manifest the existence of what Kit Fine called `penumbral connections', phenomena that the logics Pinillos considers are already known not to handle well. (shrink)

Read as a comment on Crispin Wright's \"Vagueness: A Fifth Column Approach\", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.