In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.

In this paper, I take issue with a core commitment of logical conventionalism: that we impose a logic on ourselves by adopting general linguistic conventions governing our use of logical terms, thereby determining the meanings of the logical constants and which of our inferences are valid. Drawing on Kripke’s ‘adoption problem’, I argue that general logical principles cannot be adopted, either explicitly or implicitly. I go on to argue that the meanings of our logical terms, and the validity of our (...) inferences, cannot depend on our adoption of logico-linguistic conventions. (shrink)

What is the relation between meaning and use? This chapter first defends a non-reductionist understanding of Wittgenstein’s suggestion that ‘the meaning of a word is its use in the language’; facts about meaning cannot be reduced to, or explained in terms of, facts about use, characterized non-semantically. Nonetheless, it is contended, facts about meaning do supervene on non-semantic facts about use. That supervenience thesis is suggested by comments of Wittgenstein’s and is consistent with his view of meaning and rule-following. Semantic (...) supervenience is then defended against two criticisms: first, John McDowell’s suggestion that the supervenience thesis falsifies the epistemology of meaning and fails to accommodate common-sense truths about meaning; second, a series of counter-examples proposed by Stephen Kearns and Ofra Magidor, who argue that worlds may differ semantically without differing non-semantically. It is argued that neither criticism is convincing: we should accept the thesis that semantic facts supervene on non-semantic facts. (shrink)

If the semantic values of predicates are, as Williamson assumes (_Philsophical Perspectives,_ _13_, 505–517, 1999, 509) properties in the intensional sense, then epistemicism is immediate. Epistemicism fails, so also this properties account of predicates. I deploy examination of Williamson’s account as a foil against properties as semantic values, showing that his two positive arguments for bivalence fail, as do his efforts to rescue epistemicism from obvious problems. In Part II I argue that, despite the properties account’s problems, it has an (...) important role to play in compositional semantics. We may separate the problem of how smallest parts of language get attached to the world from the problem of how those parts compose to form complex semantic values. For the latter problem we idealize and treat the smallest semantic values as properties (and referents). So doing functions to put to one side how the smallest parts get worldly attachment, a problem that would just get in the way of understanding composition. Attachment to the world must be studied separately, and I review some of the options. As a bonus we see why the requirement of higher order vagueness is an artifact of taking properties as semantic values literally instead of as a simplifying idealization. (shrink)

Semantic normativism, which is the view that semantic properties/concepts are some kind of normative properties/concepts, has become increasingly influential in contemporary meta-semantics. In this paper, I aim to argue that semantic normativism has difficulty accommodating the causal efficacy of semantic properties. In specific, I raise an exclusion problem for semantic normativism, inspired by the exclusion problem in the philosophy of mind. Moreover, I attempt to show that the exclusion problem for semantic normativism is peculiarly troublesome: while we can solve mental-physical (...) exclusion by adopting the so-called ‘autonomy approach’, a similar autonomy solution to semantic exclusion is implausible if semantic properties are understood as normative properties. (shrink)

What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson’s Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an epistemicist semantics (...) from that model theory, one of which I will find to be more plausible than the other. (shrink)

Sometimes it is indeterminate what an agent morally ought do. This generates a Decision Ought Challenge—to give moral guidance to agents in such a scenario. This article is a field guide to the options for a theory of the decision ought for cases of indeterminacy. Three categories of view are evaluated, and the best representative for each is identified.

The aim of this paper is to introduce, elucidate and defend the usefulness of a variant of grounding, or metaphysical explanation, that has the feature that the grounds explain of some states of affairs that one of them obtains without explaining which one obtains. I will dub this variant arbitrary grounding. After informally elucidating the basic idea in the first section, I will provide three metaphysical hypotheses that are best formulated in terms of arbitrary grounding in the second section. The (...) third section will be concerned with the relation between arbitrary grounding and non-arbitrary grounding. The fourth section will compare arbitrary grounding to two extant proposals in the literature. (shrink)

There is a well-known argument against irreducibly normative properties that appeals to the following claim about supervenience: for all possible worlds W and W*, if the instantiation of descriptive properties in W and W* is exactly the same, then the instantiation of normative properties in W and W* is also exactly the same. This claim used to be uncontroversial, but recently several philosophers have challenged it. Do these challenges undermine this argument? I argue that they do not, since the negation (...) of this claim about supervenience has consequences that are much more implausible than the negations of key premises in these challenges. (shrink)

This paper offers a noncognitivist characterization of moral attitudes, according to which moral attitudes count as such because of their inclusion of moral concepts. Moral concepts are distinguished by their contribution to the functional roles of some of the attitudes in which they can occur. They have no particular functional role in other attitudes, and should instead be viewed as evolutionary spandrels. In order to make the counter-intuitive implications of the view more palatable, the paper ends with an account of (...) the evolution of normative judgments as exaptations of the cognitive structures that underlie beliefs. (shrink)

Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the problem by canvassing (...) what we may call the arbitrary reference strategy. The main claims of such strategy are 2. First, we do not know which objects are the referents of proposition and numerical terms since their reference is fixed arbitrarily. Second, our ignorance of which object is picked out as the referent does not entail that no object is referred to by the relevant expression. Different articulations of the strategy are assessed, and a new one is defended. (shrink)

This paper is a response to Haze’s brief argument for the falsity of the theory that instantial terms refer arbitrarily, proposed by Breckenridge and Magidor in 2012. In this paper, I characterise instantial terms and outline the theory of arbitrary reference; then I reconstruct Haze’s argument and contend that it fails in its purpose. Haze’s argument is supposed to be a _reductio ad absurdum:_ according to Haze, it proves that a contradiction follows from the most basic tenets of the theory (...) of arbitrary reference. I will argue, however, that the contradiction in question follows not from these tenets, but from the surreptitious use that Haze makes of a self-referential expression. I conclude, consequently, that Haze’s argument is nothing more than an illustration of the well-known fact that self-referential expressions produce paradoxical results. (shrink)

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 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. (shrink)

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how (...) epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)

Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully (...) support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy. (shrink)

Sentences in context have semantic contents determined by a range of factors both internal and external to speakers. I argue against the thesis that semantic content is transparent to speakers in the sense of being immediately accessible to speakers in virtue of their linguistic competence.

This paper takes issue with an influential interpretationist argument for physicalism about intentionality based on the possibility of radical interpretation. The interpretationist defends the physicalist thesis that the intentional truths supervene on the physical truths by arguing that it is possible for a radical interpreter, who knows all of the physical truths, to work out the intentional truths about what an arbitrary agent believes, desires, and means without recourse to any further empirical information. One of the most compelling arguments for (...) the possibility of radical interpretation, associated most closely with David Lewis and Donald Davidson, gives a central role to decision theoretic representation theorems, which demonstrate that if an agent’s preferences satisfy certain constraints, it is possible to deduce probability and utility functions that represent her beliefs and desires. We argue that an interpretationist who wants to rely on existing representation theorems in defence of the possibility of radical interpretation faces a trilemma, each horn of which is incompatible with the possibility of radical interpretation. (shrink)

In metasemantics, semantic dispositionalism is the view that what makes it the case that, given the value of the relevant parameters, a certain linguistic expression refers to what it does are the speakers’ dispositions. In the literature, there is something like a consensus that the fate of dispositionalism hinges on the status of three arguments, first put forward by Saul Kripke ‒ or at least usually ascribed to him. This paper discusses a different, and strangely neglected, anti-dispositionalist argument, which develops (...) some remarks first put forward by Paul Boghossian and Anandi Hattiangadi and revolves around the idea that semantic dispositionalists have no way to justify their privileging certain dispositions, the ones they take to be reference-determining, over all the others. After some background (Section 1) and a first presentation of the argument (Section 2), I discuss three ways a dispositionalist might try to answer it and find them all wanting (Section 3). (shrink)

Kripkenstein’s challenge is usually described as being essentially about the use of a word in new kinds of cases ‒ the old kinds of cases being commonly considered as non-problematic. I show that this way of conceiving the challenge is neither true to Kripke’s intentions nor philosophically defensible: the Kripkean skeptic can question my answering “125” to the question “What is 68 plus 57?” even if that problem is one I have already encountered and answered. I then argue that once (...) the real nature of Kripkenstein’s challenge is properly appreciated, one extremely popular strategy to try to meet it, what usually goes by the name of “semantic dispositionalism”, loses much of its appeal. Along the way, I also explain that Kripkenstein’s challenge is actually two distinct challenges ‒ one concerning the mental state of meaning, or intending, something by a sign and the other concerning the meaning (referentially conceived) of linguistic expressions. (shrink)

Most meanings we express belong to large families of variant meanings, among which it would be implausible to suppose that some are much more apt for being expressed than others. This abundance of candidate meanings creates pressure to think that the proposition attributing any particular meaning to an expression is modally plastic: its truth depends very sensitively on the exact microphysical state of the world. However, such plasticity seems to threaten ordinary counterfactuals whose consequents contain speech reports, since it is (...) hard to see how we could reasonably be confident in a counterfactual whose consequent can be true only if a certain very finely tuned microphysical configuration obtains. This essay develops the foregoing puzzle and explores several possible solutions. (shrink)

Epistemicism associates vagueness with ignorance produced by semantic plasticity: the shiftiness of intensions in our language resulting from small changes in usage. The recent literature (Caie 2012; Magidor 2018; Yli-Vakkuri 2016) points to a missing piece in the epistemicist theory of vagueness, namely a clear account of the semantics of the definiteness operator Δ. The fundamentals of the epistemicist theory are well understood. However, the technical work of defining the definiteness operator has proven difficult. There are several desiderata that we (...) would like Δ to satisfy. For instance, we would like the epistemicist notion of ‘definiteness’ to interact well with modal operators and validate intuitive principles like ‘necessarily, if φ is definitely true, then φ is true’. Providing an account that would meet all such desiderata has eluded the epistemicists so far. In this paper, I present a novel version of a multidimensional model inspired by the work of Robert Stalnaker and David Kaplan. Using this model, I provide an account of epistemicist definiteness that meets our desiderata. (shrink)

In an addendum to Naming and Necessity, Saul Kripke argues against his earlier view that Sherlock Holmes is a possible person. In this paper, I suggest a nonstandard interpretation of the addendum. A key feature of this non-standard interpretation is that it attempts to make sense of why Kripke would be rejecting the view that Sherlock Holmes is a possible person without asserting that it is not the case that Sherlock Holmes is a possible person.

Two fundamental rules of reasoning are Universal Generalisation and Existential Instantiation. Applications of these rules involve stipulations such as ‘Let n be an arbitrary number’ or ‘Let John be an arbitrary Frenchman’. Yet the semantics underlying such stipulations are far from clear. What, for example, does ‘n’ refer to following the stipulation that n be an arbitrary number? In this paper, we argue that ‘n’ refers to a number—an ordinary, particular number such as 58 or 2,345,043. Which one? We do (...) not and cannot know, because the reference of ‘n’ is fixed arbitrarily. Underlying this proposal is a more general thesis: Arbitrary Reference : It is possible to fix the reference of an expression arbitrarily. When we do so, the expression receives its ordinary kind of semantic-value, though we do not and cannot know which value in particular it receives. Our aim in this paper is defend AR. In particular, we argue that AR can be used to provide an account of instantial reasoning, and we suggest that AR can also figure in offering new solutions to a range of difficult philosophical puzzles. (shrink)

I would like to attack a certain view: The view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. I introduce the Received View in Section 1. In Section 2 I explain what I mean by entity, and I argue (...) that supporters of the Received View should agree with my characterization of the corresponding notion of entity. I also explain what I mean by identity, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved. (shrink)

It is common belief that semantic properties supervene on non-semantic properties: no two possible worlds can be non-semantic duplicates and fail to be semantic duplicates. The view enjoys somewhat of an orthodoxy status in contemporary philosophy of language and metaphysics, and is often assumed without argument. Yet, work by Stephen Kearns and Ofra Magidor has claimed that it is vulnerable to a variant of the classical arguments against the supervenience of the phenomenal on the physical. This paper does three things: (...) it clarifies what semantic supervenience is about, it responds to the objections that have been leveled against it, and provides a new battery of arguments in its favor. I argue that the thesis of semantic supervenience is safe from classical anti-supervenience arguments, and show that its rejection generates unwelcome consequences. I conclude that there are substantial reasons to embrace the received wisdom: semantic properties supervene. (shrink)

The view that it is possible for someone to think at a time without existing at that time is not only perfectly coherent but in harmony with an attractive externalist view of the mental. Furthermore, it offers plausible solutions to various puzzles of personal identity.