The modal fictionalist faces a problem due to the fact that her chosen story seems to be incomplete—certain things are neither fictionally true nor fictionally false. The significance of this problem is not localized to modal fictionalism, however, since many fictionalists will face it too. By examining how the fictionalist should analyze the notion of truth according to her story, and, in particular, the role that conditionals play for the fictionalist, I develop a novel and elegant solution to the incompleteness (...) problem. (shrink)

Stephen Yablo (2001) argues that traditional fictionalist strategies run into trouble due to a mismatch between the modal status of a claim like ‘2 + 3 = 5’ and the modal status of its fictionalist paraphrase. I argue here that Yablo is best seen as confronting the fictionalist with a dilemma, and then go on to show how this dilemma can be resolved.

Epistemic utility theory is generally coupled with veritism. Veritism is the view that truth is the sole fundamental epistemic value. Veritism, when paired with EUT, entails a methodological commitment: norms of epistemic rationality are justified only if they can be derived from considerations of accuracy alone. According to EUT, then, believing truly has epistemic value, while believing falsely has epistemic disvalue. This raises the question as to how the rational believer should balance the prospect of true belief against the risk (...) of error. A strong intuitive case can be made for a kind of epistemic conservatism – that we should disvalue error more than we value true belief. I argue that none of the ways in which advocates of veritist EUT have sought to motivate conservatism can be squared with their methodological commitments. Short of any such justification, they must therefore either abandon their most central methodological principle or else adopt a permissive line with respect to epistemic risk. (shrink)

Fictionalists maintain that possible worlds, numbers or composite objects exist only according to theories which are useful but false. Hale, Divers and Woodward have provided arguments which threaten to show that fictionalists must be prepared to regard the theories in question as contingently, rather than necessarily, false. If warranted, this conclusion would significantly limit the appeal of the fictionalist strategy rendering it unavailable to anyone antecedently convinced that mathematics and metaphysics concern non-contingent matters. I try to show that their arguments (...) can be resisted by developing and defending a strategy suggested by Rosen, Nolan and Dorr, according to which the fiction-operator is to be analysed in terms of a counterfactual that admits of non-trival truth-values even when the antecedent is impossible. (shrink)

Modal fictionalists face a problem that arises due to their possible-world story being incomplete in the sense that certain relevant claims are neither true nor false according to it. It has recently been suggested that this incompleteness problem generalises to other brands of fictionalism, such as fictionalism about composite or mathematical objects. In this paper, I argue that these fictionalist positions are particularly threatened by a generalised incompleteness problem since they cannot emulate the modal fictionalists’ most attractive response. I then (...) defend mathematical and compositional fictionalism by showing that the reasons for which the incompleteness problem has been thought to affect them are mistaken. This leads to the question of whether there are other fictionalist positions to which the problem does in fact generalise. I give a general account of the features of a fictionalist position that generate the incompleteness problem and argue that whenever a fictionalist position does exemplify these features then the problem can be addressed in analogy to the modal fictionalists’ preferred response. (shrink)

Accounts of modality in terms of fictional possible worlds face an objection based on the idea that when modal claims are analysed in terms of fictions, the connection between analysans and analysandum seems artificial. Strong modal fictionalism, the theory according to which modal claims are analysed in terms of a fiction, has been defended by, among others, Seahwa Kim, who has recently claimed that the philosophical objection that the connection between modality and fictions is artificial can be met. I propose (...) a new way of spelling out the intuition of artificiality and show that strong modal fictionalism should be rejected. (shrink)

A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

In this paper, I argue that for the purposes of ordinary reasoning, sentences about properties of concrete objects can be replaced with sentences concerning how things in our universe would be related to inscriptions were there a pluriverse. Speaking loosely, pluriverses are composites of universes that collectively realize every way a universe could possibly be. As such, pluriverses exhaust all possible meanings that inscriptions could take. Moreover, because universes necessarily do not influence one another, our universe would not be any (...) different intrinsically if there were a pluriverse. These two facts enable anti-realists about abstract objects to replace, e.g. talk of anatomical features with talk of the inscriptions concerning anatomical structure that would exist were there a pluriverse. The availability of such replacements enables anti-realists to carry out essential ordinary reasoning without referring to properties, thereby making room for a consistent anti-realist worldview. The inscriptions of the would-be pluriverse are so numerous and varied that sentences about them can play the roles in ordinary reasoning served by simple sentences about properties of concrete objects. (shrink)

Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove some (...) facts about that function and facts about some sound logics for those languages. In doing so, I prove that, given some plausible metaphysical assumptions, a large class of sentences about properties of concrete objects are “safe” on nominalistic grounds. Whenever some true sentences about concrete objects and some sentences belonging to this class that are true according to platonists collectively entail a conclusion about concrete objects, some nominalistically acceptable sentences are true and entail the same conclusion. Because the proof can itself be formulated without abstract objects, it provides a nominalistic explanation of the success of theories that invoke properties of concrete objects. (shrink)

In this paper, I develop a "safety result" for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are "correct": roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages (...) over existing nominalistic accounts of applied mathematics. It also provides a nominalistic account of pure mathematics. (shrink)

Despite protestations to the contrary, philosophers have always been renowned for espousing theories that do violence to common-sense opinion. In the last twenty years or so there has been a growing number of philosophers keen to follow in this tradition. According to these philosophers, if a story of pure fic-tion tells us that an individual exists, then there really is such an individual. According to these realists about fictional characters, ‘Scarlett O’Hara,’ ‘Char-lie Brown,’ ‘Batman,’ ‘Superman,’ ‘Tweedledum’ and ‘Tweedledee’ are not (...) denotationless terms, but names that really refer. What is truly surprising about this situation is that almost no one has inveighed against this unfortunate real-ist tendency. My aim here will be to challenge this new orthodoxy, and to defend an anti-realist position against the arguments proffered by the realist. (shrink)

Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as “mathematical surrealists” by contrast appeal to facts about the intrinsic character of the concrete world, not (...) to explain why our best mathematically imbued scientific theories and explanations are acceptable in spite of having false components, but in order to replace those theories and explanations with parasitic, nominalistically acceptable alternatives. I argue that easy-road fictionalism is viable only if mathematical surrealism is and that the latter constitutes a superior nominalist strategy. Two advantages of mathematical surrealism are that it neither begs the question concerning the explanatory role of mathematics in science nor requires rejecting the cogency of inference to the best explanation. (shrink)

In this paper, after clarifying certain features of Gideon Rosen’s Modal Fictionalism, I raise two problems for that view and argue that these problems strongly suggest that advocates of a “Deflationist Strategy” ought not to endorse, or adopt Rosen-style Modal Fictionalism.

Questions about necessity (or what has to be, or what cannot be otherwise) and possibility (or what can be, or what could be otherwise) are questions about modality. Fictionalism is an approach to theoretical matters in a given area which treats the claims in that area as being in some sense analogous to fictional claims: claims we do not literally accept at face value, but which we nevertheless think serve some useful function. However, despite its name, “Modal Fictionalism” in its (...) usual manifestations is not primarily fictionalism about claims of necessity and possibility, but rather a fictionalist approach to claims about possible worlds. (For instance, modal fictionalism is not normally fictionalist about the claim that “it is possible that there be a species of tail-less kangaroo”, but rather about the claim that “there is a possible world in which there is a species of tail-less kangaroo”.) The practice of taking possible worlds to be merely convenient fictions, or of treating talk about possible worlds as being useful without being literally correct, is quite common in philosophical circles. It is only recently, however, that philosophers have seriously examined the implications of taking possible worlds to be merely fictional objects, like Sherlock Holmes or a frictionless surface. (shrink)