Conversational exculpature is a pragmatic process whereby information is subtracted from, rather than added to, what the speaker literally says. This pragmatic content subtraction explains why we can say “Rob is six feet tall” without implying that Rob is between 5'0.99" and 6'0.01" tall, and why we can say “Ellen has a hat like the one Sherlock Holmes always wears” without implying Holmes exists or has a hat. This article presents a simple formalism for understanding this pragmatic mechanism, specifying how, (...) in context, the result of such subtractions is determined. And it shows how the resulting theory of conversational exculpature accounts for a varied range of linguistic phenomena. A distinctive feature of the approach is the crucial role played by the question under discussion in determining the result of a given exculpature. (shrink)

State of the art paper on the topic realism/anti-realism. The first part of the paper elucidates the notions of existence and independence of the metaphysical characterization of the realism/anti-realism dispute. The second part of the paper presents a critical taxonomy of the most important positions and doctrines in the contemporary literature on the domains of science and mathematics: scientific realism, scientific anti-realism, constructive empiricism, structural realism, mathematical Platonism, mathematical indispensability, mathematical empiricism, intuitionism, mathematical fictionalism and second philosophy.

In this entry I will offer a survey of the contemporary debate on fic- tionalism, which is a distinctive anti-realist view about certain regions of discourse that are valued for their usefulness rather than their truth.

The new explanatory or enhanced indispensability argument alleges that our mathematical beliefs are justified by their indispensable appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories. I argue that the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense the new argument is an oblique restatement of the standard argument. On the other sense, it is vulnerable to an instrumentalist (...) response. Either way, the explanatory indispensability argument is no improvement on the standard one. (shrink)

In this paper I do three things. Firstly, I defend the view that in his most familiar arguments about morality and the theological postulates, the arguments which appeal to the epistemological doctrines of the first Critique, Kant is as much of a fictionalist as anybody not working explicitly with that conceptual apparatus could be: his notion of faith as subjectively and not objectively grounded is precisely what fictionalists are concerned with in their talk of nondoxastic attitudes. Secondly, I reconstruct a (...) logically distinct argument to a fictionalist conclusion which I argue Kant also gives us, this time an argument to the conclusion that it is a good thing if our commitment to the existence of God is nondoxastic. And finally, I argue that this argument is of continuing interest, to Kantians and non-Kantians alike, not only because it raises interesting questions about the relation of morality to belief in God (which go in the opposite direction to most discussions, which focus on whether and to what extent belief in God can be an aid to morality), but also because this ‘Moral Hazard Argument’ seems to be available to religious realists and non-realists alike, thus suggesting that religious fictionalism is not by any means just an interesting version of religious non-realism. (shrink)

Yablo argued that some metaphors are representationally essential: they enable us to express contents that we would not be able to express without them. He defended a fictionalist view of mathematical language by making the case that it similarly serves as a representational aid. Against this, Colyvan argued that metaphorical/figurative language can never play an essential role in explanation and that mathematical language often does, hence concluding that Yablo’s fictionalism is untenable. I show that Colyvan’s thesis about explanation is highly (...) implausible in the absence of a challenge to Yablo’s position on representationally essential metaphors, which Colyvan does not attempt. I also briefly discuss other attempts to produce a simple knock-out argument against fictionalism and show them wanting. (shrink)

Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s (...) mathematical aspects to obtain, as remainder, what it says ‘mathematics aside’. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quine’s three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvan’s example that the third grade really obtains. (shrink)

Questions regarding what exists are central to various forms of Buddhist philosophy, as they are to many traditions of philosophy. Interestingly, there is perhaps a clearer consensus in Buddhist thought regarding what does not exist than there may be regarding precisely what does exist, at least insofar as the doctrine of anātman (no self, absence of self) is taken to be a fundamental Buddhist doctrine. It may be noted that many forms of Mahāyāna Buddhist philosophy in particular are considered to (...) offer a quite austere ontology—a rather ‘empty’ account of what exists. Continuing in this vein of ontological austerity, here I will attempt to lay out a relatively novel approach to Buddhist ontology, viz. Buddhist fictionalism. (shrink)

Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...) Replies5.1 Yablo’s likely response5.2 Charity6 Conclusion. (shrink)

I contend that mathematical domains are freestanding institutional entities that, at least typically, are introduced to serve representational functions. In this paper, I outline an account of institutional reality and a supporting metaontological perspective that clarify the content of this thesis. I also argue that a philosophy of mathematics that has this thesis as its central tenet can account for the objectivity, necessity, and atemporality of mathematics.

This is a survey of contemporary work on ‘fictionalism in metaphysics’, a term that is taken to signify both the place of fictionalism as a distinctive anti‐realist metaphysics in which usefulness rather than truth is the norm of acceptance, and the fact that philosophers have given fictionalist treatments of a range of specifically metaphysical notions.

It is our contention that an ontological commitment to propositions faces a number of problems; so many, in fact, that an attitude of realism towards propositions—understood the usual “platonistic” way, as a kind of mind- and language-independent abstract entity—is ultimately untenable. The particular worries about propositions that marshal parallel problems that Paul Benacerraf has raised for mathematical platonists. At the same time, the utility of “proposition-talk”—indeed, the apparent linguistic commitment evident in our use of 'that'-clauses (in offering explanations and making (...) predictions)—is also in need of explanation. We account for this with a fictionalist analysis of our use of 'that'-clauses. Our account avoids certain problems that arise for the usual error-theoretic versions of fictionalism because we apply the notion of semantic pretense to develop an alternative, pretense-involving, non-error-theoretic, fictionalist account of proposition-talk. (shrink)

I take up the task of examining how someone who takes seriously the ambitious programme of conceptual analysis advocated by the Canberra School can minimise the eliminative consequences which I argue the Ramsey-Carnap-Lewis recipe of conceptual analysis is likely to have for many folk discourses. The objective is to find a stable means to preserve the constative appearance of folk discourse and to find it generally successful in its attempts to describe an external world, albeit in non-scientific terms that do (...) not reflect the nature of things. The view I settle on, quasi-fictionalism, is modelled on a modified descriptivist version of Kendall Walton’s account of prop-oriented games of make-believe. (shrink)

Philosophy of mathematics for the last half-century has been dominated in one way or another by Quine’s indispensability argument. The argument alleges that our best scientific theory quantifies over, and thus commits us to, mathematical objects. In this paper, I present new considerations which undermine the most serious challenge to Quine’s argument, Hartry Field’s reformulation of Newtonian Gravitational Theory.

One familiar form of argument for rejecting entities of a certain kind is that, by rejecting them, we avoid certain difficult problems associated with them. Such problem-avoidance arguments backfire if the problems cited survive the elimination of the rejected entities. In particular, we examine one way problems can survive: a question for the realist about which of a set of inconsistent statements is false may give way to an equally difficult question for the eliminativist about which of a set of (...) inconsistent statements fail to be 'factual'. Much of the first half of the paper is devoted to explaining a notion of factuality that does not imply truth but still consists in 'getting the world right'. The second half of the paper is a case study. Some 'compositional nihilists' have argued that, by rejecting composite objects (and so by denying the composition ever takes place), we avoid the notorious puzzles of coincidence, for example, the statue/lump and the ship of Theseus puzzles. Using the apparatus developed in the first half of the paper, we explore the question of whether these puzzles survive the elimination of composite objects. (shrink)

Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number of (...) themes in recent philosophy of mathematics (concerning a priority and fictionalism, for example) in revealing new light. (shrink)

Imaginative and creative capacities seem to be at the heart of both games of make-believe and figurative uses of language. But how exactly might cases of metaphor or idiom involve make-believe? In this paper, I argue against the pretense-based accounts of Walton (1990, 1993), Hills (1997), and Egan (this journal, 2008) that pretense plays no role in the interpretation of metaphor or idiom; instead, more general capacities for manipulating concepts (which are also called on within the use of pretense) do (...) the real explanatory work. This result has consequences for both our understanding of metaphor and idiom as well as for the use of figurative language by fictionalists in ontology. (shrink)

It is common for contemporary metaphysical realists to adopt Quine's criterion of ontological commitment while at the same time repudiating his ontological pragmatism. 2 Drawing heavily from the work of others—especially Joseph Melia and Stephen Yablo—I will argue that the resulting approach to meta-ontology is unstable. In particular, if we are metaphysical realists, we need not accept ontological commitment to whatever is quantified over by our best first-order theories.

I defend pretence hermeneutic fictionalism against the Autism Objection. The objection is this: since people with autism have no difficulty in engaging with mathematics even if they cannot pretend, it is not the case that engagement with mathematics involves pretence. I show that a previous response to the objection is inadequate as a defence of the kind of pretence hermeneutic fictionalism put forward as a semantic thesis about the discourse in question. I claim that a more general response to the (...) Autism Objection is to deny the premise that people with autism cannot pretend. To motivate this response, I appeal to psychological studies suggesting that people with autism can understand pretence and they can pretend under certain conditions. Finally, I provide explanations for why it is the case that people with autism do not have a problem with engaging in mathematics whereas they have so much difficulty with other kinds of figurative language and pretence. (shrink)

Non-actual model systems discussed in scientific theories are compared to fictions in literature. This comparison may help with the understanding of similarity relations between models and real-world target systems. The ontological problems surrounding fictions in science may be particularly difficult, however. A comparison is also made to ontological problems that arise in the philosophy of mathematics.

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.

ABSTRACTA ‘sceptical’ approach to easy arguments involves reducing our confidence in the supposedly uncontroversial premise with which the arguments begin. Here I address the question: if we accept Yablo's new version of a sceptical proposal, what difference might that make for the relevant meta-ontological debates? I argue that serious difficulties remain for even this ‘best’ version of a sceptical approach. Noting these difficulties might motivate us to look again at the alternative strategy—of reading the uncontroversial premise straightforwardly and thinking that (...) doubts about the conclusion were based on artificial inflation or confusion. (shrink)

There are two doctrines for which Quine is particularly well known: the doctrine of ontological commitment and the inscrutability thesis—the thesis that reference and quantification are inscrutable. At first glance, the two doctrines are squarely at odds. If there is no fact of the matter as to what our expressions refer to, then it would appear that no determinate commitments can be read off of our best theories. We argue here that the appearance of a clash between the two doctrines (...) is illusory. The reason that there is no real conflict is not simply that in determining our theories’ ontological commitments we naturally rely on our home language but also (and more importantly) that ontological commitment is not intimately tied to objectual quantification and a reference-first approach to language. Or so we will argue. We conclude with a new inscrutability argument which rests on the observation that the notion of objectual quantification, when properly cashed out, deflates. (shrink)

In the recent literature on all things metaontological, discussion of a notorious Meinongian doctrine—the thesis that some objects have no kind of being at all—has been conspicuous by its absence. And this is despite the fact that this thesis is the central element of the noneist metaphysics of Richard Routley (1980) and Graham Priest (2005). In this paper, we therefore examine the metaontological foundations of noneism, with a view to seeing exactly how the noneist's approach to ontological inquiry differs from (...) the orthodox Quinean one. We proceed by arguing that the core anti-Quinean element in noneism has routinely been misidentified: rather than concerning Quine's thesis that to be is to be the value of a variable, the real difference is that the noneist rejects what we identify as Quine's “translate-and-deflate” methodology. In rejecting this aspect of Quinean orthodoxy, the noneist is in good company: many of those who think that questions of fundamentality should be the proper focus of ontological inquiry can be read as rejecting it too. Accordingly, we then examine the differences between the noneist's conception of ontology and that offered by the fundamentalist. We argue that these two anti-Quinean approaches differ in terms of their respective conceptions of the theoretical role associated with the notion of being. And the contrast that emerges between them is, in the end, an explanatory one. (shrink)

I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...) by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type. (shrink)

Fictionalists claim that instead of believing certain controversial propositions they accept them nonseriously, as useful make-believe. In this way they present themselves as having an austere ontology despite the apparent ontological commitments of their discourse. Some philosophers object that this plays on a distinction without a difference: the fictionalist’s would-be nonserious acceptance is the most we can do for the relevant content acceptance-wise, hence such acceptance is no different from what we ordinarily call ‘belief’ and should be so called. They (...) conclude that it is subject to the norms applicable to paradigmatic empirical beliefs, and hence, pace fictionalists, ontological commitments must be taken seriously. I disentangle three strands in the objector’s thought: the ‘What more can you ask for?’ intuition, a linguistic/ conceptual claim, and a claim about norms. I argue that the former two are compatible with ontological deflationism, and therefore do not entail applicability of the norms. Nevertheless, if indeed there is no more robust acceptance with which to contrast the supposed nonserious acceptance, then the fictionalist’s claim to austere ontology must be abandoned. Is there a reason to suppose there is any merit to the distinction-without-a-difference charge? I argue that there is, clarify it, and defend against objections, focusing on Daly 2008. (shrink)