This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters. The essay proceeds by questioning traditional assumptions about the connection between the objects that are used to specify the truth-conditions of a sentence, on the one hand, and the objects whose existence is required in order for (...) the truth-conditions thereby specified to be satisfied, on the other. This allows one to set forth an assignment of truth-conditions to arithmetical sentences whereby nothing is required of the world in order for the truth-conditions of a truth of pure arithmetic to be satisfied. The essay then argues that such an assignment can be used to account for the a priori knowability of certain arithmetical truths. (shrink)

There is no doughnut without a hole, the saying goes. And that’s true. If you think you can come up with an exception, it simply wouldn’t be a doughnut. Holeless doughnuts are like extensionless color, or durationless sound—nonsense. Does it follow, then, that when we buy a doughnut we really purchase two sorts of thing—the edible stuff plus the little chunk of void in the middle? Surely we cannot just take the doughnut and leave the hole at the grocery store, (...) as we cannot just eat the doughnut and save the hole for later. But then, again, surely when we eat a doughnut we do not also eat the hole. Or do we? (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)

We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...) Langford find themselves in conflict with mathematical and scientific practice. (shrink)

There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...) can be swiftly and decisively dispatched by appeal to disciplines other than philosophy. In this paper we will argue that such an attitude of uncritical deference to any non-philosophical discipline is badly misguided. With reference to the work of John Burgess and David Lewis, we consider deference to mathematics. We show that deference to mathematics is implausible and that main arguments for it fail. With reference to the work of Michael Blome-Tillmann, we consider deference to linguistics. We show that his arguments appealing to deference to linguistics are unsuccessful. We then show that naturalism does not entail deferentialism and that naturalistic considerations even motivate some anti-deferentialist views. Finally, we set out deferentialism’s failings and present our own anti-deferentialist approach to philosophical inquiry. (shrink)

This essay explains why creationism about fictional characters is an abject failure. Creationism about fictional characters is the view that fictional objects are created by the authors of the novels in which they first appear. This essay shows that, when the details of creationism are filled in, the hypothesis becomes far more puzzling than the linguistic data it is used to explain. No matter how the creationist identifies where, when and how fictional objects are created, the proposal conflicts with other (...) strong intuitions we have about fictional characters. (shrink)

According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world (...) is just as it in fact is, then T’ bear on this claim. It concludes that, while analogies with theories that attempt to eliminate unobservable concrete entities provide good reason to regard theories of the former sort as explanatorily bad, this reason does not apply to theories of the latter sort. (shrink)

Virtually everyone agrees that, even after having presented the arguments for their positions, proponents of revisionary philosophical theories are required to provide some sort of account of the conflict between their theories and what the folk believe. I examine various strategies for answering the challenge from folk belief. The examination proceeds as a case study, whose focus is eliminativism about ordinary material objects. I critically assess eliminativist attempts to explain folk belief by appeal to paraphrase, experience, and intuition.

In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.

Much attention has been given to the question of ontic vagueness, and the issues usually center around whether certain paradigmatically concrete entities – cats, clouds, mountains, etc. – are vague in the sense of having indeterminate spatial boundaries. In this paper, however, I wish to focus on a way in which some abstracta seem to be locationally vague. To begin, I will briefly cover some territory already covered regarding certain types of “traditional” abstracta and the ways they are currently alleged (...) to be vague. I then wish to discuss two types of “nontraditional” abstracta and the sense in which I think some of these objects are locationally vague. I will next reexamine some of the traditional abstracta and discuss whether any of these objects are locationally vague in the novel way suggested for the nontraditional sorts. I’ll finish by discussing objections, and conclude with some remarks about characterizing the abstract/concrete distinction. (shrink)

Jackendoff defends a mentalist approach to semantics that investigates conceptual structures in the mind/brain and their interfaces with other structures, including specifically linguistic structures responsible for syntactic and phonological competence. He contrasts this approach with one that seeks to characterize the intentional relations between expressions and objects in the world. The latter, he argues, cannot be reconciled with mentalism. He objects in particular that intentionality cannot be naturalized and that the relevant notion of object is suspect. I critically discuss these (...) objections, arguing in part that Jackendoff’s position rests on questionable philosophical assumptions. (shrink)

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...) with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics. (shrink)

This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.

Platonism in the philosophy of mathematics is the doctrine that there are mathematical objects such as numbers. John Burgess and Gideon Rosen have argued that that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either rely on a dubious epistemology, or resemble a dubious sceptical argument concerning perceptual knowledge. Against Burgess and Rosen, I show that an epistemological anti- platonist argument proposed by Hartry Field avoids both horns of their dilemma.

This entry focuses on two of the more historically important monisms: existence monism and priority monism . Existence monism targets concrete objects and counts by tokens. This is the doctrine that exactly one concrete object exists. Priority monism also targets concrete objects, but counts by basic tokens. This is the doctrine that exactly one concrete object is basic, which will turn out to be the classical doctrine that the whole is prior to its parts.

Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.

For Quine, the ontological commitments of a discourse are what fall under its (objectual) quantifiers. The recent literature, however, is beginning to move away from this picture. There are direct challenges to Quine's criterion, and there are also attempts to provide alternatives. Azzouni suggests that the ontological commitments of a discourse should be determined by an existence predicate instead. The availability of this alternative forces an adjudication between Qune's criterion and the predicate approach to ontological commitment. I argue that to (...) adjudicate between these criteria for ontological commitment, we need first to adjudicate between criteria for what exists. (shrink)

Fictionalism has recently returned as a standard response to ontologically problematic domains. This article assesses moral fictionalism. It argues (i) that a correct understanding of the dialectical situation in contemporary metaethics shows that fictionalism is only an interesting new alternative if it can provide a new account of normative content: what is it that I am thinking or saying when I think or say that I ought to do something; and (ii) that fictionalism, qua fictionalism, does not provide us with (...) any new resources for providing such an account. (shrink)

Probably there is no position in Goodman’s corpus that has generated greater perplexity and criticism than Goodman’s “nominalism”. As is abundantly clear from Goodman’s writings, it is not “abstract entities” generally that he questions—indeed, he takes sensory qualia as “basic” in his Carnap-inspired constructional system in Structure—but rather just those abstracta that are so crystal clear in their identity conditions, so fundamental to our thought, so prevalent and seemingly unavoidable in our discourse and theorizing that they have come to form (...) the generally accepted framework for the most time-honored, exact, sophisticated, refined, central, and secure branch of human knowledge yet devised, mathematics itself! Of all the abstracta to question, why sets? Of course, Goodman gave his “reasons”, the unintelligibility of “generating” an infinitude of “constructed objects” automatically from any given object or objects. But critics have been quick to point out that set theory is intended not as a theory of what can be “generated” or “constructed” from given objects in any literal sense but rather as a theory of a certain realm of objects independently existing in their own right. “Construction” is a metaphor. (shrink)

Much recent discussion in the philosophy of mathematics has concerned the indispensability argument—an argument which aims to establish the existence of abstract mathematical objects through appealing to the role that mathematics plays in empirical science. The indispensability argument is standardly attributed to W. V. Quine and Hilary Putnam. In this paper, I show that this attribution is mistaken. Quine's argument for the existence of abstract mathematical objects differs from the argument which many philosophers of mathematics ascribe to him. Contrary to (...) appearances, Putnam did not argue for the existence of abstract mathematical objects at all. I close by suggesting that attention to Quine and Putnam's writings reveals some neglected arguments for platonism which may be superior to the indispensability argument. (shrink)

Mathematicalnominalists have argued that we can reformulate scientific theories without quantifying over mathematical objects.However, worries about the nature and meaningfulness of these nominalistic reformulations have been raised, like Burgess and Rosen’s dilemma. In this paper, I’ll review (what I take to be) a kind of emerging consensus response to this dilemma: appeal to the idea of different levels of analysis and explanation, with philosophy providing an extra layer of analysis “below” physics, much as physics does below chemistry. I’ll argue that (...) one can address certain lingering worries for this approach by appeal to the apparent usefulness of a distinction between foundational and non-foundational contexts within mathematics and certain (admittedly controversial) arguments for Potentialism about set theory. (shrink)

In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to (...) exist and the teleological why-question asks for what purpose numbers exist. I argue that in a psychologist constructivist account, in which numbers are understood to exist as referents of a particular type of culturally shared concepts, both why-questions can get plausible answers. (shrink)

It is well known that Carnap, early in his philosophical career, took most of metaphysics to consist of meaningless pseudostatements. In contrast to this meaning-theoretic critique of metaphysics, we develop what we take to be Carnap’s later value-based critique. We argue that this later critique is forceful against several central contemporary metaphysical debates, its origin in the principle of tolerance notwithstanding.

There are compelling reasons to believe that musical works are abstract. However, this hypothesis conflicts with the platitude that musical works are appreciated by means of audition: the things that enter our ear canals and make our eardrums vibrate must be concrete, so how can musical works be listened to if they are abstract? This question constitutes the audibility problem. In this paper, I assess Julian Dodd’s elaborate attempt to solve it, and contend that Dodd’s attempt is unsuccessful. Then I (...) discuss what I take to be the ideal response to the audibility problem, and show that it ultimately fails. I contend, consequently, that the project of construing musical works as audible is disheartening. Accordingly, in my last section, I will argue the audibility problem may be satisfactorily resolved without ascribing audibility to musical works. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

In this paper, I develop a theory on which each of a thing’s abundant properties is immanent in that thing. On the version of the theory I will propose, universals are abundant, each instantiated universal is immanent, and each uninstantiated universal is such that it could have been instantiated, in which case it would have been immanent. After setting out the theory, I will defend it from David Lewis’s argument that such a combination of immanence and abundance is absurd. I (...) will then advocate the theory on the grounds that it accomplishes all of Lewis’s “new work” while providing a gain in parsimony and a new account of fine-grained content. I will close with a discussion of how the theory also affords a new reply to two objections to uninstantiated universals: Armstrong’s charge that they are inconsistent with naturalism, and a Benacerraf-Field-style objection about epistemic access. (shrink)

Conventionalism about mathematics has much in common with two other views: fictionalism and the multiverse view (aka plenitudinous platonism). The three views may differ over the existence of mathematical objects, but they agree in rejecting a certain kind of objectivity claim about mathematics, advocating instead an extreme pluralism. The early parts of the paper will try to elucidate this anti‐objectivist position, and question whether conventionalism really offers a third form of it distinct from fictionalism and the multiverse view. The paper (...) then turns to anti‐objectivism about logic, and suggests that here too conventionalism offers no distinct alternative, and that there are limits on the extent of pluralism/anti‐objectivism. It also argues that these limits can't be used to argue for more extensive objectivity within mathematics, and also that they do allow for more limited pluralism within logic, e.g. as regards resolution of semantic and property‐theoretic paradoxes. (shrink)

The aim of this article is to argue against the real possibility of languages without subject‐predicate structure, so‐called feature‐placing languages. They were first introduced by Strawson (1959/1990), later given formal expression through Quine's Predicate Functor Logic (Quine, 1960, Quine, 1971/Quine, 1976, Quine, 1992), and further elaboration in (Hawthorne & Cortens, 1995). I argue that, on the presumption that feature‐placing languages are not mere notational variants on first‐order languages, the idea of such languages is incoherent. The argument for this view rests (...) on two highly plausible views about the conditions for the possibility of sentential meaning in natural languages. If accepted, these two views jointly imply that the sentences of feature‐placing languages lack sufficient internal structure to meet the conditions for sentential meaning. Feature‐placing languages cannot then count as genuine languages. (shrink)

Neo-Fregeanism aims to provide a possible route to knowledge of arithmetic via Hume’s principle, but this is of only limited significance if it cannot account for how the vast majority of arithmetic knowledge, accrued by ordinary people, is obtained. I argue that Hume’s principle does not capture what is ordinarily meant by numerical identity, but that we can do much better by buttressing plural logic with plural versions of the ancestral operator, obtaining natural and plausible characterizations of various key arithmetic (...) concepts, including finiteness, equinumerosity and addition and multiplication of cardinality—revealing these to be logical concepts, and obtaining much of ordinary arithmetic knowledge as logical knowledge. Supplementing this with an abstraction principle and a simple axiom of infinity (known either empirically or modally) we obtain a full interpretation of arithmetic. (shrink)

Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...) applies to any binary operator and propositional quantifier. It is also shown that the result essentially arises out of giving a negative answer to both questions, as each negative answer is consistent by itself. (shrink)

Can we do science without numbers? How much contingency is there? These seemingly unrelated questions--one in the philosophy of math and science and the other in metaphysics--share an unexpectedly close connection. For as it turns out, a radical answer to the second leads to a breakthrough on the first. The radical answer is new view about modality called compossible immutabilism. The breakthrough is a new strategy for doing science without numbers. One of the chief benefits of the new strategy is (...) that, unlike the existing substantialism approach from Field (1980), the new strategy naturally generalizes to theories formulated in terms of state space. (shrink)

Las teorías que usamos para representar el mundo pueden ser extremadamente complejas. Abordan temas tales como electrones, campos cuánticos, estrellas de neutrones, materia oscura, redes neuronales, mercados económicos, la atmósfera y muchas otras entidades que suponemos existen en el universo. Al formular nuestras teorías, recurrimos a lenguajes exactos que nos permiten minimizar la vaguedad y expresarnos lo más precisa y cuantitativamente posible. Recurrimos a la matemática. Cuando formulamos nuestras teorías fácticas en lenguaje matemático, estas se refieren no solamente a objetos (...) que nosotros interpretamos como materiales, tales como partículas o personas, sino también a entidades más raras de un mundo abstracto: conjuntos, números, funciones, espacios algebraicos, variedades, topologías, y otras entidades similares. Estos objetos no son materiales en el sentido en que nosotros decimos que una manzana es material. Ellos no existen en el espacio-tiempo, no interactúan, no cambian o evolucionan. Sin embargo, allí están, profundamente arraigados en nuestras teorías más apreciadas acerca del mundo. (shrink)

To Shape a New World, ShelbyTommie and TerryBrandon. Cambridge, MA: Harvard University Press, 2018. Pp. x + 449.

Many philosophers think all abstract objects are causally inert. Here, focusing on novels, I argue that some abstracta are causally efficacious. First, I defend a straightforward argument for this view. Second, I outline an account of object causation—an account of how objects cause effects. This account further supports the view that some abstracta are causally efficacious.

According to a growing consensus in the secondary literature on Quine, the judgment Quine makes in favor of the nominalism outlined in “Steps Toward a Constructive Nominalism” is in tension with the naturalism he later adopts. In this paper, I show the consensus view is mistaken by showing that Quine’s judgment is rooted in a naturalistic standard of clarity. Moreover, I argue that Quine late in his career is committed to accepting one plausible reading of his judgment in 1947. In (...) making these arguments, I draw attention to a version of naturalism that misreadings of Quine have prevented philosophers from appreciating, and thereby articulate and clarify a version of naturalism I recommend philosophers investigate today. (shrink)

In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...) to other philosophically problematic entities. The moral is that puzzle avoidance fails to motivate deflationary nominalism. (shrink)

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...) for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.

I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable (...) to such arguments while mathematical, logical, and normative beliefs are not—the very construction of Harman-style skeptical arguments requires the truth of significant fragments of our mathematical, logical, and normative beliefs, but requires no such thing of our moral beliefs. Given this property, Harman-style skeptical arguments against logical, mathematical, and normative beliefs are self-effacing; doubting these beliefs on the basis of such arguments results in the loss of our reasons for doubt. But we can cleanly doubt the truth of morality. (shrink)

Mental fictionalism is the view that, even if mental states do not exist, it is useful to talk as if they do. Mental states are useful fictions. Recent philosophy of mind has seen a growing interest in mental fictionalism. To date, much of the discussion has concerned the general features of the approach. In this paper, I develop a specific form of mental fictionalism by drawing on Kendall Walton’s work on make-believe. According to the approach I propose, talk of mental (...) states is a useful pretence for describing people and their behaviour. I try to clarify and motivate this approach by comparing it to well-known alternatives, including behaviourism, instrumentalism and eliminativism. I also consider some of the challenges that it faces. (shrink)

We naturally think of the material world as being populated by a large number of individuals . These are things, such as my laptop and the particles that compose it, that we describe as being propertied and related in various ways when we describe the material world around us. In this paper I argue that, fundamentally speaking at least, there are no such things as material individuals. I then propose and defend an individual-less view of the material world I call (...) “generalism”. (shrink)

Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...) scientific theories range over. In this paper, I argue that all three arguments fail and they fail for much the same reason; would-be nominalists are thus left facing Field's hard road. (shrink)

Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...) this, I argue that semantics can fail to deliver determinate ontological commitments and determinate answers to ontological questions, more generally. (shrink)

In this essay, the tension that Benacerraf identifies for theories of mathematical truth is used as the vehicle for arguing against a particular desideratum for semantic theories. More specifically, I place in question the desideratum that a semantic theory, provided for some area of discourse, should run in parallel with the semantic theory holding for the rest of the language. The importance of this desideratum is also made clear by means of tracing out the subtle implications of its rejection.