There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a (...) liberalized version of Field’s response—and I discuss its significance. I argue that if it succeeds, it provides a new refutation of the indispensability argument; and that, even if it fails, its failure may bolster some of the fictionalist responses to the indispensability argument already under discussion. In addition, I use grounding to reply to a recent challenge to these responses. (shrink)

ABSTRACT‘expressionist’ accounts of applied mathematics seek to avoid the apparent Platonistic commitments of our scientific theories by holding that we ought only to believe their mathematics-free nominalistic content. The notion of ‘nominalistic content’ is, however, notoriously slippery. Yablo's account of non-catastrophic presupposition failure offers a way of pinning down this notion. However, I argue, its reliance on possible worlds machinery begs key questions against Platonism. I propose instead that abstract expressionists follow Geoffrey Hellman's lead in taking the assertoric content of (...) empirical science to be irreducibly modal, using the ‘non-interference’ of mathematical objects as justification for detaching nominalistic consequences. (shrink)

We consider to what extent the fundamental question of spacetime singularities is relevant for the philosophical debate about the nature of spacetime. After reviewing some basic aspects of the spacetime singularities within general relativity, we argue that the well known difficulty to localize them in a meaningful way may challenge the received metaphysical view of spacetime as a set of points possessing some intrinsic properties together with some spatiotemporal relations. Considering the algebraic formulation of general relativity, we argue that the (...) spacetime singularities highlight the philosophically misleading dependence on the standard geometric representation of spacetime. †To contact the author, please write to: Department of Philosophy, University of Lausanne, CH-1015 Lausanne, Switzerland; e-mail: [email protected]. (shrink)

Homotopy Type Theory is a putative new foundation for mathematics grounded in constructive intensional type theory that offers an alternative to the foundations provided by ZFC set theory and category theory. This article explains and motivates an account of how to define, justify, and think about HoTT in a way that is self-contained, and argues that, so construed, it is a candidate for being an autonomous foundation for mathematics. We first consider various questions that a foundation for mathematics might be (...) expected to answer, and find that many of them are not answered by the standard formulation of HoTT as presented in the ‘HoTT Book’. More importantly, the presentation of HoTT given in the HoTT Book is not autonomous since it explicitly depends upon other fields of mathematics, in particular homotopy theory. We give an alternative presentation of HoTT that does not depend upon ideas from other parts of mathematics, and in particular makes no reference to homotopy theory, and argue that it is a candidate autonomous foundation for mathematics. Our elaboration of HoTT is based on a new interpretation of types as mathematical concepts, which accords with the intensional nature of the type theory. 1 Introduction2 What Is a Foundation for Mathematics?2.1 A characterization of a foundation for mathematics2.2 Autonomy3 The Basic Features of Homotopy Type Theory3.1 The rules3.2 The basic ways to construct types3.3 Types as propositions and propositions as types3.4 Identity3.5 The homotopy interpretation4 Autonomy of the Standard Presentation?5 The Interpretation of Tokens and Types5.1 Tokens as mathematical objects?5.2 Tokens and types as concepts6 Justifying the Elimination Rule for Identity7 The Foundations of Homotopy Type Theory without Homotopy7.1 Framework7.2 Semantics7.3 Metaphysics7.4 Epistemology7.5 Methodology8 Possible Objections to this Account8.1 A constructive foundation for mathematics?8.2 What are concepts?8.3 Isn’t this just Brouwerian intuitionism?8.4 Duplicated objects8.5 Intensionality and substitution salva veritate9 Conclusion9.1 Advantages of this foundation. (shrink)

This paper explores some variants and aspects of multi-quantificational criteria of existence, examining these in the context of the debate between monism and pluralism in analytical philosophy. Assuming familiarity with the findings to date, we seek to apply to these the newly introduced concepts of “substitution” and “substitutional model”. Possible applications of formal theories involving multiple types of existential quantifier are highlighted, together with their methods of construction. These considerations then lead to a thesis asserting the irrelevance of both multi-quantificational (...) criteria and assumptions involving quantificational ontology to the debate between monism and pluralism in ontology. Many quantifiers cannot properly distinguish different modes of existence–as we aim to show by furnishing a general method for constructing counter-examples to any theory that assumes that different types of existential quantifier correspond to different modes of existence. (shrink)

Indispensability arguments purport to show that empirical data provide evidence for the existence of mathematical entities. In this paper we argue that indispensability arguments fail to show that empirical data bears on the mathematical. In order to show this we attempt to clarify what it is to be mathematical , and separate the question whether abstracta in general exist from whether distinctively mathematical abstracta exist. We introduce the notion of an ‘agnostified’ empirical theory as a heuristic device for clarifying the (...) role of mathematical terminology in empirical theories. The special case of spaces is then briefly considered. (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)

Physics presents us with a symphony of natural constants: G, h, c, etc. Up to this point, constants have received comparatively little philosophical attention. In this paper I provide an account of dimensionful constants, in particular the gravitational constant. I propose that they represent inter-quantity structure in the form of relations between quantities with different dimensions. I use this account of G to settle a debate over whether mass scalings are symmetries of Newtonian Gravitation. I argue that they are not, (...) but only if we interpret mass anti-quidditistically. This is analogous to anti-haecceitism in the presence of spacetime symmetries. (shrink)

It is now standard to interpret symmetry-related models of physical theories as representing the same state of affairs. Recently, a debate has sprung up around the question when this interpretational move is warranted. In particular, Møller-Nielsen :1253–1264, 2017) has argued that one is only allowed to interpret symmetry-related models as physically equivalent when one has a characterisation of their common content. I disambiguate two versions of this claim. On the first, a perspicuous interpretation is required: an account of the models’ (...) common ontology. On the second, stricter, version of this claim, a perspicuous formalism is required in addition: one whose mathematical structures ‘intrinsically’ represent the physical world, in the sense of Field. Using Dewar’s :485–521, 2019) distinction between internal and external sophistication as a case study, I argue that the second requirement is decisive. This clarifies the conditions under which it is warranted to interpret symmetry-related models as physically equivalent. (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)

It is not uncommon for philosophers to maintain that one is obliged to believe nothing beyond the observable consequences of a successful scientific theory. This doctrine is variously known as instrumentalism, fictionalism, constructive empiricism, theoretical skepticism and the philosophy of "as if". The purpose of the present paper is to subject such forms of scientific antirealism to a two-pronged critique. In the first place it is argued that there is no genuine difference between believing a theory and being disposed to (...) use it to make predictions, design experiments, and so on; so traditional instrumentalism is incoherent. In the second place, a retrenched position is considered in which theoretical belief would be tolerated but said to be justified on merely pragmatic, and not epistemic, grounds. In criticizing this point of view it is shown that the onus of proof rests on anyone who maintains it; furthermore, the only possible rationale for it (which is based on underdetermination of theory by data) is described, and various deficiencies in this argument are exposed. (shrink)

Kitcher urges us to think of mathematics as an idealized science of human operations, rather than a theory describing abstract mathematical objects. I argue that Kitcher's invocation of idealization cannot save mathematical truth and avoid platonism. Nevertheless, what is left of Kitcher's view is worth holding onto. I propose that Kitcher's account should be fictionalized, making use of Walton's and Currie's make-believe theory of fiction, and argue that the resulting ideal-agent fictionalism has advantages over mathematical-object fictionalism.

It has commonly been argued that certain types of mental descriptions, specifically those characterized in terms of propositional attitudes, are part of a folk psychological understanding of the mind. Recently, however, it has also been argued that this is the case even when such descriptions are employed as part of scientific theories in domains like social psychology and comparative psychology. In this paper, I argue that there is no plausible way to understand the distinction between folk and scientific psychology that (...) can support such claims. Moreover, these sorts of claims can have adverse consequences for the neuroscientific study of the brain by downplaying the value of many psychological theories that provide information neuroscientists need in order to build and test neurological models. (shrink)

In this paper, I argue that various disputes in ontology have important ramifications and so are worth taking seriously. I employ a criterion according to which whether a dispute matters depends on how integrated it is with the rest of our theoretical projects. Disputes that arise from previous tensions in our theorizing and have additional implications for other issues matter, while insular disputes do not. I apply this criterion in arguing that certain ontological disputes matter; specifically, the disputes over concrete (...) possible worlds and coincident material objects. Finally, I consider how one could show that some ontological disputes do not matter, using a Platonism/nominalism dispute as an example. (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.

In this paper I present the Discrete Space-Time Thesis, in a way which enables me to defend it against various well-known objections, and which extends to the discrete versions of Special and General Relativity with only minor difficulties. The point of this presentation is not to convince readers that space-time really is discrete but rather to convince them that we do not yet know whether or not it is. Having argued that it is an open question whether or not space-time (...) is discrete, I then turn to some possible empirical evidence, which we do not yet have. This evidence is based on some slight differences between commonly occurring differential equations and their discrete analogs. (shrink)

Earman (1993) distinguishes three notions of empirical indistinguishability and offers a rigorous framework to investigate how each of these notions relates to the problem of underdetermination of theory choice. He uses some of the results obtained in this framework to argue for a version of scientific anti- realism. In the present paper we first criticize Earman's arguments for that position. Secondly, we propose and motivate a modification of Earman's framework and establish several results concerning some of the notions of indistinguishability (...) in this modified framework. Finally, we interpret these results in the light of the realism/anti- realism debate. (shrink)

According to ontological nihilism there are, fundamentally, no individuals. Both natural languages and standard predicate logic, however, appear to be committed to a picture of the world as containing individual objects. This leads to what I call the \emph{expressibility challenge} for ontological nihilism: what language can the ontological nihilist use to express her account of how matters fundamentally stand? One promising suggestion is for the nihilist to use a form of \emph{predicate functorese}, a language developed by Quine. This proposal faces (...) a difficult objection, according to which any theory in predicate functorese will be a notational variant of the corresponding theory stated in standard predicate logic. Jason Turner (2011) has provided the most detailed and convincing version of this objection. In the present paper, I argue that Turner's case for the notational variance thesis relies on a faulty metasemantic principle and, consequently, that an objection long thought devastating is in fact misguided. (shrink)

Steven French’s new book is a bold and ambitious look at the question of what sorts of things scientific theories are—or rather, what they are not. For the purp.

In recent work, Adlam (2022b), Chen & Goldstein (2022), and Meacham (2023) have defended accounts of laws that take laws to be primitive global constraints. A major advantage of these accounts is that they’re able to accommodate the many different kinds of laws that appear in physical theories. In this paper I’ll present these three accounts, highlight their distinguishing features, and note some key differences that might lead one to favor one of these accounts over the others. I’ll conclude by (...) briefly discussing a version of a “constraint” account that I think is especially attractive. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...) to mathematics and a top-down naturalisation. Articulating my particular understanding of what realism and naturalism should commit us to, I propose a creative fusion of Badiou’s attention to metamathematical results with a structural-informational metaphysics, proposing a ‘matherialism’ uniting the more daring speculative insights of the former with the naturalist and empiricist commitments motivating the latter. (shrink)

In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by (...) mathematics in our scientific explanations is a purely expressive one, merely allowing us to say more about the physical world than we would otherwise be able to. Mathematical objects do not need to exist for mathematics to play this role. This proposal puts a normative constraint on our use of mathematical language: we ought to use mathematically presented theories to express belief only in the consequences they have for non-mathematical things. In Part II, I will argue that what the normative proposal recommends is in fact what people generally do in both pure and applied mathematical contexts. I motivate this claim by showing that it is predicted by our best general means of analysing natural language. I provide a semantic theory of applied arithmetical sentences that reveals they do not purport to refer to numbers, as well as a pragmatic theory for pure mathematical language use which reveals that pure mathematical utterances do not typically communicate content that implies the existence of mathematical objects. In conclusion, I show that the emerging hermeneutic fictionalist position is preferable to any alternative interpretation of mathematical discourse as aimed at describing a domain of independently existing abstract mathematical objects. (shrink)

General discussion of grounding, including its formal features, relations to other notions, and applications. (Originally published 2014; revised 2021).

Quine has famously put forward the indispensability argument to force belief in the existence of mathematical objects (such as classes) due to their indispensability to our best theories of the world (Quine 1960). Quine has also advocated the indeterminacy of reference argument, according to which reference is dramatically indeterminate: given a language, there’s no unique reference relation for that language (see Quine 1969a). In this paper, I argue that these two arguments are in conflict with each other. Whereas the indispensability (...) argument supports realism about mathematics, the indeterminacy of reference argument, when applied to mathematics, provides a powerful strategy in support of mathematical anti-realism. I conclude the paper by indicating why the indeterminacy of reference phenomenon should be preferred over the considerations regarding indispensability. In the end, even the Quinean shouldn’t be a realist (platonist) about mathematics. (shrink)

The predisposition of the Indispensability Argument to objections, rephrasing and versions associated with the various views in philosophy of mathematics grants it a special status of a “blueprint” type rather than a debatable theme in the philosophy of science. From this point of view, it follows that the Argument has more an epistemic character than ontological.

Most empirical accounts of design suggest that designing is an activity where objects and representations are progressively constructed. Despite this fact, whether design is a constructive process or not is not a question directly addressed in the current design research. By contrast, in other fields such as Mathematics or Psychology, the notion of constructivism is seen as a foundational issue. The present paper defends the point of view that forms of constructivism in design need to be identified and integrated as (...) a founda- tional element in design research as well. In fact, a look at the literature reveals at least two types of constructive processes that are well embedded in design research: first, an interac- tive constructivism, where a designer engages a conversation with media, that allows changing the course of the activity as a result of this interaction; second, a social constructivism, where designers need to handle communication and nego- tiation aspects, that allows integrating individuals' expertise into the global design process. A key feature lacking these well-established paradigms is the explicit consideration of creativity as a central issue of design. To explore how cre- ative and constructivist aspects of design can be taken into account conjointly, the present paper pursues a theoretical approach. We consider the roots of constructivism in math- ematics, namely the Intuitionist Mathematics, in order to shed light on the original insights that led to the development of a notion of constructivism. Intuitionists describe mathe- matics as the process of mental mathematical constructions realized by a creative subject over time. One of the most original features of intuitionist constructivism is the intro- duction of incomplete objects into the heart of mathematics by means of lawless sequences and free choices. This allows the possibility to formulate undecided propositions and the consideration of creative acts within a formal constructive process. We provide an in-depth analysis of intuitionism from a design standpoint showing that the original notion is more than a pure constructivism where new objects are a mere bottom-up combination of already known objects. Rather, intuitionism describes an imaginative constructivist process that allows combining bottom-up and top-down processes and the expansion of both propositions and objects with free choices of a creative subject. We suggest that this new form of constructivism we identify is also relevant in interpreting conventional design processes and discuss its status with respect to other forms of constructivism in design. (shrink)

There are advantages to thrift over honest toil. If we can make do without numbers we avoid challenging questions over the metaphysics and epistemology of such entities; and we have a good idea, I think, of what a nominalistic metaphysics should look like. But minimizing ontology brings its own problems; for it seems to lead to error theory— saying that large swathes of common-sense and best science are false. Should recherche philosophical arguments really convince us to give all this up? (...) Such Moorean considerations are explicitly part of the motivation for the recent resurgence of structured metaphysics, which allow a minimal (perhaps nominalistic) fundamental ontology, while avoiding error-theory by adopting a permissive stance towards ontology that can be argued to be grounded in the fundamental. This paper evaluates the Moorean arguments, identifying key epistemological assumptions. On the assumption that Moorean arguments can be used to rule out error-theory, I examine deflationary ‘representationalist’ rivals to the structured metaphysics reaction. Quinean paraphrase, fictionalist claims about syntax and semantics are considered and criticized. In the final section, a ‘direct’ deflationary strategy is outlined and the theoretical obligations that it faces are articulated. The position advocated may have us talking a lot like a friend of structured metaphysics—but with a very different conception of what we’re up to. (shrink)

In this paper, I propose a fictionalist approach to the problem of color. On my view, which I call prescriptive color fictionalism, we can continue to employ our color discourse as we have thus far even if it turns out that there are no colored objects. My proposal is a species of error theory. As such, it does not describe our current practices. It is rather proposed as a prescription to a problem, namely that the color theory we accept (according (...) to which there are colored objects) is false. By formulating a fictionalist account of color and showing that we can preserve ordinary color discourse in the absence of colored objects, I provide a solution to the problem of color. (shrink)

This thesis articulates the resonances between J. M. Coetzee's lifelong engagement with mathematics and his practice as a novelist, critic, and poet. Though the critical discourse surrounding Coetzee's literary work continues to flourish, and though the basic details of his background in mathematics are now widely acknowledged, his inheritance from that background has not yet been the subject of a comprehensive and mathematically- literate account. In providing such an account, I propose that these two strands of his intellectual trajectory not (...) only developed in parallel, but together engendered several of the characteristic qualities of his finest work. The structure of the thesis is essentially thematic, but is also broadly chronological. Chapter 1 focuses on Coetzee's poetry, charting the increasing involvement of mathematical concepts and methods in his practice and poetics between 1958 and 1979. Chapter 2 situates his master's thesis alongside archival materials from the early stages of his academic career, and thus traces the development of his philosophical interest in the migration of quantificatory metaphors into other conceptual domains. Concentrating on his doctoral thesis and a series of contemporaneous reviews, essays, and lecture notes, Chapter 3 details the calculated ambivalence with which he therein articulates, adopts, and challenges various statistical methods designed to disclose objective truth. Chapter 4 explores the thematisation of several mathematical concepts in Dusklands and In the Heart of the Country. Chapter Five considers Waiting for the Barbarians and Foe in the context provided by Coetzee's interest in the attempts of Isaac Newton to bridge the gap between natural language and the supposedly transparent language of mathematics. Finally, Chapter 6 locates in Elizabeth Costello and Diary of a Bad Year a cognitive approach to the use of mathematical concepts in ethics, politics, and aesthetics, and, by analogy, a central aspect of the challenge Coetzee's late fiction poses to the contemporary literary landscape. (shrink)

The object of this paper is to study the analogy, drawn both positively and negatively, between mathematics and fiction. The analogy is more subtle and interesting than fictionalism, which was discussed in part I. Because analogy is not common coin among philosophers, this particular analogy has been discussed or mentioned for the most part just in terms of specific similarities that writers have noticed and thought worth mentioning without much attention's being paid to the larger picture. I intend with this (...) analogy (looking at others' comparisons) to shed a little light on what is going on in mathematics, how one can understand it a bit other than experientially. This intention is philosophical and the way that I am attempting to accomplish it is also philosophical. I shall conclude my attempt to explain how it is possible and even natural for mathematics and fiction to have the analogy they have, taking it for granted, as argued in part I, that they are not to be identified. To this end I shall discuss philosophers' comparisons, mainly those of Hodes, Resnik, Tharp, and Wagner, who are the writers that seem to me to have written most thoughtfully and sufficiently extensively about fiction in making the comparison and of Körner, whose comparison is different. Whether either of these comparisons or the more general analogy is of permanent philosophical interest will have to be decided by philosophers now that they have had a fuller examination. I shall mention some other writers' reference to fiction, but not all; indeed, I am sure that I have not even found all the comparisons that there are. (shrink)

Recent attempts to answer ontological questions through conceptual analysis have been controversial. Still, it seems reasonable to assume that if the existence of certain things analytically follows from sentences we already accept, then there is no further ontological commitment involved in affirming the existence of those things. More generally, it is plausible that whenever a sentence analytically entails another, the conjunction of those sentences requires nothing more of the world for its truth than the former sentence alone. In his ‘Analyticity (...) and Ontology’, Louis deRosset tries to produce counterexamples to these principles by means of linguistic stipulations. I aim to show where his arguments go wrong. (shrink)

I describe three extant attempts to identify the global external symmetries within a Humean framework with theorems of some or other deductive systematization of the world, respectively, the best system, a meta-best system and a maximally simple system. Each has merits, but also serious flaws. Instead, I propose a view of global external symmetries as consequences of the structure of Humean-consistent world-making relations.

The paper first argues that if one takes current fundamental physics seriously, one gets to a metaphysics of events and relations in contrast to substances and intrinsic properties. Against that background, the paper discusses Heil’s theory of properties being both categorical and dispositional and his rejection of levels of being. I contrast these views with a Humean metaphysics. My concluding claim is that Heil’s account of properties opens up the perspective of a conservative reductionism, which avoids the common reservations against (...) reductionism. (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)

Words and phrases specifying similarity and distance abound in musical discourse. This essay explores such pitch-predicates as "matches", "is in the vicinity of, and "is closer to ... than to". Sought here are ways in which pitch and pitch-interval predicates might be inter-connected logically. Within a nominalist framework, an orderly progression from pitch- to pitch-interval-predicates can be proven and interpreted in terms of simplicity. Also indicated are connections between the present formulation and issues of (i) dimensionality and explanation in psychoacoustics, (...) Gestalt psychology, and behaviorism, and (ii) nominalism and the "numerological fallacy" in music theory. (shrink)

The paper traces some of the assumptions that have informed conservative naturalism in linguistic theory, critically examines their justification, and proposes a more liberal alternative.

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

The metaphysics of representation poses questions such as: in virtue of what does a sentence, picture, or mental state represent that the world is a certain way? In the first instance, I have focused on the semantic properties of language: for example, what is it for a name such as ‘London’ to refer to something? Interpretationism concerning what it is for linguistic expressions to have meaning, says that constitutively, semantic facts are fixed by best semantic theory. As here developed, it (...) promises to give a reductive, universal and non-revisionary account of the nature of linguistic representation. -/- Interpretationism in general, however, is threatened by severe internal tension, due to arguments for radical inscrutability. These contend that, given the interpretationist setting, there can be no fact of the matter what object an individual word refers to: for example, that there is no fact of the matter as to whether “London” refers to London or to Sydney. -/- A series of challenges emerge, forming the basis for this thesis. 1. What sort of properties is the interpretationist trying to reduce, and what kind of reductive story is she offering? 2. How are inscrutability theses best formulated? Are arguments for inscrutability effective in their own terms? What kinds of inscrutability arise? 3. Is endorsing radical inscrutability a stable position? 4. Are there theoretical virtues—such as simplicity—that can be appealed to in discrediting the rival (empirically equivalent) theories that underpin inscrutability arguments? -/- In addressing these questions, I concentrate on diagnosing the source of inscrutability, mapping the space of ways of resisting the arguments for radical inscrutability, and examining the challenges faced in developing a principled account of linguistic content that avoids radical inscrutability. -/- The effect is not to close down the original puzzles, but rather to sharpen them into a set of new and deeper challenges. (shrink)

Timothy Williamson’s Knowledge and its Limits has been highly influential since the beginning of this century. It can be read as a systematic response to scepticism. One of the most important notions in this response is the notion of «evidence,» which will be the focus of the present paper. I attempt to show primarily two things. First, the notion of evidence invoked by Williamson does not address the sceptical worry: he stipulates an objective notion of evidence, but this begs the (...) question against his opponent. Second, his related thesis «Evidence equals Knowledge» does not sit well with his own content externalism: he promises to relate epistemology to philosophy of mind, but he fails to live up to this commitment in his crucial chapter on scepticism. Other minor problems concerning evidence will also be discussed in due course. (shrink)