This paper has three aims: to define autonomism clearly and charitably, to offer a positive argument in its favour, and to defend a larger view about what is at stake in the debate between autonomism and its critics. Autonomism is here understood as the claim that a valuer does not make an error in failing to bring her moral and aesthetic judgements together, unless she herself values doing so. The paper goes on to argue that reason does not require the (...) valuer to make coherent her aesthetic and moral evaluations. Finally, the paper shows that the denial of autonomism has realist commitments that autonomism does not have, and concludes that issues of value realism and irrealism are relevant to the debates about autonomism in ways that have not hitherto been recognized. (shrink)

Immoralists hold that in at least some cases, moral fl aws in artworks can increase their aesthetic value. They deny what I call the valence constraint: the view that any effect that an artwork’s moral value has on its aesthetic merit must have the same valence. The immoralist offers three arguments against the valence constraint. In this paper I argue that these arguments fail, and that this failure reveals something deep and interesting about the relationship between cognitive and moral value. (...) In the fi nal section I offer a positive argument for the valence constraint. (shrink)

Ancient Chinese and Greek thinkers alike were preoccupied with the moral value of music; they distinguished between good and bad music by looking at the music’s effect on moral character. The idea can be understood in terms of two closely related questions. Does music have the power to affect the ethical character of either listener or performer? If it does, is it better as music for doing so? I argue that an affirmative answers to both questions are more plausible than (...) it might seem at first. (shrink)

Aesthetic internalism claims a link between judgement and motivation: aesthetic judgements bring with them motivations to act in characteristic ways. Critics object that there is a difference between merely liking something and judging it to be aesthetically good, and that it is our likings, not our aesthetic judgements, that motivate us. This paper develops a version of aesthetic internalism that can respond to this criticism. Wholehearted aesthetic judgements are characterized by stability, attention, and motivation. Making such judgements is an important (...) part of a good life, and so at least some aesthetic judgements are motivating. So we have reason to think that this version of aesthetic internalism is true. This paper defends wholehearted aesthetic internalism against objections, and assesses an argument from aesthetic internalism to aesthetic non-cognitivism. While wholehearted aesthetic internalism can only offer qualified support to non-cognitivism, it nonetheless offers a number of fruitful avenues for further work. (shrink)

The topic of this essay is how non-realistic novels challenge our philosophical understanding of the moral significance of literature. I consider just one case: Joseph Heller’s Catch-22. I argue that standard philosophical views, based as they are on realistic models of literature, fail to capture the moral significance of this work. I show that Catch-22 succeeds morally because of the ways it resists using standard realistic techniques, and suggest that philosophical discussion of ethics and literature must be pluralistic if it (...) is to include all morally salient literature, and not just novels in the “Great Tradition” and their ilk. (shrink)

I explore the claim that “fictive imagining” – imagining what it is like to be a character – can be morally dangerous. In particular, I consider the controversy over William Styron’s imagining the revolutionary protagonist in his Confessions of Nat Turner. I employ Ted Cohen’s model of fictive imagining to argue, following a generally Kantian line of thought, that fictive imagining can be dangerous if one has the wrong motives. After considering several possible motives, I argue that only internally directed (...) motives can satisfy the moral concern. Finally, I suggest that when one has the right motives, fictive imagining is morally praiseworthy since it improves one’s ability to imagine the lives of others. (shrink)

© British Society of Aesthetics 2018. Published by Oxford University Press on behalf of the British Society of Aesthetics. All rights reserved. For Permissions, please email: [email protected] adaptation of literary works into films has been almost completely neglected as a philosophical topic. I discuss two questions about this phenomenon:What do we mean when we say that a film is faithful to its source?Is being faithful to its source a merit in a film adaptation?In response to, I set out two distinct (...) senses of fidelity: story fidelity and thematic fidelity. I then argue, in response to, that thematic fidelity, but not story fidelity, is an aesthetic merit in a film adaptation. The key steps in this argument involve showing that merely preserving the story from one medium to another does not typically involve an aesthetically... (shrink)

One important but infrequently discussed difficulty with expressivism is the attitude type individuation problem.1 Expressivist theories purport to provide a unified account of normative states. Judgments of moral goodness, beauty, humor, prudence, and the like, are all explicated in the same way: as expressions of attitudes, what Allan Gibbard calls “states of norm-acceptance”. However, expressivism also needs to explain the difference between these different sorts of attitude. It is possible to judge that a thing is both aesthetically good and morally (...) bad. While the realist can explain the difference by suggesting that each judgment makes reference to a different property (or set of properties), the expressivist cannot. She must show that what is expressed by the speaker is different in each case. This has proven to be difficult to do. (shrink)

In recent years it has become more and more difficult to distinguish between metaethical cognitivism and non-cognitivism. For example, proponents of the minimalist theory of truth hold that moral claims need not express beliefs in order to be (minimally) truth-apt, and yet some of these proponents still reject the traditional cognitivist analysis of moral language and thought. Thus, the dispute in metaethics between cognitivists and non-cognitivists has come to be seen as a dispute over the correct way to characterize our (...) psychology: are moral judgments beliefs, or a kind of pro-attitude? In this paper, I argue that this distinction, too, is difficult to maintain in the light of a reasonable skepticism about folk psychology. I conclude by suggesting some new possibilities for the analysis of moral language that look beyond this distinction. I begin by briefly reviewing some contemporary positions in metaethics on cognitivism and non-cognitivism, that are intended to emphasize the supposed psychological differences between the two views. I show that the appearance of a clear difference between these views depends on one's having a very strong commitment to the context-independence and completeness of certain concepts of folk psychology. I then argue for a moderate skepticism about folk psychology. I conclude that folk concepts like ?belief? are not sufficiently well-defined to settle this metaethical dispute. (shrink)

Two recent novels, Ian McEwan’s Atonement and Margaret Atwood’s The Blind Assassin, are philosophically instructive. These books are interesting, I argue, because they reveal something about understanding and appreciating narrative. They show us that audience’s participation in narrative is much more subtle and complex than philosophers generally acknowledge. An analysis of these books reveals that narrative imagining is not static or unified, but dynamic and multipolar. I argue that once the complexity of narrative engagement is better understood, some prominent philosophical (...) problems and debates concerning narrative dissolve. (shrink)

Some films scare us; some make us cry; some thrill us. Some of the most interesting films, however, leave us suspended between feelings – both joyous and sad, or angry and serene. This paper attempts to explain how this can happen and why it is important. I look closely at one film that creates and exploits these conflicted responses. I argue that cases of conflict in film illuminate a pair of vexing questions about emotion in film: (1) To what extent (...) are emotional responses rational, or in need of rationalization?; and (2) What relationship is there between emotional response and value (moral, filmic, or otherwise)? Conflict, I argue, can be revealing, and can help us better understand emotional responses to narrative film1 in general. The paper is divided into four sections. First, I sketch a theory of emotional engagement that makes sense of the notion of a “conflicted emotional response” to a film. Second, I turn to a particular case of a film that produces this sort of conflict, Fritz Lang’s M (1931), and show that the conflict engendered by that film is both more significant and less unusual than it may appear. In the final two sections, I argue that there is no need to rationalize or make consistent such mixed emotional responses, and that there is real moral, aesthetic, and cognitive value to be had from such conflict. (shrink)

In this essay I argue that if Kantian and consequentialist ethical theories are vulnerable to the so-called “problem of alienation,” a virtue ethics based on Xunzi’s ethical writings will also be vulnerable to this problem. I outline the problem of alienation, and then show that the role of ritual ( li ) in Xunzi’s theory renders his view susceptible to the problem as it has been traditionally understood. I consider some replies on Xunzi’s behalf, and also discuss whether the problem (...) affects other Confucian and eudaimonian approaches to virtue ethics. I close by considering some solutions to the problem and the affect that this result has on the argumentative dialectic between the three major ethical traditions. (shrink)

Psychopaths are the bugbears of moral philosophy. They are often used as examples of perfectly rational people who are nonetheless willing to do great moral wrong without regret; hence the disorder has received the epithet “moral insanity” (Pritchard 1835). But whereas philosophers have had a great deal to say about psychopaths’ glaring and often horrifying lack of moral conscience, their aesthetic capacities have received hardly any attention, and are generally assumed to be intact or even enhanced. Popular culture often portrays (...) psychopaths in ways that suggest a great gap between their amorality and their aesthetic sensitivity. In The Silence of the Lambs (Jonathan Demme, 1991), Hannibal Lecter appreciates fine art, fashion, and wine, while he eats his way through his enemies. His real-life counterparts, however, do not demonstrate the same sensitivities. There is no evidence that psychopaths are capable of real aesthetic appreciation, and some evidence that they are not. In this paper, we set out the limited evidence for the psychopath’s deficient aesthetic sensitivity. The best explanations of what the psychopath lacks turn out to implicate abilities that are also thought to be central to moral thought and action: an impaired capacity for empathizing with others and deficient ability to take a disinterested attitude towards things (socalled distance). We endorse the latter explanation. Thinking about what underlies the psychopath’s deficient aesthetic understanding turns out to throw light on a difficult problem: the connection between ethics and aesthetics. (shrink)

The hermeneutic pragmatism explored in this article timely examines how “post-truth” claims over-estimate semantic freedoms while at the same time underestimating semantic and pre-semantic restraints. Such pragmatism also timely examines how formalists err by committing the reverse errors. Drawing on insights from James, Peirce, Putnam, Rorty, Gadamer, Derrida, and others, such hermeneutic pragmatism explores (1) the necessary role of both internal and objective experience in meaning, (2) the resulting instrumental nature of concepts required to deal with such experience, (3) (...) the related need for workability to apply to the “the collectivity of experience’s demands, nothing being omitted,” (4) the inherent role of morality and other norms in measuring such workability, (5) the semantic as well as experiential nature of our workable realities, (6) the semantic freedoms involved in constructing, framing, and retaining our workable realities and concepts, and (7) the semantic, pre-semantic, and other restraints on constructing, framing, and retaining our workable realities and concepts. -/- Such hermeneutic pragmatism also introduces Eunomia, a real-world alternative to Dworkin’s superhuman judge Hercules. Named after the Greek goddess of good order, the human Eunomia represents the reasonable judge excellently versed in (among other things) legal theory, legal practice, linguistics, and philosophy of language. Additionally, in its appendices, this article surveys the pragmatic restraints of “implementives” and provides a detailed overview of pragmatic “workability” restraints for both law and fact. -/- (By “sense” the title of this article means not only “meaning conveyed or intended” but also “capacity for effective application of the powers of the mind as a basis for action or response.” See Sense, MERRIAM-WEBSTER’S COLLEGIATE DICTIONARY (11th ed. 2014) “Workable” has the broad meaning discussed in Sections II, IV, and Appendix C of the Article, and "good" is further explored in the section on Eunomia, namesake of the Greek goddess of good order.) -/- Keywords: Pragmatism, Hermeneutic, Truth, Rule of Law, William James, C.S. Peirce, Hilary Putnam, Richard Rorty, Gadamer, Habermas, Derrida, Lon Fuller, H.L.A. Hart, Post-truth, Postmodernism, Trump, Rhetoric, Meaning, Interpretation, Metaphor, Category, Lifeworld, Formalism, Framing, Deconstruction. (shrink)

This chapter presents the formalist account of the moral status of an artwork as an aesthetically significant and autonomous form, with due emphasis on the Anglo-American art-for-art’s-sake aesthetic, as it developed between 1870 and 1960. The author shows that the formalist art-is-above-morals approach is a substantive moral stance in itself. Formalist aesthetics is usually presented in the literature as evincing a purist indifference to ethics, construing moral properties as external to art, in opposition to the internal pure properties of art’s (...) composition. The chapter demonstrates that this is a misrepresentation of the complex formalist prescriptive idea of the relations between art and ethics. Through its autonomy and imperviousness to external co-opting—which is accomplished by due focus on aesthetic form—art on the formalist account is held to be a paradigm of the liberalist principles of individual freedom and self-fulfillment, thus an inherent means to the good. (shrink)

Hubert Dreyfus has argued that cases of absorbed bodily coping show that there is no room for self-awareness in flow experiences of experts. In this paper, I argue against Dreyfus’ maxim of vanishing self-awareness by suggesting that awareness of agency is present in expert bodily action. First, I discuss the phenomenon of absorbed bodily coping by discussing flow experiences involved in expert bodily action: merging into the flow; immersion in the flow; emergence out of flow. I argue against the claim (...) that flow experience does not involve an awareness of agency for each of these features, while conceding that fluent agency does not involve self-awareness in the thetic sense. I challenge the assumption that the awareness of fluent agency must be understood in terms of a thetic awareness of agency. Instead, I develop an Anscombean account of the awareness of fluent agency in terms of the phenomenal character of knowing one’s aims. I respond to the challenge that if an Anscombean account of the awareness of agency is to succeed, then agents must be able to answer Anscombean questions. I consider the objection that awareness of agency is not a form of self-awareness by outlining an account of self-awareness as self-synthesis that is distinct from self-perception and self-ascription, but which makes room for self-awareness in expert bodily action. (shrink)

The paper discusses the arguments for and against animalism and concludes that a pluralist position which rejects animalism and embraces a multiplicity of thinkers is the best option.

This paper presents a model-theoretic semantics for discourse "about" natural numbers, one that captures what I call "the mathematical-object picture", but avoids what I can "the mathematical-object theory".

The Monad’s components are as follows: 1: Monism as the state of eternal undifferentiation 2: Dualism as the state of infinite differentiations -/- MONAD = ET = INF ET Ψ INF.

Scepticism about ought simpliciter is the view that there is no such thing as what one ought simpliciter to do. Instead, practical deliberation is governed by a plurality of normative standpoints, each authoritative from their own perspective but none authoritative simpliciter. This paper aims to resist such scepticism. After setting out the challenge in general terms, I argue that scepticism can be resisted by rejecting a key assumption in the sceptic’s argument. This is the assumption that standpoint-relative ought judgments bring (...) with them a commitment to act in accordance with those judgments. Instead, I propose an alternative account of our normative concepts according to which only ought simpliciter judgments commit one to acting in accordance with those judgments. In addition to answering the sceptical challenge, the proposal offers an independently motivated account of what makes a concept normatively authoritative. (shrink)

A lineage of prominent philosophers who have discussed the second-person relation can be regarded as advancing structural accounts. They posit that the second-person relation effects one transformative change to the structure of practical reasoning. In this paper, I criticise this orthodoxy and offer an alternative, substantive account. That is, I argue that entering into second-personal relations with others does indeed affect one's practical reasoning, but it does this not by altering the structure of one's agential thought, but by changing what (...) reasons can become available. The importance of second-personal thought for action is heterogenous. Second-person relations make possible the emergence of a wide variety of different kinds of practical reasons: creating some, revealing others. Recognising this diminishes the appeal of the traditional, structural accounts of the practical significance of such second-personal relations. Moving away from structural accounts facilitates a more thorough understanding of the intersubjective form of action. (shrink)

In this volume, leading philosophers of psychiatry examine psychiatric classification systems, including the Diagnostic and Statistical Manual of Mental Disorders, asking whether current systems are sufficient for effective diagnosis, treatment, and research. Doing so, they take up the question of whether mental disorders are natural kinds, grounded in something in the outside world. Psychiatric categories based on natural kinds should group phenomena in such a way that they are subject to the same type of causal explanations and respond similarly to (...) the same type of causal interventions. When these categories do not evince such groupings, there is reason to revise existing classifications. The contributors all question current psychiatric classifications systems and the assumptions on which they are based. They differ, however, as to why and to what extent the categories are inadequate and how to address the problem. Topics discussed include taxometric methods for identifying natural kinds, the error and bias inherent in DSM categories, and the complexities involved in classifying such specific mental disorders as "oppositional defiance disorder" and pathological gambling. -/- Contributors George Graham, Nick Haslam, Allan Horwitz, Harold Kincaid, Dominic Murphy, Jeffrey Poland, Nancy Nyquist Potter, Don Ross, Dan Stein, Jacqueline Sullivan, Serife Tekin, Peter Zachar. (shrink)

From the mid-1960s until the late 1980s, the well-known general philosophies of science of the time were applied to economics. The result was disappointing: none seemed to fit. This paper argues that this is due to a special feature of economics: it possesses ‘orientational paradigms’ in high number. Orientational paradigms are similar to Kuhn’s paradigms in that they are shared across scientific communities, but dissimilar to Kuhn’s paradigms in that they are not generally accepted as valid guidelines for further research. (...) As will be shown by several examples, orientational paradigms provide economics with common points of reference that support its epistemic coherence and make scientific discourse more easily possible across school boundaries. With the help of systematicity theory, a newer general philosophy of science, one can further elucidate the role of orientational paradigms with regard to scientific progress. (shrink)

Goetz outlined legal models of identical entities that include natural persons who are identical to a coregency and natural persons who are identical to a general partnership. Those entities cohere with the formula logic of relative identity. This essay outlines the coexistence of relative identity and numerical identity in the models of identical legal entities, which is impure relative identity. These models support the synthesis of Relative Trinitarianism and Social Trinitarianism, which I call Relative-Social Trinitarianism.

This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...) The second reason is conditional on a substitutional interpretation of quantification over types other than that of individuals. This reason stands up to investigation: a simple-type language will not sustain such an interpretation, but a ramified-type language will. And there is evidence that Russell was tacitly inclined towards such an interpretation. A strong construal of that interpretation opens a way to make sense of Russell’s simultaneous repudiation of propositions and his willingness to quantify over them. But that way runs into trouble with Russell’s commitment to the finitude of human understanding. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

A model of metaphysics associated with EJ Lowe and Tuomas Tahko sees metaphysics as involving a priori knowledge of possible essences, or at least modal facts, and delimiting the actual ‘ontological categories,’ the ultimate and essential divisions of what exists, based on the results of a posteriori scientific investigation. Their approach to metaphysics has been criticized by those who argue that such metaphysics is unsuitably a priori, disconnected with empirical research in natural science, and ends up failing to provide meaningful (...) constraints on metaphysical theorization. I present different epistemological and semantic worries about these accounts to motivate an alternative perspective on which metaphysics centers on form, rather than possibility. This scholastic perspective is shown to incorporate the skeptical insights as constitutive of its approach to existence, by way of the position that ‘being’ is not a genus. Rather, ‘being’ is a determinable. The scholastic approach can thus provide responses to the skeptics, since it denies that ontological categories – in the Lowe/Tahko sense – are what metaphysicians investigate and proposes a different view of ontological categories as classes of forms. (shrink)

Coincidence comes in two varieties – permanent and temporary. Moderate monism is the position that permanent coincidence, but not temporary coincidence, entails identity. Extreme monism is the position that even temporary coincidence entails identity. Pluralists are opponents of monism tout court. The intuitively obvious, commonsensical position is moderate monism. It is therefore important to see if it can be sustained.

My aim in this paper is to show that the natural idea that humiliation is harmful calls explanation and to argue that the most straightforward ways of responding to this explanatory demand fall short in important ways. I end by considering a line of response which I take to be promising, which appeals to our need, as social animals, for interpersonal connection.

Amie Thomasson’s work provides numerous ways to rethink and improve our approach to metaphysics. This chapter is my attempt to begin to sketch why I still think the easy approach leaves room for substantive metaphysical work, and why I do not think that metaphysics need rely on any ‘epistemically metaphysical’ knowledge. After distinguishing two possible forms of deflationism, I argue that the easy ontologist needs to accept (implicitly or explicitly) that there are worldly constraints on what sorts of entities could (...) exist, and could co-exist. I argue this leaves room for a substantive role for metaphysics if (following the work of E.J. Lowe) we take metaphysics to be concerned with the possible ways that reality could be. I explain how this conception does not need to appeal to any ‘epistemically metaphysical’ knowledge, and need only make use of conceptual and/or empirical means to arrive at views on what could exist (and co-exist). Thus, the answer I propose to the question posed in the title, at least in my view, is no-one. Or, at least, no-one should be afraid of conceptual analysis. Not even metaphysicians. (shrink)

It is a plausible and compelling theoretical assumption that epistemic rationality is just a matter of having doxastic attitudes that are the correct responses to one’s epistemic reasons, or that all requirements of epistemic rationality reduce to requirements on doxastic attitudes. According to this idea, all instances of epistemic rationality are instances of rational belief. Call this assumption, and any theory working under it, _belief-centered_. In what follows, I argue that we should not accept belief-centered theories of epistemic rationality. This (...) is an argument in three acts. In the first, I present counterexamples that problematize the belief-centered assumption: cases whose protagonists (i) fail to meet any plausible requirements on belief but (ii) nevertheless appear epistemically rational. In the second act, I consider alternative explanations of the counterexamples, friendly to the belief-centered theorist, and find them wanting. In the third and final act, I show that there are significant theoretical benefits to acknowledging a distinct agent-centered dimension of epistemic rationality and sketch a candidate agent-centered approach: a view that grounds an agent’s epistemic rationality in the possession of _good epistemic policies_. In the end, we see that a complete theory of epistemic rationality is as much of a theory of rational _agents_ as it is of rational _belief_. (shrink)

Experimental philosophy brings empirical methods to philosophy. These methods are used to probe how people think about philosophically interesting things such as knowledge, morality, and freedom. This paper explores the contribution that qualitative methods have to make in this enterprise. I argue that qualitative methods have the potential to make a much greater contribution than they have so far. Along the way, I acknowledge a few types of resistance that proponents of qualitative methods in experimental philosophy might encounter, and provide (...) reasons to think they are ill-founded. (shrink)

Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...) is logic?” drives us to the question “What is a logical constant?” Though what follows contains some argument, limitations of space constrain me in large part to express my Credo on this topic with the broad brush of bold assertion and some promissory gestures. (shrink)

Many of us think human extinction would be a very bad thing, and that we have moral reasons to prevent it. But there is disagreement over what would make extinction so bad, and thus over what grounds these moral reasons. Recently, several theorists have argued that our reasons to prevent extinction stem not just from the value of the welfare of future lives, but also from certain additional values relating to the existence of humanity itself (for example, humanity's “final” value, (...) or the value of humanity in itself). In this paper, I argue against these “additional value” views. Despite their initial appeal, these views will inevitably face conflicts between the additional values to which they appeal, and the value of the welfare of future lives. And, I argue, the views cannot plausibly resolve these conflicts. In contrast, these conflicts do not arise for a rival view, on which our reasons to prevent extinction stem just from the value of the welfare of future lives. I conclude that this gives us reason to prefer the latter view, despite the greater initial plausibility of additional value views. (shrink)

This paper examines the general prospects for conceptual role expressivism, expressivist theories that embrace conceptual role semantics. It has two main aims. The first aim is to provide a general characterisation of the view. The second aim is to raise a challenge for the general view. The challenge is to explain why normative concepts are not a species of defective concepts, where defective concepts are those that cannot meaningfully embed and participate in genuine inference. After rejecting existing attempts to answer (...) the challenge, I propose an alternative solution. However, the solution leaves conceptual role expressivism a far less distinctive and interesting position than its proponents claim. I conclude that we should be sceptical about how much expressivists gain by appealing to conceptual role semantics. (shrink)

Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role (...) of number-words is not designation but rather the encoding of cardinality-quantifiers. I also present some reasons for preferring this view. (shrink)