Department of Philosophy

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Semantics and the Ontology of Number

It is currently fashionable to take Putnamian model-theoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. However, I will argue that (under certain mild assumptions) merely securing determinate reference to physical possibility suffices to rule out the kind of nonstandard interpretations of our number talk Putnam invokes. So, anyone who accepts determinate reference to physical possibility should not reject determinate reference to the natural numbers on Putnamian model-theoretic grounds. © 2021 The Authors. Published by Oxford University Press. All rights reserved.

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Philosophia Mathematica

Physical Possibility and Determinate Number Theory

The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting three necessary and independently motivated restrictions on the metalinguistic predicates ‘atom’ and ‘non-atom’: both are sort, property, and context-relative. With these restrictions in place, Schein’s problematic assumption becomes evident: his presumed singularist analysis of ‘non-atom’ conflates the metalanguage with the meta-metalanguage, i.e. the language used to talk about the metalanguage. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.

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Erkenntnis

Mereological Singularism and Paradox

Philosophers have long been interested in love and its general role in morality. This volume focuses on and explores the complex relation between love and justice as it appears within loving relationships, between lovers and their wider social context, and the broader political realm. Special attention is paid to the ensuing challenge of understanding and respecting the lovers’ personal autonomy in all three contexts. Accordingly, the essays in this volume are divided into three thematic sections. Section I aims at shedding further light on conceptual and practical issues concerning the compatibility or incompatibility of love and justice within relationships of love. For example, are loving relations inherently unjust? Might love require justice? Or do love and justice belong to distinct moral domains? The essays in Section II consider the relation between the lovers on the one hand and their broader societal environment on the other. Specifically, how exactly are love and impartiality related? Are they compatible or not? Is it unjust to favor one’s beloved? Finally, Section III looks at the political dimensions of love and justice. How, for instance, do various accounts of love inform how we are to relate to our fellow citizens? If love is taken to play an important role in fostering or hindering the development of personal autonomy, what are the political implications that need to be addressed, and how? In addressing these questions, this book engenders a better understanding both of conceptual and practical issues regarding the relation between love, justice, and autonomy as well as their broader societal and political implications. It will be of interest to advanced students and scholars working on the philosophy of love from ethical, political, and psychological angles.&nbsp;

Love, Justice, and Autonomy: Philosophical Perspectives

A core commitment of Bob Hale and Crispin Wright’s neologicism is their invocation of Frege’s Constraint—roughly, the requirement that the core empirical applications for a class of numbers be “built directly into” their formal characterization. According to these neologicists, if legitimate, Frege’s Constraint adjudicates in favor of their preferred foundation—Hume’s Principle—and against alternatives, such as the Dedekind–Peano axioms. In this paper, we consider a recent argument for legitimating Frege’s Constraint due to Hale, according to which the primary empirical application of the naturals is transitive counting, or answering ‘how many’-questions using numerals. We make two claims regarding Hale’s argument. First, it fails to legitimate Frege’s Constraint in virtue of resting on unsupported and highly contentious assumptions. Secondly, even if sound, Hale’s argument would vindicate a version of Frege’s Constraint which fails to adjudicate in favor of Hume’s Principle over alternative characterizations of the naturals. © 2019, Springer Nature B.V.

Synthese

Hale’s argument from transitive counting

Definite group nouns, such as “the deck of cards,” raise two important kinds of problems. Philosophically, they raise the ancient Problem of the Many: How can one deck be many cards? Linguistically, they threaten paradox: If such expressions singularly refer to groups as set-like entities, then analyses employing such entities threaten to be incoherent, due to Russell's paradox. On the other hand, no paradox is threatened if, per the suggestion of Alex Oliver and Timothy Smiley, “the deck of cards” is a pseudo-singular term, that is, a term which is syntactically singular but semantically plural, exploiting the primitive relation of plural reference. Against this, we argue that pseudo-singularity is linguistically and logically untenable. As such, it will not plausibly solve either kind of problem raised by definite group nouns. © 2021 The Thought Trust and Wiley Periodicals LLC.

Thought

Group nouns and pseudo-singularity

Clarke and Beck import certain assumptions about the nature of numbers. Although these are widespread within research on number cognition, they are highly contentious among philosophers of mathematics. In this commentary, we isolate and critically evaluate one core assumption: the identity thesis. Copyright © The Author(s), 2021. Published by Cambridge University Press.

Behavioral and Brain Sciences

Unwarranted philosophical assumptions in research on ANS

Experience, it is widely agreed, constrains our thinking and is also thoroughly theory-laden. But how can it constrain our thinking while depending on what it purports to constrain? To address this issue, I revisit and carefully analyze the account of (scientific) observation provided by Norwood Russell Hanson, who introduced the term ‘theory-ladenness of observation’ in the first place. I show that Hanson’s account provides an original and coherent response to the initial question and argue that, if suitably developed, his account provides a distinctive, powerful, and attractive alternative to relationalist and standard representationalist conceptions of experience. © 2019, Springer Nature B.V.

Norwood Russell Hanson’s account of experience: an untimely defense

According to what I call the Traditional View, there is a fundamental semantic distinction between counting and measuring, which is reflected in two fundamentally different sorts of scales: discrete cardinality scales and dense measurement scales. Opposed to the Traditional View is a thesis known as the Universal Density of Measurement: there is no fundamental semantic distinction between counting and measuring, and all natural language scales are dense. This paper considers a new argument for the latter, based on a puzzle I call the Fractional Cardinalities Puzzle: if answers to ‘how many’-questions always designate cardinalities, and if cardinalities are necessarily discrete, then how can e.g. ‘2.38’ be a correct answer to the question ‘How many ounces of water are in the beaker?’? If cardinality scales are dense, then the answer is obvious: ‘2.38’ designates a fractional cardinality, contra the Traditional View. However, I provide novel evidence showing that ‘many’ is not uniformly associated with the dimension of cardinality across contexts, and so ‘how many’-questions can ask about other kinds of measures, including e.g. volume. By combining independently motivated analyses of cardinal adjectives, measure phrases, complex fractions, and degrees, I develop a semantics intended to defend the Traditional View against purported counterexamples like this and others which have received a fair amount of recent philosophical attention. © 2020, Springer Nature B.V.

Linguistics and Philosophy

Counting, measuring, and the fractional cardinalities puzzle

How to conceptualize loving relationships so as to accommodate that just love is geared toward preserving and fostering individual autonomy? To develop an answer, this paper draws on the recent debate on the rational role of experience to motivate a view dubbed Murdochian presentationalism. Murdochian presentationalism takes seriously two presentationalist ideas: 1) individuals harboring different world views who respond to identical situations differently can be equally rational; 2) our views and concepts develop under the constant pressure of experience. It combines these ideas with Murdoch’s tenet that coming to know others (and thus being able to do well by them) requires unselfish love, construed as just attention that involves a continuous refinement of our evaluative concepts and makes us better attuned to what is real. Complemented with a broadly Kantian notion of autonomy, the resulting view fits the bill. The paper ends on a sketch of what is dubbed the ideal lovers’ pledge and a comment on what metaphor the view arrived at suggests for thinking about loving relationships.