Ashoka University is a private university located in Sonipat, Haryana, India, focusing on liberal arts and sciences. It was established in 2014.&nbsp;It is guided by an academic council of academics and scholars from around the world. The council sets the university&#39;s academic standard, advising on matters of curriculum, faculty hiring and research.&nbsp;

Ashoka University offers a full-time 3 (+ 1) year undergraduate programme. The University comprises of&nbsp;2500 plus students, with a mix of both national and international students.&nbsp; &nbsp;

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Ashoka University

Perhaps the most pressing challenge for singularism—the predominant view that definite plurals like ‘the students’ singularly refer to a collective entity, such as a mereological sum or set—is that it threatens paradox. Indeed, this serves as a primary motivation for pluralism—the opposing view that definite plurals refer to multiple individuals simultaneously through the primitive relation of plural reference. Groups represent one domain in which this threat is immediate. After all, groups resemble sets in having a kind of membership-relation and iterating: we can have groups of groups, groups of groups of groups, etc. Yet there cannot be a group of all non-self-membered groups. In response, we develop a potentialist theory of groups according to which we always can, but do not have to, form a group from any sum. Modalizing group-formation makes it a species of potential, as opposed to actual or completed, infinity. This allows for a consistent, plausible, and empirically adequate treatment of natural language plurals, one which is motivated by the iterative nature of syntactic and semantic processes more generally .

Department of Philosophy

World University root node

Linguistics and Philosophy

Groups, sets, and paradox

In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.

Boston Studies in the Philosophy and History of Science

Hofweber’s Nominalist Naturalism

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Fulltext

Philosophies

Computability, Notation, and de re Knowledge of Numbers

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting.

Philosophia Mathematica

Resolving Frege's Other Puzzle

Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium

Link’s Revenge: A Case Study in Natural Language Mereology

Semantics and the Ontology of Number

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.

Erkenntnis

Mereological Singularism and Paradox

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

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.

Counting, measuring, and the fractional cardinalities puzzle

One of the more distinctive features of Bob Hale and Crispin Wright's neologicism about arithmetic 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. In particular, they maintain that, if adopted, Frege's Constraint adjudicates in favor of their preferred foundation – Hume's Principle – and against alternatives, such as the Dedekind-Peano axioms. In what follows we establish two main claims. First, we show that, if sound, Hale and Wright's arguments for Frege's Constraint at most establish a version on which the relevant application of the naturals is transitive counting – roughly, the counting procedure by which numerals are used to answer “how many”-questions. Second, we show that this version of Frege's Constraint fails to adjudicate in favor of Hume's Principle. If this is the version of Frege's Constraint that a foundation for arithmetic must respect, then Hume's Principle no more – and no less – meets the requirement than the Dedekind-Peano axioms do. © 2018 Wiley Periodicals, Inc.

Nous

Neologicism, Frege's Constraint, and the Frege-Heck Condition

Essays on Frege's Basic Laws of Arithmetic

Frege on the Real Numbers

We address a puzzle about the meanings of fraction words, due to Nathan Salmon. Counting 2 (Formula presented.) oranges seemingly requires enumerating a collection of objects with a non-whole cardinal number, which is incoherent by the lights of traditional analyses of cardinality expressions. Thus, some argue that counting 2 (Formula presented.) oranges really amounts to measuring quantities of orange-stuff. However, we claim that ‘2 (Formula presented.) oranges’ is ambiguous between counting- and measuring-interpretations; and recognizing this affords a novel solution to Salmon’s puzzle that is consistent with traditional analyses. © 2019, © 2019 Australasian Association of Philosophy.

Australasian Journal of Philosophy

How To Count 2 Oranges

This paper investigates a certain puzzling argument concerning number expressions and their meanings, the Easy Argument for Numbers. After finding faults with previous views, I offer a new take on what’s ultimately wrong with the Argument: it equivocates. I develop a semantics for number expressions which relates various of their uses, including those relevant to the Easy Argument, via type-shifting. By marrying Romero ’s (Linguist Philos 28(6):687–737, 2005) analysis of specificational clauses with Scontras ’ (The semantics of measurement, 2014) semantics for Degree Nouns, I show how to extend Landman ’s (Indefinites and the type of sets, Blackwell, Oxford, 2004) Adjectival Theory to numerical specificational clauses. The resulting semantics can explain various contrasts observed by Moltmann (Philos Stud 162:499–536, 2013a), but only if Scontras’ contention that degrees and numbers are sortally distinct is correct. At the same time, the Easy Argument can establish its intended conclusion only if numbers and degrees are mistakenly assumed to be identical. © 2017, Springer Science+Business Media B.V.

Numbers and Cardinalities: What’s Really Wrong with the Easy Argument for Numbers?

Proceedings of Sinn und Bedeutung

The Universal Measurer

A number of recent accounts for vague terms postulate a kind of context-sensitivity, one that kicks in after the usual ‘external’ contextual factors like comparison class are established and held fixed. In a recent paper, ‘Vagueness without Context Change’(Mind 116 (2007): 275–92), Rosanna Keefe criticizes all such accounts. The arguments are variations on considerations that have been brought against context-sensitive accounts of knowledge, predicates of personal taste, epistemic modals, and the like. The issues are well known and there are variety of options available in reply. More important, the arguments rely on an overly narrow conception of context-sensitivity, suggesting that one size fits all. If Keefe’s arguments were cogent, they would tell against the context-sensitivity of just about any expression, beyond the typical indexicals, including the variation of vague terms with comparison class. However, the criticisms raised by Keefe do highlight certain questions that must be answered by an advocate of a context-sensitive account of vagueness, essentially the same sorts of questions that must be answered by a contextualist or relativist about knowledge, epistemic modals, predicates of personal taste, etc. The main purpose of this paper is to use replies to the relevant objections raised by Keefe as a springboard for further articulation of the underlying view of vagueness. © 2015 Taylor & Francis.

Inquiry (United Kingdom)

Vagueness and Context

I argue for two major claims in this paper. First, I argue that the linguistic evidence best supports a certain form of contextualism about predicates of personal taste (PPTs) like 'fun' and 'tasty'. In particular, I argue that these adjectives are both individual-level predicates (ILPs) and anaphoric implicit argument taking predicates (IATPs). As ILPs, these naturally form generics. As anaphoric IATPs, PPTs show the same dependencies on context and distributional behavior as more familiar anaphoric IATPs, for example, 'local' and 'apply'. Moreover, they are subject to important binding-related phenomena, for example, various kinds of anaphora, binding arguments, and strict-sloppy ambiguities. The latter are particularly problematic for relativism, contextualism's major competitor. I argue that relativism cannot account for these binding facts in a non-ad hoc manner. Second, I argue that disagreement is a predictable feature of dialogues involving PPTs in conjunction with the contextualist semantics defended. Appealing to 'off the shelf' analyses of genericity, I show how disagreement arises in just the cases we would expect, licensing just the kinds of responses we would expect. They also suggest promising explanations, unavailable to relativists, of various otherwise puzzling features of disagreements involving PPTs. © 2013 Copyright Taylor and Francis Group, LLC.