22 found
Order:
Disambiguations
Eric Snyder [26]Eric Andrew Snyder [1]
  1. Resolving Frege’s Other Puzzle.Eric Snyder, Richard Samuels & Stewart Shapiro - 2022 - Philosophica Mathematica 30 (1):59-87.
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  2. Number Concepts: An Interdisciplinary Inquiry.Richard Samuels & Eric Snyder - 2024 - Cambridge University Press.
    This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...)
  3.  74
    Numbers and Cardinalities: What’s Really Wrong with the Easy Argument for Numbers?Eric Snyder - 2017 - Linguistics and Philosophy 40 (4):373-400.
    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 :687–737, 2005) analysis of specificational clauses with Scontras ’ semantics for Degree Nouns, I show how to (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  4. Hofweber’s Nominalist Naturalism.Eric Snyder, Richard Samuels & Stewart Shapiro - 2022 - In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo (eds.), Objects, Structures, and Logics. Cham (Switzerland): Springer. pp. 31-62.
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  5.  46
    Semantics and the Ontology of Number.Eric Snyder - 2021 - Cambridge University Press.
    What are the meanings of number expressions, and what can they tell us about questions of central importance to the philosophy of mathematics, specifically 'Do numbers exist?' This Element attempts to shed light on this question by outlining a recent debate between substantivalists and adjectivalists regarding the semantic function of number words in numerical statements. After highlighting their motivations and challenges, I develop a comprehensive polymorphic semantics for number expressions. I argue that accounting for the numerous meanings and how they (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  6.  70
    Binding, Genericity, and Predicates of Personal Taste.Eric Snyder - 2013 - Inquiry: An Interdisciplinary Journal of Philosophy 56 (2-3):278-306.
    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?. (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  7. Restricted nominalism about number and its problems.Stewart Shapiro, Richard Samuels & Eric Snyder - 2024 - Synthese 203 (5):1-23.
    Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  8.  98
    Neologicism, Frege's Constraint, and the Frege‐Heck Condition.Eric Snyder, Richard Samuels & Stewart Shapiro - 2018 - Noûs 54 (1):54-77.
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  9.  68
    (1 other version)Cardinals, Ordinals, and the Prospects for a Fregean Foundation.Eric Snyder, Stewart Shapiro & Richard Samuels - 2018 - Royal Institute of Philosophy Supplement 82:77-107.
    There are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is ‘more basic’ or ‘more fundamental’ than the others. This paper addresses two related issues. First, we review some of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  10.  41
    Counting, measuring, and the fractional cardinalities puzzle.Eric Snyder - 2020 - Linguistics and Philosophy 44 (3):513-550.
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  11. (1 other version)How To Count 2.5 Oranges.Eric Snyder & Jefferson Barlew - 2019 - Australasian Journal of Philosophy 97 (4):792-808.
    We address a puzzle about the meanings of fraction words due to Nathan Salmon. Counting 2 1/2 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 1/2 oranges really amounts to measuring quantities of orange-stuff . However, we claim that `2 1/2 oranges' is ambiguous between counting and measuring interpretations, and recognizing this affords a novel solution to Salmon's (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  12.  29
    (1 other version)Mereological Singularism and Paradox.Eric Snyder & Stewart Shapiro - 2021 - Erkenntnis 88 (1):1-20.
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  13.  68
    Groups, sets, and paradox.Eric Snyder & Stewart Shapiro - 2022 - Linguistics and Philosophy 45 (6):1277-1313.
    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: (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  14.  61
    Group nouns and pseudo‐singularity.Eric Snyder & Stewart Shapiro - 2021 - Thought: A Journal of Philosophy 10 (1):66-77.
    Thought: A Journal of Philosophy, EarlyView.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  15.  32
    Unwarranted philosophical assumptions in research on ANS.John Opfer, Richard Samuels, Stewart Shapiro & Eric Snyder - 2021 - Behavioral and Brain Sciences 44.
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  16.  50
    Hale’s argument from transitive counting.Eric Snyder, Richard Samuels & Stewart Shapiro - 2019 - Synthese 198 (3):1905-1933.
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17. Link's Revenge: A Case Study in Natural Language Mereology.Eric Snyder & Stewart Shapiro - 2018 - In Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 3-36.
    Most philosophers are familiar with the metaphysical puzzle of the statue and the clay. A sculptor begins with some clay, eventually sculpting a statue from it. Are the clay and the statue one and the same thing? Apparently not, since they have different properties. For example, the clay could survive being squashed, but the statue could not. The statue is recently formed, though the clay is not, etc. Godehart Link 1983’s highly influential analysis of the count/mass distinction recommends that English (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  18. Computability, Notation, and de re Knowledge of Numbers.Stewart Shapiro, Eric Snyder & Richard Samuels - 2022 - Philosophies 1 (7):20.
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  19.  23
    Link’s Revenge: A Case Study in Natural Language Mereology.Eric Snyder & Stewart Shapiro - 2018 - In Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 3-36.
    Most philosophers are familiar with the metaphysical puzzle of the statue and the clay. A sculptor begins with some clay, eventually sculpting a statue from it. Are the clay and the statue one and the same thing? Apparently not, since they have different properties. For example, the clay could survive being squashed, but the statue could not. The statue is recently formed, though the clay is not, etc. Godehart Link 1983’s highly influential analysis of the count/mass distinction recommends that English (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  20.  35
    Leon HorstenThe Metaphysics and Mathematics of Ordinary Objects. [REVIEW]Eric Snyder - forthcoming - Philosophia Mathematica:nkaa006.
    HorstenLeon* * _ The Metaphysics and Mathematics of Ordinary Objects. _Cambridge University Press, 2019. Pp. xviii + 231. ISBN: 978-1-107-03941-4 ; 978-1-10860177-1. doi: 10.1017/9781139600293.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  21.  37
    Leon Horsten*The Metaphysics and Mathematics of Arbitrary Objects. [REVIEW]Eric Snyder - 2020 - Philosophia Mathematica 28 (1):79-95.
  22.  42
    M. Carrara, A. Arapinis, and F. Moltmann, editors. Unity and Plurality: Logic, Philosophy, and Linguistics. Oxford University Press, 2016. [REVIEW]Eric Snyder - 2016 - Bulletin of Symbolic Logic 22 (4):530-532.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark