Results for 'number'

999 found
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  1. Number adaptation: A critical look.Sami Yousif, Sam Clarke & Elizabeth Brannon - forthcoming - Cognition.
    It is often assumed that adaptation — a temporary change in sensitivity to a perceptual dimension following exposure to that dimension — is a litmus test for what is and is not a “primary visual attribute”. Thus, papers purporting to find evidence of number adaptation motivate a claim of great philosophical significance: That number is something that can be seen in much the way that canonical visual features, like color, contrast, size, and speed, can. Fifteen years after its (...)
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  2. Reference to numbers in natural language.Friederike Moltmann - 2013 - Philosophical Studies 162 (3):499 - 536.
    A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated (...)
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  3. Numbers, Empiricism and the A Priori.Olga Ramírez Calle - 2020 - Logos and Episteme 11 (2):149-177.
    The present paper deals with the ontological status of numbers and considers Frege ́s proposal in Grundlagen upon the background of the Post-Kantian semantic turn in analytical philosophy. Through a more systematic study of his philosophical premises, it comes to unearth a first level paradox that would unset earlier still than it was exposed by Russell. It then studies an alternative path, that departin1g from Frege’s initial premises, drives to a conception of numbers as synthetic a priori in a more (...)
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  4. Leibniz on Number Systems.Lloyd Strickland - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Springer. pp. 167-197.
    This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems that (...)
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  5. Constructing a concept of number.Karenleigh Overmann - 2018 - Journal of Numerical Cognition 2 (4):464–493.
    Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics (...)
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  6. Rational Number Representation by the Approximate Number System.Chuyan Qu, Sam Clarke & Elizabeth Brannon - manuscript
    The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence (...)
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  7. The number sense represents (rational) numbers.Sam Clarke & Jacob Beck - 2021 - Behavioral and Brain Sciences 44:1-57.
    On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds (...)
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  8. Numbers and Manifolds.Peter Simons - 1982 - In Barry Smith (ed.), Parts and Moments. Studies in Logic and Formal Ontology. Munich: Philosophia. pp. 160-197.
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  9. Of Numbers and Electrons.Cian Dorr - 2010 - Proceedings of the Aristotelian Society 110 (2pt2):133-181.
    According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world (...)
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  10. 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 (...)
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  11. Numbers without aggregation.Tim Henning - 2023 - Noûs.
    Suppose we can save either a larger group of persons or a distinct, smaller group from some harm. Many people think that, all else equal, we ought to save the greater number. This article defends this view (with qualifications). But unlike earlier theories, it does not rely on the idea that several people's interests or claims receive greater aggregate weight. The argument starts from the idea that due to their stakes, the affected people have claims to have a say (...)
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  12. Number words as number names.Friederike Moltmann - 2017 - Linguistics and Philosophy 40 (4):331-345.
    This paper criticizes the view that number words in argument position retain the meaning they have on an adjectival or determiner use, as argued by Hofweber :179–225, 2005) and Moltmann :499–534, 2013a, 2013b). In particular the paper re-evaluates syntactic evidence from German given in Moltmann to that effect.
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  13. Numbers, numerosities, and new directions.Jacob Beck & Sam Clarke - 2021 - Behavioral and Brain Sciences 44:1-20.
    In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.
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  14. Number Words and Ontological Commitment.Berit Brogaard - 2007 - Philosophical Quarterly 57 (226):1–20.
    With the aid of some results from current linguistic theory I examine a recent anti-Fregean line with respect to hybrid talk of numbers and ordinary things, such as ‘the number of moons of Jupiter is four’. I conclude that the anti-Fregean line with respect to these sentences is indefensible.
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  15. The Number of Planets, a Number-Referring Term?Friederike Moltmann - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford, England: Oxford University Press UK. pp. 113-129.
    The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to numbers as (...)
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  16. Number and natural language.Stephen Laurence & Eric Margolis - 2005 - In Peter Carruthers, Stephen Laurence & Stephen P. Stich (eds.), The Innate Mind: Structure and Contents. New York, US: Oxford University Press USA. pp. 1--216.
    One of the most important abilities we have as humans is the ability to think about number. In this chapter, we examine the question of whether there is an essential connection between language and number. We provide a careful examination of two prominent theories according to which concepts of the positive integers are dependent on language. The first of these claims that language creates the positive integers on the basis of an innate capacity to represent real numbers. The (...)
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  17. Incomparable numbers.Kenneth Walden - 2020 - Oxford Studies in Normative Ethics 10.
    This chapter presents arguments for two slightly different versions of the thesis that the value of persons is incomparable. Both arguments allege an incompatibility between the demands of a certain kind of practical reasoning and the presuppositions of value comparisons. The significance of these claims is assessed in the context of the “Numbers problem”—the question of whether one morally ought to benefit one group of potential aid recipients rather than another simply because they are greater in number. It is (...)
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  18. Rational Numbers: A Non‐Consequentialist Explanation Of Why You Should Save The Many And Not The Few.Tom Dougherty - 2013 - Philosophical Quarterly 63 (252):413-427.
    You ought to save a larger group of people rather than a distinct smaller group of people, all else equal. A consequentialist may say that you ought to do so because this produces the most good. If a non-consequentialist rejects this explanation, what alternative can he or she give? This essay defends the following explanation, as a solution to the so-called numbers problem. Its two parts can be roughly summarised as follows. First, you are morally required to want the survival (...)
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  19. Numbers and Propositions: Reply to Melia.Tim Crane - 1992 - Analysis 52 (4):253-256.
    Is the way we use propositions to individuate beliefs and other intentional states analogous to the way we use numbers to measure weights and other physical magnitudes? In an earlier paper [2], I argued that there is an important disanalogy. One and the same weight can be 'related to' different numbers under different units of measurement. Moreover, the choice of a unit of measurement is arbitrary,in the sense that which way we choose doesn't affect the weight attributed to the object. (...)
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  20. Real Numbers are the Hidden Variables of Classical Mechanics.Nicolas Gisin - 2020 - Quantum Studies: Mathematics and Foundations 7:197–201.
    Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.
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  21. Numbers and functions in Hilbert's finitism.Richard Zach - 1998 - Taiwanese Journal for History and Philosophy of Science 10:33-60.
    David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far (...)
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  22. Why Numbers Are Sets.Eric Steinhart - 2002 - Synthese 133 (3):343-361.
    I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all (...)
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  23. Theoretical implications of the study of numbers and numerals in mundurucu.Pierre Pica & Alain Lecomte - 2008 - Philosophical Psychology 21 (4):507 – 522.
    Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...)
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  24. Updating the “abstract–concrete” distinction in Ancient Near Eastern numbers.Karenleigh Overmann - 2018 - Cuneiform Digital Library Journal 1:1–22.
    The characterization of early token-based accounting using a concrete concept of number, later numerical notations an abstract one, has become well entrenched in the literature. After reviewing its history and assumptions, this article challenges the abstract–concrete distinction, presenting an alternative view of change in Ancient Near Eastern number concepts, wherein numbers are abstract from their inception and materially bound when most elaborated. The alternative draws on the chronological sequence of material counting technologies used in the Ancient Near East—fingers, (...)
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  25. Pro Tanto Rights and the Duty to Save the Greater Number.Benjamin Kiesewetter - 2023 - Oxford Studies in Normative Ethics 13:190-214.
    This paper has two aims. The first is to present and defend a new argument for rights contributionism – the view that the notion of a moral claim-right is a contributory (or pro tanto) rather than overall normative notion. The argument is an inference to the best explanation: it is argued that (i) there are contributory moral factors that contrast with standard moral reasons by way of having a number of formal properties that are characteristic of rights, even though (...)
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  26. The number of senses.Kevin C. Klement - 2003 - Erkenntnis 58 (3):303 - 323.
    Many philosophers still countenance senses or meanings in the broadly Fregean vein. However, it is difficult to posit the existence of senses without positing quite a lot of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are (...)
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  27. Where Do the Cardinal Numbers Come From?Harold T. Hodes - 1990 - Synthese 84 (3):347-407.
    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".
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  28. Numbers versus Nominalists.Nathan Salmon - 2008 - Analysis 68 (3):177–182.
    A nominalist account of statements of number (e.g., ‘There are exactly two moons of Mars’) is rebutted.
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  29. Intuitions about large number cases.Theron Pummer - 2013 - Analysis 73 (1):37-46.
    Is there some large number of very mild hangnail pains, each experienced by a separate person, which would be worse than two years of excruciating torture, experienced by a single person? Many people have the intuition that the answer to this question is No. However, a host of philosophers have argued that, because we have no intuitive grasp of very large numbers, we should not trust such intuitions. I argue that there is decent intuitive support for the No answer, (...)
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  30. Why the numbers should sometimes count.John T. Sanders - 1988 - Philosophy and Public Affairs 17 (1):3-14.
    John Taurek has argued that, where choices must be made between alternatives that affect different numbers of people, the numbers are not, by themselves, morally relevant. This is because we "must" take "losses-to" the persons into account (and these don't sum), but "must not" consider "losses-of" persons (because we must not treat persons like objects). I argue that the numbers are always ethically relevant, and that they may sometimes be the decisive consideration.
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  31. Infinite numbers are large finite numbers.Jeremy Gwiazda - unknown
    In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to be counted (...)
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  32. Fair Numbers: What Data Can and Cannot Tell Us About the Underrepresentation of Women in Philosophy.Yann Benétreau-Dupin & Guillaume Beaulac - 2015 - Ergo: An Open Access Journal of Philosophy 2:59-81.
    The low representation (< 30%) of women in philosophy in English-speaking countries has generated much discussion, both in academic circles and the public sphere. It is sometimes suggested (Haslanger 2009) that unconscious biases, acting at every level in the field, may be grounded in gendered schemas of philosophers and in the discipline more widely, and that actions to make philosophy a more welcoming place for women should address such schemas. However, existing data are too limited to fully warrant such an (...)
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  33. The Small Number System.Eric Margolis - 2020 - Philosophy of Science 87 (1):113-134.
    I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific (...)
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  34. Numbers, Ontologically Speaking: Plato on Numerosity.Calian Florin George - 2021 - In Numbers and Numeracy in the Greek Polis. Brill.
    The conceptualisation of numbers is culturally bound. This may seem like a counterintuitive claim, but one illustration thereof is the limitations of the resemblance of the ancient Greek concept of number to that in modern mathematics.
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  35. Numbers without Science.Russell Marcus - 2007 - Dissertation, The Graduate School and University Center of the City University of New York
    Numbers without Science opposes the Quine-Putnam indispensability argument, seeking to undermine the argument and reduce its profound influence. Philosophers rely on indispensability to justify mathematical knowledge using only empiricist epistemology. I argue that we need an independent account of our knowledge of mathematics. The indispensability argument, in broad form, consists of two premises. The major premise alleges that we are committed to mathematical objects if science requires them. The minor premise alleges that science in fact requires mathematical objects. The most (...)
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  36. The Number of Bricks in a Ziggurat.Ben Blumson & Jarinah Jabbar - 2020 - Mathematics Magazine 93 (3):226-227.
    The number of bricks in a ziggurat is a sum of consecutive squares.
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  37. Number and Reality: Sources of Scientific Knowledge.Alex V. Halapsis - 2016 - ScienceRise 23 (6):59-64.
    Pythagoras’s number doctrine had a great effect on the development of science. Number – the key to the highest reality, and such approach allowed Pythagoras to transform mathematics from craft into science, which continues implementation of its project of “digitization of being”. Pythagoras's project underwent considerable transformation, but it only means that the plan in knowledge is often far from result.
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  38. Number, Language, and Mathematics.Joosoak Kim - manuscript
    Number is a major object in mathematics. Mathematics is a discipline which studies the properties of a number. The object is expressible by mathematical language, which has been devised more rigorously than natural language. However, the language is not thoroughly free from natural language. Countability of natural number is also originated from natural language. It is necessary to understand how language leads a number into mathematics, its’ main playground.
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  39. African Numbers Games and Gambler Motivation: 'Fahfee' in Contemporary South African.Stephen Louw - 2018 - African Affairs 117 (466):109-129.
    Since independence, at least 28 African countries have legalized some form of gambling. Yet a range of informal gambling activities have also flourished, often provoking widespread public concern about the negative social and economic impact of unregulated gambling on poor communities. This article addresses an illegal South African numbers game called fahfee. Drawing on interviews with players, operators, and regulatory officials, this article explores two aspects of this game. First, it explores the lives of both players and runners, as well (...)
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  40. Numbers, Fairness and Charity.Adam Hosein - manuscript
    This paper discusses the "numbers problem," the problem of explaining why you should save more people rather than fewer when forced to choose. Existing non-consequentialist approaches to the problem appeal to fairness to explain why. I argue that this is a mistake and that we can give a more satisfying answer by appealing to requirements of charity or beneficence.
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  41. Frege's Changing Conception of Number.Kevin C. Klement - 2012 - Theoria 78 (2):146-167.
    I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...)
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  42. Applied Mathematics without Numbers.Jack Himelright - 2023 - Philosophia Mathematica 31 (2):147-175.
    In this paper, I develop a "safety result" for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are "correct": roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages (...)
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  43. Transfinite Number in Wittgenstein's Tractatus.James R. Connelly - 2021 - Journal for the History of Analytical Philosophy 9 (2).
    In his highly perceptive, if underappreciated introduction to Wittgenstein’s Tractatus, Russell identifies a “lacuna” within Wittgenstein’s theory of number, relating specifically to the topic of transfinite number. The goal of this paper is two-fold. The first is to show that Russell’s concerns cannot be dismissed on the grounds that they are external to the Tractarian project, deriving, perhaps, from logicist ambitions harbored by Russell but not shared by Wittgenstein. The extensibility of Wittgenstein’s theory of number to the (...)
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  44.  73
    The number of downloads for the bayesvl program increased significantly in January 2024.A. I. S. D. L. Team - 2024 - Sm3D Portal.
    In the first month of 2024, there was a significant increase in the number of downloads for the Bayesian stats / MCMC computing program, bayesvl, developed by AISDL running on R and Stan. The following RDocumentation (CRAN) graph illustrates the noticeable leap in data for January 2024.
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  45. Lower and Upper Estimates of the Quantity of Algebraic Numbers.Yaroslav Sergeyev - 2023 - Mediterranian Journal of Mathematics 20:12.
    It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is (...)
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  46. Innate Mathematical Characteristics and Number Sense Competencies of Junior High School Students.Raymundo A. Santos, Leila M. Collantes, Edwin D. Ibañez, Florante P. Ibarra & Jupeth Pentang - 2022 - International Journal of Learning, Teaching and Educational Research 21 (10):325-340.
    The study determined the influence of innate mathematical characteristics on the number sense competencies of junior high school students in a Philippine public school. The descriptive-correlational research design was used to accomplish the study involving a nonrandom sample of sixty 7th-grade students attending synchronous math sessions. Data obtained from the math-specific Learning Style and Self-Efficacy questionnaires and the modified Number Sense Test (NST) were analyzed and interpreted using descriptive statistics, Pearson’s Chi-Square, and Simple Linear Regression analysis. The research (...)
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  47. Platonism by the Numbers.Steven M. Duncan - manuscript
    In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.
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  48. Does the number sense represent number?Sam Clarke & Jacob Beck - 2020 - In Blair Armstrong, Stephanie Denison, Michael Mack & Yang Xu (eds.), Proceedings of the 42nd Meeting of the Cognitive Science Society.
    On a now orthodox view, humans and many other animals are endowed with a “number sense”, or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques, with critics maintaining either that numerical content is absent altogether, or else that some primitive analog of number (‘numerosity’) is represented as opposed to number itself. We distinguish three arguments for these claims – the arguments from congruency, confounds, and imprecision – (...)
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  49. The SignalGlyph Project and Prime Numbers.Michael Joseph Winkler - 2021 - In Michael Winkler (ed.), The Image of Language. Northeast, NY: Artists Books Editions. pp. 158-163.
    An excerpt of "The SignalGlyph Project and Prime Numbers" (a chapter of the book THE IMAGE OF LANGUAGE) that attempts to illustrate how dimensional limitations of mathematical language have obscured recognition of the system of patterning in the distribution of prime numbers.
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  50. Show me the numbers: a quantitative portrait of the attitudes, experiences, and values of philosophers of science regarding broadly engaged work.Kathryn Plaisance, Alexander V. Graham, John McLevey & Jay Michaud - 2019 - Synthese 198 (5):4603-4633.
    Philosophers of science are increasingly arguing for the importance of doing scientifically- and socially-engaged work, suggesting that we need to reduce barriers to extra-disciplinary engagement and broaden our impact. Yet, we currently lack empirical data to inform these discussions, leaving a number of important questions unanswered. How common is it for philosophers of science to engage other communities, and in what ways are they engaging? What barriers are most prevalent when it comes to broadly disseminating one’s work or collaborating (...)
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