Results for 'Ordinal numbers'

999 found
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  1. Eliminating the Ordinals From Proofs. An Analysis of Transfinite Recursion.Edoardo Rivello - 2014 - In Proceedings of the conference "Philosophy, Mathematics, Linguistics. Aspects of Interaction", St. Petersburg, April 21-25, 2014. pp. 174-184.
    Transfinite ordinal numbers enter mathematical practice mainly via the method of definition by transfinite recursion. Outside of axiomatic set theory, there is a significant mathematical tradition in works recasting proofs by transfinite recursion in other terms, mostly with the intention of eliminating the ordinals from the proofs. Leaving aside the different motivations which lead each specific case, we investigate the mathematics of this action of proof transforming and we address the problem of formalising the philosophical notion of elimination (...)
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  2. 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. I give a detailed mathematical demonstration that 0 is {} and for every natural number n, n is the set of all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals.
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  3. On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators.Jake Chandler & Richard Booth - 2018 - In Michael Thielscher, Francesca Toni & Frank Wolter (eds.), Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR2018). Palo Alto, CA, USA: pp. 210-219.
    Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...)
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  4. On the Number of Gods.Eric Steinhart - 2012 - International Journal for Philosophy of Religion 72 (2):75-83.
    A god is a cosmic designer-creator. Atheism says the number of gods is 0. But it is hard to defeat the minimal thesis that some possible universe is actualized by some possible god. Monotheists say the number of gods is 1. Yet no degree of perfection can be coherently assigned to any unique god. Lewis says the number of gods is at least the second beth number. Yet polytheists cannot defend an arbitrary plural number of gods. An alternative is that, (...)
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  5. Strong Normalization via Natural Ordinal.Daniel Durante Pereira Alves - 1999 - Dissertation,
    The main objective of this PhD Thesis is to present a method of obtaining strong normalization via natural ordinal, which is applicable to natural deduction systems and typed lambda calculus. The method includes (a) the definition of a numerical assignment that associates each derivation (or lambda term) to a natural number and (b) the proof that this assignment decreases with reductions of maximal formulas (or redex). Besides, because the numerical assignment used coincide with the length of a specific sequence (...)
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  6. Measuring the Intelligence of an Idealized Mechanical Knowing Agent.Samuel Alexander - 2020 - Lecture Notes in Computer Science 12226.
    We define a notion of the intelligence level of an idealized mechanical knowing agent. This is motivated by efforts within artificial intelligence research to define real-number intelligence levels of compli- cated intelligent systems. Our agents are more idealized, which allows us to define a much simpler measure of intelligence level for them. In short, we define the intelligence level of a mechanical knowing agent to be the supremum of the computable ordinals that have codes the agent knows to be codes (...)
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  7. Surreal Time and Ultratasks.Haidar Al-Dhalimy & Charles J. Geyer - 2016 - Review of Symbolic Logic 9 (4):836-847.
    This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (...)
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  8.  44
    The Symmetries of Quantum and Classical Information. The Ressurrected “Ether" of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (41):1-36.
    The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...)
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  9. On the Plurality of Gods.Eric Steinhart - 2013 - Religious Studies 49 (3):289-312.
    Ordinal polytheism is motivated by the cosmological and design arguments. It is also motivated by Leibnizian–Lewisian modal realism. Just as there are many universes, so there are many gods. Gods are necessary concrete grounds of universes. The god-universe relation is one-to-one. Ordinal polytheism argues for a hierarchy of ranks of ever more perfect gods, one rank for every ordinal number. Since there are no maximally perfect gods, ordinal polytheism avoids many of the familiar problems of monotheism. (...)
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  10. Quantum-Information Conservation. The Problem About “Hidden Variables”, or the “Conservation of Energy Conservation” in Quantum Mechanics: A Historical Lesson for Future Discoveries.Vasil Penchev - 2020 - Energy Engineering (Energy) eJournal (Elsevier: SSRN) 3 (78):1-27.
    The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...)
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  11. God, Logic, and Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-10.
    Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what (...)
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  12. Set Theory, Topology, and the Possibility of Junky Worlds.Thomas Mormann - 2014 - Notre Dame Journal of Formal Logic 55 (1): 79 - 90.
    A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...)
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  13.  76
    Matter as Information. Quantum Information as Matter.Vasil Penchev - 2016 - Nodi. Collana di Storia Della Filosofia 2016 (2):127-138.
    Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what (...)
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  14.  53
    Quantum Information as the Information of Infinite Collections or Series.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (14):1-8.
    The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after (...)
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  15. Five problems for the moral consensus about sins.Mike Ashfield - 2021 - International Journal for Philosophy of Religion 90 (3):157-189.
    A number of Christian theologians and philosophers have been critical of overly moralizing approaches to the doctrine of sin, but nearly all Christian thinkers maintain that moral fault is necessary or sufficient for sin to obtain. Call this the “Moral Consensus.” I begin by clarifying the relevance of impurities to the biblical cataloguing of sins. I then present four extensional problems for the Moral Consensus on sin, based on the biblical catalogue of sins: (1) moral over-demandingness, (2) agential unfairness, (3) (...)
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  16. Perception and Attention.Ronald A. Rensink - 2013 - In Oxford Handbook of Cognitive Psychology. pp. 97-116.
    Our visual experience of the world is one of diverse objects and events, each with particular colors, shapes, and motions. This experience is so coherent, so immediate, and so effortless that it seems to result from a single system that lets us experience everything in our field of view. But however appealing, this belief is mistaken: there are severe limits on what can be visually experienced. -/- For example, in a display for air-traffic control it is important to track all (...)
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  17. Cantor’s Proof in the Full Definable Universe.Laureano Luna & William Taylor - 2010 - Australasian Journal of Logic 9:10-25.
    Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on (...)
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  18. On the Weak Kleene Scheme in Kripke's Theory of Truth.James Cain & Zlatan Damnjanovic - 1991 - Journal of Symbolic Logic 56 (4):1452-1468.
    It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...)
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  19. Fast-Collapsing Theories.Samuel A. Alexander - 2013 - Studia Logica (1):1-21.
    Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.
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  20. The Quantity of Quantum Information and Its Metaphysics.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (18):1-6.
    The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after (...)
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  21. Halfway Up To the Mathematical Infinity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transfinite Design.Edward G. Belaga - manuscript
    Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of (...)
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  22. The Sense and Nonsense of Criminalizing Transfers of Obscene.Dennis J. Baker - 2008 - Singapore Law Review 26:126-160.
    The recent distribution of nude photos of a number of high profile Hong Kong celebrities has provoked intense discussion about the state of Hong Kong's obscenity and indecency laws. In this paper, I argue that Hong Kong's laws prohibiting the transfer of obscene and indecent information and images between consenting adults are both under-inclusive and over-inclusive. The Control of Obscene and Indecent Articles Ordinance is under-inclusive in that it does not adequately criminalise grave violations of privacy. It is also over-inclusive (...)
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  23. 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 or exotic substitutes (...)
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  24. 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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  25. 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 (...)
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  26. 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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  27. 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 University Press. 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 (...) as abstract objects. (shrink)
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  28. 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 (...)
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  29. 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: Oxford University Press New York. 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 second (...)
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  30. 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 received (...)
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  31.  99
    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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  32.  80
    The Existence of Numbers (Or: What is the Status of Arithmetic?).Andrew Boucher - manuscript
    I begin with a personal confession. Philosophical discussions of existence have always bored me. When they occur, my eyes glaze over and my attention falters. Basically ontological questions often seem best decided by banging on the table--rocks exist, fairies do not. Argument can appear long-winded and miss the point. Sometimes a quick distinction resolves any apparent difficulty. Does a falling tree in an earless forest make noise, ie does the noise exist? Well, if noise means that an ear must be (...)
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  33.  31
    Caos e ordine: genesi e sviluppo dello stile deduttivo nell’Antica Grecia.Luca Sciortino - 2021 - Informazione Filosofica 3 (2):6-24.
    ABSTRACT (ENG) One of the concerns of Greek philosophy centred on the question of how a manifold and ordered universe arose out of the primitive state of things. From the mythical accounts dating around the seventh century B.C. to the cosmologies of the Classical period in Ancient Greece, many theories have been proposed in order to answer to this question. How these theories differ in positing a “something” that pre-existed the ordered cosmos has been widely discussed. However, scholars have rarely (...)
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  34.  51
    Against Prohibition (Or, When Using Ordinal Scales to Compare Groups Is OK).Cristian Larroulet Philippi - forthcoming - The British Journal for the Philosophy of Science.
    There is a widely held view on measurement inferences, that goes back to Stevens’s ([1946]) theory of measurement scales and ‘permissible statistics’. This view defends the following prohibition: you should not make inferences from averages taken with ordinal scales (versus quantitative scales: interval or ratio). This prohibition is general—it applies to all ordinal scales—and it is sometimes endorsed without qualification. Adhering to it dramatically limits the research that the social and biomedical sciences can conduct. I provide a Bayesian (...)
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  35. 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 (...)
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  36. 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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  37. The Neural Correlates of Visual Imagery: A Co-Ordinate-Based Meta-Analysis.C. Winlove, F. Milton, J. Ranson, J. Fulford, M. MacKisack, Fiona Macpherson & A. Zeman - 2018 - Cortex 105 (August 2018):4-25.
    Visual imagery is a form of sensory imagination, involving subjective experiences typically described as similar to perception, but which occur in the absence of corresponding external stimuli. We used the Activation Likelihood Estimation algorithm (ALE) to identify regions consistently activated by visual imagery across 40 neuroimaging studies, the first such meta-analysis. We also employed a recently developed multi-modal parcellation of the human brain to attribute stereotactic co-ordinates to one of 180 anatomical regions, the first time this approach has been combined (...)
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  38. 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 (...)
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  39.  86
    Georg Cantor’s Ordinals, Absolute Infinity & Transparent Proof of the Well-Ordering Theorem.Hermann G. W. Burchard - 2019 - Philosophy Study 9 (8).
    Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add Zermelo's choice function. (...)
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  40. 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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  41. 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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  42. 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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  43. 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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  44. 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 (...)
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  45. 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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  46. 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 with (...)
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  47. Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures.Pierre Pica, Stanislas Dehaene, Elizabeth Spelke & Véronique Izard - 2008 - Science 320 (5880):1217-1220.
    The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic (...) and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)
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  48. 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 (...)
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    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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  50. 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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