Results for 'cardinality'

145 found
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  1. Cardinal Composition.Lisa Vogt & Jonas Werner - forthcoming - Erkenntnis.
    The thesis of Weak Unrestricted Composition says that every pair of objects has a fusion. This thesis has been argued by Contessa and Smith to be compatible with the world being junky and hence to evade an argument against the necessity of Strong Unrestricted Composition proposed by Bohn. However, neither Weak Unrestricted Composition alone nor the different variants of it that have been proposed in the literature can provide us with a satisfying answer to the special composition question, or so (...)
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  2. A Cardinal Worry for Permissive Metaontology.Simon Hewitt - 2015 - Metaphysica 16 (2):159-166.
    Permissivist metaontology proposes answering customary existence questions in the affirmative. Many of the existence questions addressed by ontologists concern the existence of theoretical entities which admit precise formal specification. This causes trouble for the permissivist, since individually consistent formal theories can make pairwise inconsistent demands on the cardinality of the universe. We deploy a result of Gabriel Uzquiano’s to show that this possibility is realised in the case of two prominent existence debates and propose rejecting permissivism in favour of (...)
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  3. The Cardinal Role of Respect and Self-Respect for Rawls’s and Walzer’s Theories of Justice.Manuel Dr Knoll - 2017 - In Giovanni Giorgini & Elena Irrera (eds.), The Roots of Respect. A Historic-Philosophical Itinerary. De Gruyter. pp. 207–227.
    The cardinal role that notions of respect and self-respect play in Rawls’s A Theory of Justice has already been abundantly examined in the literature. However, it has hardly been noticed that these notions are also central for Michael Walzer’s Spheres of Justice. Respect and self-respect are not only central topics of his chapter on “recognition”, but constitute a central aim of his whole theory of justice. This paper substantiates this thesis and elucidates Walzer’s criticism of Rawls’s that we need to (...)
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  4. Choice-Based Cardinal Utility. A Tribute to Patrick Suppes.Jean Baccelli & Philippe Mongin - 2016 - Journal of Economic Methodology 23 (3):268-288.
    We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes's contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes's doctrine with the major deviation from ordinalism that conceives of utility functions as (...)
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  5. The Cardinal Role of Respect and Self-Respect for Rawls’s and Walzer’s Theories of Justice.Manuel Knoll - 2017 - In Elena Irrera & Giovanni Giorgini (eds.), The Roots of Respect: A Historic-Philosophical Itinerary. De Gruyter. pp. 207-224.
    The cardinal role that notions of respect and self-respect play in Rawls’s A Theory of Justice has already been abundantly examined in the literature. In contrast, it has hardly been noticed that these notions are also central to Michael Walzer’s Spheres of Justice. Respect and self-respect are not only central topics of his chapter “Recognition”, but constitute a central aim of a “complex egalitarian society” and of Walzer’s theory of justice. This paper substantiates this thesis and elucidates Walzer’s criticism of (...)
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  6. Creationism and Cardinality.Daniel Nolan & Alexander Sandgren - 2014 - Analysis 74 (4):615-622.
    Creationism about fictional entities requires a principle connecting what fictions say exist with which fictional entities really exist. The most natural way of spelling out such a principle yields inconsistent verdicts about how many fictional entities are generated by certain inconsistent fictions. Avoiding inconsistency without compromising the attractions of creationism will not be easy.
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  7. Thomas Hobbes and Cardinal Bellarmine: Leviathan and 'He Ghost of the Roman Empire'.Patricia Springborg - 1995 - History of Political Thought 16 (4):503-531.
    As a representative of the papacy Bellarmine was an extremely moderate one. In fact Sixtus V in 1590 had the first volume of his Disputations placed on the Index because it contained so cautious a theory of papal power, denying the Pope temporal hegemony. Bellarmine did not represent all that Hobbes required of him either. On the contrary, he proved the argument of those who championed the temporal powers of the Pope faulty. As a Jesuit he tended to maintain the (...)
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  8. Are Large Cardinal Axioms Restrictive?Neil Barton - manuscript
    The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal axioms are restrictive. (...)
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  9.  29
    Nota: ¿CUÁL ES EL CARDINAL DEL CONJUNTO DE LOS NÚMEROS REALES?Franklin Galindo - manuscript
    ¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...)
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  10.  32
    Cardinality Logics, Part I: Inclusions Between Languages Based on ‘Exactly’.Harold Hodes - 1988 - Annals of Pure and Applied Logic 39 (3):199-238.
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  11.  25
    Cardinality Logics. Part II: Definability in Languages Based on `Exactly'.Harold Hodes - 1988 - Journal of Symbolic Logic 53 (3):765-784.
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  12. A Happy Possibility About Happiness (And Other Subjective) Scales: An Investigation and Tentative Defence of the Cardinality Thesis.Michael Plant - manuscript
    There are long-standing doubts about whether data from subjective scales—for instance, self-reports of happiness—are cardinally comparable. It is unclear how to assess whether these doubts are justified without first addressing two unresolved theoretical questions: how do people interpret subjective scales? Which assumptions are required for cardinal comparability? This paper offers answers to both. It proposes an explanation for scale interpretation derived from philosophy of language and game theory. In short: conversation is a cooperative endeavour governed by various maxims (Grice 1989); (...)
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  13. The Basic Laws of Cardinal Number.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 1-30.
    An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.
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  14. Generalized Löb’s Theorem. Strong Reflection Principles and Large Cardinal Axioms.Jaykov Foukzon - 2013 - Advances in Pure Mathematics (3):368-373.
    In this article, a possible generalization of the Löb’s theorem is considered. Main result is: let κ be an inaccessible cardinal, then ¬Con( ZFC +∃κ) .
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  15. Can an Ancient Argument of Carneades on Cardinal Virtues and Divine Attributes Be Used to Disprove the Existence of God?Douglas Walton - 1999 - Philo 2 (2):5-13.
    An ancient argument attributed to the philosopher Carneades is presented that raises critical questions about the concept of an all-virtuous Divine being. The argument is based on the premises that virtue involves overcoming pains and dangers, and that only a being that can suffer or be destroyed is one for whom there are pains and dangers. The conclusion is that an all-virtuous Divine (perfect) being cannot exist. After presenting this argument, reconstructed from sources in Sextus Empiricus and Cicero, this paper (...)
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  16. The Nineteenth-Century Thomist From the Far East: Cardinal Zeferino González, OP (1831–1894).Levine Andro Lao - 2021 - Philippiniana Sacra 56 (167):277-306.
    This article reintroduces Fr. Zeferino González, OP (1831-1894) to scholars of Church history, philosophy, and cultural heritage. He was an alumnus of the University of Santo Tomás in Manila, a Cardinal, and a champion of the revival of Catholic Philosophy that led to the promulgation of Leo XIII’s encyclical Aeterni Patris. Specifically, this essay presents, firstly, the Cardinal’s biography in the context of his experience as a missionary in the Far East; secondly, the intellectual tradition in Santo Tomás in Manila, (...)
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  17. Inconsistent Countable Set in Second Order ZFC and Nonexistence of the Strongly Inaccessible Cardinals.Jaykov Foukzon - 2015 - British Journal of Mathematics and Computer Science 9 (5):380-393.
    In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.
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  18. Generalized Löb’s Theorem.Strong Reflection Principles and Large Cardinal Axioms. Consistency Results in Topology.Jaykov Foukzon - 2015 - Pure and Applied Mathematics Journal (Vol. 4, No. 1-1):1-5.
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  19. Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.
    This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...)
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  20. Relativism, Today and Yesterday.Barbara Herrnstein Smith - 2007 - Common Knowledge 13 (2-3):227-249.
    An analysis of Cardinal Joseph Ratzinger's statements regarding relativism in his 2005 homily to the conclave meeting to elect the new pope in the context of the charge of "relativism" in 20th-century philosophy. Parts of this essay are adapted from Barbara Herrnstein Smith,"Pre-Post-Modern Relativism," in *Scandalous Knowledge: Science, Truth and the Human* (Edinburgh: Edinburgh University Press, 2005; Durham, NC: Duke University Press, 2006), 18 – 45.
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  21. Composition and Relative Counting.Massimiliano Carrara & Giorgio Lando - 2017 - Dialectica 71 (4):489-529.
    According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as (...)
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  22. First-Order Modal Logic in the Necessary Framework of Objects.Peter Fritz - 2016 - Canadian Journal of Philosophy 46 (4-5):584-609.
    I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the (...)
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  23. The Transition Within Virtue Ethics in the Context of Benevolence.Prasasti Pandit - 2022 - Philosophia (Philippines) 23 (1):135-151.
    This paper explores the value of benevolence as a cardinal virtue by analyzing the evolving history of virtue ethics from ancient Greek tradition to emotivism and contemporary thoughts. First, I would like to start with a brief idea of virtue ethics. Greek virtue theorists recognize four qualities of moral character, namely, wisdom, temperance, courage, and justice. Christianity recognizes unconditional love as the essence of its theology. Here I will analyze the transition within the doctrine of virtue ethics in the Christian (...)
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  24. Overgeneration in the Higher Infinite.Salvatore Florio & Luca Incurvati - forthcoming - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning. Cambridge: Cambridge University Press.
    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...)
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  25. Countabilism and Maximality Principles.Neil Barton & Sy-David Friedman - manuscript
    It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...)
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  26. Two Mereological Arguments Against the Possibility of an Omniscient Being.Joshua T. Spencer - 2006 - Philo 9 (1):62-72.
    In this paper I present two new arguments against the possibility of an omniscient being. My new arguments invoke considerations of cardinality and resemble several arguments originally presented by Patrick Grim. Like Grim, I give reasons to believe that there must be more objects in the universe than there are beliefs. However, my arguments will rely on certain mereological claims, namely that Classical Extensional Mereology is necessarily true of the part-whole relation. My first argument is an instance of a (...)
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  27. Logic of Paradoxes in Classical Set Theories.Boris Čulina - 2013 - Synthese 190 (3):525-547.
    According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...)
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  28. Iterated Ultrapowers and Prikry Forcing.Patrick Dehornoy - 1978 - Annals of Mathematical Logic 15 (2):109.
    If $U$ is a normal ultrafilter on a measurable cardinal $\kappa$, then the intersection of the $\omega$ first iterated ultrapowers of the universe by $U$ is a Prikry generic extension of the $\omega$th iterated ultrapower.
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  29. There is No Standard Model of ZFC and ZFC_2. Part I.Jaykov Foukzon - 2017 - Journal of Advances in Mathematics and Computer Science 2 (26):1-20.
    In this paper we view the first order set theory ZFC under the canonical frst order semantics and the second order set theory ZFC_2 under the Henkin semantics. Main results are: (i) Let M_st^ZFC be a standard model of ZFC, then ¬Con(ZFC + ∃M_st^ZFC ). (ii) Let M_stZFC_2 be a standard model of ZFC2 with Henkin semantics, then ¬Con(ZFC_2 +∃M_stZFC_2). (iii) Let k be inaccessible cardinal then ¬Con(ZFC + ∃κ). In order to obtain the statements (i) and (ii) examples of (...)
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  30. There is No Standard Model of ZFC and ZFC2. Part II.Jaykov Foukzon & Elena Men’Kova - 2019 - Advanced in Pure Mathematic 9 (9):685-744.
    In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models or nonstandard model with standard part. An posible generalization of Lob’s theorem is considered.Main results are: (i) ConZFC  Mst ZFC, (ii) ConZF  V  L, (iii) ConNF  Mst NF, (iv) ConZFC2, (v) let k be inaccessible cardinal then ConZFC  .
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  31. All Things Must Pass Away.Joshua Spencer - 2012 - Oxford Studies in Metaphysics 7:67.
    Are there any things that are such that any things whatsoever are among them. I argue that there are not. My thesis follows from these three premises: (1) There are two or more things; (2) for any things, there is a unique thing that corresponds to those things; (3) for any two or more things, there are fewer of them than there are pluralities of them.
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  32. Size and Function.Bruno Whittle - 2018 - Erkenntnis 83 (4):853-873.
    Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: for (...)
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  33. Parity, Imprecise Comparability, and the Repugnant Conclusion.Ruth Chang - 2016 - Theoria 82 (2):183-215.
    This article explores the main similarities and differences between Derek Parfit’s notion of imprecise comparability and a related notion I have proposed of parity. I argue that the main difference between imprecise comparability and parity can be understood by reference to ‘the standard view’. The standard view claims that 1) differences between cardinally ranked items can always be measured by a scale of units of the relevant value, and 2) all rankings proceed in terms of the trichotomy of ‘better than’, (...)
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  34. Modality and Hyperintensionality in Mathematics.Hasen Khudairi - manuscript
    This paper aims to contribute to the analysis of the nature of mathematical modality, and to the applications of the latter to unrestricted quantification and absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the (...)
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  35. Infinite Aggregation and Risk.Hayden Wilkinson - forthcoming - Australasian Journal of Philosophy:1-20.
    For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...)
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  36. The Measure of Knowledge.Nick Treanor - 2013 - Noûs 47 (3):577-601.
    What is it to know more? By what metric should the quantity of one's knowledge be measured? I start by examining and arguing against a very natural approach to the measure of knowledge, one on which how much is a matter of how many. I then turn to the quasi-spatial notion of counterfactual distance and show how a model that appeals to distance avoids the problems that plague appeals to cardinality. But such a model faces fatal problems of its (...)
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  37.  83
    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 (...)
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  38. Public Attitudes Toward Cognitive Enhancement.Nicholas S. Fitz, Roland Nadler, Praveena Manogaran, Eugene W. J. Chong & Peter B. Reiner - 2014 - Neuroethics 7 (2):173-188.
    Vigorous debate over the moral propriety of cognitive enhancement exists, but the views of the public have been largely absent from the discussion. To address this gap in our knowledge, four experiments were carried out with contrastive vignettes in order to obtain quantitative data on public attitudes towards cognitive enhancement. The data collected suggest that the public is sensitive to and capable of understanding the four cardinal concerns identified by neuroethicists, and tend to cautiously accept cognitive enhancement even as they (...)
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  39. Wide Sets, ZFCU, and the Iterative Conception.Christopher Menzel - 2014 - Journal of Philosophy 111 (2):57-83.
    The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow for (...)
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  40.  84
    Apical Amplification—a Cellular Mechanism of Conscious Perception?Tomas Marvan, Michal Polák, Talis Bachmann & William A. Phillips - 2021 - Neuroscience of Consciousness 7 (2):1-17.
    We present a theoretical view of the cellular foundations for network-level processes involved in producing our conscious experience. Inputs to apical synapses in layer 1 of a large subset of neocortical cells are summed at an integration zone near the top of their apical trunk. These inputs come from diverse sources and provide a context within which the transmission of information abstracted from sensory input to their basal and perisomatic synapses can be amplified when relevant. We argue that apical amplification (...)
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  41. Absolutely No Free Lunches!Gordon Belot - forthcoming - Theoretical Computer Science.
    This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in that (...)
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  42.  41
    On the Expressive Power of Łukasiewicz Square Operator.Marcelo E. Coniglio, Francesc Esteva, Tommaso Flaminio & Lluis Godo - forthcoming - Journal of Logic and Computation.
    The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...)
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  43.  78
    Absence Perception and the Philosophy of Zero.Neil Barton - 2020 - Synthese 197 (9):3823-3850.
    Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...)
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  44. Review of Øystein Linnebo, Thin Objects. [REVIEW]Thomas Donaldson - forthcoming - Philosophia Mathematica:6.
    A brief review of Øystein Linnebo's Thin Objects. The review ends with a brief discussion of cardinal number and metaphysical ground.
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  45.  59
    Virtues Are Excellences.Paul Bloomfield - 2022 - Ratio 35 (1):49-60.
    Ratio, Volume 35, Issue 1, Page 49-60, March 2022.
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  46.  64
    What is Logical in First-Order Logic?Boris Čulina - manuscript
    In this article, logical concepts are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language.
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  47. Higher-Order Contingentism, Part 3: Expressive Limitations.Peter Fritz - 2018 - Journal of Philosophical Logic 47 (4):649-671.
    Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists (...)
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  48. Two-Sorted Frege Arithmetic is Not Conservative.Stephen Mackereth & Jeremy Avigad - 2022 - Review of Symbolic Logic:1-34.
    Neo-Fregean logicists claim that Hume's Principle (HP) may be taken as an implicit definition of cardinal number, true simply by fiat. A longstanding problem for neo-Fregean logicism is that HP is not deductively conservative over pure axiomatic second-order logic. This seems to preclude HP from being true by fiat. In this paper, we study Richard Kimberly Heck's Two-sorted Frege Arithmetic (2FA), a variation on HP which has been thought to be deductively conservative over second-order logic. We show that it isn't. (...)
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  49. Uninstantiated Properties and Semi-Platonist Aristotelianism.James Franklin - 2015 - Review of Metaphysics 69 (1):25-45.
    A problem for Aristotelian realist accounts of universals (neither Platonist nor nominalist) is the status of those universals that happen not to be realised in the physical (or any other) world. They perhaps include uninstantiated shades of blue and huge infinite cardinals. Should they be altogether excluded (as in D.M. Armstrong's theory of universals) or accorded some sort of reality? Surely truths about ratios are true even of ratios that are too big to be instantiated - what is the truthmaker (...)
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  50. Value Neutrality and the Ranking of Opportunity Sets.Michael Garnett - 2016 - Economics and Philosophy 32 (1):99-119.
    I defend the idea that a liberal commitment to value neutrality is best honoured by maintaining a pure cardinality component in our rankings of opportunity or liberty sets. I consider two challenges to this idea. The first holds that cardinality rankings are unnecessary for neutrality, because what is valuable about a set of liberties from a liberal point of view is not its size but rather its variety. The second holds that pure cardinality metrics are insufficient for (...)
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