Results for 'Endogenous fixed point'

973 found
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  1. The Child of Fortune: Envy and the Constitution of the Social Space.Emanuele Antonelli - 2013 - Contagion: Journal of Violence, Mimesis, and Culture 20:117-140.
    In this paper, we sketch out a simple scheme to evaluate different ways in which Western society has coped with the momentous and hidden problem of envy; afterward, we consider the consequences for the constitution of the social space that these changes entail. We will argue that envy, when considered as a primal feeling, can shed light on René Girard’s notion of metaphysical desire and on diasparagmos rituals. Then, taking into account Jean-Pierre Dupuy’s endogenous fixed point thesis—concerning (...)
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  2.  38
    From Text to Image: The Sacred Foundation of Western Institutional Order: Legal-Semiotic Perspectives. [REVIEW]Paolo Heritier - 2013 - International Journal for the Semiotics of Law - Revue Internationale de Sémiotique Juridique 26 (1):163-190.
    The paper analyzes the sacred foundations of Western institutional order, moving from an epistemological, historical and legal–aesthetic perspective. Firstly, it identifies an epistemological theory of complexity which, pursuing Hayek’s theory of complexity, Robilant’s notion of informative–normative systems, Popper’s theory of the Worlds, and Dupuy’s theory of endogenous fixed point, will conclusively lead to presenting the hypothesis of World 0 as the World of the foundation of legal thinking, the home of the sacred and the aesthetic. Secondly, it (...)
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  3. On Loss Aversion in Bimatrix Games.Bram Driesen, Andrés Perea & Hans Peters - 2010 - Theory and Decision 68 (4):367-391.
    In this article three different types of loss aversion equilibria in bimatrix games are studied. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points—points below which they consider payoffs to be losses—are endogenous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000; Int. J. Game Theory 29(2):269) under the name of ‘myopic loss aversion equilibrium.’ There, the players’ reference points (...)
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  4.  4
    Fixed-pointed Involutive Micanorm-based Logics.Eunsuk Yang - 2022 - Korean Journal of Logic 25 (2):121-137.
    This paper considers standard completeness for fixed-pointed involutive micanorm-based logics. For this, we first discuss fixed-pointed involutive micanorm-based logics together with their algebraic semantics. Next, after introducing some examples of fixed-pointed involutive micanorms, we provide standard completeness results for those logics.
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  5.  57
    Fixed points and unfounded chains.Claudio Bernardi - 2001 - Annals of Pure and Applied Logic 109 (3):163-178.
    By an unfounded chain for a function f:X→X we mean a sequence nω of elements of X s.t. fxn+1=xn for every n. Unfounded chains can be regarded as a generalization of fixed points, but on the other hand are linked with concepts concerning non-well-founded situations, as ungrounded sentences and the hypergame. In this paper, among other things, we prove a lemma in general topology, we exhibit an extensional recursive function from the set of sentences of PA into itself without (...)
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  6.  26
    Fixed-point models for paradoxical predicates.Luca Castaldo - 2021 - Australasian Journal of Logic 18 (7):688-723.
    This paper introduces a new kind of fixed-point semantics, filling a gap within approaches to Liar-like paradoxes involving fixed-point models à la Kripke (1975). The four-valued models presented below, (i) unlike the three-valued, consistent fixed-point models defined in Kripke (1975), are able to differentiate between paradoxical and pathological-but-unparadoxical sentences, and (ii) unlike the four-valued, paraconsistent fixed-point models first studied in Visser (1984) and Woodruff (1984), preserve consistency and groundedness of truth.
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  7. Supervaluation fixed-point logics of truth.Philip Kremer & Alasdair Urquhart - 2008 - Journal of Philosophical Logic 37 (5):407-440.
    Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as (...)
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  8.  37
    Fixed points in Peano arithmetic with ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.
    Jäger, G., Fixed points in Peano arithmetic with ordinals, Annals of Pure and Applied Logic 60 119-132. This paper deals with some proof-theoretic aspects of fixed point theories over Peano arithmetic with ordinals. It studies three such theories which differ in the principles which are available for induction on the natural numbers and ordinals. The main result states that there is a natural theory in this framework which is a conservative extension of Peano arithmeti.
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  9.  29
    Explicit Fixed Points in Interpretability Logic.Dick de Jongh & Albert Visser - 1991 - Studia Logica 50 (1):39-49.
    The problem of Uniqueness and Explicit Definability of Fixed Points for Interpretability Logic is considered. It turns out that Uniqueness is an immediate corollary of a theorem of Smoryński.
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  10.  39
    The fixed points of belief and knowledge.Daniela Schuster - forthcoming - Logic Journal of the IGPL.
    Self-referential sentences have troubled our understanding of language for centuries. The most famous self-referential sentence is probably the Liar, a sentence that says of itself that it is false. The Liar Paradox has encouraged many philosophers to establish theories of truth that manage to give a proper account of the truth predicate in a formal language. Kripke’s Fixed Point Theory from 1975 is one famous example of such a formal theory of truth that aims at giving a plausible (...)
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  11.  34
    Moral Fixed Points, Error Theory and Intellectual Vice.Christos Kyriacou - 2023 - Philosophia 51 (4):1785-1794.
    Ingram (2015) has argued that Cuneo and Shafer-Landau’s (2014) ‘moral fixed points’ theory entails that error theorists are conceptually deficient with moral concepts. They are conceptually deficient with moral concepts because they do not grasp moral fixed points (e.g. ‘Torture for fun is pro tanto wrong’). Ingram (2015) concluded that moral fixed points theory cannot substantiate the conceptual deficiency charge and, therefore, the theory is defeated. In defense of moral fixed points theory, Kyriacou (2017a) argued that (...)
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  12. Structural fixed-point theorems.Brian Rabern & Landon Rabern - manuscript
    The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to (...)
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  13.  27
    Fixed-points of Set-continuous Operators.O. Esser, R. Hinnion & D. Dzierzgowski - 2000 - Mathematical Logic Quarterly 46 (2):183-194.
    In this paper, we study when a set-continuous operator has a fixed-point that is the intersection of a directed family. The framework of our study is the Kelley-Morse theory KMC– and the Gödel-Bernays theory GBC–, both theories including an Axiom of Choice and excluding the Axiom of Foundation. On the one hand, we prove a result concerning monotone operators in KMC– that cannot be proved in GBC–. On the other hand, we study conditions on directed superclasses in GBC– (...)
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  14. Comparing fixed-point and revision theories of truth.Philip Kremer - 2009 - Journal of Philosophical Logic 38 (4):363-403.
    In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to (...)
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  15. Fixed Point Theorems with Applications to Economics and Game Theory.Kim C. Border - 1989 - Cambridge University Press.
    One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the (...)
     
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  16.  91
    A fixed point theorem for the weak Kleene valuation scheme.Anil Gupta & Robert L. Martin - 1984 - Journal of Philosophical Logic 13 (2):131 - 135.
  17.  53
    The Fixed Point Property in Modal Logic.Lorenzo Sacchetti - 2001 - Notre Dame Journal of Formal Logic 42 (2):65-86.
    This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every has the explicit fixed point property. Our main result states that every complete modal logic L having the Craig's interpolation property and such that , where and are suitable modal formulas, has the explicit (...)
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  18.  34
    A fixed-point problem for theories of meaning.Niklas Dahl - 2022 - Synthese 200 (1):1-15.
    In this paper I argue that it’s impossible for there to be a single universal theory of meaning for a language. First, I will consider some minimal expressiveness requirements a language must meet to be able to express semantic claims. Then I will argue that in order to have a single unified theory of meaning, these expressiveness requirements must be satisfied by a language which the semantic theory itself applies to. That is, we would need a language which can express (...)
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  19.  56
    Fixed-point extensions of first-order logic.Yuri Gurevich & Saharon Shelah - 1986 - Annals of Pure and Applied Logic 32:265-280.
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  20.  38
    Fixed points and well-ordered societies.Paul Weithman - 2023 - Politics, Philosophy and Economics 22 (2):197-212.
    Recent years have seen a certain impatience with John Rawls's approach to political philosophy and calls for the discipline to move beyond it. One source of dissatisfaction is Rawls's idea of a well-ordered society. In a recent article, Alex Schaefer has tried to give further impetus to this movement away from Rawlsian theorizing by pursuing a question about well-ordered societies that he thinks other critics have not thought to ask. He poses that question in the title of his article: “Is (...)
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  21.  23
    A fixed-point theorem for definably amenable groups.Juan Felipe Carmona, Kevin Dávila, Alf Onshuus & Rafael Zamora - 2020 - Archive for Mathematical Logic 60 (3-4):413-424.
    We prove an analogue of the fixed-point theorem for the case of definably amenable groups.
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  22.  36
    Intuitionistic fixed point theories over set theories.Toshiyasu Arai - 2015 - Archive for Mathematical Logic 54 (5-6):531-553.
    In this paper we show that the intuitionistic fixed point theory FiXi over set theories T is a conservative extension of T if T can manipulate finite sequences and has the full foundation schema.
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  23.  24
    Fixed point theory in weak second-order arithmetic.Naoki Shioji & Kazuyuki Tanaka - 1990 - Annals of Pure and Applied Logic 47 (2):167-188.
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  24. On Fixed Points, Diagonalization, and Self-Reference.Bernd Buldt - unknown
    We clarify the respective roles fixed points, diagonalization, and self- reference play in proofs of Gödel’s first incompleteness theorem.
     
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  25.  30
    Fixed Point Results of Dynamic Process D ˇ ϒ, μ 0 through F I C -Contractions with Applications.Amjad Ali, Eskandar Ameer, Muhammad Arshad, Hüseyin Işık & Mustafa Mudhesh - 2022 - Complexity 2022:1-8.
    This article constitutes the new fixed point results of dynamic process D through FIC-integral contractions of the Ciric kind and investigates the said contraction to iterate a fixed point of set-valued mappings in the module of metric space. To do so, we use the dynamic process instead of the conventional Picard sequence. The main results are examined by tangible nontrivial examples which display the motivation for such investigation. The work is completed by giving an application to (...)
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  26.  42
    Intuitionistic fixed point logic.Ulrich Berger & Hideki Tsuiki - 2021 - Annals of Pure and Applied Logic 172 (3):102903.
    We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We also (...)
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  27.  20
    Short note: Least fixed points versus least closed points.Gerhard Jäger - 2021 - Archive for Mathematical Logic 60 (7):831-835.
    This short note is on the question whether the intersection of all fixed points of a positive arithmetic operator and the intersection of all its closed points can proved to be equivalent in a weak fragment of second order arithmetic.
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  28.  59
    Definable fixed points in modal and temporal logics — a survey.Sergey Mardaev - 2007 - Journal of Applied Non-Classical Logics 17 (3):317-346.
    The paper presents a survey of author's results on definable fixed points in modal, temporal, and intuitionistic propositional logics. The well-known Fixed Point Theorem considers the modalized case, but here we investigate the positive case. We give a classification of fixed point theorems, describe some classes of models with definable least fixed points of positive operators, special positive operators, and give some examples of undefinable least fixed points. Some other interesting phenomena are discovered (...)
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  29.  37
    Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application.A. Asif, M. Alansari, N. Hussain, M. Arshad & A. Ali - 2021 - Complexity 2021:1-12.
    This manuscript investigates fixed point of single-valued Hardy-Roger’s type F -contraction globally as well as locally in a convex b -metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom of the F -contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b -metric space is not necessarily complete, the (...)
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  30.  20
    Fixed-points for relations and the back and forth method.Janusz Czelakowski - 2006 - Bulletin of the Section of Logic 35 (2/3):63-71.
  31.  14
    Autonomous Fixed Point Progressions and Fixed Point Transfinite Recursion.Thomas Strahm - 2001 - Bulletin of Symbolic Logic 7 (4):535-536.
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  32.  39
    The Mermin Fixed Point.Veit Elser - 2003 - Foundations of Physics 33 (11):1691-1698.
    The most efficient known method for solving certain computational problems is to construct an iterated map whose fixed points are by design the problem's solution. Although the origins of this idea go back at least to Newton, the clearest expression of its logical basis is an example due to Mermin. A contemporary application in image recovery demonstrates the power of the method.
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  33.  34
    Intuitionistic Fixed Point Theories for Strictly Positive Operators.Christian Rüede & Thomas Strahm - 2002 - Mathematical Logic Quarterly 48 (2):195-202.
    In this paper it is shown that the intuitionistic fixed point theory equation image for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and equation image sentences over the theory equation image for α times iterated arithmetic comprehension without set parameters. This generalizes results previously due to Buchholz [5] and Arai [2].
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  34.  26
    Fixed point theorems for precomplete numberings.Henk Barendregt & Sebastiaan A. Terwijn - 2019 - Annals of Pure and Applied Logic 170 (10):1151-1161.
    In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. We discuss various generalizations of this result. Among other things, we show that Arslanov's completeness criterion also holds for every precomplete numbering, and we discuss the relation with Visser's ADN theorem, as well as the uniformity or nonuniformity of the various fixed point theorems. Finally, we base numberings on partial combinatory algebras and prove a generalization of Ershov's theorem in (...)
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  35.  84
    ŁΠ logic with fixed points.Luca Spada - 2008 - Archive for Mathematical Logic 47 (7-8):741-763.
    We study a system, μŁΠ, obtained by an expansion of ŁΠ logic with fixed points connectives. The first main result of the paper is that μŁΠ is standard complete, i.e., complete with regard to the unit interval of real numbers endowed with a suitable structure. We also prove that the class of algebras which forms algebraic semantics for this logic is generated, as a variety, by its linearly ordered members and that they are precisely the interval algebras of real (...)
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  36.  22
    Largest fixed points of set continuous operators and Boffa's Anti-Foundation.Hisato Muraki - 2005 - Mathematical Logic Quarterly 51 (4):365.
    In Aczel [1], the existence of largest fixed points of set continuous operators is proved assuming the schema version of dependent choices in Zermelo-Fraenkel set theory without the axiom of Foundation. In the present paper, we study whether the existence of largest fixed points of set continuous operators is provable without the schema version of dependent choices, using Boffa's weak antifoundation axioms.
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  37. Fixed Point Constructions in Various Theories of Mathematical Logic.Giovanni Sommaruga-Rosolemos - 1991
     
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  38.  29
    Incompleteness and Fixed Points.Lorenzo Sacchetti - 2002 - Mathematical Logic Quarterly 48 (1):15-28.
    Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property.
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  39.  22
    Fixed Point Theorems for Inconsistent and Incomplete Formation of Large Categories.J. Cole & Christian Edward Mortensen - 1995 - Logique Et Analyse 139 (140):223-238.
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  40.  21
    (1 other version)Fixed points and diagonal method.Maurizio Negri - 1990 - Mathematical Logic Quarterly 36 (4):319-329.
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  41. From Moral Fixed Points to Epistemic Fixed Points.Christos Kyriacou - 2018 - In Christos Kyriacou & Robin McKenna (eds.), Metaepistemology: Realism & Antirealism. Cham: Palgrave Macmillan.
    Cuneo and Shafer-Landau (2014) argued that there are moral conceptual truths that are substantive in content, what they called ‘moral fixed points’. I argue that insofar as we have some reason to postulate moral fixed points, we have equal reason to postulate epistemic fixed points (e.g. the factivity condition). To this effect, I show that the two basic reasons Cuneo and Shafer-Landau (2014) offer in support of moral fixed points naturally carry over to epistemic fixed (...)
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  42. Rationality’s Fixed Point.Michael G. Titelbaum - 2015 - Oxford Studies in Epistemology 5.
    This article defends the Fixed Point Thesis: that it is always a rational mistake to have false beliefs about the requirements of rationality. The Fixed Point Thesis is inspired by logical omniscience requirements in formal epistemology. It argues to the Fixed Point Thesis from the Akratic Principle: that rationality forbids having an attitude while believing that attitude is rationally forbidden. It then draws out surprising consequences of the Fixed Point Thesis, for instance (...)
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  43.  9
    Infinite fixed-point algebras.Robert M. Solovay - 1985 - In Anil Nerode & Richard A. Shore (eds.), Recursion theory. Providence, R.I.: American Mathematical Society. pp. 42--473.
  44. The fixed point non-classical theory of truth value gaps by S. Kripke.Artyom Ukhov - 2017 - Vestnik SPbSU. Philosophy and Conflict Studies 33 (2):224-233.
    The article is about one of the vital problem for analytic philosophy which is how to define truth value for sentences which include their own truth predicate. The aim of the article is to determine Saul Kripke’s approach to widen epistemological truth to create a systemic model of truth. Despite a lot of work on the subject, the theme of truth is no less relevant to modern philosophy. With the help of S. Kripke’s article “Outline of the Theory of Truth” (...)
     
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  45.  23
    Fixed-point properties for predicate modal logics.Sohei Iwata & Taishi Kurahashi - 2020 - Annals of the Japan Association for Philosophy of Science 29:1-25.
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  46. Fixed-point solutions to the regress problem in normative uncertainty.Philip Trammell - 2019 - Synthese 198 (2):1177-1199.
    When we are faced with a choice among acts, but are uncertain about the true state of the world, we may be uncertain about the acts’ “choiceworthiness”. Decision theories guide our choice by making normative claims about how we should respond to this uncertainty. If we are unsure which decision theory is correct, however, we may remain unsure of what we ought to do. Given this decision-theoretic uncertainty, meta-theories attempt to resolve the conflicts between our decision theories...but we may be (...)
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  47.  36
    A fixed point theorem for o-minimal structures.Kam-Chau Wong - 2003 - Mathematical Logic Quarterly 49 (6):598.
    We prove a definable analogue to Brouwer's Fixed Point Theorem for o-minimal structures of real closed field expansions: A continuous definable function mapping from the unit simplex into itself admits a fixed point, even though the underlying space is not necessarily topologically complete. Our proof is direct and elementary; it uses a triangulation technique for o-minimal functions, with an application of Sperner's Lemma.
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  48.  63
    Fixed point logics.Anuj Dawar & Yuri Gurevich - 2002 - Bulletin of Symbolic Logic 8 (1):65-88.
    We consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory, and also consider the expressive power of the resulting logics on infinite structures. In particular, we establish the relationship between inflationary and nondeterministic fixed point logics and second (...)
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  49.  6
    How strong are single fixed points of normal functions?Anton Freund - 2020 - Journal of Symbolic Logic 85 (2):709-732.
    In a recent paper by M. Rathjen and the present author it has been shown that the statement “every normal function has a derivative” is equivalent to $\Pi ^1_1$ -bar induction. The equivalence was proved over $\mathbf {ACA_0}$, for a suitable representation of normal functions in terms of dilators. In the present paper, we show that the statement “every normal function has at least one fixed point” is equivalent to $\Pi ^1_1$ -induction along the natural numbers.
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  50.  46
    Two kinds of fixed point theorems and reverse mathematics.Weiguang Peng & Takeshi Yamazaki - 2017 - Mathematical Logic Quarterly 63 (5):454-461.
    In this paper, we investigate the logical strength of two types of fixed point theorems in the context of reverse mathematics. One is concerned with extensions of the Banach contraction principle. Among theorems in this type, we mainly show that the Caristi fixed point theorem is equivalent to math formula over math formula. The other is dedicated to topological fixed point theorems such as the Brouwer fixed point theorem. We introduce some variants (...)
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