Results for 'choice sequence'

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  1. Free Choice Sequences: A Temporal Interpretation Compatible with Acceptance of Classical Mathematics.Saul Kripke - 2019 - Indagationes Mathematicae 30 (3):492-499.
    This paper sketches a way of supplementing classical mathematics with a motivation for a Brouwerian theory of free choice sequences. The idea is that time is unending, i.e. that one can never come to an end of it, but also indeterminate, so that in a branching time model only one branch represents the ‘actual’ one. The branching can be random or subject to various restrictions imposed by the creating subject. The fact that the underlying mathematics is classical makes such (...)
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  2.  51
    Choice sequences: a chapter of intuitionistic mathematics.Anne Sjerp Troelstra - 1977 - Oxford [Eng.]: Clarendon Press.
  3.  51
    Busy choice sequences refraining formulas and modalities.Ming Xu - 1995 - Studia Logica 54 (3):267 - 301.
    The purpose of this paper is to present some results instit theory, a theory of agency proposed by N. Belnap and M. Perloff. We will establish a correspondence between the numbers ofstit modalities and the complexity degrees ofbusy choice sequences in semantic structures, and consequently, a correspondence between the number of modes of actions/inactions instit theory and the complexity degrees ofbusy choice sequences in semantic structures.
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  4.  70
    Choice Sequences and the Continuum.Casper Storm Hansen - 2020 - Erkenntnis 87 (2):517-534.
    According to L.E.J. Brouwer, there is room for non-definable real numbers within the intuitionistic ontology of mental constructions. That room is allegedly provided by freely proceeding choice sequences, i.e., sequences created by repeated free choices of elements by a creating subject in a potentially infinite process. Through an analysis of the constitution of choice sequences, this paper argues against Brouwer’s claim.
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  5.  72
    Choice sequences and informal rigour.A. S. Troelstra - 1985 - Synthese 62 (2):217 - 227.
    In this paper we discuss a particular example of the passage from the informal, but rigorous description of a concept to the axiomatic formulation of principles holding for the concept; in particular, we look at the principles of continuity and lawlike choice in the theory of lawless sequences. Our discussion also leads to a better understanding of the rôle of the so-called density axiom for lawless sequences.
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  6. Free choice sequences I».Amitabha Ghose - 1968 - In P. Braffort & F. van Scheepen (eds.), Automation in language translation and theorem proving. Brussels,: Commission of the European Communities, Directorate-General for Dissemination of Information. pp. 245.
     
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  7.  68
    Analysing choice sequences.A. S. Troelstra - 1983 - Journal of Philosophical Logic 12 (2):197 - 260.
  8.  30
    Choice Sequences and Knowledge States: Extending the Notion of Finite Information to Produce a Clearer Foundation for Intuitionistic Analysis, Keele University, UK, 2017. Supervised by Peter Fletcher.James Firoze Appleby - 2018 - Bulletin of Symbolic Logic 24 (2):196-197.
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  9. On choice sequences determined by spreads.Gerritder Hoeven & Ieke Moerdijk - 1984 - Journal of Symbolic Logic 49 (3):908 - 916.
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  10.  42
    Spreads or choice sequences?H. C. M. De Swart - 1992 - History and Philosophy of Logic 13 (2):203-213.
    Intuitionistically. a set has to be given by a finite construction or by a construction-project generating the elements of the set in the course of time. Quantification is only meaningful if the range of each quantifier is a well-circumscribed set. Thinking upon the meaning of quantification, one is led to insights?in particular, the so-called continuity principles?which are surprising from a classical point of view. We believe that such considerations lie at the basis of Brouwer?s reconstruction of mathematics. The predicate ?α (...)
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  11.  27
    Choice sequences: A chapter of intuitionistic mathematics. [REVIEW]Mary Tiles - 1978 - Philosophical Books 19 (2):77-80.
  12.  49
    (1 other version)A remark on free choice sequences and the topological completeness proofs.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (4):369-388.
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  13. Divergent Potentialism: A Modal Analysis With an Application to Choice Sequences.Ethan Brauer, Øystein Linnebo & Stewart Shapiro - 2022 - Philosophia Mathematica 30 (2):143-172.
    Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic logic, we overcome (...)
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  14.  38
    Individual Choice Sequences in the Work of L.E.J. Brouwer.Joop Niekus - 2005 - Philosophia Scientiae 9 (S2):217-232.
    Par des suites de choix, nous comprenons des suites qui ne sont pas déterminées complètement par une loi arithmétique. Elles sont des objets caractéristiques de l’intuitionnisme de Brouwer. Nous prétendons qu’à partir de 1927, l’utilisation par Brouwer de suites de choix particulières n’est pas reconnu comme tel. Nous prétendons que l’utilisation de ces suites dans la méthode du sujet créatif, après la seconde guerre mondiale, n’a pas à être mis en relation avec l’utilisation de celles-ci dans les années vingt et (...)
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  15.  13
    Brouwer meets Husserl. On the Phenomenology of Choice Sequences.Mark van Atten (ed.) - 2006 - Springer.
    Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? The mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice (...)
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  16.  65
    Mark Van atten. Brouwer meets Husserl: On the phenomenology of choice sequences.Miriam Franchella - 2008 - Philosophia Mathematica 16 (2):276-281.
    This book summarizes the intense research that the author performed for his Ph.D. thesis , revised and with the addition of an intuitionistic critique of Husserl's concept of number. His starting point consisted of a double conviction: 1) Brouwerian intuitionism is a valid way of doing mathematics but is grounded on a weak philosophy; 2) Husserlian phenomenology can provide a suitable philosophical ground for intuitionism. In order to let intuitionism and phenomenology match, he had to solve in general two problems: (...)
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  17.  88
    Brouwer meets Husserl: on the phenomenology of choice sequences.Markus Sebastiaan Paul Rogier van Atten - 2007 - Dordrecht: Springer.
    Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice (...). But other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl. (shrink)
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  18. A.S. TROELSTRA "Choice sequences. A chapter of intuitionistic mathematics". [REVIEW]R. E. Grandy - 1983 - History and Philosophy of Logic 4 (2):241.
     
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  19.  49
    On Choice Sequences Determined by Spreads.Gerrit van der Hoeven & Ieke Moerdijk - 1984 - Journal of Symbolic Logic 49 (3):908 - 916.
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  20.  13
    The Theory of Choice Sequences.A. S. Troelstra, B. van Rootselaar & J. F. Staal - 1973 - Journal of Symbolic Logic 38 (2):332-332.
  21.  42
    Informal theory of choice sequences.A. S. Troelstra - 1969 - Studia Logica 25 (1):31 - 54.
  22.  56
    Sheaf models for choice sequences.Gerrit Van Der Hoeven & Ieke Moerdijk - 1984 - Annals of Pure and Applied Logic 27 (1):63-107.
  23.  62
    Troelstra A. S.. Choice sequences. A chapter of intuitionistic mathematics. Oxford logic guides. Clarendon Press, Oxford 1977, ix + 170 pp. [REVIEW]Richard Vesley - 1979 - Journal of Symbolic Logic 44 (2):275-276.
  24.  7
    Phenomenology's reception of Brouwer's choice sequences.Mark van Atten - 2005 - In Volker Peckhaus (ed.), Oskar Becker undie Philosophie der Mathematik. Wilhelm Fink Verlag. pp. 101-117.
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  25.  66
    Varieties of indeterminacy in the theory of general choice sequences.Carl J. Posy - 1976 - Journal of Philosophical Logic 5 (1):91 - 132.
  26. From the axiom of choice to choice sequences.H. Jervell - 1996 - Nordic Journal of Philosophical Logic 1 (1):95-98.
  27.  6
    No Decreasing Sequence of Cardinals in the Hierarchy of Choice Principles.Eleftherios Tachtsis - 2024 - Notre Dame Journal of Formal Logic 65 (3):311-331.
    In set theory without the axiom of choice (AC), we study the relative strength of the principle “No decreasing sequence of cardinals,” that is, “There is no function f on ω such that |f(n+1)|<|f(n)| for all n∈ω” (NDS) with regard to its position in the hierarchy of weak choice principles. We establish the following results: (1) The Boolean prime ideal theorem plus countable choice does not imply NDS in ZF; (2) “Every non-well-orderable set has a well-orderable (...)
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  28.  51
    Whole genome sequencing in children: ethics, choice and deliberation.Ainsley J. Newson - 2017 - Journal of Medical Ethics 43 (8):540-542.
    Implementing whole genome sequencing (WGS) in paediatric settings demands sensitive and nuanced examination. Critical reflection as to how and when to use this technology is particularly important. This commentary on Anderson et al's (2017) evaluation of the Genome Clinic study, which involved paediatric clinical WGS, provides an opportunity for such reflection. I scrutinise three issues raised in the study: (1) the non-separation of the choice over agreeing to diagnostic WGS and whether to receive adult-onset SVs; (2) the value of (...)
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  29.  29
    (1 other version)Troelstra A. S.. The theory of choice sequences. Logic, methodology and philosophy of science III, Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science, Amsterdam 1967, edited by van Rootselaar B. and Staal J. F., Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam 1968, pp. 201–223. [REVIEW]R. E. Vesley - 1973 - Journal of Symbolic Logic 38 (2):332-332.
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  30.  42
    G. Kreisel. A remark on free choice sequences and the topological completeness proofs. The journal of symbolic logic, vol. 23 no. 4 , pp. 369–388. [REVIEW]Joan Rand Moschovakis - 1967 - Journal of Symbolic Logic 32 (2):283-283.
  31.  32
    Patients' Choices for Return of Exome Sequencing Results to Relatives in the Event of Their Death.Laura M. Amendola, Martha Horike-Pyne, Susan B. Trinidad, Stephanie M. Fullerton, Barbara J. Evans, Wylie Burke & Gail P. Jarvik - 2015 - Journal of Law, Medicine and Ethics 43 (3):476-485.
    The informed consent process for genetic testing does not commonly address preferences regarding disclosure of results in the event of the patient's death. Adults being tested for familial colorectal cancer were asked whether they want their exome sequencing results disclosed to another person in the event of their death prior to receiving the results. Of 78 participants, 92% designated an individual and 8% declined to. Further research will help refine practices for informed consent.
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  32.  37
    James sequences and Dependent Choices.Marianne Morillon - 2005 - Mathematical Logic Quarterly 51 (2):171-186.
    We prove James's sequential characterization of reflexivity in set-theory ZF + DC, where DC is the axiom of Dependent Choices. In turn, James's criterion implies that every infinite set is Dedekind-infinite, whence it is not provable in ZF. Our proof in ZF + DC of James' criterion leads us to various notions of reflexivity which are equivalent in ZFC but are not equivalent in ZF. We also show that the weak compactness of the closed unit ball of a reflexive space (...)
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  33.  37
    Patient Choice and Preventive Genomic Sequencing—More Trouble Upstream.Søren Holm & Thomas Ploug - 2015 - American Journal of Bioethics 15 (7):24-26.
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  34.  23
    Resistance to extinction following sequences of partial and continuous reinforcement in a human choice task.Sherwin B. Cotler & John E. Nygaard - 1969 - Journal of Experimental Psychology 81 (2):270.
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  35.  16
    A Classical Modal Theory of Lawless Sequences.Ethan Brauer - 2023 - Bulletin of Symbolic Logic 29 (3):406-452.
    Free choice sequences play a key role in the intuitionistic theory of the continuum and especially in the theorems of intuitionistic analysis that conflict with classical analysis, leading many classical mathematicians to reject the concept of a free choice sequence. By treating free choice sequences as potentially infinite objects, however, they can be comfortably situated alongside classical analysis, allowing a rapprochement of these two mathematical traditions. Building on recent work on the modal analysis of potential infinity, (...)
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  36.  27
    The Continuing Evolution of Ethical Standards for Genomic Sequencing in Clinical Care: Restoring Patient Choice.Susan M. Wolf - 2017 - Journal of Law, Medicine and Ethics 45 (3):333-340.
    Developing ethical standards for clinical use of large-scale genome and exome sequencing has proven challenging, in part due to the inevitability of incidental or secondary findings. Policy of the American College of Medical Genetics and Genomics has evolved but remains problematic. In 2013, ACMG issued policy recommending mandatory analysis of 56 extra genes whenever sequencing was ordered for any indication, in order to ascertain positive findings in pathogenic and actionable genes. Widespread objection yielded a 2014 amendment allowing patients to opt-out (...)
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  37.  30
    Observations on sequences of choices made at five successive choice points.Malcolm G. Preston & Pearl M. Zeid - 1943 - Journal of Experimental Psychology 32 (4):275.
  38. Online choice and hierarchical representation of sequences.Hl Roitblat, Tg Bever, He Harley & D. Helweg - 1988 - Bulletin of the Psychonomic Society 26 (6):508-508.
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  39.  53
    Looking for Trouble: Preventive Genomic Sequencing in the General Population and the Role of Patient Choice.Gabriel Lázaro-Muñoz, John M. Conley, Arlene M. Davis, Marcia Van Riper, Rebecca L. Walker & Eric T. Juengst - 2015 - American Journal of Bioethics 15 (7):3-14.
    Advances in genomics have led to calls for developing population-based preventive genomic sequencing programs with the goal of identifying genetic health risks in adults without known risk factors. One critical issue for minimizing the harms and maximizing the benefits of PGS is determining the kind and degree of control individuals should have over the generation, use, and handling of their genomic information. In this article we examine whether PGS programs should offer individuals the opportunity to selectively opt out of the (...)
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  40.  28
    Realizing Brouwer's sequences.Richard E. Vesley - 1996 - Annals of Pure and Applied Logic 81 (1-3):25-74.
    When Kleene extended his recursive realizability interpretation from intuitionistic arithmetic to analysis, he was forced to use more than recursive functions to interpret sequences and conditional constructions. In fact, he used what classically appears to be the full continuum. We describe here a generalization to higher type of Kleene's realizability, one case of which, -realizability, uses general recursive functions throughout, both to realize theorems and to interpret choice sequences. -realizability validates a version of the bar theorem and the usual (...)
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  41.  14
    Effects of sample-specific ratios on free-choice matching-order sequences.Richard Pisacreta & Jeffrey Rautio - 1984 - Bulletin of the Psychonomic Society 22 (3):244-247.
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  42.  31
    Response to Open Peer Commentaries on “Looking for Trouble: Preventive Genomic Sequencing in the General Population and the Role of Patient Choice”.Gabriel Lázaro-Muñoz, John M. Conley, Arlene M. Davis, Marcia Van Riper, Rebecca L. Walker & Eric T. Juengst - 2015 - American Journal of Bioethics 15 (12):6-9.
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  43.  29
    Predicting Outcomes in a Sequence of Binary Events: Belief Updating and Gambler's Fallacy Reasoning.Kariyushi Rao & Reid Hastie - 2023 - Cognitive Science 47 (1):e13211.
    Beliefs like the Gambler's Fallacy and the Hot Hand have interested cognitive scientists, economists, and philosophers for centuries. We propose that these judgment patterns arise from the observer's mental models of the sequence-generating mechanism, moderated by the strength of belief in an a priori base rate. In six behavioral experiments, participants observed one of three mechanisms generating sequences of eight binary events: a random mechanical device, an intentional goal-directed actor, and a financial market. We systematically manipulated participants’ beliefs about (...)
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  44.  21
    Factorials and the finite sequences of sets.Nattapon Sonpanow & Pimpen Vejjajiva - 2019 - Mathematical Logic Quarterly 65 (1):116-120.
    We write for the cardinality of the set of finite sequences of a set which is of cardinality. With the Axiom of Choice (), for every infinite cardinal where is the cardinality of the permutations on a set which is of cardinality. In this paper, we show that “ for every cardinal ” is provable in and this is the best possible result in the absence of. Similar results are also obtained for : the cardinality of the set of (...)
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  45.  85
    Dynamic Choice Mechanisms.Ludwig von Auer - 1999 - Theory and Decision 46 (3):295-312.
    A dynamic choice mechanism (e.g. sophisticated choice) is a rule transforming a sequence of orderings into actual choices. The dynamic choice literature analysing such rules is restricted to the case of strict preferences. The present paper allows also for weak preferences. This generalisation is necessary since in dynamic utility models decision makers are typically endowed with orderings which can be represented by continuous utility functions. Such a representation, however, requires the orderings to be a weak ordering. (...)
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  46.  30
    The permutations with N non-fixed points and the sequences with length N of a set.Jukkrid Nuntasri & Pimpen Vejjajiva - 2024 - Journal of Symbolic Logic 89 (3):1067-1076.
    We write $\mathcal {S}_n(A)$ for the set of permutations of a set A with n non-fixed points and $\mathrm {{seq}}^{1-1}_n(A)$ for the set of one-to-one sequences of elements of A with length n where n is a natural number greater than $1$. With the Axiom of Choice, $|\mathcal {S}_n(A)|$ and $|\mathrm {{seq}}^{1-1}_n(A)|$ are equal for all infinite sets A. Among our results, we show, in ZF, that $|\mathcal {S}_n(A)|\leq |\mathrm {{seq}}^{1-1}_n(A)|$ for any infinite set A if ${\mathrm {AC}}_{\leq n}$ (...)
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  47.  51
    Cofinally Invariant Sequences and Revision.Edoardo Rivello - 2015 - Studia Logica 103 (3):599-622.
    Revision sequences are a kind of transfinite sequences which were introduced by Herzberger and Gupta in 1982 as the main mathematical tool for developing their respective revision theories of truth. We generalise revision sequences to the notion of cofinally invariant sequences, showing that several known facts about Herzberger’s and Gupta’s theories also hold for this more abstract kind of sequences and providing new and more informative proofs of the old results.
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  48.  47
    Does Presentation Order Impact Choice After Delay?Jonah Berger - 2016 - Topics in Cognitive Science 8 (3):670-684.
    Options are often presented incidentally in a sequence, but does serial position impact choice after delay, and if so, how? We address this question in a consequential real-world choice domain. Using 25 years of citation data, and a unique identification strategy, we examine the relationship between article order and citation count. Results indicate that mere serial position affects the prominence that research achieves: Earlier-listed articles receive more citations. Furthermore, our identification strategy allows us to cast doubt on (...)
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  49.  20
    Pigeonhole and Choice Principles.Wolfgang Degen - 2000 - Mathematical Logic Quarterly 46 (3):313-334.
    We shall investigate certain set-theoretic pigeonhole principles which arise as generalizations of the usual pigeonhole principle; and we shall show that many of them are equivalent to full AC. We discuss also several restricted cases and variations of those principles and relate them to restricted choice principles. In this sense the pigeonhole principle is a rich source of weak choice principles. It is shown that certain sequences of restricted pigeonhole principles form implicational hierarchies with respect to ZF. We (...)
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  50.  10
    The Definability of the Extender Sequence From In.Farmer Schlutzenberg - 2024 - Journal of Symbolic Logic 89 (2):427-459.
    Let M be a short extender mouse. We prove that if $E\in M$ and $M\models $ “E is a countably complete short extender whose support is a cardinal $\theta $ and $\mathcal {H}_\theta \subseteq \mathrm {Ult}(V,E)$ ”, then E is in the extender sequence $\mathbb {E}^M$ of M. We also prove other related facts, and use them to establish that if $\kappa $ is an uncountable cardinal of M and $\kappa ^{+M}$ exists in M then $(\mathcal {H}_{\kappa ^+})^M$ satisfies (...)
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