14 found
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Frederik Herzberg [12]Frederik S. Herzberg [2]
  1.  9
    Minimal Axiomatic Frameworks for Definable Hyperreals with Transfer.Frederik S. Herzberg, Vladimir Kanovei, Mikhail Katz & Vassily Lyubetsky - 2018 - Journal of Symbolic Logic 83 (1):385-391.
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  2.  52
    The Consistency of Probabilistic Regresses. A Reply to Jeanne Peijnenburg and David Atkinson.Frederik Herzberg - 2010 - Studia Logica 94 (3):331-345.
    In a recent paper, Jeanne Peijnenburg and David Atkinson [ Studia Logica, 89:333-341 ] have challenged the foundationalist rejection of infinitism by giving an example of an infinite, yet explicitly solvable regress of probabilistic justification. So far, however, there has been no criterion for the consistency of infinite probabilistic regresses, and in particular, foundationalists might still question the consistency of the solvable regress proposed by Peijnenburg and Atkinson.
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  3.  53
    Impossibility Results for Infinite-Electorate Abstract Aggregation Rules.Frederik Herzberg & Daniel Eckert - 2012 - Journal of Philosophical Logic 41 (1):273-286.
    Following Lauwers and Van Liedekerke (1995), this paper explores in a model-theoretic framework the relation between Arrovian aggregation rules and ultraproducts, in order to investigate a source of impossibility results for the case of an infinite number of individuals and an aggregation rule based on a free ultrafilter of decisive coalitions.
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  4.  67
    The Consistency of Probabilistic Regresses: Some Implications for Epistemological Infinitism. [REVIEW]Frederik Herzberg - 2013 - Erkenntnis 78 (2):371-382.
    This note employs the recently established consistency theorem for infinite regresses of probabilistic justification (Herzberg in Stud Log 94(3):331–345, 2010) to address some of the better-known objections to epistemological infinitism. In addition, another proof for that consistency theorem is given; the new derivation no longer employs nonstandard analysis, but utilises the Daniell–Kolmogorov theorem.
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  5.  17
    A Definable Nonstandard Enlargement.Frederik Herzberg - 2008 - Mathematical Logic Quarterly 54 (2):167-175.
    This article establishes the existence of a definable , countably saturated nonstandard enlargement of the superstructure over the reals. This nonstandard universe is obtained as the union of an inductive chain of bounded ultrapowers . The underlying ultrafilter is the one constructed by Kanovei and Shelah [10].
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  6. The Dialectics of Infinitism and Coherentism: Inferential Justification Versus Holism and Coherence.Frederik Herzberg - 2014 - Synthese 191 (4):701-723.
    This paper formally explores the common ground between mild versions of epistemological coherentism and infinitism; it proposes—and argues for—a hybrid, coherentist–infinitist account of epistemic justification. First, the epistemological regress argument and its relation to the classical taxonomy regarding epistemic justification—of foundationalism, infinitism and coherentism—is reviewed. We then recall recent results proving that an influential argument against infinite regresses of justification, which alleges their incoherence on account of probabilistic inconsistency, cannot be maintained. Furthermore, we prove that the Principle of Inferential Justification (...)
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  7.  34
    Aggregating Infinitely Many Probability Measures.Frederik Herzberg - 2015 - Theory and Decision 78 (2):319-337.
    The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference and judgment (...)
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  8.  27
    Internal Laws of Probability, Generalized Likelihoods and Lewis' Infinitesimal Chances–a Response to Adam Elga.Frederik Herzberg - 2007 - British Journal for the Philosophy of Science 58 (1):25-43.
    The rejection of an infinitesimal solution to the zero-fit problem by A. Elga ([2004]) does not seem to appreciate the opportunities provided by the use of internal finitely-additive probability measures. Indeed, internal laws of probability can be used to find a satisfactory infinitesimal answer to many zero-fit problems, not only to the one suggested by Elga, but also to the Markov chain (that is, discrete and memory-less) models of reality. Moreover, the generalization of likelihoods that Elga has in mind is (...)
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  9.  20
    A Note on “The No Alternatives Argument” by Richard Dawid, Stephan Hartmann and Jan Sprenger.Frederik Herzberg - 2014 - European Journal for Philosophy of Science 4 (3):375-384.
    The defence of The No Alternatives Argument in a recent paper by R. Dawid, S. Hartmann and J. Sprenger rests on the assumption that the number of acceptable alternatives to a scientific hypothesis is independent of the complexity of the scientific problem. This note proves a generalisation of the main theorem by Dawid, Hartmann and Sprenger, where this independence assumption is no longer necessary. Some of the other assumptions are also discussed, and the limitations of the no-alternatives argument are explored.
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  10.  11
    Addendum to “A Definable Nonstandard Enlargement”.Frederik Herzberg - 2008 - Mathematical Logic Quarterly 54 (6):666-667.
    Łoś's theorem for bounded D -ultrapowers, D being the ultrafilter introduced by Kanovei and Shelah [4], is established.
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  11. Hyperreal Expected Utilities and Pascal's Wager.Frederik Herzberg - 2011 - Logique Et Analyse 54 (213):69-108.
     
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  12.  39
    A Graded Bayesian Coherence Notion.Frederik Herzberg - 2014 - Erkenntnis 79 (4):843-869.
    Coherence is a key concept in many accounts of epistemic justification within ‘traditional’ analytic epistemology. Within formal epistemology, too, there is a substantial body of research on coherence measures. However, there has been surprisingly little interaction between the two bodies of literature. The reason is that the existing formal literature on coherence measure operates with a notion of belief system that is very different from—what we argue is—a natural Bayesian formalisation of the concept of belief system from traditional epistemology. Therefore, (...)
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  13.  15
    Arrovian Aggregation of Generalised Expected-Utility Preferences: Possibility Results by Means of Model Theory.Frederik Herzberg - 2018 - Studia Logica 106 (5):947-967.
    Cerreia-Vioglio et al. :341–375, 2011) have proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences—and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory, is employed.
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  14.  9
    The Birth of Social Choice Theory From the Spirit of Mathematical Logic: Arrow’s Theorem in the Framework of Model Theory.Daniel Eckert & Frederik S. Herzberg - 2018 - Studia Logica 106 (5):893-911.
    Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...)
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