Results for 'Bolzano Weierstrass theorem'

893 found
Order:
  1. Linguistic Functions.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of the linguistic continuum we (...)
    Download  
     
    Export citation  
     
    Bookmark  
  2. Szemerédi’s theorem: An exploration of impurity, explanation, and content.Patrick J. Ryan - 2023 - Review of Symbolic Logic 16 (3):700-739.
    In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  3. Non-archimedean analysis on the extended hyperreal line *R_d and the solution of some very old transcendence conjectures over the field Q.Jaykov Foukzon - 2015 - Advances in Pure Mathematics 5 (10):587-628.
    In 1980 F. Wattenberg constructed the Dedekind completiond of the Robinson non-archimedean field  and established basic algebraic properties of d [6]. In 1985 H. Gonshor established further fundamental properties of d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completiond in transcendental number theory were considered. We dealing using set theory ZFC  (-model of ZFC).Given (...)
    Download  
     
    Export citation  
     
    Bookmark  
  4. Set Theory INC_{∞^{#}}^{#} Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part III).Hyper inductive definitions. Application in transcendental number theory.Jaykov Foukzon - 2021 - Journal of Advances in Mathematics and Computer Science 36 (8):43.
    Main results are: (i) number e^{e} is transcendental; (ii) the both numbers e+π and e-π are irrational.
    Download  
     
    Export citation  
     
    Bookmark  
  5. Dimensional theoretical properties of some affine dynamical systems.Jörg Neunhäuserer - 1999 - Dissertation,
    In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  6. Zu Bolzanos Wahrscheinlichkeitslehre.Georg J. W. Dorn - 1987 - Philosophia Naturalis 24 (4):423–441.
    Bolzano hat seine Wahrscheinlichkeitslehre in 15 Punkten im § 14 des zweiten Teils seiner Religionswissenschaft sowie in 20 Punkten im § 161 des zweiten Bandes seiner Wissenschaftslehre niedergelegt. (Ich verweise auf die Religionswissenschaft mit 'RW II', auf die Wissenschaftslehre mit 'WL II'.) In der RW II (vgl. p. 37) ist seine Wahrscheinlichkeitslehre eingebettet in seine Ausführungen "Über die Natur der historischen Erkenntniß, besonders in Hinsicht auf Wunder", und die Lehrsätze, die er dort zusammenstellt, dienen dem ausdrücklichen Zweck, mit mathematischem (...)
    Download  
     
    Export citation  
     
    Bookmark  
  7. Kant, Bolzano, and the Formality of Logic.Nicholas Stang - 2014 - In Sandra Lapointe & Clinton Tolley (eds.), The New Anti-Kant. pp. 193–234.
    In §12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that “In the new logic textbooks one reads almost constantly that ‘in logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal science’” (WL §12, 46).1 The sentence Bolzano quotes is his own summary of others’ philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  8. The Reasons Aggregation Theorem.Ralph Wedgwood - 2022 - Oxford Studies in Normative Ethics 12:127-148.
    Often, when one faces a choice between alternative actions, there are reasons both for and against each alternative. On one way of understanding these words, what one “ought to do all things considered (ATC)” is determined by the totality of these reasons. So, these reasons can somehow be “combined” or “aggregated” to yield an ATC verdict on these alternatives. First, various assumptions about this sort of aggregation of reasons are articulated. Then it is shown that these assumptions allow for the (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  9. On Bolzano’s Alleged Explicativism.Jacques Dubucs & Sandra Lapointe - 2006 - Synthese 150 (2):229-246.
    Bolzano was the first to establish an explicit distinction between the deductive methods that allow us to recognise the certainty of a given truth and those that provide its objective ground. His conception of the relation between what we, in this paper, call "subjective consequence", i.e., the relation from epistemic reason to consequence and "objective consequence", i.e., grounding however allows for an interpretation according to which Bolzano advocates an "explicativist" conception of proof: proofs par excellence are those that (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  10. Bolzano’s Mathematical Infinite.Anna Bellomo & Guillaume Massas - 2021 - Review of Symbolic Logic:1-55.
    Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  11. Bolzano versus Kant: mathematics as a scientia universalis.Paola Cantù - 2011 - Philosophical Papers Dedicated to Kevin Mulligan.
    The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  12. Representation theorems and the foundations of decision theory.Christopher J. G. Meacham & Jonathan Weisberg - 2011 - Australasian Journal of Philosophy 89 (4):641 - 663.
    Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...)
    Download  
     
    Export citation  
     
    Bookmark   70 citations  
  13. Bolzano' s Theory of Science.Kenneth Archer - 2008 - Dissertation, Catholic University of America
    This thesis presents a Bolzano whose genius resulted not from his freedom from powerful philosophical influences, but precisely from his response to the powerful philosophical influences of his day. Chief amongst these were the voices engaged in debate about the nature of science. It was precisely Bolzano's commanding synthesis of the views of those advocating progress through mathematical physics with the views of those advocating a classical model of a science as the study of causes that set the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  14. Jury Theorems.Franz Dietrich & Kai Spiekermann - 2021 - The Stanford Encyclopedia of Philosophy.
    Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans across various disciplines such (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  15. Bolzano a priori knowledge, and the Classical Model of Science.Sandra Lapointe - 2010 - Synthese 174 (2):263-281.
    This paper is aimed at understanding one central aspect of Bolzano's views on deductive knowledge: what it means for a proposition and for a term to be known a priori. I argue that, for Bolzano, a priori knowledge is knowledge by virtue of meaning and that Bolzano has substantial views about meaning and what it is to know the latter. In particular, Bolzano believes that meaning is determined by implicit definition, i.e. the fundamental propositions in a (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  16. Incompleteness and Computability: An Open Introduction to Gödel's Theorems.Richard Zach - 2019 - Open Logic Project.
    Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  17. Jury Theorems.Franz Dietrich & Kai Spiekermann - 2019 - In M. Fricker, N. J. L. L. Pedersen, D. Henderson & P. J. Graham (eds.), The Routledge Handbook of Social Epistemology. Routledge.
    We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  18. Jury Theorems for Peer Review.Marcus Arvan, Liam Kofi Bright & Remco Heesen - forthcoming - British Journal for the Philosophy of Science.
    Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  19. Representation Theorems and Radical Interpretation.Edward J. R. Elliott - manuscript
    This paper begins with a puzzle regarding Lewis' theory of radical interpretation. On the one hand, Lewis convincingly argued that the facts about an agent's sensory evidence and choices will always underdetermine the facts about her beliefs and desires. On the other hand, we have several representation theorems—such as those of (Ramsey 1931) and (Savage 1954)—that are widely taken to show that if an agent's choices satisfy certain constraints, then those choices can suffice to determine her beliefs and desires. In (...)
    Download  
     
    Export citation  
     
    Bookmark  
  20. Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
    Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  21. A Representation Theorem for Frequently Irrational Agents.Edward Elliott - 2017 - Journal of Philosophical Logic 46 (5):467-506.
    The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  22.  96
    Theorem proving in artificial neural networks: new frontiers in mathematical AI.Markus Pantsar - 2024 - European Journal for Philosophy of Science 14 (1):1-22.
    Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  23. A Kantian Response to Bolzano’s Critique of Kant’s Analytic-Synthetic Distinction.Nicholas F. Stang - 2012 - Grazer Philosophische Studien 85 (1):33-61.
    One of Bolzano’s objections to Kant’s way of drawing the analytic-synthetic distinction is that it only applies to judgments within a narrow range of syntactic forms, namely, universal affirmative judgments. According to Bolzano, Kant cannot account for judgments of other syntactic forms that, intuitively, are analytic. A recent paper by Ian Proops also attributes to Kant the view that analytic judgments beyond a limited range of syntactic forms are impossible. I argue that, correctly understood, Kant’s conception of analyticity (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  24. Tense Logic and Ontology of Time.Avril Styrman - 2021 - Emilio M. Sanfilippo Et Al, Eds., Proceedings of FOUST 2021: 5th Workshop on Foundational Ontology, Held at JOWO 2021: Episode VII The Bolzano Summer of Knowledge, September 11–18, 2021, Bolzano, Italy, CEURWS, Vol. 2969, 2021.
    This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are developed, and mapped to (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  25. Theorems and Models in Political Theory: An Application to Pettit on Popular Control.Sean Ingham - 2015 - The Good Society 24 (1):98-117.
    Pettit (2012) presents a model of popular control over government, according to which it consists in the government being subject to those policy-making norms that everyone accepts. In this paper, I provide a formal statement of this interpretation of popular control, which illuminates its relationship to other interpretations of the idea with which it is easily conflated, and which gives rise to a theorem, similar to the famous Gibbard-Satterthwaite theorem. The theorem states that if government policy is (...)
    Download  
     
    Export citation  
     
    Bookmark  
  26. Bell’s Theorem, Quantum Probabilities, and Superdeterminism.Eddy Keming Chen - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge.
    In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  27. Theoremizing Yablo's Paradox.Ahmad Karimi & Saeed Salehi - manuscript
    To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these (...)
    Download  
     
    Export citation  
     
    Bookmark  
  28. Arrow's theorem in judgment aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.
    In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we (...)
    Download  
     
    Export citation  
     
    Bookmark   83 citations  
  29. Agreement theorems for self-locating belief.Michael Caie - 2016 - Review of Symbolic Logic 9 (2):380-407.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  30. Collections in Early Bolzano.Stefania Centrone & Mark Siebel - 2018 - Journal for the History of Analytical Philosophy 6 (7).
    There are quite a few studies on late Bolzano’s notion of a collection (Inbegriff). We try to broaden the perspective by introducing the forerunner of collections in Bolzano’s early writings, namely the entities referred to by expressions with the technical term ‘et’. Special emphasis is laid on the question whether these entities are set-theoretical or mereological plenties. Moreover, similarities and differences to Bolzano’s mature conception are pointed out.
    Download  
     
    Export citation  
     
    Bookmark  
  31. Some theorems on the expressive limitations of modal languages.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):13 - 26.
    Download  
     
    Export citation  
     
    Bookmark   35 citations  
  32. The Beyträge at 200: Bolzano's quiet revolution in the philosophy of mathematics.Jan Sebestik & Paul Rusnock - 2013 - Journal for the History of Analytical Philosophy 1 (8).
    This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  33. Stefan Roski, Bolzano’s Conception of Grounding. [REVIEW]Petter Sandstad - 2017 - Phenomenological Reviews.
    I review Stefan Roski's "Bolzano's Conception of Grounding".
    Download  
     
    Export citation  
     
    Bookmark  
  34. Making Theorem-Proving in Modal Logic Easy.Paul Needham - 2009 - In Lars-Göran Johansson, Jan Österberg & Rysiek Śliwiński (eds.), Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel. Uppsala, Sverige: pp. 187-202.
    A system for the modal logic K furnishes a simple mechanical process for proving theorems.
    Download  
     
    Export citation  
     
    Bookmark  
  35. The Craig interpolation theorem for prepositional logics with strong negation.Valentin Goranko - 1985 - Studia Logica 44 (3):291 - 317.
    This paper deals with, prepositional calculi with strong negation (N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  36. An impossibility theorem for amalgamating evidence.Jacob Stegenga - 2013 - Synthese 190 (12):2391-2411.
    Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  37. The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism.Mahmoud Jalloh - forthcoming - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics. Oxford: Oxford University Press.
    In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are (...)
    Download  
     
    Export citation  
     
    Bookmark  
  38. Gegenstandslose Vorstellungen: Bolzano und seine Kritiker.Guillaume Fréchette - 2010 - Sankt Augustin: Academia Verlag.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  39. The Kochen - Specker theorem in quantum mechanics: a philosophical comment (part 2).Vasil Penchev - 2013 - Philosophical Alternatives 22 (3):74-83.
    The text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum mechanics (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  40. Fermat’s Last Theorem Proved by Induction (and Accompanied by a Philosophical Comment).Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (8):1-8.
    A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  41. Oversights in the Respective Theorems of von Neumann and Bell are Homologous.Joy Christian - manuscript
    We show that the respective oversights in the von Neumann's general theorem against all hidden variable theories and Bell's theorem against their local-realistic counterparts are homologous. When latter oversight is rectified, the bounds on the CHSH correlator work out to be ±2√2 instead of ±2.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  42. Bell's Theorem Begs the Question.Joy Christian - manuscript
    I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument (...)
    Download  
     
    Export citation  
     
    Bookmark  
  43. Judgment aggregation: (Im)possibility theorems.Franz Dietrich - 2006 - Journal of Economic Theory 1 (126):286-298.
    The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore (...)
    Download  
     
    Export citation  
     
    Bookmark   75 citations  
  44. The impartial observer theorem of social ethics.Philippe Mongin - 2001 - Economics and Philosophy 17 (2):147-179.
    Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.
    Download  
     
    Export citation  
     
    Bookmark   21 citations  
  45. The Kochen - Specker theorem in quantum mechanics: a philosophical comment (part 1).Vasil Penchev - 2013 - Philosophical Alternatives 22 (1):67-77.
    Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  46. An Impossibility Theorem for Base Rate Tracking and Equalized Odds.Rush T. Stewart, Benjamin Eva, Shanna Slank & Reuben Stern - forthcoming - Analysis.
    There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby (...)
    Download  
     
    Export citation  
     
    Bookmark  
  47. On the Martingale Representation Theorem and on Approximate Hedging a Contingent Claim in the Minimum Deviation Square Criterion.Nguyen Van Huu & Quan-Hoang Vuong - 2007 - In Ta-Tsien Li Rolf Jeltsch (ed.), Some Topics in Industrial and Applied Mathematics. World Scientific. pp. 134-151.
    In this work we consider the problem of the approximate hedging of a contingent claim in the minimum mean square deviation criterion. A theorem on martingale representation in case of discrete time and an application of the result for semi-continuous market model are also given.
    Download  
     
    Export citation  
     
    Bookmark  
  48. Quantum no-go theorems and consciousness.Danko Georgiev - 2013 - Axiomathes 23 (4):683-695.
    Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the standard Hilbert (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  49. Why Arrow's Theorem Matters for Political Theory Even If Preference Cycles Never Occur.Sean Ingham - forthcoming - Public Choice.
    Riker (1982) famously argued that Arrow’s impossibility theorem undermined the logical foundations of “populism”, the view that in a democracy, laws and policies ought to express “the will of the people”. In response, his critics have questioned the use of Arrow’s theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I argue (...)
    Download  
     
    Export citation  
     
    Bookmark  
  50. The multiple-computations theorem and the physics of singling out a computation.Orly Shenker & Meir Hemmo - 2022 - The Monist 105 (1):175-193.
    The problem of multiple-computations discovered by Hilary Putnam presents a deep difficulty for functionalism (of all sorts, computational and causal). We describe in out- line why Putnam’s result, and likewise the more restricted result we call the Multiple- Computations Theorem, are in fact theorems of statistical mechanics. We show why the mere interaction of a computing system with its environment cannot single out a computation as the preferred one amongst the many computations implemented by the system. We explain why (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
1 — 50 / 893