Results for 'Formalism'

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  1.  10
    Formalism.Michael Detlefsen - 2005 - In Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 236--317.
    A comprehensive historical overview of formalist ideas in the philosophy of mathematics.
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  2.  44
    Why Did Weyl Think That Formalism's Victory Against Intuitionism Entails a Defeat of Pure Phenomenology?Iulian D. Toader - 2014 - History and Philosophy of Logic 35 (2):198-208.
    It has been contended that it is unjustified to believe, as Weyl did, that formalism's victory against intuitionism entails a defeat of the phenomenological approach to mathematics. The reason for this contention, recently put forth by Paolo Mancosu and Thomas Ryckman, is that, unlike intuitionistic Anschauung, phenomenological intuition could ground classical mathematics. I argue that this indicates a misinterpretation of Weyl's view, for he did not take formalism to prevail over intuitionism with respect to grounding classical mathematics. I (...)
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  3.  83
    A Critique of Moderate Formalism.Simon Fokt - 2013 - Estetika 50 (1):41-52.
    Moderate formalism is the view that all artworks which have aesthetic properties have formal aesthetic properties, and some but not all of those works also have non-formal aesthetic properties. Nick Zangwill develops this view in his Metaphysics of Beauty after having argued against its alternatives – extreme formalism and anti-formalism. This article reviews his arguments against the rivals of moderate formalism, and argues that the rejection of anti-formalism is unjustified. Zangwill does not succeed in proving (...)
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  4.  30
    Form and Freedom: The Kantian Ethos of Musical Formalism.Hanne Appelqvist - 2011 - Nordic Journal of Aesthetics 22 (22):75-88.
    Musical formalism is often portrayed as the enemy of artistic freedom. Its main representative, Eduard Hanslick, is seen as a purist who, by emphasizing musical rules, aims at restricting music criticism and even musical practices themselves. It may also seem that formalism is depriving music of its ability to have moral significance, as the semantic connection to the extramusical is denied by the formalistic view. In my paper, I defend formalism by placing Hanslick’s argument in a Kantian (...)
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  5.  77
    The Classical Trinity and Kant's Aesthetic Formalism.Jennifer A. McMahon - 2010 - Critical Horizons 11 (3):419-441.
    I identify two mutually exclusive notions of formalism in Kant’s Critique of Aesthetic Judgement: a thin concept of aesthetic formalism and a thick concept of aesthetic formalism. Arguably there is textual support for both concepts in Kant’s third critique. I offer interpretations of three key elements in the Critique of Aesthetic Judgement which support a thick formalism. The three key elements are: Harmony of the Faculties, Aesthetic Ideas and Sensus Communis. I interpret these concepts in relation (...)
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  6.  9
    From Formalism to Psychology: Metaphilosophical Studies in Wilfrid Sellars's Early Works.Peter Olen - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):24-63.
    When discussing Wilfrid Sellars’s philosophy, very little work has been done to offer a developmental account of his systematic views. More often than not, Sellars’s complex views are presented in a systematic and holistic fashion that ignores any periodization of his work. I argue that there is a metaphilosophical shift in Sellars’s early philosophy that results in substantive changes to his conception of language, linguistic rules, and normativity. Specifically, I claim that Sellars’s shift from a formalist metaphilosophy to one more (...)
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  7.  26
    Husserl Between Frege's Logicism And Hilbert's Formalism.Ulrich Majer - 2009 - The Baltic International Yearbook of Cognition, Logic and Communication 4 (1):4.
    The traditional view regarding the philosophy of mathematics in the twentieth century is the dogma of three schools: Logicism, Intuitionism and Formalism. The problem with this dogma is not, at least not first and foremost, that it is wrong, but that it is biased and essentially incomplete. 'Biased' because it was formulated by one of the involved parties, namely the logical empiricists - if I see it right - in order to make their own position look more agreeable by (...)
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  8.  52
    Musical Formalism and Political Performances.Jonathan A. Neufeld - 2009 - Contemporary Aesthetics 7.
    Musical formalism, which strictly limits the type of thing any description of the music can tell us, is ill-equipped to account for contemporary performance practice. If performative interpretations are in a position to tell us something about musical works—that is if performance is a kind of description, as Peter Kivy argues—then we have to loosen the restrictions on notions of musical relevance to make sense of performance. I argue that musical formalism, which strictly limits the type of thing (...)
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  9.  6
    The Formalism for Energy Changing Rate of an Accelerated Atom Coupled with Electromagnetic Vacuum Fluctuations.Anwei Zhang - 2016 - Foundations of Physics 46 (9):1199-1207.
    The structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom in interaction with a quantum electromagnetic field is investigated. Our main purpose is to rewrite the formalism in Zhu et al. and to deduce the general expressions of the Einstein A coefficients of an atom on an arbitrary stationary trajectory. The total rate of change of the energy and Einstein coefficients of the atom near a plate with finite temperature or (...)
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  10.  10
    Against Zangwill’s Extreme Formalism About Inorganic Nature.Min Xu & Guifang Deng - 2015 - Philosophia 43 (1):249-257.
    Extreme formalism is a radical and important position in the aesthetics of inorganic nature. Zangwill offers a new formulation of what formal aesthetic properties are, according to which a formal aesthetic property of a thing is an aesthetic property that is determined merely by its appearance properties. An appearance property of a thing is the way it seems if perceived under certain conditions. With the notion of formal aesthetic properties formulated as such, extreme formalism, the claim that all (...)
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  11.  13
    Curry's Formalism as Structuralism.Jonathan P. Seldin - 2011 - Logica Universalis 5 (1):91-100.
    In 1939, Curry proposed a philosophy of mathematics he called formalism. He made this proposal in two works originally written then, although one of them was not published until 1951. These are the two philosophical works for which Curry is known, and they have left a false impression of his views. In this article, I propose to clarify Curry’s views by referring to some of his later writings on the subject. I claim that Curry’s philosophy was not what is (...)
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  12.  19
    Receiving Newman. Formalism, Minimalism, and Their Philosophical Preconditions.Espen Dahl - 2012 - Nordic Journal of Aesthetics 23 (42).
    Despite the divide between American formalism and theoreticians of minimalism, Barnett Newman’s art received great acclaim from both schools of thought. Attempting to unearth the philosophical preconditions of this strange constellation, this article argues that the closeness between minimalism and formalism is due to their mutual reliance upon phenomenology and ordinary language philosophy. However, their proximity also conveys their distance, since they imply different interpretations and applications of the philosophical schools in question. Such theoretical differences shed light on (...)
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  13. ‘‘‘Hegel, Formalism, and Robert Turner’s Ceramic Art’.Kenneth R. Westphal - 1997 - Jahrbuch für Hegelforschung 3:259–283.
    Hegel’s aesthetic ideal is the perfect integration of form and content within a work of art. This ideal is incompatible with the predominant 20th-century principle of formalist criticism, that form is the sole important factor in a work of art. Although the formalist dichotomy between form and content has been criticized on philosophical grounds, that does not suffice to justify Hegel’s ideal. Justifying Hegel’s ideal requires detailed art criticism that shows how form and content are, and why they should be, (...)
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  14.  6
    Internet Websites Statistics Expressed in the Framework of the Ursell—Mayer Cluster Formalism.D. Bar - 2004 - Foundations of Physics 34 (8):1203-1223.
    We show that it is possible to generalize the Ursell–Mayer cluster formalism so that it may cover also the statistics of Internet websites. Our starting point is the introduction of an extra variable that is assumed to take account, as will be explained, of the nature of the Internet statistics. We then show, following the arguments in Mayer, that one may obtain a phase transition-like phenomena.
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  15. Aestheticism: Deep Formalism and the Emergence of Modernist Aesthetics.Michalle Gal - 2015 - Peter Lang.
    This book offers, for the first time in aesthetics, a comprehensive account of aestheticism of the 19<SUP>th</SUP> century as a philosophical theory of its own right. Taking philosophical and art-historical viewpoints, this cross-disciplinary book presents aestheticism as the foundational movement of modernist aesthetics of the 20<SUP>th</SUP> century. Emerging in the writings of the foremost aestheticists - Oscar Wilde, Walter Pater, James Whistler, and their formalist successors such as Clive Bell, Roger Fry, and Clement Greenberg - aestheticism offers a uniquely synthetic (...)
     
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  16. Badiou and the Consequences of Formalism.Paul Livingston - 2012 - Cosmos and History 8 (1):131-150.
    I consider the relationship of Badiou’s schematism of the event to critical thought following the linguistic turn as well as to the mathematical formalisms of set theory. In Being and Event, Badiou uses formal argumentation to support his sweeping rejection of the linguistic turn as well as much of contemporary critical thought. This rejection stems from his interpretation of set theory as barring thought from the 'One-All' of totality; but I argue that, by interpreting it differently, we can understand this (...)
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  17.  42
    Formalism and Interpretation in Quantum Theory.Alexander Wilce - 2010 - Foundations of Physics 40 (4):434-462.
    Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally (...)
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  18.  22
    Representing the Negotiation Process with a Rule-Based Formalism.Gregory E. Kersten, Wojtek Michalowski, Stan Matwin & Stan Szpakowicz - 1988 - Theory and Decision 25 (3):225-257.
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  19. Hilbert's Formalism.Michael Detlefsen - 1993 - Revue Internationale de Philosophie 47 (186):285-304.
    Various parallels between Kant's critical program and Hilbert's formalistic program for the philosophy of mathematics are considered.
     
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  20. Formalism and Psychological Explanation.John Heil - 1986 - Journal of Mind and Behavior 7 (1):1-10.
     
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  21.  2
    Open Systems’ Density Matrix Properties in a Time Coarsened Formalism.Robert Englman & Asher Yahalom - 2015 - Foundations of Physics 45 (6):673-690.
    The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties of the bath. It is also applicable when an open microscopic sub-system is coupled to another finite system. By use of a time-periodic minimal coupling model between these two (...)
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  22.  11
    Formalism and Marxism.Tony Bennett - 1979 - Methuen.
    Placing the work of key figures in context and addressing such issues as aesthetics, linguistics and the category of literature, form and function or literary ...
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  23.  13
    Dialogue, Rationality, Formalism. Interdisciplinary Works in Logic, Epistemology, Psychology and Linguistics.Manuel Rebuschi, Martine Batt, Gerhard Heinzmann, Franck Lihoreau, Michel Musiol & Alain Trognon (eds.) - forthcoming - Springer.
  24. An Interpretation of the Formalism of Quantum Mechanics in Terms of Epistemological Realism.Arthur Jabs - 1992 - British Journal for the Philosophy of Science 43 (3):405-421.
    We present an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. Elementary particles are considered as extended objects and nonlocal effects are included. The role of the new concepts in the problems of measurement and of the Einstein–Podolsky–Rosen correlations is described. Experiments to distinguish the proposed interpretation from the Copenhagen one (...)
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  25.  53
    A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices.Yehuda Rav - 2007 - Philosophia Mathematica 15 (3):291-320.
    In a recent article, Azzouni has argued in favor of a version of formalism according to which ordinary mathematical proofs indicate mechanically checkable derivations. This is taken to account for the quasi-universal agreement among mathematicians on the validity of their proofs. Here, the author subjects these claims to a critical examination, recalls the technical details about formalization and mechanical checking of proofs, and illustrates the main argument with aanalysis of examples. In the author's view, much of mathematical reasoning presents (...)
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  26.  27
    Tracking Down Gauge: An Ode to the Constrained Hamiltonian Formalism.John Earman - 2003 - In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press. pp. 140--62.
    Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the (...)
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  27.  33
    Formalism, Ontology and Methodology in Bohmian Mechanics.Darrin W. Belousek - 2003 - Foundations of Science 8 (2):109-172.
    The relationship between mathematical formalism, physical interpretation and epistemological appraisal in the practice of physical theorizing is considered in the context of Bohmian mechanics. After laying outthe formal mathematical postulates of thetheory and recovering the historical roots ofthe present debate over the meaning of Bohmianmechanics from the early debate over themeaning of Schrödinger's wave mechanics,several contemporary interpretations of Bohmianmechanics in the literature are discussed andcritiqued with respect to the aim of causalexplanation and an alternative interpretationis proposed. Throughout, the over-arching (...)
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  28.  1
    Formalism and Strategic Fouls.Eric Moore - 2017 - Journal of the Philosophy of Sport 44 (1):95-107.
    It is sometimes claimed that formalism and the logical incompatibility thesis together imply that fouls cannot be part of the game. Some philosophers think this proves that therefore strategic fouls are always morally wrong, but other philosophers think this result undermines formalism itself, since strategic fouls clearly are part of the game and are at least sometimes morally permissible. I show that formalism in fact does accommodate strategic fouls and that it is neutral about whether strategic fouls (...)
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  29.  33
    Density Formalism for Quantum Theory.Roderick I. Sutherland - 1998 - Foundations of Physics 28 (7):1157-1190.
    A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a picture of an external reality. The new formalism, developed first for the single-particle case, has the advantage of generalizing immediately to quantum field theory and to the description of relativistic phenomena such as particle creation and annihilation.
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  30.  83
    Idealization and Formalism in Bohr's Approach to Quantum Theory.Scott Tanona - 2004 - Philosophy of Science 71 (5):683-695.
    I reinterpret Bohr's attitude towards quantum mechanical formalism and its empirical content, based on his understanding of the correspondence principle and its approximate applicability. I suggest that Bohr understood complementarity as a limitation imposed by the commutation relations upon the applicability of the idealizations which had grounded the use of the correspondence principle. By discussing this interpretation against the contemporary background of discussions regarding “naïve realism” about operators (as observables), I suggest that a Bohrian view on the empirical content (...)
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  31. Feasible Aesthetic Formalism.Nick Zangwill - 1999 - Noûs 33 (4):610-629.
    Aesthetic Formalism has fallen on hard times. At best it receives unsympathetic discussion and swift rejection. At worst it is the object of abuse and derision. But I think that there is something to be said for it. In this paper, I shall try to find and secure the truth in formalism. I shall not try to defend formalism against all of the objections to it.1 Instead I shall articulate a moderate formalist view that draws on aesthetic0nonaesthetic (...)
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  32.  6
    Husserlian and Fichtean Leanings: Weyl on Logicism, Intuitionism, and Formalism.Norman Sieroka - 2009 - Philosophia Scientiae 13 (2):85-96.
    Around 1918 Hermann Weyl resisted the logicists’ attempt to reduce mathematics to logic and set theory. His philosophical points of reference were Husserl and Fichte. In the 1920s, Weyl distinguished between the position of these two philosophers and separated the conceptual affinity between intuitionism and phenomenology from the affinity between formalism and constructivism. Not long after Weyl had done so, Oskar Becker adopted a similar distinction. In contrast to the phenomenologist Becker, however, Weyl assumed the superiority of active Fichtean (...)
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  33. In Defence of Moderate Aesthetic Formalism.Nick Zangwill - 2000 - Philosophical Quarterly 50 (201):476-493.
    Most of the debate for and against aesthetic formalism in the twentieth century has been little more than a sequence of assertions, on both sides. But there is one discussion that stands out for its argumentative subtlety and depth, and that is Kendall Walton’s paper ‘Categories of Art’.1 In what follows I shall defend a certain version of formalism against the antiformalist arguments which Walton deploys. I want to show that while Walton’s arguments do indeed create insurmountable difficulties (...)
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  34.  18
    Truth Through Proof: A Formalist Foundation for Mathematics.Alan Weir - 2010 - Oxford University Press.
    Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.
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  35. The Purposiveness of Form: A Reading of Kant's Aesthetic Formalism.Rachel Zuckert - 2006 - Journal of the History of Philosophy 44 (4):599-622.
    Rachel Zuckert - The Purposiveness of Form: A Reading of Kant's Aesthetic Formalism - Journal of the History of Philosophy 44:4 Journal of the History of Philosophy 44.4 599-622 Muse Search Journals This Journal Contents The Purposiveness of Form: A Reading of Kant's Aesthetic Formalism Rachel Zuckert In the "critique of aesthetic judgment," Kant claims that when we find an object beautiful, we are appreciating its "purposive form." Many of Kant's readers have found this claim one of his (...)
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  36.  43
    Contextualizing Concepts Using a Mathematical Generalization of the Quantum Formalism.Liane Gabora & Diederik Aerts - 2002 - Philosophical Explorations.
    We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal (...)
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  37. Review of Susan Haack, Deviant Logic, Fuzzy Logic: Beyond the Formalism[REVIEW]Achille C. Varzi - 1998 - Philosophical Review 107 (3):468-471.
    Book information: Deviant Logic, Fuzzy Logic: Beyond The Formalism. By SUSAN HAACK. Chicago, Ill.: University of Chicago Press, 1996. Pp. xxvi, 291.
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  38.  93
    In Defence of Extreme Formalism About Inorganic Nature: Reply to Parsons.Nick Zangwill - 2005 - British Journal of Aesthetics 45 (2):185-191.
    I defend extreme formalism about inorganic nature against arguments put forward by Glenn Parsons. I begin by laying out the general issue over aesthetic formalism, and I describe the position of extreme formalism about inorganic nature. I then reconsider -Ronald Hepburn's beach/seabed example. Next I discuss the notions of function in play in our thinking about inorganic nature. And lastly I consider Parsons's flooding river example. I conclude that extreme formalism about inorganic nature is safe from (...)
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  39. Defusing Anti-Formalist Arguments.Nick Zangwill - 2000 - British Journal of Aesthetics 40 (3):376-383.
    ANTI-FORMALISM has become the consensus in aesthetics. But in my view anti-formalism is not true to our aesthetic experience; it gives a revisionary account of the aesthetic properties that we think we find in works of art. The thesis I think we should hold is not extreme formalism—the view that all or almost all aesthetic properties are formal—but the moderate thesis that many are. This view has not been given its due because so many aestheticians have been (...)
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  40.  54
    A Constructive Type-Theoretical Formalism for the Interpretation of Subatomically Sensitive Natural Language Constructions.Bartosz Więckowski - 2012 - Studia Logica 100 (4):815-853.
    The analysis of atomic sentences and their subatomic components poses a special problem for proof-theoretic approaches to natural language semantics, as it is far from clear how their semantics could be explained by means of proofs rather than denotations. The paper develops a proof-theoretic semantics for a fragment of English within a type-theoretical formalism that combines subatomic systems for natural deduction [20] with constructive (or Martin-Löf) type theory [8, 9] by stating rules for the formation, introduction, elimination and equality (...)
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  41.  47
    A Formalist Philosophy of Mathematics Part I: Arithmetic.Michael Gabbay - 2010 - Studia Logica 96 (2):219-238.
    In this paper I present a formalist philosophy mathematics and apply it directly to Arithmetic. I propose that formalists concentrate on presenting compositional truth theories for mathematical languages that ultimately depend on formal methods. I argue that this proposal occupies a lush middle ground between traditional formalism, fictionalism, logicism and realism.
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  42.  5
    Formalist and Relationalist Theory in Social Network Analysis.Emily Erikson - 2013 - Sociological Theory 31 (3):219-242.
    Social network research is widely considered atheoretical. In contrast, in this article I argue that network analysis often mixes two distinct theoretical frameworks, creating a logically inconsistent foundation. Relationalism rejects essentialism and a priori categories and insists upon the intersubjectivity of experience and meaning as well as the importance of the content of interactions and their historical setting. Formalism is based on a structuralist interpretation of the theoretical works of Georg Simmel. Simmel laid out a neo-Kantian program of identifying (...)
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  43.  83
    Quantum Formalism with State-Collapse and Superluminal Communication.George Svetlichny - 1998 - Foundations of Physics 28 (2):131-155.
    Given the collapse hypothesis (CH) of quantum measurement, EPR-type correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves purity of states must also be linear. A gedanken experiment shows that Lorentz covariance along with the second law of thermodynamics imply a nonentropic version (...)
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  44.  4
    Formalism , Behavioral Realism and the Interdisciplinary Challenge in Sociological Theory.O. Lizardo - 2009 - Journal for the Theory of Social Behaviour 39 (1):39-80.
    In this paper, I argue that recent sociological theory has become increasingly bifurcated into two mutually incompatible styles of theorizing that I label formalist and behavioral-realist. Formalism favors mathematization and proposes an instrumentalist ontology of abstract processes while behavioral-realist theory takes at its basis the "real" physical individual endowed with concrete biological, cognitive and neurophysiological capacities and constraints and attempts to derive the proper conceptualization of social behavior from that basis. Formalism tends to lead toward a conceptually independent (...)
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  45.  72
    Quantum Theory: A Hilbert Space Formalism for Probability Theory. [REVIEW]R. Eugene Collins - 1977 - Foundations of Physics 7 (7-8):475-494.
    It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrödinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL 2 representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of two (...)
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  46.  50
    New Formalism and the Aesthetic Appreciation of Nature.Glenn Parsons & Allen Carlson - 2004 - Journal of Aesthetics and Art Criticism 62 (4):363–376.
    Recently, several authors have defended a new version of formalism in the aesthetics of nature and attempted to refute earlier arguments against the doctrine. In this essay, we assess this new formalism by reconsidering the force of antiformalist arguments against both traditional formalism and new formalism. While we find that these arguments remain effective against traditional formalism, new formalism falls largely beyond their scope. We therefore provide a novel line of argument for the insignificance (...)
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  47.  63
    The Quantum Formalism and the Grw Formalism.Sheldon Goldstein - unknown
    The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has (...)
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  48.  22
    Formalism, Hamilton and Complex Numbers.John O'Neill - 1986 - Studies in History and Philosophy of Science Part A 17 (3):351-372.
    The development and applicability of complex numbers is often cited in defence of the formalist philosophy of mathematics. This view is rejected through an examination of hamilton's development of the notion of complex numbers as ordered pairs of reals, And his later development of the quaternion theory, Which subsequently formed the basis of vector analysis. Formalism, By protecting informal assumptions from critical scrutiny, Constrained rather than encouraged the development of mathematics.
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  49.  1
    A Formalism for Action Representation Inspired by Mīmāṁsā.Parthasarathi Ranjani & Srinivasan Bama - 2012 - Journal of Intelligent Systems 21 (1):45-77.
    . This paper endeavors to formalize imperatives that convey actions. Imperatives, unlike propositions, do not hold the value of true or false. Peter Vranas proposed an alternate logical formalism in the literature of imperative logic with three values, namely: Satisfaction (), Violation () and Avoidance (). Although this formalism takes into account the conditional imperatives, it does not address imperatives from the perspective of actions. According to Mīmāṁsā, the prime motive of an imperative is to carry out action (...)
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    The Coordinate-Independent 2-Component Spinor Formalism and the Conventionality of Simultaneity.Jonathan Bain - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (2):201-226.
    In recent articles, Zangari (1994) and Karakostas (1997) observe that while an &unknown;-extended version of the proper orthochronous Lorentz group O + (1,3) exists for values of &unknown; not equal to zero, no similar &unknown;-extended version of its double covering group SL(2, C) exists (where &unknown;=1-2&unknown; R , with &unknown; R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence for (...)
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