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Introduction to Logic

Philosophical Quarterly 10 (40):287-288 (1960)

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  1. Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective).Richard Zach - 2015 - Journal of Philosophical Logic 45 (2):183-197.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...)
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  • Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions.John Corcoran & Hassan Masoud - 2015 - History and Philosophy of Logic 36 (1):39-61.
    Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...)
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  • A verisimilitudinarian analysis of the Linda paradox.Gustavo Cevolani, Vincenzo Crupi & Roberto Festa - 2012 - VII Conference of the Spanish Society for Logic, Methodology and Philosphy of Science.
    The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.
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  • The Model-Theoretic Approach in the Philosophy of Science.Newton C. A. Da Costa & Steven French - 1990 - Philosophy of Science 57 (2):248 - 265.
    An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.
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  • Formalization, primitive concepts, and purity: Formalization, primitive concepts, and purity.John T. Baldwin - 2013 - Review of Symbolic Logic 6 (1):87-128.
    We emphasize the role of the choice of vocabulary in formalization of a mathematical area and remark that this is a particular preoccupation of logicians. We use this framework to discuss Kennedy’s notion of ‘formalism freeness’ in the context of various schools in model theory. Then we clarify some of the mathematical issues in recent discussions of purity in the proof of the Desargues proposition. We note that the conclusion of ‘spatial content’ from the Desargues proposition involves arguments which are (...)
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  • Confirmation of ecological and evolutionary models.Elisabeth A. Lloyd - 1987 - Biology and Philosophy 2 (3):277-293.
    In this paper I distinguish various ways in which empirical claims about evolutionary and ecological models can be supported by data. I describe three basic factors bearing on confirmation of empirical claims: fit of the model to data; independent testing of various aspects of the model, and variety of evident. A brief description of the kinds of confirmation is followed by examples of each kind, drawn from a range of evolutionary and ecological theories. I conclude that the greater complexity and (...)
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  • Approaches to reduction.Kenneth F. Schaffner - 1967 - Philosophy of Science 34 (2):137-147.
    Four current accounts of theory reduction are presented, first informally and then formally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an "isomorphic model" schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation of (...)
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  • Reviewing Reduction in a Preferential Model‐Theoretic Context.Emma Ruttkamp & Johannes Heidema - 2005 - International Studies in the Philosophy of Science 19 (2):123 – 146.
    In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of a reducing theory (...)
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  • Translation, reduction and commensurability: A note on Schroeder-heister and Schaefer.David Pearce - 1989 - Philosophy of Science 56 (1):158-164.
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  • Models and the Semantic View.Martin Thomson-Jones - 2006 - Philosophy of Science 73 (5):524-535.
    I begin by distinguishing two notions of model, the notion of a truth-making structure and the notion of a mathematical model (in one specific sense). I then argue that although the models of the semantic view have often been taken to be both truth-making structures and mathematical models, this is in part due to a failure to distinguish between two ways of truth-making; in fact, the talk of truth-making is best excised from the view altogether. The result is a version (...)
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  • A semantic approach to the structure of population genetics.Elisabeth A. Lloyd - 1984 - Philosophy of Science 51 (2):242-264.
    A precise formulation of the structure of modern evolutionary theory has proved elusive. In this paper, I introduce and develop a formal approach to the structure of population genetics, evolutionary theory's most developed sub-theory. Under the semantic approach, used as a framework in this paper, presenting a theory consists in presenting a related family of models. I offer general guidelines and examples for the classification of population genetics models; the defining features of the models are taken to be their state (...)
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  • Erotetic logic and the structure of scientific revolution.Scott A. Kleiner - 1970 - British Journal for the Philosophy of Science 21 (2):149-165.
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  • Scientific Structuralism: Presentation and Representation.Katherine Brading & Elaine Landry - 2006 - Philosophy of Science 73 (5):571-581.
    This paper explores varieties of scientific structuralism. Central to our investigation is the notion of `shared structure'. We begin with a description of mathematical structuralism and use this to point out analogies and disanalogies with scientific structuralism. Our particular focus is the semantic structuralist's attempt to use the notion of shared structure to account for the theory-world connection, this use being crucially important to both the contemporary structural empiricist and realist. We show why minimal scientific structuralism is, at the very (...)
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  • Optimal-design models and the strategy of model building in evolutionary biology.John Beatty - 1980 - Philosophy of Science 47 (4):532-561.
    The prevalence of optimality models in the literature of evolutionary biology is testimony to their popularity and importance. Evolutionary biologist R. C. Lewontin, whose criticisms of optimality models are considered here, reflects that "optimality arguments have become extremely popular in the last fifteen years, and at present represent the dominant mode of thought." Although optimality models have received little attention in the philosophical literature, these models are very interesting from a philosophical point of view. As will be argued, optimality models (...)
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  • Reduction, integration, and the unity of science: Natural, behavioral, and social sciences and the humanities.William P. Bechtel & Andrew Hamilton - 2007 - In T. Kuipers (ed.), Philosophy of Science: Focal Issues (Volume 1 of the Handbook of the Philosophy of Science). Elsevier.
    1. A Historical Look at Unity 2. Field Guide to Modern Concepts of Reduction and Unity 3. Kitcher's Revisionist Account of Unification 4. Critics of Unity 5. Integration Instead of Unity 6. Reduction via Mechanisms 7. Case Studies in Reduction and Unification across the Disciplines.
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  • Tarski’s Theory of the Formal Correctness of Definitions.David Hitchcock - 2024 - Journal of Philosophical Logic 53 (1):181-221.
    In his 1933 monograph on the concept of truth, Alfred Tarski claimed that his definition of truth satisfied “the usual conditions of methodological correctness”, which in a 1935 article he identified as consistency and back-translatability. Following the rules of defining for an axiomatized theory was supposed to ensure satisfaction of the two conditions. But Tarski neither explained the two conditions nor supplied rules of defining for any axiomatized theory. We can make explicit what Tarski understood by consistency and back-translatability, with (...)
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  • Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - 2023 - Journal of Logic, Language and Information 32 (2):247-273.
    The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent logic (...)
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  • Ramsification and Semantic Indeterminacy.Hannes Leitgeb - 2022 - Review of Symbolic Logic 16 (3):900-950.
    Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully (...)
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  • Rational Intransitive Preferences.Peter Baumann - 2022 - Politics, Philosophy and Economics 21 (1):3-28.
    According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the transitivity (...)
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  • Against ‘Interpretation’: Quantum Mechanics Beyond Syntax and Semantics.Raoni Wohnrath Arroyo & Gilson Olegario da Silva - 2022 - Axiomathes 32 (6):1243-1279.
    The question “what is an interpretation?” is often intertwined with the perhaps even harder question “what is a scientific theory?”. Given this proximity, we try to clarify the first question to acquire some ground for the latter. The quarrel between the syntactic and semantic conceptions of scientific theories occupied a large part of the scenario of the philosophy of science in the 20th century. For many authors, one of the two currents needed to be victorious. We endorse that such debate, (...)
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  • Analysis in Prior Analytics I.45.Igor Martinjak - 2022 - History and Philosophy of Logic 43 (3):207-231.
    I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent is just (...)
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  • Mario Bunge (1919–2020): Conjoining Philosophy of Science and Scientific Philosophy.Martin Mahner - 2021 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 52 (1):3-23.
    The leitmotif of Mario Bunge’s work was that the philosophy of science should be informed by a comprehensive scientific philosophy, and vice versa; with both firmly rooted in realism and materialism. Now Bunge left such a big oeuvre, comprising more than 70 books and hundreds of articles, that it is impossible to review it in its entirety. In addition to biographical remarks, this obituary will therefore restrict itself to some select issues of his philosophy: his scientific metaphysics, his philosophy of (...)
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  • Are Metaphysical Claims Testable?Chrysovalantis Stergiou - 2020 - Philosophia 49 (2):801-818.
    To consider metaphysical claims a priori and devoid of empirical content, is a rather commonplace received opinion. This paper attempts an exploration of a contemporary philosophical heresy: it is possible to test metaphysical claims if they play an indispensable role in producing empirical success, i.e. novel predictions. To do so one, firstly, needs to express the metaphysical claims employed in the logico-mathematical language of a scientific theory, i.e. to explicate them. Secondly, one should have an understanding of what it is (...)
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  • Rumos da Epistemologia v. 11.Luiz Dutra & Alexandre Meyer Luz (eds.) - 2011 - Núcleo de Epistemologia e Lógica.
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  • Supervenience, Reduction, and Translation.Neil Dewar - 2019 - Philosophy of Science 86 (5):942-954.
    This article considers the following question: What is the relationship between supervenience and reduction? I investigate this formally: first, by introducing a recent argument by Christian List to the effect that one can have supervenience without reduction; then, by considering how the notion of Nagelian reduction can be related to the formal apparatus of definability and translation theory; then, by showing how, in the context of propositional theories, topological constraints on supervenience serve to enforce reducibility; and, finally, by showing how (...)
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  • Definition in mathematics.Carlo Cellucci - 2018 - European Journal for Philosophy of Science 8 (3):605-629.
    In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.
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  • Die Architektur der Synthese. Entstehung und Philosophie der modernen Evolutionstheorie.Marcel Weber - 1996 - Dissertation, University of Konstanz
    This Ph.D. thesis provides a pilosophical account of the structure of the evolutionary synthesis of the 1930s and 40s. The first, more historical part analyses how classical genetics came to be integrated into evolutionary thinking, highlighting in particular the importance of chromosomal mapping of Drosophila strains collected in the wild by Dobzansky, but also the work of Goldschmidt, Sumners, Timofeeff-Ressovsky and others. The second, more philosophical part attempts to answer the question wherein the unity of the synthesis consisted. I argue (...)
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  • Paradoxical hypodoxes.Alexandre Billon - 2019 - Synthese 196 (12):5205-5229.
    Most paradoxes of self-reference have a dual or ‘hypodox’. The Liar paradox (Lr = ‘Lr is false’) has the Truth-Teller (Tt = ‘Tt is true’). Russell’s paradox, which involves the set of sets that are not self-membered, has a dual involving the set of sets which are self-membered, etc. It is widely believed that these duals are not paradoxical or at least not as paradoxical as the paradoxes of which they are duals. In this paper, I argue that some paradox’s (...)
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  • Knowledge: Genuine and Bogus.Mario Bunge - 2011 - Science & Education 20 (5-6):411-438.
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  • Burn all your textbooks.Varol Akman - 2017 - Australasian Journal of Logic 14 (3).
    The standard propositional exposition of necessary and sufficient conditions, as available in introductory logic texts, leads to a contradiction. It should be abolished.
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  • Essentially Comparative Value Does Not Threaten Transitivity.Toby Handfield - 2016 - Thought: A Journal of Philosophy 5 (1):3-12.
    The essentially comparative conception of value entails that the value of a state of affairs does not depend solely upon features intrinsic to the state of affairs, but also upon extrinsic features, such as the set of feasible alternatives. It has been argued that this conception of value gives us reason to abandon the transitivity of the better than relation. This paper shows that the support for intransitivity derived from this conception of value is very limited. On its most plausible (...)
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  • Scientific Theories.Hans Halvorson - 2014 - In Paul Humphreys (ed.), The Oxford Handbook of Philosophy of Science. New York, NY, USA: Oxford University Press. pp. 585-608.
    Since the beginning of the 20th century, philosophers of science have asked, "what kind of thing is a scientific theory?" The logical positivists answered: a scientific theory is a mathematical theory, plus an empirical interpretation of that theory. Moreover, they assumed that a mathematical theory is specified by a set of axioms in a formal language. Later 20th century philosophers questioned this account, arguing instead that a scientific theory need not include a mathematical component; or that the mathematical component need (...)
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  • La structure du temps est-elle indécidable? Sous-détermination et structure du temps chez Newton-Smith.Vincent Ardourel - 2014 - Dialogue 53 (4):623-649.
    In his book, The Structure of Time, William H. Newton-Smith claims that we cannot decide whether the structure of time is continuous or merely dense. I discuss here the extent to which he is correct. I argue that he fails to provide strong enough arguments to defend his claim, but I then suggest how he might overcome this issue. I also argue that we must reconsider the consequences that he draws from his “undecidability result”.
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  • McTaggart and the Neo-Positive Entropists.William R. Shea - 1975 - Philosophy 50 (193):346 - 351.
    John King-Farlow's ‘The Positive McTaggart on Time’ brings out extremely important likenesses between ‘abstract’ metaphysicians and ‘concrete’ philosophers of science. These striking similarities illustrate a perennial human quest for Something More Basic than Time, a quest which characterizes not only mystics who rejoice in contradictions but hard-headed philosophers who submit to the rigours of logic. King-Farlow is largely concerned with the McTaggart of 1908 and his motivation for writing ‘The Unreality of Time’. I should like to explore further the surprising (...)
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  • Identity, Individuation and Substance.David Wiggins - 2012 - European Journal of Philosophy 20 (1):1-25.
    The paper takes off from the problem of finding a proper content for the relation of identity as it holds or fails to hold among ordinary things or substances. The necessary conditions of identity are familiar, the sufficient conditions less so. The search is for conditions at once better usable than the Leibnizian Identity of Indiscernibles (independently suspect) and strong enough to underwrite all the formal properties of the relation.It is contended that the key to this problem rests at the (...)
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  • Problems of axiomatizing religion.Paul Weingartner - 2021 - Studies in East European Thought 74 (2):149-163.
    The paper discusses problems which arise in attempts to axiomatize parts of religion or religious belief systems. Besides those problems already investigated by Bochenski, like that of the propositional content or the meaning of religious discourse there are several further ones. This paper deals with the question whether full Classical Logic is suitable, whether one universe of discourse is sufficient, how to use definitions and analogous concepts and whether justifications satisfy credibility criteria.
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  • One or Two Gentle Remarks about Hans Halvorson’s Critique of the Semantic View.Bas C. van Fraassen - 2014 - Philosophy of Science 81 (2):276-283,.
    In recent papers Hans Halvorson has offered a critique of the semantic view of theories, showing that theories may be the same although the corresponding sets of models are different and, conversely, that theories may be different although the corresponding sets of models are the same. This critique will be assessed, first, as it pertains to issues concerning scientific models in the empirical sciences and, second, independent of any concern with empirical science.
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  • The problem of counterfactuals.R. F. Tredwell - 1965 - Philosophy of Science 32 (3/4):310-323.
    The "problem of counterfactuals," as proposed by Goodman and Chisholm, cannot be solved. However, a similar program, pioneered by Hiż and Mrs. Milmed, but largely neglected, can be completed and promises a satisfactory analysis of subjunctive conditionals.
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  • Applying Ramseyfication to Infrared Spectroscopy.Michael Toppel - 2023 - Erkenntnis 88 (8):3357-3373.
    The so-called Ramsey–Carnap approach, or Ramseyfication, has gone out of fashion in the philosophy of science. Advocates have tried to argue for a revival by writing methodological and metatheoretical studies of Ramseyfication. For this paper I have chosen a different approach; I will apply Ramseyfication to infrared spectroscopy—a method used in analytical chemistry—in order to logically analyse the relation between measurements and mathematical structures. My aim in doing so is to contribute to the debate about the _Application Problem of Mathematics_, (...)
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  • Conceptual and Logical Aspects of the ‘New’ Evolutionary Epistemology.Paul Thompson - 1988 - Canadian Journal of Philosophy 18 (sup1):235-253.
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  • The conjunction fallacy: a misunderstanding about conjunction?K. Tentori - 2004 - Cognitive Science 28 (3):467-477.
    It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X‐and‐Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners' interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems.
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  • 分析形而上学と経験科学の連続主義に対する批判的検討.Masahiro Takatori - 2023 - Kagaku Tetsugaku 56 (1):59.
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  • Understanding Scientific Theories: An Assessment of Developments, 1969–1998.Frederick Suppe - 2000 - Philosophy of Science 67 (3):115.
    The positivistic Received View construed scientific theories syntactically as axiomatic calculi where theoretical terms were given a partial semantic interpretation via correspondence rules connecting them to observation statements. This paper assesses what, with hindsight, seem the most important defects in the Received View; surveys the main proposed successor analyses to the Received View--various Semantic Conception versions and the Structuralist Analysis; evaluates how well they avoid those defects; examines what new problems they face and where the most promising require further development (...)
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  • Alf Ross on the Concept of a Legal Right.Torben Spaak - 2014 - Ratio Juris 27 (4):461-476.
    In this article, I discuss Alf Ross's claim that the concept of a legal right is best understood as a technical tool of presentation, which ties together a disjunction of operative facts and a conjunction of legal consequences, and that rights statements render the content of a number of legal norms in a convenient manner. I argue that while Ross's analysis is appealing, it is problematic in at least three respects. I also argue, however, that despite these difficulties Ross's analysis (...)
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  • The axiomatization of physical theories.Herbert A. Simon - 1970 - Philosophy of Science 37 (1):16-26.
    The task of axiomatizing physical theories has attracted, in recent years, some interest among both empirical scientists and logicians. However, the axiomatizations produced by either one of these two groups seldom appear satisfactory to the members of the other. It is the purpose of this paper to develop an approach that will satisfy the criteria of both, hence permit us to construct axiomatizations that will meet simultaneously the standards and needs of logicians and of empirical scientists.
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  • Reduction, representation and commensurability of theories.Peter Schroeder-Heister & Frank Schaefer - 1989 - Philosophy of Science 56 (1):130-157.
    Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...)
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  • Behavior at the organismal and molecular levels: The case of C. elegans.Kenneth F. Schaffner - 2000 - Philosophy of Science 67 (3):288.
    Caenorhabditis elegans (C. elegans) is a tiny worm that has become the focus of a large number of worldwide research projects examining its genetics, development, neuroscience, and behavior. Recently several groups of investigators have begun to tie together the behavior of the organism and the underlying genes, neural circuits, and molecular processes implemented in those circuits. Behavior is quintessentially organismal--it is the organism as a whole that moves and mates--but the explanations are devised at the molecular and neurocircuit levels, and (...)
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  • Some problems concerning language and physics.Adonai Sant’Anna & Gabriel Guerrer - 2007 - Synthese 154 (3):467-484.
    We discuss three problems concerning the use of formal languages in theoretical physics: (i) the definability of time and spacetime in classical physical theories; (ii) how to cope with indistinguishable elementary particles in quantum mechanics without labeling them; and (iii) how to get a formal picture of quantum states jumping.
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  • Perception, illusion, and hallucination.Kazem Sadegh-Zadeh - 1982 - Theoretical Medicine and Bioethics 3 (2):159-191.
    Patrick Suppes'' set-theoretical approach to the analysis of theories, and Joseph D. Sneed''s metatheory are briefly outlined. The notions of observation, illusion and hallucination are reconstructed according to these approaches. It is argued that the terms perception and truth are theoretical with respect to observation but nontheoretical with respect to illusion and hallucination. Hallucination is construed as a special kind of illusion.
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  • How to Derive Aristotle’s Categories from First Principles.Karl Reed & Humphrey P. van Polanen Petel - 2021 - Axiomathes 32 (Suppl 2):113-147.
    We propose a model of cognition grounded in ancient Greek philosophy which encompasses Aristotle’s categories. Taking for First Principles the brute facts of the mental actions of separation, aggregation and ordering, we derive Aristotle’s categories as follows. First, Separation lets us see single entities, giving the simple concept of an individual. Next, Aggregation lets us see instances of some kind, giving the basic concept of a particular. Then, Ordering lets us see both wholes-with-parts as well as parts-of-some-whole, giving the subtle (...)
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