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On rigorous definitions

Philosophical Studies 72 (2-3):115 - 146 (1993)

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  1. Alfred Tarski: philosophy of language and logic.Douglas Patterson - 2012 - New York: Palgrave-Macmillan.
    This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.
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  • Open texture, rigor, and proof.Benjamin Zayton - 2022 - Synthese 200 (4):1-20.
    Open texture is a kind of semantic indeterminacy first systematically studied by Waismann. In this paper, extant definitions of open texture will be compared and contrasted, with a view towards the consequences of open-textured concepts in mathematics. It has been suggested that these would threaten the traditional virtues of proof, primarily the certainty bestowed by proof-possession, and this suggestion will be critically investigated using recent work on informal proof. It will be argued that informal proofs have virtues that mitigate the (...)
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  • Busting a Myth about Leśniewski and Definitions.Rafal Urbaniak & K. Severi Hämäri - 2012 - History and Philosophy of Logic 33 (2):159-189.
    A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Leśniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Leśniewski's published or unpublished work is known where the standard conditions are discussed. Second, Leśniewski's own logical theories allow for creative definitions. Third, Leśniewski's celebrated ‘rules of definition’ lay (...)
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  • Work is Meaningful if There are Good Reasons to do it: A Revisionary Conceptual Analysis of ‘Meaningful Work’.Jens Jørund Tyssedal - 2022 - Journal of Business Ethics 185 (3):533-544.
    Meaningful work is an important ideal, but it seems hard to give an adequate account of meaningful work. In this article, I conduct a revisionary conceptual analysis of ‘meaningful work’, i.e. a conceptual analysis that aims at finding a better and more useful way to use this term. I argue for a distinction between cases where work itself is meaningful and cases where other sources of meaning are found at work. The term ‘meaningful work’ is most useful for the former (...)
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  • Proper Names and their Fictional Uses.Heidi Tiedke - 2011 - Australasian Journal of Philosophy 89 (4):707 - 726.
    Fictional names present unique challenges for semantic theories of proper names, challenges strong enough to warrant an account of names different from the standard treatment. The theory developed in this paper is motivated by a puzzle that depends on four assumptions: our intuitive assessment of the truth values of certain sentences, the most straightforward treatment of their syntactic structure, semantic compositionality, and metaphysical scruples strong enough to rule out fictional entities, at least. It is shown that these four assumptions, taken (...)
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  • Resilience: Some Philosophical Remarks on Defining Ostensively and Stipulatively.Henrik Thorén & Johannes Persson - 2015 - Sustainability: Science, Practice, and Policy 11 (1):64-74.
    Although contentious, the concept of resilience is common in sustainability research. Critique of the concept have often focused on the content of the concept. In this paper we focus on another feature of concepts, namely how they are defined. We distinguish between concepts that are ostensively defined, that aim to point to some phenomena, and stipulatively defined concepts, where the content of the concept is given in the definition itself. We argue that although definitions themselves are similar across many different (...)
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  • The metaphysics of words.Roy Sorensen - 1996 - Philosophical Studies 81 (2-3):193 - 214.
    Semantic indeterminacy is the ether of philosophy of language. It fills the interstices of our intentions and pervades accounts of presupposition, tense, fiction, translation, and especially, vagueness. Yet semantic indeterminacy is as impossible as ectoplasm. Indeed, more so! The demonstration need only borrow a few assumptions used elsewhere in widely accepted impossibility results. Since an impossibility is never a necessary condition for anything actual, semantic indeterminacy must be superfluous. Language is no more explained by semantic indeterminacy than calculus is explained (...)
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  • X - Phi and Carnapian Explication.Joshua Shepherd & James Justus - 2015 - Erkenntnis 80 (2):381-402.
    The rise of experimental philosophy has placed metaphilosophical questions, particularly those concerning concepts, at the center of philosophical attention. X-phi offers empirically rigorous methods for identifying conceptual content, but what exactly it contributes towards evaluating conceptual content remains unclear. We show how x-phi complements Rudolf Carnap’s underappreciated methodology for concept determination, explication. This clarifies and extends x-phi’s positive philosophical import, and also exhibits explication’s broad appeal. But there is a potential problem: Carnap’s account of explication was limited to empirical and (...)
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  • Revision Without Revision Sequences: Circular Definitions.Edoardo Rivello - 2019 - Journal of Philosophical Logic 48 (1):57-85.
    The classical theory of definitions bans so-called circular definitions, namely, definitions of a unary predicate P, based on stipulations of the form $$Px =_{\mathsf {Df}} \phi,$$where ϕ is a formula of a fixed first-order language and the definiendumP occurs into the definiensϕ. In their seminal book The Revision Theory of Truth, Gupta and Belnap claim that “General theories of definitions are possible within which circular definitions [...] make logical and semantic sense” [p. IX]. In order to sustain their claim, they (...)
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  • Tarski on the Necessity Reading of Convention T.Douglas Eden Patterson - 2006 - Synthese 151 (1):1-32.
    Tarski’s Convention T is often taken to claim that it is both sufficient and necessary for adequacy in a definition of truth that it imply instances of the T-schema where the embedded sentence translates the mentioned sentence. However, arguments against the necessity claim have recently appeared, and, furthermore, the necessity claim is actually not required for the indefinability results for which Tarski is justly famous; indeed, Tarski’s own presentation of the results in the later Undecidable Theories makes no mention of (...)
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  • Truth-definitions and Definitional Truth.Douglas Patterson - 2008 - Midwest Studies in Philosophy 32 (1):313-328.
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  • On the determination argument against deflationism.Douglas Patterson - 2007 - Pacific Philosophical Quarterly 88 (2):243–250.
    (Pacific Philosophical Quarterly 2007) > Another look at Bar-On, Horisk and Lycan’s criticism of deflationism. I claim that their argument turns on a simple confusion about definitions and thereby fails to establish that deflationism somehow requires meaning to be explained in terms of truth conditions.
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  • Rejectivism and the Challenge of Pragmatic Contradictions.Ben Martin - 2016 - Disputatio 8 (43):253-267.
    Rejectivism is one of the most influential embodiments of pragmatism within contemporary philosophy of logic, advancing an explanation of the meaning of a logical notion, negation, in terms of the speech act of denial. This paper offers a challenge to rejectivism by proposing that in virtue of explaining negation in terms of denial, the rejectivist ought to be able to explain the concept of contradiction partially in terms of denial. It is argued that any failure to achieve this constitutes an (...)
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  • Concept Formation in Ethical Theories: Dealing with Polar Predicates.Sebastian Lutz - 2010 - Journal of Ethics and Social Philosophy 2010 (August):1-8.
    In "A Danger of Definition: Polar Predicates in Metaethics," Mark Alfano (2009) concludes that the response-dependence theory of Prinz and others and the fitting-attitudes theory first articulated by Brentano are false because they imply empirically false statements. He further concludes that these statements cannot be avoided by revising the definitions of the terms 'good' and 'bad' used in the two theories. I strengthen Alfano's first conclusion by arguing that the two theories are false even if they imply empirically true but (...)
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  • Carnap on Empirical Significance.Sebastian Lutz - 2017 - Synthese 194 (1):217-252.
    Carnap’s search for a criterion of empirical significance is usually considered a failure. I argue that the results from two out of his three different approaches are at the very least problematic, but that one approach led to success. Carnap’s criterion of translatability into logical syntax is too vague to allow for definite results. His criteria for terms—introducibility by chains of reduction sentences and his criterion from “The Methodological Character of Theoretical Concepts”—are almost trivial and have no clear relation to (...)
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  • Humility and constraints on O-language.Stephan Leuenberger - 2010 - Philosophical Studies 149 (3):327-354.
    In "Ramseyan Humility," David Lewis argues that we cannot know what the fundamental properties in our world are. His arguments invoke the possibility of permutations and replacements of fundamental properties. Most responses focus on Lewis’s view on the relationship between properties and roles, and on the assumptions about knowledge that he makes. I argue that no matter how the debates about knowledge and about the metaphysics of properties turn out, Lewis’s arguments are unconvincing since they rely on a highly implausible (...)
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  • Why “is at”? —On Quine’s Objection to Carnap’s Aufbau in “Two Dogmas of Empiricism”.Ka Ho Lam - 2018 - Journal for the History of Analytical Philosophy 6 (4).
    In “Two Dogmas”, Quine indicates that Carnap’s Aufbau fails “in principle” to reduce our knowledge of the external world to sense data. This is because in projecting the sensory material to reconstruct the physical world, Carnap gives up the use of operating rules and switches to a procedure informed by general principles. This procedure falls short of providing an eliminative translation for the connective “is at”, which is necessary for the reduction. In dissecting Quine’s objection, I argue that Quine has (...)
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  • Carnap on concept determination: methodology for philosophy of science. [REVIEW]James Justus - 2012 - European Journal for Philosophy of Science 2 (2):161-179.
    Abstract Recent criticisms of intuition from experimental philosophy and elsewhere have helped undermine the authority of traditional conceptual analysis. As the product of more empirically informed philosophical methodology, this result is compelling and philosophically salutary. But the negative critiques rarely suggest a positive alternative. In particular, a normative account of concept determination—how concepts should be characterized—is strikingly absent from such work. Carnap's underappreciated theory of explication provides such a theory. Analyses of complex concepts in empirical sciences illustrates and supports this (...)
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  • Truth, Meaning, and Circularity.Claire Horisk - 2008 - Philosophical Studies 137 (2):269-300.
    It is often argued that the combination of deflationism about truth and the truth-conditional theory of meaning is impossible for reasons of circularity. I distinguish, and reject, two strains of circularity argument. Arguments of the first strain hold that the combination has a circular account of the order in which one comes to know the meaning of a sentence and comes to know its truth condition. I show that these arguments fail to identify any circularity. Arguments of the second strain (...)
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  • Understanding and Defining Institutions: The Contribution of Francesco Gual. [REVIEW]Geoffrey M. Hodgson - 2018 - Journal of Economic Methodology 25 (1):111-116.
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  • Recent Truth Theories: A Case Study.Guillermo Rosado Haddock - 2001 - Global Philosophy 12 (1-2):87-115.
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  • A unified social ontology.Francesco Guala & Frank Hindriks - 2015 - Philosophical Quarterly 65 (259):177-201.
    Current debates in social ontology are dominated by approaches that view institutions either as rules or as equilibria of strategic games. We argue that these two approaches can be unified within an encompassing theory based on the notion of correlated equilibrium. We show that in a correlated equilibrium each player follows a regulative rule of the form ‘if X then do Y’. We then criticize Searle's claim that constitutive rules of the form ‘X counts as Y in C’ are fundamental (...)
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  • What are Implicit Definitions?Eduardo N. Giovannini & Georg Schiemer - 2019 - Erkenntnis 86 (6):1661-1691.
    The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely as specifications of the meaning of the primitive terms of a theory and as definitions of higher-order mathematical concepts or structures. We analyze these (...)
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  • On Anselm’s Ontological Argument in Proslogion II.Paul E. Oppenheimer & Edward N. Zalta - 2021 - History of Philosophy & Logical Analysis 25 (2):327-351.
    Formulations of Anselm’s ontological argument have been the subject of a number of recent studies. We examine these studies in light of Anselm’s text and (a) respond to criticisms that have surfaced in reaction to our earlier representations of the argument, (b) identify and defend a more refined representation of Anselm’s argument on the basis of new research, and (c) compare our representation of the argument, which analyzes that than which none greater can be conceived as a definite description, to (...)
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  • A Formal Explication of Blanchette's Conception of Fregean Consequence.Günther Eder - 2023 - History and Philosophy of Logic 44 (3):287-310.
    Over the past decades, Patricia Blanchette has developed a sophisticated account of Frege's conception of logic and his views on logical consequence. One of the central components of her interpretation is the idea that Frege's conception of logical consequence is ‘semantically laden’ and not purely formal. The aim of the present paper is to provide precise explications of this as well as related ideas that inform her account, and to discuss their significance for the philosophy of logic in general and (...)
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  • Definitions in practice: An interview study.V. J. W. Coumans & L. Consoli - 2023 - Synthese 202 (1):1-32.
    In the philosophy of mathematical practice, the aim is to understand the various aspects of this practice. Even though definitions are a central element of mathematical practice, the study of this aspect of mathematical practice is still in its infancy. In particular, there is little empirical evidence to substantiate claims about definitions in practice. In this article, we address this gap by reporting on an empirical investigation on how mathematicians create definitions and which roles and properties they attribute to them. (...)
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  • The Opacity of Law: On the Hidden Impact of Experts’ Opinion on Legal Decision-making.Damiano Canale - 2021 - Law and Philosophy 40 (5):509-543.
    It is well known that experts’ opinion and testimony take on a decisive weight in judicial fact-finding, raising issues and perplexities that have long been under scholarly scrutiny. In this paper I argue that expert’s opinions have a much wider impact on legal decision-making. In particular, they may generate a problem that I will call ‘the opacity of law’. A legal text, such as a statute or regulation, becomes opaque if a legal authority is not able to grasp its full (...)
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  • Explication as a Method of Conceptual Re-engineering.Georg Brun - 2016 - Erkenntnis 81 (6):1211-1241.
    Taking Carnap’s classic exposition as a starting point, this paper develops a pragmatic account of the method of explication, defends it against a range of challenges and proposes a detailed recipe for the practice of explicating. It is then argued that confusions are involved in characterizing explications as definitions, and in advocating precising definitions as an alternative to explications. Explication is better characterized as conceptual re-engineering for theoretical purposes, in contrast to conceptual re-engineering for other purposes and improving exactness for (...)
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  • Frege on the Fruitfulness of Definitions.Rachel Boddy - 2021 - Journal for the History of Analytical Philosophy 9 (11).
    What, in Frege’s view, makes definitions fruitful? In Grundlagen §70, Frege offers an answer: Unfruitful definitions are definitions that “could just as well be omitted and leave no link missing in the chain of our proofs”. The §70 passage, however, poses an interpretive puzzle as its characterization of fruitfulness appears to conflict with other conditions that Frege imposes on definitions, namely, eliminability and conservativeness. It appears that the only way to resolve this conflict is to attribute to Frege a notion (...)
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  • Frege’s Unification.Rachel Boddy - 2018 - History and Philosophy of Logic 40 (2):135-151.
    What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the (...)
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  • What Is a Stand Up Special?Frank Boardman - 2021 - Aesthetic Investigations 5 (1):51-63.
    The stand-up special is growing cultural significance just as it is maturing and becoming more distinct as an art form. Philosophical treatments of the special are therefore neither frivolous nor redundant. I argue here that such inquiry can be aided by a definitional account of “special” and that an essential definition – if one is available- would serve us best. I then offer a candidate definition of this kind and reply to some likely objections to it.
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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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  • Leśniewski's Systems of Logic and Foundations of Mathematics.Rafal Urbaniak - 2013 - Cham, Switzerland: Springer.
    With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...
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  • The Golden Age of Polish Philosophy. Kaziemierz Twardowski’s philosophical legacy.Sandra Lapointe, Jan Wolenski, Mathieu Marion & Wioletta Miskiewicz (eds.) - 2009 - Dordrecht, Netherland: Springer.
    This volume portrays the Polish or Lvov-Warsaw School, one of the most influential schools in analytic philosophy, which, as discussed in the thorough introduction, presented an alternative working picture of the unity of science.
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  • Definitions.Anil Gupta - 2008 - Stanford Encyclopedia of Philosophy.
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  • Taking Control : The role of manipulation in theories of causation.Henning Strandin - 2019 - Dissertation, Stockholm University
    Causation has always been a philosophically controversial subject matter. While David Hume’s empiricist account of causation has been the dominant influence in analytic philosophy and science during modern times, a minority view has instead connected causation essentially to agency and manipulation. A related approach has for the first time gained widespread popularity in recent years, due to new powerful theories of causal inference in science that are based in a technical notion of intervention, and James Woodward’s closely connected interventionist theory (...)
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  • Truth, meaning, and translation.Panu Raatikainen - 2008 - In Douglas Patterson (ed.), New essays on Tarski and philosophy. O.University Press. pp. 247.
    Philosopher’s judgements on the philosophical value of Tarski’s contributions to the theory of truth have varied. For example Karl Popper, Rudolf Carnap, and Donald Davidson have, in their different ways, celebrated Tarski’s achievements and have been enthusiastic about their philosophical relevance. Hilary Putnam, on the other hand, pronounces that “[a]s a philosophical account of truth, Tarski’s theory fails as badly as it is possible for an account to fail.” Putnam has several alleged reasons for his dissatisfaction,1 but one of them, (...)
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  • Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Naming and Referring: Table of Contents.Heidi Savage - manuscript
    This book is about whether reference to an individual is the essential feature of a proper name -- a widely held view -- or whether referring to an individual is simply a contingent feature. Three questions need resolving, then. First, whether all names in particular contexts are themselves referring devices. Second, whether recognizing names types and the consequent issue of their ambiguity can be resolved simply by distinguishing between name types and tokens thereof. Last, whether names are ever referential in (...)
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  • Criteria of empirical significance: a success story.Sebastian Lutz - manuscript
    The sheer multitude of criteria of empirical significance has been taken as evidence that the pre-analytic notion being explicated is too vague to be useful. I show instead that a significant number of these criteria—by Ayer, Popper, Przełęcki, Suppes, and David Lewis, among others—not only form a coherent whole, but also connect directly to the theory of definition, the notion of empirical content as explicated by Ramsey sentences, and the theory of measurement; two criteria by Carnap and Sober are trivial, (...)
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  • The Hammer and the Nail : Interdisciplinarity and Problem Solving in Sustainability Science.Henrik Thorén - 2015 - Dissertation, Lund University
    This is a thesis about interdisciplinarity, scientific integration, and problem solving in sustainability science. Sustainability science is an emerging and highly interdisciplinary field that seeks to integrate vastly differentiated bodies of knowledge in addressing the challenge of transitioning contemporary societies towards sustainability. Interdisciplinarity is paramount. Interdisciplinarity in general, and in the context of sustainability science in particular, has often been associated with solving particular problems and problem solving is one important theme in this thesis. A central idea that is developed (...)
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  • Objective Expertise and Functionalist Constraints: A Comment on Croce.Christian Quast - 2019 - Social Epistemology Review and Reply Collective 8 (8):15-28.
    Any conceptual investigation into a given phenomenon may fail in several ways. It may be, for instance, inconsistent, too inclusive or exclusive, or even materially inappropriate. In a recent reply, Michel Croce raises all of these objections to what I have called a “balanced account of expertise” (2018). First, he claims there is a “compromising tension” between two basic components of my account (cf. sect. 3.1). This would be the charge of inconsistency, as Croce states, “Quast cannot have his cake (...)
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  • Notes on the art of logic.Nuel Belnap - manuscript
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  • On Sober's Criterion of Contrastive Testability.Sebastian Lutz - manuscript
    Elliott Sober has suggested his criterion of contrastive testability as an improvement over previous criteria of empirical significance like falsifiability. I argue that his criterion renders almost any theory empirically significant because its restrictions on auxiliary assumptions are to weak. Even when the criterion is modified to avoid this trivialization, it fails to meet other conditions of adequacy for a criterion of empirical significance that follow from Sober's position. I suggest to define empirical significance as empirical non-equivalence to a tautology, (...)
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  • Tarski's Method of Truth Definition: Its Nature and Significance.Ladislav Koreň - 2010 - In Jaroslav Peregrin (ed.), Foundations of Logic. Charles University in Prague/Karolinum Press.
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  • Criteria of Empirical Significance: Foundations, Relations, Applications.Sebastian Lutz - 2012 - Dissertation, Utrecht University
    This dissertation consists of three parts. Part I is a defense of an artificial language methodology in philosophy and a historical and systematic defense of the logical empiricists' application of an artificial language methodology to scientific theories. These defenses provide a justification for the presumptions of a host of criteria of empirical significance, which I analyze, compare, and develop in part II. On the basis of this analysis, in part III I use a variety of criteria to evaluate the scientific (...)
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  • Information, Security, Privacy, and Anonymity : Definitional and Conceptual Issues.Björn Lundgren - 2018 - Dissertation, Kth Royal Institute of Technology
    This doctoral thesis consists of five research papers that address four tangential topics, all of which are relevant for the challenges we are facing in our socio-technical society: information, security, privacy, and anonymity. All topics are approached by similar methods, i.e. with a concern about conceptual and definitional issues. In Paper I—concerning the concept of information and a semantic conception thereof—it is argued that the veridicality thesis is false. In Paper II—concerning information security—it is argued that the current leading definitions (...)
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  • Theories of truth and convention T.Douglas Patterson - 2002 - Philosophers' Imprint 2:1-16.
    Partly due to the influence of Tarski's work, it is commonly assumed that any good theory of truth implies biconditionals of the sort mentioned in Convention T: instances of the T-Schema "s is true in L if and only if p" where the sentence substituted for "p" is equivalent in meaning to s. I argue that we must take care to distinguish the claim that implying such instances is sufficient for adequacy in an account of truth from the claim that (...)
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