Results for 'extensions'

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  1.  27
    Indefinite Extensibility.Timothy Williamson - 1998 - Grazer Philosophische Studien 55 (1):1-24.
    Dummett's account of the semantic paradoxes in terms of his theory of indefinitely extensible concepts is compared with Bürge's account in terms of indexicality. Dummett's appeal to intuitionistic logic does not block the paradoxes but Bürge's attempt to avoid the Strengthened Liar is unconvincing. It is argued that in order to avoid the Strengthened Liar and other semantic paradoxes involving nonindexical expressions, one must postulate that when we reflect on the paradoxes there are slight shifts in the meaning we ascribe (...)
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  2. Indefinite Extensibility.Timothy Williamson - 1998 - Grazer Philosophische Studien 55 (1):1-24.
    Of all the cases made against classical logic, Michael Dummett's is the most deeply considered. Issuing from a systematic and original conception of the discipline, it constitutes one of the most distinctive achievements of twentieth century British philosophy. Although Dummett builds on the work of Brouwer and Heyting, he provides the case against classical logic with a new, explicit and general foundation in the philosophy of language. Dummett's central arguments, widely celebrated if not widely endorsed, concern the implications of the (...)
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  3. Body-Extension Versus Body-Incorporation: Is There a Need for a Body-Model? [REVIEW]Helena De Preester & Manos Tsakiris - 2009 - Phenomenology and the Cognitive Sciences 8 (3):307-319.
    This paper investigates the role of a pre-existing body-model that is an enabling constraint for the incorporation of objects into the body. This body-model is also a basis for the distinction between body extensions (e.g., in the case of tool-use) and incorporation (e.g., in the case of successful prosthesis use). It is argued that, in the case of incorporation, changes in the sense of body-ownership involve a reorganization of the body-model, whereas extension of the body with tools does not (...)
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  4.  24
    Connexive Extensions of Regular Conditional Logic.Yale Weiss - 2019 - Logic and Logical Philosophy 28 (3):611-627.
    The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. (...)
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  5.  87
    Extensive Games as Process Models.Johan van Benthem - 2002 - Journal of Logic, Language and Information 11 (3):289-313.
    We analyze extensive games as interactive process models, using modallanguages plus matching notions of bisimulation as varieties of gameequivalences. Our technical results show how to fit existing modalnotions into this new setting.
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  6. Extensive Enactivism: Why Keep It All In?Daniel D. Hutto, Michael D. Kirchhoff & Erik Myin - 2014 - Frontiers in Human Neuroscience 8 (706).
    Radical enactive and embodied approaches to cognitive science oppose the received view in the sciences of the mind in denying that cognition fundamentally involves contentful mental representation. This paper argues that the fate of representationalism in cognitive science matters significantly to how best to understand the extent of cognition. It seeks to establish that any move away from representationalism toward pure, empirical functionalism fails to provide a substantive “mark of the cognitive” and is bereft of other adequate means for individuating (...)
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  7.  7
    Canonical Extensions and Kripke–Galois Semantics for Non-Distributive Logics.Chrysafis Hartonas - 2018 - Logica Universalis 12 (3-4):397-422.
    This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames, the semantic approach presented in this article is suitable for modeling applied logics, as it respects the intended interpretation of the logical operators. This is made possible by restricting admissible interpretations.
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  8.  62
    Indefinite Extensibility—Dialetheic Style.Graham Priest - 2013 - Studia Logica 101 (6):1263-1275.
    In recent years, many people writing on set theory have invoked the notion of an indefinitely extensible concept. The notion, it is usually claimed, plays an important role in solving the paradoxes of absolute infinity. It is not clear, however, how the notion should be formulated in a coherent way, since it appears to run into a number of problems concerning, for example, unrestricted quantification. In fact, the notion makes perfectly good sense if one endorses a dialetheic solution to the (...)
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  9. Cognitive Extension, Enhancement, and the Phenomenology of Thinking.Philip J. Walsh - 2017 - Phenomenology and the Cognitive Sciences 16 (1):33-51.
    This paper brings together several strands of thought from both the analytic and phenomenological traditions in order to critically examine accounts of cognitive enhancement that rely on the idea of cognitive extension. First, I explain the idea of cognitive extension, the metaphysics of mind on which it depends, and how it has figured in recent discussions of cognitive enhancement. Then, I develop ideas from Husserl that emphasize the agential character of thought and the distinctive way that conscious thoughts are related (...)
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  10. Extension and Measurement: A Constructivist Program From Leibniz to Grassmann.Erik C. Banks - 2013 - Studies in History and Philosophy of Science Part A 44 (1):20-31.
    Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.
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  11. Properly Extensive Quantities.Zee R. Perry - 2015 - Philosophy of Science 82 (5):833-844.
    This article introduces and motivates the notion of a “properly extensive” quantity by means of a puzzle about the reliability of certain canonical length measurements. An account of these measurements’ success, I argue, requires a modally robust connection between quantitative structure and mereology that is not mediated by the dynamics and is stronger than the constraints imposed by “mere additivity.” I outline what it means to say that length is not just extensive but properly so and then briefly sketch an (...)
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  12. Varieties of Indefinite Extensibility.Gabriel Uzquiano - 2015 - Notre Dame Journal of Formal Logic 56 (1):147-166.
    We look at recent accounts of the indefinite extensibility of the concept set and compare them with a certain linguistic model of indefinite extensibility. We suggest that the linguistic model has much to recommend over alternative accounts of indefinite extensibility, and we defend it against three prima facie objections.
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  13.  81
    Extensions of First Order Logic.María Manzano - 1996 - Cambridge University Press.
    Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them (...)
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  14. Cognitive Extension: The Parity Argument, Functionalism, and the Mark of the Cognitive.Sven Walter - 2010 - Synthese 177 (2):285-300.
    During the past decade, the so-called “hypothesis of cognitive extension,” according to which the material vehicles of some cognitive processes are spatially distributed over the brain and the extracranial parts of the body and the world, has received lots of attention, both favourable and unfavourable. The debate has largely focussed on three related issues: (1) the role of parity considerations, (2) the role of functionalism, and (3) the importance of a mark of the cognitive. This paper critically assesses these issues (...)
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  15. On Extensions of Elementary Logic.Per Lindström - 1969 - Theoria 35 (1):1-11.
  16.  63
    Life Extension, Human Rights, and the Rational Refinement of Repugnance.A. D. N. J. de Grey - 2005 - Journal of Medical Ethics 31 (11):659-663.
    On the ethics of extending human life: healthy people have a right to carry on livingHumanity has long demonstrated a paradoxical ambivalence concerning the extension of a healthy human lifespan. Modest health extension has been universally sought, whereas extreme health extension has been regarded as a snare and delusion—a dream beyond all others at first blush, but actually something we are better off without. The prevailing pace of biotechnological progress is bringing ever closer the day when humanity will be able (...)
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  17. Defending Extension Theory: A Response to Kiran and Verbeek.Richard Heersmink - 2012 - Philosophy and Technology 25 (1):121-128.
    In a recent publication in this journal, Asle Kiran and Peter-Paul Verbeek (hereafter K&V) argue that extension theory and the notion of trust it implies are flawed. In this commentary, I defend extension theory against their critique. I first briefly introduce extension theory, then reconstruct K&V’s five arguments against extension theory and demonstrate that four of their five arguments are misplaced.
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  18. Extensions of Priest-da Costa Logic.Thomas Macaulay Ferguson - 2014 - Studia Logica 102 (1):145-174.
    In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed (...)
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  19.  38
    On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
    In this paper we will study the properties of the least extension n(Λ) of a given intermediate logic Λ by a strong negation. It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n(Λ). This summarizes results that can be found already in [13, 14] and [4]. Furthermore, we determine the (...)
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  20.  79
    Extensions of Some Theorems of Gödel and Church.Barkley Rosser - 1936 - Journal of Symbolic Logic 1 (3):87-91.
  21.  14
    End Extensions of Models of Weak Arithmetic Theories.Costas Dimitracopoulos & Vasileios S. Paschalis - 2016 - Notre Dame Journal of Formal Logic 57 (2):181-193.
    We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of $B\Sigma_{1}$, that is, the theory of $\Sigma_{1}$ collection.
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  22.  72
    Canonical Extensions and Relational Completeness of Some Substructural Logics.J. Michael Dunn, Mai Gehrke & Alessandra Palmigiano - 2005 - Journal of Symbolic Logic 70 (3):713 - 740.
    In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.
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  23.  42
    Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming.Yining Wu, Martin Caminada & Dov M. Gabbay - 2009 - Studia Logica 93 (2):383-403.
    In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3-valued stable models in logic programming. This result is in line with earlier work of [6] that identified the correspondence between the grounded extension in abstract argumentation and the well-founded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming.
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  24.  50
    Extension of Family Resemblance Concepts as a Necessary Condition of Interpretation Across Traditions.Jaap Van Brakel & Lin Ma - 2015 - Dao: A Journal of Comparative Philosophy 14 (4):475-497.
    In this paper we extend Wittgenstein’s notion of family resemblance to translation, interpretation, and comparison across traditions. There is no need for universals. This holds for everyday concepts such as green and qing 青, philosophical concepts such as emotion and qing 情, as well as philosophical categories such as form of life and dao 道. These notions as well as all other concepts from whatever tradition are family resemblance concepts. We introduce the notion of quasi-universal, which connects family resemblance concepts (...)
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  25.  88
    Pure Extensions, Proof Rules, and Hybrid Axiomatics.Patrick Blackburn & Balder Ten Cate - 2006 - Studia Logica 84 (2):277-322.
    In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language to the strong Priorean language . We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the (...)
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  26.  40
    Logical Extensions of Aristotle’s Square.Dominique Luzeaux, Jean Sallantin & Christopher Dartnell - 2008 - Logica Universalis 2 (1):167-187.
    . We start from the geometrical-logical extension of Aristotle’s square in [6,15] and [14], and study them from both syntactic and semantic points of view. Recall that Aristotle’s square under its modal form has the following four vertices: A is □α, E is , I is and O is , where α is a logical formula and □ is a modality which can be defined axiomatically within a particular logic known as S5 (classical or intuitionistic, depending on whether is involutive (...)
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  27.  64
    Hazy Totalities and Indefinitely Extensible Concepts: An Exercise in the Interpretation of Dummett’s Philosophy of Mathematics.Alex Oliver - 1998 - Grazer Philosophische Studien 55 (1):25-50.
    Dummctt argues that classical quantification is illegitimate when the domain is given as the objects which fall under an indefinitely extensible concept, since in such cases the objects are not the required definite totality. The chief problem in understanding this complex argument is the crucial but unexplained phrase 'definite totality' and the associated claim that it follows from the intuitive notion of set that the objects over which a classical quantifier ranges form a set. 'Definite totality' is best understood as (...)
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  28. Extensive Philosophical Agreement and Progress.Bryan Frances - 2017 - Metaphilosophy 48 (1-2):47-57.
    This article argues, first, that there is plenty of agreement among philosophers on philosophically substantive claims, which fall into three categories: reasons for or against certain views, elementary truths regarding fundamental notions, and highly conditionalized claims. This agreement suggests that there is important philosophical progress. It then argues that although it's easy to list several potential kinds of philosophical progress, it is much harder to determine whether the potential is actual. Then the article attempts to articulate the truth that the (...)
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  29. Extensive Measurement and Ratio Functions.Brent Mundy - 1988 - Synthese 75 (1):1 - 23.
    Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. This is interpreted as involving (...)
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  30.  15
    Mencius’ Extension of Moral Feelings: Implications for Cosmopolitan Education.Charlene Tan - 2019 - Ethics and Education 14 (1):70-83.
    ABSTRACTThis article explores Mencius’ extension of moral feelings and its potential to address a key challenge in cosmopolitan education: how to motivate students to expand their existing affection and obligations towards their family and community to the rest of the world. Rather than strong universalism, a Mencian orientation is aligned with rooted cosmopolitanism that takes into account localised and cultural contexts that underpin, determine and give value to social practices. Mencius’ approach, as argued in this essay, highlights the spontaneous human (...)
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  31.  39
    Extensive Social Choice and the Measurement of Group Fitness in Biological Hierarchies.Walter Bossert, Chloe X. Qi & John A. Weymark - 2013 - Biology and Philosophy 28 (1):75-98.
    Extensive social choice theory is used to study the problem of measuring group fitness in a two-level biological hierarchy. Both fixed and variable group size are considered. Axioms are identified that imply that the group measure satisfies a form of consequentialism in which group fitness only depends on the viabilities and fecundities of the individuals at the lower level in the hierarchy. This kind of consequentialism can take account of the group fitness advantages of germ-soma specialization, which is not possible (...)
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  32.  87
    Loops, Constitution and Cognitive Extension.S. Orestis Palermos - 2014 - Cognitive Systems Research 27:25-41.
    The ‘causal-constitution’ fallacy, the ‘cognitive bloat’ worry, and the persisting theoretical confusion about the fundamental difference between the hypotheses of embedded (HEMC) and extended (HEC) cognition are three interrelated worries, whose common point—and the problem they accentuate—is the lack of a principled criterion of constitution. Attempting to address the ‘causal-constitution’ fallacy, mathematically oriented philosophers of mind have previously suggested that the presence of non-linear relations between the inner and the outer contributions is sufficient for cognitive extension. The abstract idea of (...)
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  33.  6
    Body-Extension Versus Body-Incorporation: Is There a Need for a Body-Model?Helena Preester & Manos Tsakiris - 2009 - Phenomenology and the Cognitive Sciences 8 (3):307-319.
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  34.  29
    Life Extension Research: An Analysis of Contemporary Biological Theories and Ethical Issues. [REVIEW]Jennifer Marshall - 2005 - Medicine, Health Care and Philosophy 9 (1):87-96.
    Many opinions and ideas about aging exist. Biological theories have taken hold of the popular and scientific imagination as potential answers to a “cure” for aging. However, it is not clear what exactly is being cured or whether aging could be classified as a disease. Some scientists are convinced that aging will be biologically alterable and that the human lifespan will be vastly extendable. Other investigators believe that aging is an elusive target that may only be “statistically” manipulatable through a (...)
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  35.  61
    Life Extension and Mental Ageing.Christopher Wareham - 2012 - Philosophical Papers 41 (3):455-477.
    Abstract Objections to life extension often focus on its effects for individual well-being. Prominent amongst these concerns is the possibility that life extending technologies will extend lifespan without preventing the ageing of the mind. Writers on the subject express the fear that life extending drugs will keep us physically youthful whilst our minds decay, succumbing to dementia, boredom, and loneliness. Generally these fears remain speculative, in part due to the absence of genuine life extending technologies. In this paper, however, I (...)
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  36.  8
    Extensions of Paraconsistent Weak Kleene Logic.Francesco Paoli & Michele Pra Baldi - forthcoming - Logic Journal of the IGPL.
    Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued logic, (...)
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  37.  41
    Life Extension Research: Health, Illness, and Death.Leigh Turner - 2004 - Health Care Analysis 12 (2):117-129.
    Scientists, bioethicists, and policy makers are currently engaged in a contentious debate about the scientific prospects and morality of efforts to increase human longevity. Some demographers and geneticists suggest that there is little reason to think that it will be possible to significantly extend the human lifespan. Other biodemographers and geneticists argue that there might well be increases in both life expectancy and lifespan. Bioethicists and policy makers are currently addressing many of the ethical, social, and economic issues raised by (...)
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  38.  48
    Extensions of the Lewis System S5.Schiller Joe Scroggs - 1951 - Journal of Symbolic Logic 16 (2):112-120.
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  39.  15
    Two Extensions of the Structurally Free Logic LC.K. Bimbó & J. Dunn - 1998 - Logic Journal of the IGPL 6 (3):403-424.
    The paper considers certain extensions of the system LC introduced in Dunn & Meyer 1997. LC is a structurally free system , but it has combinators as formulas in the place of structural rules. We consider two ways to extend LC with conjunction and disjunction depending on whether they distribute over each other or not. We prove the elimination theorem for the systems. At the end of the paper we give a Routley-Meyer style semantics for the distributive extension, including (...)
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  40. Extensive and Strategic Forms: Games and Models for Games.Robert Stalnaker - 1999 - Research in Economics 53 (3):293 - 319.
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  41.  17
    Whither Extensions?David Pereplyotchik - 2020 - Mind and Language 35 (2):237-250.
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  42. Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain I. Scattering Processes.P. C. W. Davies - unknown
    Institute of Theoretical Astronomy, University of Cambridge, Cambridge, UK 3fS. received 28th August 1970, in final revised form 1st July 1971..
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  43. Judgment, Extension, Logical Form.Luciano Codato - 2008 - In Kant-Gesellschaft E. V. Walter de Gruyter (ed.), Law and Peace in Kant’s Philosophy / Recht und Frieden in der Philosophie Kants. Walter de Gruyter. pp. 1--139.
    In Kant’s logical texts the reference of the form S is P to an “unknown = x” is well known, but its understanding still remains controversial. Due to the universality of all concepts, the subject as much as the predicate is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, this Kantian interpretation of the S-P relationship leads to the question about the relations between intuition and concept in judgment. (...)
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  44.  8
    Hazy Totalities and Indefinitely Extensible Concepts: An Exercise in the Interpretation of Dummett’s Philosophy of Mathematics.Alex Oliver - 1998 - Grazer Philosophische Studien 55 (1):25-50.
    Dummctt argues that classical quantification is illegitimate when the domain is given as the objects which fall under an indefinitely extensible concept, since in such cases the objects are not the required definite totality. The chief problem in understanding this complex argument is the crucial but unexplained phrase 'definite totality' and the associated claim that it follows from the intuitive notion of set that the objects over which a classical quantifier ranges form a set. 'Definite totality' is best understood as (...)
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  45. Life-Extension and the Malthusian Objection.John K. Davis - 2005 - Journal of Medicine and Philosophy 30 (1):27 – 44.
    The worst possible way to resolve this issue is to leave it up to individual choice. There is no known social good coming from the conquest of death (Bailey, 1999). - Daniel Callahan Dramatically extending the human lifespan seems increasingly possible. Many bioethicists object that life-extension will have Malthusian consequences as new Methuselahs accumulate, generation by generation. I argue for a Life-Years Response to the Malthusian Objection. If even a minority of each generation chooses life-extension, denying it to them deprives (...)
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  46.  16
    A Conservative Negation Extension of Positive Semilattice Logic Without the Finite Model Property.Yale Weiss - 2021 - Studia Logica 109 (1):125-136.
    In this article, I present a semantically natural conservative extension of Urquhart’s positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further research.
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  47.  19
    Extension and Comprehension in Logic.Joseph C. Frisch - 1969 - New York: Philosophical Library.
  48.  69
    The Extension of Color Sensations: Reid, Stewart, and Fearn.Giovanni B. Grandi - 2011 - Canadian Journal of Philosophy 41 (S1):50-79.
    According to Reid, color sensations are not extended nor are they arranged in figured patterns. Reid further claimed that ‘there is no sensation appropriated to visible figure.’ Reid justified these controversial claims by appeal to Cheselden's report of the experiences of a young man affected by severe cataracts, and by appeal to cases of perception of visible figure without color. While holding fast to the principle that sensations are not extended, Dugald Stewart tried to show that ‘a variety of colour (...)
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  49.  12
    Linear Extensions of Partial Orders and Reverse Mathematics.Emanuele Frittaion & Alberto Marcone - 2012 - Mathematical Logic Quarterly 58 (6):417-423.
    We introduce the notion of τ-like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω-like means that every element has finitely many predecessors, while being ζ-like means that every interval is finite. We consider statements of the form “any τ-like partial order has a τ-like linear extension” and “any τ-like partial order is embeddable into τ” . Working in the framework of reverse mathematics, we show that these (...)
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  50. Continuities and Extensions of Ethical Climate Theory: A Meta-Analytic Review.Kelly D. Martin & John B. Cullen - 2006 - Journal of Business Ethics 69 (2):175-194.
    Using traditional meta-analytic techniques, we compile relevant research to enhance conceptual appreciation of ethical climate theory (ECT) as it has been studied in the descriptive and applied ethics literature. We explore the various treatments of ethical climate to understand how the theoretical framework has developed. Furthermore, we provide a comprehensive picture of how the theory has been extended by describing the individual-level work climate outcomes commonly studied in this theoretical context. Meta-analysis allows us to resolve inconsistencies in previous findings as (...)
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