Results for 'Topological semantics'

968 found
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  1. Modal logic S4 as a paraconsistent logic with a topological semantics.Marcelo E. Coniglio & Leonardo Prieto-Sanabria - 2017 - In Caleiro Carlos, Dionisio Francisco, Gouveia Paula, Mateus Paulo & Rasga João (eds.), Logic and Computation: Essays in Honour of Amilcar Sernadas. College Publications. pp. 171-196.
    In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new (...)
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  2. Topological Aspects of Epistemology and Metaphysics.Thomas Mormann - 2020 - In Silvano Zipoli Caiani & Alberto Peruzzi (eds.), Structures Mères: Semantics, Mathematics, and Cognitive Science. Springer. pp. 135 - 152.
    The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be (...)
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  3. Completeness and Doxastic Plurality for Topological Operators of Knowledge and Belief.Thomas Mormann - 2023 - Erkenntnis: 1 - 34, ONLINE.
    The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of (...)
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  4. Prototypes, Poles, and Topological Tessellations of Conceptual Spaces.Thomas Mormann - 2021 - Synthese 199 (1):3675 - 3710.
    Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type (...)
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  5.  69
    On the Gettier Problem for Topological Logic of Knowledge and Belief.Thomas Mormann - manuscript
    Abstract. Gettier’s famous examples intended to show that knowledge cannot always be equated with justified true belief. The Gettier problem can also be considered as a problem for topological epistemic logic: If knowledge and justified belief are conceived as topological operators K and B on topological spaces (to be considered as universes of possible worlds), one may ask whether it happens that there is a proposition A such that KA ≠ A & BA or not. If this (...)
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  6. Putting the World Back into Semantics.Barry Smith - 1993 - Grazer Philosophische Studien 44 (1):91-109.
    To what in reality do the logically simple sentences with empirical content correspond? Two extreme positions can be distinguished in this regard: 'Great Fact' theories, such as are defended by Davidson; and trope-theories, which see such sentences being made the simply by those events or states to which the relevant main verbs correspond. A position midway between these two extremes is defended, one according to which sentences of the given sort are made tme by what are called 'dependence structures', or (...)
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  7. Mathematical realism and conceptual semantics.Luke Jerzykiewicz - 2012 - In Oleg Prosorov (ed.), Topologies and Sheaves Appeared as Syntax and Semantics of Natural Language. Steklov Institute of Mathematics.
    The dominant approach to analyzing the meaning of natural language sentences that express mathematical knowl- edge relies on a referential, formal semantics. Below, I discuss an argument against this approach and in favour of an internalist, conceptual, intensional alternative. The proposed shift in analytic method offers several benefits, including a novel perspective on what is required to track mathematical content, and hence on the Benacerraf dilemma. The new perspective also promises to facilitate discussion between philosophers of mathematics and cognitive (...)
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  8. Rumfitt on truth-grounds, negation, and vagueness.Richard Zach - 2018 - Philosophical Studies 175 (8):2079-2089.
    In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.
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  9. Belief Modalities Defined by Nuclei.Thomas Mormann - manuscript
    Abstract. The aim of this paper is to show that the topological interpretation of knowledge as an interior kernel operator K of a topological space (X, OX) comes along with a partially ordered family of belief modalities B that fit K in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB logic of knowledge and belief with the exception of the contentious axiom of negative introspection (NI). The new belief modalities B introduced in this (...)
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  10. Vagueness and Intuitionistic Logic.Ian Rumfitt - forthcoming - In Alexander Miller (ed.), Language, Logic,and Mathematics: Themes from the Philosophy of Crispin Wright. Oxford University Press.
    In his essay ‘“Wang’s Paradox”’, Crispin Wright proposes a solution to the Sorites Paradox (in particular, the form of it he calls the ‘Paradox of Sharp Boundaries’) that involves adopting intuitionistic logic when reasoning with vague predicates. He does not give a semantic theory which accounts for the validity of intuitionistic logic (and the invalidity of stronger logics) in that area. The present essay tentatively makes good the deficiency. By applying a theorem of Tarski, it shows that intuitionistic logic is (...)
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  11. Word Order and Incremental Update.Maria Bittner - 2003 - In Proceedings from CLS 39-1. CLS.
    The central claim of this paper is that surface-faithful word-by-word update is feasible and desirable, even in languages where word order is supposedly free. As a first step, in sections 1 and 2, I review an argument from Bittner 2001a that semantic composition is not a static process, as in PTQ, but rather a species of anaphoric bridging. But in that case the context-setting role of word order should extend from cross-sentential discourse anaphora to sentence-internal anaphoric composition. This can be (...)
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  12.  85
    The Algebras of Lewis Counterfactuals.Giuliano Rosella & Sara Ugolini - manuscript
    The logico-algebraic study of Lewis's hierarchy of variably strict conditional logics has been essentially unexplored, hindering our understanding of their mathematical foundations, and the connections with other logical systems. This work aims to fill this gap by providing a comprehensive logico-algebraic analysis of Lewis's logics. We begin by introducing novel finite axiomatizations for varying strengths of Lewis's logics, distinguishing between global and local consequence relations on Lewisian sphere models. We then demonstrate that the global consequence relation is strongly algebraizable in (...)
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  13. Reasoning about Space: The Hole Story.Achille C. Varzi - 1996 - Logic and Logical Philosophy 4:3-39.
    This is a revised and extended version of the formal theory of holes outlined in the Appendix to the book "Holes and Other Superficialities". The first part summarizes the basic framework (ontology, mereology, topology, morphology). The second part emphasizes its relevance to spatial reasoning and to the semantics of spatial prepositions in natural language. In particular, I discuss the semantics of ‘in’ and provide an account of such fallacious arguments as “There is a hole in the sheet. The (...)
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  14. Translations between logical systems: a manifesto.Walter A. Carnielli & Itala Ml D'Ottaviano - 1997 - Logique Et Analyse 157:67-81.
    The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, logics together with translations form a (...)
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  15. L'infinité des nombres premiers : une étude de cas de la pureté des méthodes.Andrew Arana - 2011 - Les Etudes Philosophiques 97 (2):193.
    Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...)
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  16. Modulated logics and flexible reasoning.Walter Carnielli & Maria Cláudia C. Grácio - 2008 - Logic and Logical Philosophy 17 (3):211-249.
    This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new monotonic logical systems are proposed here, the “Logic of (...)
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  17. Topological Explanations: An Opinionated Appraisal.Daniel Kostić - 2022 - In Insa Lawler, Kareem Khalifa & Elay Shech (eds.), Scientific Understanding and Representation: Modeling in the Physical Sciences. New York, NY: Routledge. pp. 96-115.
    This chapter provides a systematic overview of topological explanations in the philosophy of science literature. It does so by presenting an account of topological explanation that I (Kostić and Khalifa 2021; Kostić 2020a; 2020b; 2018) have developed in other publications and then comparing this account to other accounts of topological explanation. Finally, this appraisal is opinionated because it highlights some problems in alternative accounts of topological explanations, and also it outlines responses to some of the main (...)
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  18. Decoupling Topological Explanations from Mechanisms.Daniel Kostic & Kareem Khalifa - 2023 - Philosophy of Science 90 (2):245 - 268.
    We provide three innovations to recent debates about whether topological or “network” explanations are a species of mechanistic explanation. First, we more precisely characterize the requirement that all topological explanations are mechanistic explanations and show scientific practice to belie such a requirement. Second, we provide an account that unifies mechanistic and non-mechanistic topological explanations, thereby enriching both the mechanist and autonomist programs by highlighting when and where topological explanations are mechanistic. Third, we defend this view against (...)
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  19. The Topology of Communities of Trust.Mark Alfano - 2016 - Russian Sociological Review 15 (4):30-56.
    Hobbes emphasized that the state of nature is a state of war because it is characterized by fundamental and generalized distrust. Exiting the state of nature and the conflicts it inevitably fosters is therefore a matter of establishing trust. Extant discussions of trust in the philosophical literature, however, focus either on isolated dyads of trusting individuals or trust in large, faceless institutions. In this paper, I begin to fill the gap between these extremes by analyzing what I call the topology (...)
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  20. Topological Models of Columnar Vagueness.Thomas Mormann - 2020 - Erkenntnis 87 (2):693 - 716.
    This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent (...) reconstruction of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)
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  21. General Theory of Topological Explanations and Explanatory Asymmetry.Daniel Kostic - 2020 - Philosophical Transactions of the Royal Society B: Biological Sciences 375 (1796):1-8.
    In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B. Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true (...)
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  22. Topology as an Issue for History of Philosophy of Science.Thomas Mormann - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. pp. 423--434.
    Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from the central position it (...)
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  23. Topology of Balasaguni's Kutadgu Bilig. Thinking the Between.Onur Karamercan - 2021 - In Takeshi Morisato & Roman Pașca (eds.), Vanishing Subjectivity: Flower, Shame, and Direct Cultivation in Asian PhilosophiesAsian Philosophical Texts, no. 3. pp. 69-97.
    In “Topology of Balasaguni’s Kutadgu Bilig: Thinking the Between,” Onur Karamercan focuses on the philosophical dimension of Kutadgu Bilig, a poetic work of Yūsuf Balasaguni, an 11th century Central Asian thinker, poet, and statesman. Karamercan pays special attention to the meaning of betweenness and, in the first step of his argument, discusses the hermeneutic and topological implications of the between, distingushing the dynamic sense of betweenness from a static sense of in-betweenness. He then moves on to analyze Balasaguni’s notion (...)
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  24. (1 other version)Semantic normativity.Åsa Maria Wikforss - 2001 - Philosophical Studies 102 (2):203-26.
    My paper examines the popular idea, defended by Kripke, that meaning is an essentially normative notion. I consider four common versions of this idea and suggest that none of them can be supported, either because the alleged normativity has nothing to do with normativity or because it cannot plausibly be said that meaning is normative in the sense suggested. I argue that contrary to received opinion, we don’t need normativity to secure the possibility of meaning. I conclude by considering the (...)
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  25. Topological Essentialism.Roberto Casati & Achille Varzi - 2000 - Philosophical Studies 100 (3):217-236.
    Considering topology as an extension of mereology, this paper analyses topological variants of mereological essentialism (the thesis that an object could not have different parts than the ones it has). In particular, we examine de dicto and de re versions of two theses: (i) that an object cannot change its external connections (e.g., adjacent objects cannot be separated), and (ii) that an object cannot change its topological genus (e.g., a doughnut cannot turn into a sphere). Stronger forms of (...)
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  26. Semantic Internalism and Externalism In Paleolinguistics: Mind Your Language About Proto‐Indo‐European Mind And Language!Vanja Subotić - 2024 - In Janko Nešić & Vanja Subotić (eds.), Philosophy, Cognition, and Archaeology. Belgrade: University of Belgrade – Faculty of Philosophy. pp. 175-194.
    Paleolinguistics (or linguistic paleontology) is a scientific discipline that combines the methodology of historical linguistics with archaeological insights. Specifically, paleolinguists aim to reconstruct the linguistic expression of a particular archeological culture. In this paper I deal with the methodology of paleolinguistics since this has recently come under the scrutiny of philosophersfor instance, Mallory (2020) has argued that tools of the philosophy of language can be employed for charting the space of legitimate use of paleolinguistics, most notably the position of semantic (...)
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  27. Truthmaker Semantics for Relevant Logic.Mark Jago - 2020 - Journal of Philosophical Logic 49 (4):681-702.
    I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant (...)
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  28. Cosmic Topology, Underdetermination, and Spatial Infinity.Patrick James Ryan - 2024 - European Journal for Philosophy of Science 14 (17):1-28.
    It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to prefer various (...) properties over others. In particular, I favor the adoption of multiply connected universe models on grounds of (i) simplicity, (ii) Machian considerations, and (iii) explanatory power. We are able to appeal to such grounds because multiply connected topologies open up the possibility of finite universe models (consistent with our best data), which in turn avoid thorny issues concerning the postulation of an actually infinite universe. (shrink)
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  29. Semantics without semantic content.Daniel W. Harris - 2020 - Mind and Language 37 (3):304-328.
    I argue that semantics is the study of the proprietary database of a centrally inaccessible and informationally encapsulated input–output system. This system’s role is to encode and decode partial and defeasible evidence of what speakers are saying. Since information about nonlinguistic context is therefore outside the purview of semantic processing, a sentence’s semantic value is not its content but a partial and defeasible constraint on what it can be used to say. I show how to translate this thesis into (...)
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  30. The Directionality of Topological Explanations.Daniel Kostić & Kareem Khalifa - 2021 - Synthese (5-6):14143-14165.
    Proponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the ‘directionality’ of explanation, i.e., the requirement that if X explains Y , then not-Y does not explain not-X . Using topological explanations as an illustration, we argue that non-ontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which neuroscientists rely on (...)
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  31. Syntax, Semantics, and Computer Programs.William J. Rapaport - 2020 - Philosophy and Technology 33 (2):309-321.
    Turner argues that computer programs must have purposes, that implementation is not a kind of semantics, and that computers might need to understand what they do. I respectfully disagree: Computer programs need not have purposes, implementation is a kind of semantic interpretation, and neither human computers nor computing machines need to understand what they do.
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  32. Topological Aspects of Combinatorial Possibility.Thomas Mormann - 1997 - Logic and Logical Philosophy 5:75 - 92.
    The aim of this paper is to show that topology has a bearing on<br><br>combinatorial theories of possibility. The approach developed in this article is “mapping account” considering combinatorial worlds as mappings from individuals to properties. Topological structures are used to define constraints on the mappings thereby characterizing the “really possible” combinations. The mapping approach avoids the well-known incompatibility problems. Moreover, it is compatible with atomistic as well as with non-atomistic ontologies.It helps to elucidate the positions of logical atomism and (...)
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  33. Sexual topologies in the Aristotelian cosmos: revisiting Irigaray’s physics of sexual difference.Emanuela Bianchi - 2010 - Continental Philosophy Review 43 (3):373-389.
    Irigaray’s engagement with Aristotelian physics provides a specific diagnosis of women’s ontological and ethical situation under Western metaphysics: Women provide place and containership to men, but have no place of their own, rendering them uncontained and abyssal. She calls for a reconfiguration of this topological imaginary as a precondition for an ethics of sexual difference. This paper returns to Aristotelian cosmological texts to further investigate the topologies of sexual difference suggested there. In an analysis both psychoanalytic and phenomenological, the (...)
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  34. Semantics and the Computational Paradigm in Cognitive Psychology.Eric Dietrich - 1989 - Synthese 79 (1):119-141.
    There is a prevalent notion among cognitive scientists and philosophers of mind that computers are merely formal symbol manipulators, performing the actions they do solely on the basis of the syntactic properties of the symbols they manipulate. This view of computers has allowed some philosophers to divorce semantics from computational explanations. Semantic content, then, becomes something one adds to computational explanations to get psychological explanations. Other philosophers, such as Stephen Stich, have taken a stronger view, advocating doing away with (...)
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  35.  27
    Topological Analysis of Non-Commutative Scalar Fields and Fractal Patterns.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1.
    We investigate the topological properties of scalar field configurations influenced by non-commutative geometry and time-dependent perturbations. Specifically, we analyze the connectedness of level sets of scalar fields, compute the fractal dimensions of generated patterns, and study the impact of varying non-commutative parameters. Utilizing numerical simulations, we provide evidence of topological bifurcations induced by non-commutative corrections. The analysis is framed within point set topology, and the results are formalized using the theorem-proof structure.
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  36. (1 other version)Topological foundations of cognitive science.Barry Smith - 1994 - In Topological foundations of cognitive science. Hamburg: Graduiertenkolleg Kognitionswissenschaft. pp. 3-22.
    This is a revised version of the introductory essay in C. Eschenbach, C. Habel and B. Smith (eds.), Topological Foundations of Cognitive Science, Hamburg: Graduiertenkolleg Kognitionswissenschaft, 1994, the text of a talk delivered at the First International Summer Institute in Cognitive Science in Buffalo in July 1994.
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  37. Map Semantics and the Geography of Meaning.Gabriel Greenberg - 2024 - In Ernest Lepore & Luvell Anderson (eds.), The Oxford Handbook of Applied Philosophy of Language. New York, NY: Oxford University Press. pp. 489-522.
    This chapter develops a semantic theory for maps and situates it within the broader geography of meaning and semiotic significance. The discussion focuses on three central aspects of map semantics: the use of space, line marking, and linguistic tags. It is argued that the treatment of space in maps must be based on geometrical projection from a viewpoint rather than the traditional analysis in terms of spatial isomorphism. The chapter then shows how to integrate the projection-based semantics of (...)
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  38. Hyperintensional semantics: a Fregean approach.Mattias Skipper & Jens Christian Bjerring - 2020 - Synthese 197 (8):3535-3558.
    In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...)
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  39. Topological Foundations of Cognitive Science.Carola Eschenbach, Christopher Habel & Barry Smith (eds.) - 1984 - Hamburg: Graduiertenkolleg Kognitionswissenschaft.
    A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo (...)
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  40. Truthmaker Semantics in Linguistics (3rd edition).Mark Jago - forthcoming - In Hilary Nesi & Petar Milin (eds.), International Encyclopedia of Language and Linguistics. Elsevier.
    Truthmaker semantics is a recent development in formal and philosophical semantics, with similar motivation and scope to possible worlds semantics. The technical background is rather different, however, and results in a more fine-grained hyperintensional notion of content, allowing us to distinguish between classically equivalent propositions. After briefly introducing the main ideas, this entry will describe the technical apparatus of state spaces and the central notions of content and partial content. It will then outline applications of truthmaker (...) in language, logic, and other areas of philosophy. (shrink)
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  41. New Neutrosophic Crisp Topological Concepts.A. Salama, Florentin Smarandache & S. A. Alblowi - 2014 - Neutrosophic Sets and Systems 4:50-54.
    In this paper, we introduce the concept of ""neutrosophic crisp neighborhoods system for the neutrosophic crisp point ". Added to, we introduce and study the concept of neutrosophic crisp local function, and construct a new type of neutrosophic crisp topological space via neutrosophic crisp ideals. Possible application to GIS topology rules are touched upon.
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  42. Foundation of Revolutionary Topologies: An Overview, Examples, Trend Analysis, Research Issues, Challenges, and Future Directions.Florentin Smarandache - 2024 - Neutrosophic Systems with Applications 13:45-66.
    We now found nine new topologies, such as: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, and recall and improve the seven previously founded topologies in the years (2019-2023), namely: NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. They are called avantgarde topologies because of their innovative forms.
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  43. The Semantic Error Problem for Epistemic Contextualism.Patrick Michael Greenough & Dirk Kindermann - 2017 - In Jonathan Jenkins Ichikawa (ed.), The Routledge Handbook of Epistemic Contextualism. New York: Routledge. pp. 305--320.
    Epistemic Contextualism is the view that “knows that” is semantically context-sensitive and that properly accommodating this fact into our philosophical theory promises to solve various puzzles concerning knowledge. Yet Epistemic Contextualism faces a big—some would say fatal—problem: The Semantic Error Problem. In its prominent form, this runs thus: speakers just don’t seem to recognise that “knows that” is context-sensitive; so, if “knows that” really is context-sensitive then such speakers are systematically in error about what is said by, or how to (...)
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  44. Is semantics formal?Mark Schroeder - manuscript
    In this paper I will be concerned with the question of the extent to which semantics can be thought of as a purely formal exercise, which we can engage in in a way that is neutral with respect to how our formal system is to be interpreted. I will be arguing, to the contrary, that the features of the formal systems which we use to do semantics are closely linked, in several different ways, to the interpretation that we (...)
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  45. Topology and Leibniz's principle of the Identity of Indiscernibles.Mormann Thomas - manuscript
    The aim of this paper is to show that topology has a bearing on Leibniz’s Principle of the Identity of Indiscernibles (PII). According to (PII), if, for all properties F, an object a has property F iff object b has property F, then a and b are identical. If any property F whatsoever is permitted in PII, then Leibniz’s principle is trivial, as is shown by “identity properties”. The aim of this paper is to show that topology can make a (...)
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  46. Compact Open Topology and Evaluation Map via Neutrosophic Sets.R. Dhavaseelan, S. Jafari & F. Smarandache - 2017 - Neutrosophic Sets and Systems 16:35-38.
    The concept of neutrosophic locally compact and neutrosophic compact open topology are introduced and some interesting propositions are discussed.
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  47. Semantic capital: its nature, value, and curation.Luciano Floridi - 2018 - Philosophy and Technology 31 (4):481-497.
    There is a wealth of resources— ideas, insights, discoveries, inventions, traditions, cultures, languages, arts, religions, sciences, narratives, stories, poems, customs and norms, music and songs, games and personal experiences, and advertisements—that we produce, curate, consume, transmit, and inherit as humans. This wealth, which I define as semantic capital, gives meaning to, and makes sense of, our own existence and the world surrounding us. It defines who we are and enables humans to develop an individual and social life. This paper discusses (...)
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  48. Topological Games, Supertasks, and (Un)determined Experiments.Thomas Mormann - manuscript
    The general aim of this paper is to introduce some ideas of the theory of infinite topological games into the philosophical debate on supertasks. First, we discuss the elementary aspects of some infinite topological games, among them the Banach-Mazur game.Then it is shown that the Banach-Mazur game may be conceived as a Newtonian supertask.In section 4 we propose to conceive physical experiments as infinite games. This leads to the distinction between determined and undetermined experiments and the problem of (...)
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  49. Pietroski on possible worlds semantics for belief sentences.Joe Lau - 1995 - Analysis 55 (4):295-298.
    Pietroski (1993) offers a semantics for belief sentences that is supposed to address the problem of equivalence. This paper argues that his proposal fails to solve the problem.
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  50. Functorial Semantics for the Advancement of the Science of Cognition.Venkata Posina, Dhanjoo N. Ghista & Sisir Roy - 2017 - Mind and Matter 15 (2):161-184.
    Cognition involves physical stimulation, neural coding, mental conception, and conscious perception. Beyond the neural coding of physical stimuli, it is not clear how exactly these component processes constitute cognition. Within mathematical sciences, category theory provides tools such as category, functor, and adjointness, which are indispensable in the explication of the mathematical calculations involved in acquiring mathematical knowledge. More speci cally, functorial semantics, in showing that theories and models can be construed as categories and functors, respectively, and in establishing the (...)
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