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Ansten Klev [35]Ansten Mørch Klev [3]
  1.  35
    Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - Cham, Switzerland: Springer Verlag.
    This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...)
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  2.  6
    The Harmony of Identity.Ansten Klev - 2019 - Journal of Philosophical Logic 48 (5):867-884.
    The standard natural deduction rules for the identity predicate have seemed to some not to be harmonious. Stephen Read has suggested an alternative introduction rule that restores harmony but presupposes second-order logic. Here it will be shown that the standard rules are in fact harmonious. To this end, natural deduction will be enriched with a theory of definitional identity. This leads to a novel conception of canonical derivation, on the basis of which the identity elimination rule can be justified in (...)
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  3.  14
    The Justification of Identity Elimination in Martin-Löf’s Type Theory.Ansten Klev - 2019 - Topoi 38 (3):577-590.
    On the basis of Martin-Löf’s meaning explanations for his type theory a detailed justification is offered of the rule of identity elimination. Brief discussions are thereafter offered of how the univalence axiom fares with respect to these meaning explanations and of some recent work on identity in type theory by Ladyman and Presnell.
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  4. Martin-Löf on the Validity of Inference.Ansten Klev - 2024 - In Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction. Springer Verlag. pp. 171-185.
    An inference is valid if it guarantees the transferability of knowledge from the premisses to the conclusion. If knowledge is here understood as demonstrative knowledge, and demonstration is explained as a chain of valid inferences, we are caught in an explanatory circle. In recent lectures, Per Martin-Löf has sought to avoid the circle by specifying the notion of knowledge appealed to in the explanation of the validity of inference as knowledge of a kind weaker than demonstrative knowledge. The resulting explanation (...)
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  5.  18
    Dedekind and Hilbert on the foundations of the deductive sciences.Ansten Klev - 2011 - Review of Symbolic Logic 4 (4):645-681.
    We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, whereas (...)
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  6.  86
    Carnap and Husserl.Ansten Klev - forthcoming - In Christian Dambock & Georg Schiemer (eds.), Rudolf Carnap Handbuch. Metzler Verlag.
    The first part of this entry details what is known about the personal encounters between Rudolf Carnap and Edmund Husserl. The second part looks at all the places in Carnap’s works where Husserl is cited.
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  7.  23
    Eta-rules in Martin-löf type theory.Ansten Klev - 2019 - Bulletin of Symbolic Logic 25 (3):333-359.
    The eta rule for a set A says that an arbitrary element of A is judgementally identical to an element of constructor form. Eta rules are not part of what may be called canonical Martin-Löf type theory. They are, however, justified by the meaning explanations, and a higher-order eta rule is part of that type theory. The main aim of this paper is to clarify this somewhat puzzling situation. It will be argued that lower-order eta rules do not, whereas the (...)
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  8.  7
    A Comparison of Type Theory with Set Theory.Ansten Klev - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 271-292.
    This paper discusses some of the ways in which Martin-Löf type theory differs from set theory. The discussion concentrates on conceptual, rather than technical, differences. It revolves around four topics: sets versus types; syntax; functions; and identity. The difference between sets and types is spelt out as the difference between unified pluralities and kinds, or sorts. A detailed comparison is then offered of the syntax of the two languages. Emphasis is put on the distinction between proposition and judgement, drawn by (...)
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  9.  9
    Spiritus Asper versus Lambda: On the Nature of Functional Abstraction.Ansten Klev - 2023 - Notre Dame Journal of Formal Logic 64 (2):205-223.
    The spiritus asper as used by Frege in a letter to Russell from 1904 bears resemblance to Church’s lambda. It is natural to ask how they relate to each other. An alternative approach to functional abstraction developed by Per Martin-Löf some thirty years ago allows us to describe the relationship precisely. Frege’s spiritus asper provides a way of restructuring a unary function name in Frege’s sense such that the argument place indicator occurs all the way to the right. Martin-Löf’s alternative (...)
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  10. A Comparison of Type Theory with Set Theory.Ansten Klev - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 271-292.
    This paper discusses some of the ways in which Martin-Löf type theory differs from set theory. The discussion concentrates on conceptual, rather than technical, differences. It revolves around four topics: sets versus types; syntax; functions; and identity. The difference between sets and types is spelt out as the difference between unified pluralities and kinds, or sorts. A detailed comparison is then offered of the syntax of the two languages. Emphasis is placed on the distinction between proposition and judgement, drawn by (...)
     
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  11.  68
    Modality and the structure of assertion.Ansten Klev - 2023 - In Igor Sedlár (ed.), Logica Yearbook 2022. London: College Publications. pp. 39-53.
    A solid foundation of modal logic requires a clear conception of the notion of modality. Modern modal logic treats modality as a propositional operator. I shall present an alternative according to which modality applies primarily to illocutionary force, that is, to the force, or mood, of a speech act. By a first step of internalization, modality applied at this level is pushed to the level of speech-act content. By a second step of internalization, we reach a propositional operator validating the (...)
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  12.  14
    The concept horse is a concept.Ansten Klev - 2018 - Review of Symbolic Logic 11 (3):547-572.
    I offer an analysis of the sentence "the concept horse is a concept". It will be argued that the grammatical subject of this sentence, "the concept horse", indeed refers to a concept, and not to an object, as Frege once held. The argument is based on a criterion of proper-namehood according to which an expression is a proper name if it is so rendered in Frege's ideography. The predicate "is a concept", on the other hand, should not be thought of (...)
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  13.  12
    A Road Map of Dedekind’s Theorem 66.Ansten Klev - 2018 - Hopos: The Journal of the International Society for the History of Philosophy of Science 8 (2):241-277.
    Richard Dedekind’s theorem 66 states that there exists an infinite set. Its proof invokes such apparently nonmathematical notions as the thought-world and the self. This article discusses the content and context of Dedekind’s proof. It is suggested that Dedekind took the notion of the thought-world from Hermann Lotze. The influence of Kant and Bernard Bolzano on the proof is also discussed, and the reception of the proof in the mathematical and philosophical literature is covered in detail.
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  14.  17
    Identity in Martin‐Löf type theory.Ansten Klev - 2021 - Philosophy Compass 17 (2):e12805.
    The logic of identity contains riches not seen through the coarse lens of predicate logic. This is one of several lessons to draw from the subtle treatment of identity in Martin‐Löf type theory, to which the reader will be introduced in this article. After a brief general introduction we shall mainly be concerned with the distinction between identity propositions and identity judgements. These differ from each other both in logical form and in logical strength. Along the way, connections to philosophical (...)
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  15.  16
    Identity in Martin‐Löf type theory.Ansten Klev - 2021 - Philosophy Compass 17 (2):e12805.
    Philosophy Compass, Volume 17, Issue 2, February 2022.
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  16.  9
    Dedekind's Logicism.Ansten Mørch Klev - 2015 - Philosophia Mathematica:nkv027.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  17.  10
    Husserl and Carnap on Regions and Formal Categories.Ansten Klev - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag. pp. 409-429.
    Husserl, in his doctrine of categories, distinguishes what he calls regions from what he calls formal categories. The former are most general domains, while the latter are topic-neutral concepts that apply across all domains. Husserl’s understanding of these notions of category is here discussed in detail. It is, moreover, argued that similar notions of category may be recognized in Carnap’s Der logische Aufbau der Welt.
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  18.  9
    Form of apprehension and the content-apprehension model in Husserl's Logical Investigations.Ansten Klev - 2013 - History of Philosophy & Logical Analysis 16:49-69.
    An act’s form of apprehension (Auffassungsform) determines whether it is a perception, an imagination, or a signitive act. It must be distinguished from the act’s quality, which determines whether the act is, for instance, assertoric, merely entertaining, wishing, or doubting. The notion of form of apprehension is explained by recourse to the so-called content–apprehension model (Inhalt-Auffassung Schema); it is characteristic of the Logical Investigations that in it all objectifying acts are analyzed in terms of that model. The distinction between intuitive (...)
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  19.  7
    Form of Apprehension and the Content-Apprehension Model in Husserl’s Logical Investigations.Ansten Klev - 2013 - History of Philosophy & Logical Analysis 16 (1):49-69.
    An act’s form of apprehension determines whether it is a perception, an imagination, or a signitive act. It must be distinguished from the act’s quality, which determines whether the act is, for instance, assertoric, merely entertaining, wishing, or doubting. The notion of form of apprehension is explained by recourse to the so-called content-apprehension model ; it is characteristic of the Logical Investigations that in it all objectifying acts are analyzed in terms of that model. The distinction between intuitive and signitive (...)
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  20.  11
    Carnap on unified science.Ansten Klev - 2016 - Studies in History and Philosophy of Science Part A 59:53-67.
    Unified science is a recurring theme in Carnap's work from the time of the Aufbau until the end of the 1930's. The theme is not constant, but knows several variations. I shall extract three quite precise formulations of the thesis of unified science from Carnap's work during this period: from the Aufbau, from Carnap's so-called syntactic period, and from "Testability and Meaning" and related papers. My main objective is to explain these formulations and to discuss their relation, both to each (...)
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  21.  19
    The Axiom of Choice is False Intuitionistically (in Most Contexts).Charles Mccarty, Stewart Shapiro & Ansten Klev - 2023 - Bulletin of Symbolic Logic 29 (1):71-96.
    There seems to be a view that intuitionists not only take the Axiom of Choice (AC) to be true, but also believe it a consequence of their fundamental posits. Widespread or not, this view is largely mistaken. This article offers a brief, yet comprehensive, overview of the status of AC in various intuitionistic and constructivist systems. The survey makes it clear that the Axiom of Choice fails to be a theorem in most contexts and is even outright false in some (...)
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  22.  43
    Husserl's Logical Grammar.Ansten Klev - 2018 - History and Philosophy of Logic 39 (3):232-269.
    Lecture notes from Husserl's logic lectures published during the last 20 years offer a much better insight into his doctrine of the forms of meaning than does the fourth Logical Investigation or any other work published during Husserl's lifetime. This paper provides a detailed reconstruction, based on all the sources now available, of Husserl's system of logical grammar. After having explained the notion of meaning that Husserl assumes in his later logic lectures as well as the notion of form of (...)
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  23. A Brief Introduction to Constructive Type Theory.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - In Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman (eds.), Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level. Cham, Switzerland: Springer Verlag. pp. 17--55.
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  24.  9
    Identity and Sortals.Ansten Klev - 2017 - Erkenntnis 82 (1):1-16.
    According to the sortal conception of the universe of individuals every individual falls under a highest sortal, or category. It is argued here that on this conception the identity relation is defined between individuals a and b if and only if a and b fall under a common category. Identity must therefore be regarded as a relation of the form \, with three arguments x, y, and Z, where Z ranges over categories, and where the range of x and y (...)
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  25.  10
    A Proof‐Theoretic Account of the Miners Paradox.Ansten Klev - 2016 - Theoria 82 (4):351-369.
    By maintaining that a conditional sentence can be taken to express the validity of a rule of inference, we offer a solution to the Miners Paradox that leaves both modus ponens and disjunction elimination intact. The solution draws on Sundholm's recently proposed account of Fitch's Paradox.
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  26.  7
    Dedekind's Logicism†.Ansten Mørch Klev - 2015 - Philosophia Mathematica 25 (3):341-368.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  27.  15
    Immanent Reasoning or Equality in Action A Dialogical Study.Shahid Rahman, Nicolas Clerbout, Ansten Klev, Zoe Conaughey & Juan Redmond - unknown
    PREFACEProf. Göran Sundholm of Leiden University inspired the group of Logic at Lille and Valparaíso to start a fundamental review of the dialogical conception of logic by linking it to constructive type logic. One of Sundholm's insights was that inference can be seen as involving an implicit interlocutor. This led to several investigations aimed at exploring the consequences of joining winning strategies to the proof-theoretical conception of meaning. The leading idea is, roughly, that while introduction rules lay down the conditions (...)
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  28. Advanced Dialogues: Play Level.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - In Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman (eds.), Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level. Cham, Switzerland: Springer Verlag.
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  29. Advanced Dialogues: Strategy Level.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - In Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman (eds.), Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level. Cham, Switzerland: Springer Verlag.
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  30. Basic Notions for Dialogical Logic.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - In Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman (eds.), Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level. Cham, Switzerland: Springer Verlag.
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  31. Concluding Remarks: A Plaidoyer for the Play Level.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - In Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman (eds.), Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level. Cham, Switzerland: Springer Verlag.
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  32. Material Dialogues.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - In Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman (eds.), Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level. Cham, Switzerland: Springer Verlag.
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  33. The Dialogical Roots of Equality: Dialogues for Immanent Reasoning.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - In Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman (eds.), Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level. Cham, Switzerland: Springer Verlag.
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  34.  4
    Carnap et les catégories.Ansten Klev - 2020 - Cahiers Philosophiques 2:27-40.
    Cet article donne un aperçu des diverses traces de la doctrine des catégories dans les écrits de Carnap. Les notions de catégories jouent un rôle particulièrement important dans le livre Der logische Aufbau der Welt, mais on les retrouve également dans de nombreuses autres œuvres de Carnap. Sa thèse fait allusion à des catégories en plusieurs endroits. Son approche de la logique a été, pendant longtemps, fondée sur la théorie des types, incarnation de la doctrine des catégories dans la logique (...)
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  35.  15
    Carnap’s Turn to the Thing Language.Ansten Klev - 2018 - Philosophia Scientiae 22:179-198.
    Les contributions de Carnap au Congrès de 1935 marquent un triple changement dans sa philosophie: son tournant sémantique; ce qui sera appelé plus tard « la libéralisation de l’empirisme»; et son adoption du « langage des choses» comme base du langage de la science. C’est ce troisième changement qui est examiné ici. On s’interroge en particulier sur les motifs qui ont poussé Carnap à adopter le langage des choses comme langage protocolaire de la science unifiée et sur les vertus de (...)
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  36.  5
    Carnap’s Turn to the Thing Language.Ansten Klev - 2018 - Philosophia Scientiae 22:179-198.
    Les contributions de Carnap au Congrès de 1935 marquent un triple changement dans sa philosophie: son tournant sémantique; ce qui sera appelé plus tard « la libéralisation de l’empirisme»; et son adoption du « langage des choses» comme base du langage de la science. C’est ce troisième changement qui est examiné ici. On s’interroge en particulier sur les motifs qui ont poussé Carnap à adopter le langage des choses comme langage protocolaire de la science unifiée et sur les vertus de (...)
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  37.  7
    Infinite time extensions of Kleene’s $${\mathcal{O}}$$.Ansten Mørch Klev - 2009 - Archive for Mathematical Logic 48 (7):691-703.
    Using infinite time Turing machines we define two successive extensions of Kleene’s ${\mathcal{O}}$ and characterize both their height and their complexity. Specifically, we first prove that the one extension—which we will call ${\mathcal{O}^{+}}$ —has height equal to the supremum of the writable ordinals, and that the other extension—which we will call ${\mathcal{O}}^{++}$ —has height equal to the supremum of the eventually writable ordinals. Next we prove that ${\mathcal{O}^+}$ is Turing computably isomorphic to the halting problem of infinite time Turing computability, (...)
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  38.  5
    Matthias Wille.* ›Largely unknown‹ Gottlob Frege und der posthume Ruhm ›alles in den Wind geschrieben‹ Gottlob Frege wider den Zeitgeist.Ansten Klev - 2020 - Philosophia Mathematica 28 (3):426-430.