18 found
Order:
Disambiguations
Ansten Klev [16]Ansten Mørch Klev [2]
See also
Ansten Klev
Czech Academy of Sciences
  1.  5
    Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - Springer Verlag.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  2. A Comparison of Type Theory with Set Theory.Ansten Klev - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. 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 (...)
     
    Export citation  
     
    Bookmark   1 citation  
  3.  22
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  20
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  5.  52
    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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  53
    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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  7.  95
    Form of Apprehension and the Content-Apprehension Model in Husserl's Logical Investigations.Ansten Klev - 2013 - Logical Analysis and History of Philosophy 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  8.  9
    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: 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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  9.  31
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10.  14
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11.  3
    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.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  12.  72
    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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  13.  38
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  14.  35
    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, (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  15.  26
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  16.  44
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  17.  19
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  18.  10
    Carnap’s Turn to the Thing Language.Ansten Klev - 2018 - Philosophia Scientiæ. Travaux d'Histoire Et de Philosophie des Sciences 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark