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Profile: Kai Wehmeier (University of California, Irvine)
  1. Kai F. Wehmeier (2014). Nothing But D‐Truth. Analytic Philosophy 55 (1):114-117.
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  2. Kai F. Wehmeier (2014). Still Living Without Identity: Reply to Trueman. Australasian Journal of Philosophy 92 (1):173-175.
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  3. Allen P. Hazen, Benjamin G. Rin & Kai F. Wehmeier (2013). Actuality in Propositional Modal Logic. Studia Logica 101 (3):487-503.
    We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality (...)
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  4. Sven Schlotter & Kai F. Wehmeier (2013). Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians–Two Recently Discovered Documents. British Journal for the History of Philosophy 21 (3):591 - 609.
    (2012). Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians – Two Recently Discovered Documents. British Journal for the History of Philosophy. ???aop.label???. doi: 10.1080/09608788.2012.692665.
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  5. Kai Wehmeier (2013). Subjunctivity and Conditionals. Journal of Philosophy 110 (3):117-142.
     
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  6. Brian Rogers & Kaif Wehmeier (2012). Tractarian First-Order Logic: Identity and the N-Operator. Review of Symbolic Logic 5 (4):538-573.
    In the Tractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikkas, for (...)
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  7. Kai Wehmeier (2012). Subjunctivity and Cross-World Predication. Philosophical Studies 159 (1):107-122.
    The main goal of this paper is to present and compare two approaches to formalizing cross-world comparisons like John might have been taller than he is in quantified modal logics. One is the standard method employing degrees and graded positives, according to which the example just given is to be paraphrased as something like The height that John has is such that he might have had a height greater than it, which is amenable to familiar formalization strategies with respect to (...)
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  8. Kai F. Wehmeier (2012). How to Live Without Identity—And Why. Australasian Journal of Philosophy 90 (4):761 - 777.
    Identity, we're told, is the binary relation that every object bears to itself, and to itself only. But how can a relation be binary if it never relates two objects? This puzzled Russell and led Wittgenstein to declare that identity is not a relation between objects. The now standard view is that Wittgenstein's position is untenable, and that worries regarding the relational status of identity are the result of confusion. I argue that the rejection of identity as a binary relation (...)
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  9. Kai F. Wehmeier (2012). 2011 Spring Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 18 (1).
     
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  10. Anuj Dawar Colyvan, Marcelo Fiore, Noam Greenberg, Hannes Leitgeb, Rahim Moosa, Ernest Schimmerling, Carsten Schürmann & Kai Wehmeier (2011). College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW] Bulletin of Symbolic Logic 17 (1).
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  11. Mark Colyvan Burgess, Anuj Dawar, Marcelo Fiore, Noam Greenberg, Hannes Leitgeb, Ernest Schimmerling, Carsten Schürmann & Kai Wehmeier (2010). College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW] Bulletin of Symbolic Logic 16 (3).
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  12. Burgess Mark Colyvan Anuj Dawar Mirna, Marcelo Fiore Dzamonja, Hannes Leitgeb, Roger Maddux, Andre Nies Carsten Schurmann, Kai Wehmeier & Matthias Wille Au (2009). The Association for Symbolic Logic Publishes Analytical Reviews of Selected Books and Articles in the Field of Symbolic Logic. The Reviews Were Published in The Journal of Symbolic Logic From the Founding of the Journal in 1936 Until the End of 1999. The Association Moved the Reviews to This Bulletin, Beginning in 2000. The Reviews Section is Edited by Steve Awodey (Managing Editor). John Baldwin, John. [REVIEW] Bulletin of Symbolic Logic 15 (2).
     
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  13. Kai Wehmeier (2009). On Ramsey's 'Silly Delusion' Regarding Tractatus 5.53. In Giuseppe Primiero & Shahid Rahman (eds.), Acts of Knowledge - History, Philosophy and Logic. College Publications.
    We investigate a variant of the variable convention proposed at Tractatus 5.53ff for the purpose of eliminating the identity sign from logical notation. The variant in question is what Hintikka has called the strongly exclusive interpretation of the variables, and turns out to be what Ramsey initially (and erroneously) took to be Wittgenstein's intended method. We provide a tableau calculus for this identity-free logic, together with soundness and completeness proofs, as well as a proof of mutual interpretability with first-order logic (...)
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  14. Kai F. Wehmeier (2008). Wittgensteinian Tableaux, Identity, and Co-Denotation. Erkenntnis 69 (3):363 - 376.
    Wittgensteinian predicate logic (W-logic) is characterized by the requirement that the objects mentioned within the scope of a quantifier be excluded from the range of the associated bound variable. I present a sound and complete tableaux calculus for this logic and discuss issues of translatability between Wittgensteinian and standard predicate logic in languages with and without individual constants. A metalinguistic co-denotation predicate, akin to Frege’s triple bar of the Begriffsschrift, is introduced and used to bestow the full expressive power of (...)
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  15. Hans-Christoph Schmidt Am Busch & Kai F. Wehmeier (2007). On the Relations Between Heinrich Scholz and Jan Łukasiewicz. History and Philosophy of Logic 28 (1):67-81.
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  16. Hans-Christoph Schmidt Am Busch & Kai Wehmeier (2007). On the Relations Between Heinrich Scholz and Jan Łukasiewicz. History and Philosophy of Logic 28 (1):67-81.
    The aim of the present study is (1) to show, on the basis of a number of unpublished documents, how Heinrich Scholz supported his Warsaw colleague Jan ?ukasiewicz, the Polish logician, during World War II, and (2) to discuss the efforts he made in order to enable Jan ?ukasiewicz and his wife Regina to move from Warsaw to Münster under life-threatening circumstances. In the first section, we explain how Scholz provided financial help to ?ukasiewicz, and we also adduce evidence of (...)
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  17. Kai F. Wehmeier (2005). Modality, Mood, and Descriptions. In Reinhard Kahle (ed.), Intensionality: An Interdisciplinary Discussion. AK Peters.
    §1. Introduction. By means of what semantic features is a proper name tied to its bearer? This is a puzzling question indeed: proper names — like “Aristotle” or “Paris” — are syntactically simple, and it therefore does not seem possible to reduce their meanings, by means of a principle of compositionality, to the meanings of more basic, and hence perhaps more tractable, linguistic elements.
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  18. Kai Frederick Wehmeier & Peter Schroeder-Heister (2005). Frege's Permutation Argument Revisited. Synthese 147 (1):43 - 61.
    any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identiability thesis, following Schroeder-Heister [13]). As far as we are aware, there is no consensus in the literature as to (i) the proper interpretation of the permutation argument and the identiability thesis, (ii) the validity of the permutation argument, and (iii) the truth of the identiability thesis.1 In this paper, we undertake a detailed technical study of the two main lines of interpretation, (...)
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  19. Kai Wehmeier (2004). Wittgensteinian Predicate Logic. Notre Dame Journal of Formal Logic 45 (1):1-11.
    We investigate a rst-order predicate logic based on Wittgenstein's suggestion to express identity of object by identity of sign, and difference of objects by difference of signs. Hintikka has shown that predicate logic can indeed be set up in such a way; we show that it can be done nicely. More specically, we provide a perspicuous cut-free sequent calculus, as well as a Hilbert-type calculus, for Wittgensteinian predicate logic and prove soundness and completeness theorems.
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  20. Kai F. Wehmeier (2004). Russell's Paradox in Consistent Fragments of Frege's Grundgesetze der Arithmetik. In Godehard Link (ed.), One Hundred Years of Russell’s Paradox. de Gruyter.
    We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.
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  21. Kai Frederick Wehmeier (2004). In the Mood. Journal of Philosophical Logic 33 (6):607-630.
    The purpose of the present paper is to challenge some received assumptions about the logical analysis of modal English, and to show that these assumptions are crucial to certain debates in current philosophy of language. Specifically, I will argue that the standard analysis in terms of quantified modal logic mistakenly fudges important grammatical distinctions, and that the validity of Kripke's modal argument against description theories of proper names crucially depends on ensuing equivocations.
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  22. Kai F. Wehmeier (2003). World Travelling and Mood Swings. In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences II. Kluwer.
    It is not quite as easy to see that there is in fact no formula of this modal language having the same truth conditions (in terms of S5 Kripke semantics) as (1). This was rst conjectured by Allen Hazen2 and later proved by Harold Hodes3. We present a simple direct proof of this result and discuss some consequences for the logical analysis of ordinary modal discourse.
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  23. Fernando Ferreira & Kai F. Wehmeier (2002). On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze. Journal of Philosophical Logic 31 (4):301-311.
    It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension (...)
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  24. Kai F. Wehmeier (1999). Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects. Synthese 121 (3):309-328.
    In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T (...)
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  25. Kai F. Wehmeier (1998). Fragments of HA Based on B-Induction. Archive for Mathematical Logic 37 (1):37-50.
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  26. Kai Wehmeier (1997). Fragments of HA Based on Sigma_1 Induction. Archive for Mathematical Logic 37 (1):37-49.
    In the first part of this paper we investigate the intuitionistic version $iI\!\Sigma_1$ of $I\!\Sigma_1$ (in the language of $PRA$ ), using Kleene's recursive realizability techniques. Our treatment closely parallels the usual one for $HA$ and establishes a number of nice properties for $iI\!\Sigma_1$ , e.g. existence of primitive recursive choice functions (this is established by different means also in [D94]). We then sharpen an unpublished theorem of Visser's to the effect that quantifier alternation alone is much less powerful intuitionistically (...)
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  27. Kai F. Wehmeier (1997). Aspekte der frege–hilbert-korrespondenz. History and Philosophy of Logic 18 (4):201-209.
    In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine, according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert's later work (...)
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  28. Kai F. Wehmeier (1997). Fragments Of... Based On.. Archive for Mathematical Logic 37 (1).
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  29. Kai F. Wehmeier (1997). Fragments of [Mathematical Formula] Based on [Mathematical Formula]-Induction. Archive for Mathematical Logic 1.
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  30. Kai F. Wehmeier (1996). Classical and Intuitionistic Models of Arithmetic. Notre Dame Journal of Formal Logic 37 (3):452-461.
    Given a classical theory T, a Kripke model K for the language L of T is called T-normal or locally PA just in case the classical L-structure attached to each node of K is a classical model of T. Van Dalen, Mulder, Krabbe, and Visser showed that Kripke models of Heyting Arithmetic (HA) over finite frames are locally PA, and that Kripke models of HA over frames ordered like the natural numbers contain infinitely many PA-nodes. We show that Kripke models (...)
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