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Andrew Tedder
Czech Academy of Sciences
Andrew Tedder
University of Lethbridge
Andrew Tedder
University of Connecticut
  1.  29
    Currying Omnipotence: A Reply to Beall and Cotnoir.Andrew Tedder & Guillermo Badia - 2018 - Thought: A Journal of Philosophy 7 (2):119-121.
    Beall and Cotnoir (2017) argue that theists may accept the claim that God's omnipotence is fully unrestricted if they also adopt a suitable nonclassical logic. Their primary focus is on the infamous Stone problem (i.e., whether God can create a stone too heavy for God to lift). We show how unrestricted omnipotence generates Curry‐like paradoxes. The upshot is that Beall and Cotnoir only provide a solution to one version of the Stone problem, but that unrestricted omnipotence generates other problems which (...)
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  2.  11
    Axioms for Finite Collapse Models of Arithmetic.Andrew Tedder - 2015 - Review of Symbolic Logic 8 (3):529-539.
    The collapse models of arithmetic are inconsistent, nontrivial models obtained from ℕ and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom system for (...)
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  3.  17
    How Much Propositional Logic Suffices for Rosser’s Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic:1-18.
    In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in intuitionistic logic, and P. Hajek proved it in the fuzzy logic BL for Grzegorczyk's variant of Q which interprets the arithmetic operations as non-total non-functional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
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  4. How Much Propositional Logic Suffices for Rosser's Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic.
    In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
     
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  5.  10
    On Elimination of Quantifiers in Some Non-Classical Mathematical Theories.Guillermo Badia & Andrew Tedder - 2018 - Mathematical Logic Quarterly 64 (3):140-154.
    Elimination of quantifiers is shown to fail dramatically for a group of well‐known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by moving to more extensional underlying logics can we get the property back.
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  6.  8
    Correction To: Lambek Calculus with Conjugates.Igor Sedlár & Andrew Tedder - forthcoming - Studia Logica:1-1.
    We, the authors, would like to thank Guillaume Aucher for informing us of his “Displaying Updates in Logic”, published in the Journal of Logic and Computation, 26:1865-1912.
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  7.  4
    Lambek Calculus with Conjugates.Igor Sedlár & Andrew Tedder - forthcoming - Studia Logica.
    We study an expansion of the Distributive Non-associative Lambek Calculus with conjugates of the Lambek product operator and residuals of those conjugates. The resulting logic is well-motivated, under-investigated and difficult to tackle. We prove completeness for some of its fragments and establish that it is decidable. Completeness of the logic is an open problem; some difficulties with applying the usual proof method are discussed.
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  8. Information Flow In Logics in the Vicinity of BB.Andrew Tedder - 2021 - Australasian Journal of Logic 18 (1):1-24.
    Situation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. (...)
     
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  9.  14
    On Structural Features of the Implication Fragment of Frege’s Grundgesetze.Andrew Tedder - 2017 - Journal of Philosophical Logic 46 (4):443-456.
    We set out the implication fragment of Frege’s Grundgesetze, clarifying the implication rules and showing that this system extends Absolute Implication, or the implication fragment of Intuitionist logic. We set out a sequent calculus which naturally captures Frege’s implication proofs, and draw particular attention to the Cut-like features of his Hypothetical Syllogism rule.
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  10.  5
    Qua Solution, 0-Qua Has Problems.Andrew Tedder, Grace Paterson & David Ripley - 2020 - Journal of Analytic Theology 8 (1):405-411.
    We present an objection to Beall & Henderson’s recent paper defending a solution to the fundamental problem of conciliar Christology using qua or secundum clauses. We argue that certain claims the acceptance/rejection of which distinguish the Conciliar Christian from others fail to so distinguish on Beall & Henderson’s 0-Qua view. This is because on their 0-Qua account, these claims are either acceptable both to Conciliar Christians as well as those who are not Conciliar Christians or because they are acceptable to (...)
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