11 found
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  1.  37
    Bilateralism Does Not Provide a Proof Theoretic Treatment of Classical Logic.Michael Gabbay - 2017 - Journal of Applied Logic 25:S108-S122.
    In this short paper I note that a key metatheorem does not hold for the bilateralist inferential framework: harmony does not entail consistency. I conclude that the requirement of harmony will not suffice for a bilateralist to maintain a proof theoretic account of classical logic. I conclude that a proof theoretic account of meaning based on the bilateralist framework has no natural way of distinguishing legitimate definitional inference rules from illegitimate ones (such as those for tonk). Finally, as an appendix (...)
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  2.  87
    A Formalist Philosophy of Mathematics Part I: Arithmetic.Michael Gabbay - 2010 - Studia Logica 96 (2):219-238.
    In this paper I present a formalist philosophy mathematics and apply it directly to Arithmetic. I propose that formalists concentrate on presenting compositional truth theories for mathematical languages that ultimately depend on formal methods. I argue that this proposal occupies a lush middle ground between traditional formalism, fictionalism, logicism and realism.
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  3.  30
    A Proof-Theoretic Treatment of Λ-Reduction with Cut-Elimination: Λ-Calculus as a Logic Programming Language.Michael Gabbay - 2011 - Journal of Symbolic Logic 76 (2):673 - 699.
    We build on an existing a term-sequent logic for the λ-calculus. We formulate a general sequent system that fully integrates αβη-reductions between untyped λ-terms into first order logic. We prove a cut-elimination result and then offer an application of cut-elimination by giving a notion of uniform proof for λ-terms. We suggest how this allows us to view the calculus of untyped αβ-reductions as a logic programming language (as well as a functional programming language, as it is traditionally seen).
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  4. We Can Be in Harmony With Classical Logic.Michael Gabbay - unknown
    In this paper I present the strategy behind the proof-theoretic justification of logical inference. I then discuss how this strategy leads to the famous requirement that the inference rules for the logical constants should be in harmony. I argue that the proof-theoretic justification of the logical constants can be used to justify classical logic. To substantiate this I present a new normalisation theorem for first order classical logic involving Sheffer Stroke. The proof of this theorem can be modified to yield (...)
     
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  5. Properties and Universals.Michael Gabbay - unknown
    A famous proposed solution to the one over many problem is found in Plato. For example, it appears in The Parmenedies and is introduce by Zeno arguing that . . . if being is many, it must be both like and unlike, and that this is impossible, for neither can the like be unlike, nor the unlike like-is that your position? and Socrates responds: do you not further think that there is an idea of likeness in itself, and another idea (...)
     
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  6.  20
    Representation and Duality of the Untyped Λ-Calculus in Nominal Lattice and Topological Semantics, with a Proof of Topological Completeness.Murdoch J. Gabbay & Michael Gabbay - 2017 - Annals of Pure and Applied Logic 168 (3):501-621.
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  7. Causation.Michael Gabbay - unknown
    Ways out: The proper relata of causal statements are large complexes of (macroscopic) conditions. For example: the spark, in the presence of oxygen together with flammable material and low humidity etc. The entailment is made virtue of the general macroscopic laws of flammable materials, humidity etc.
     
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  8. Necessity.Michael Gabbay - unknown
    An intensional sentential context is one where such intersubstitutivity fails: It is informative that A It is known that A It is necessary that A The fact that A caused it to be that B Some authors characterise intensional contexts by the failure of the intersubstitution of co-referring terms. Such a characterisation is problematic.
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  9.  11
    A Problem and a Solution for Neo-Fregeanism.Michael Gabbay - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 11--289.
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  10. Some Formal Considerations on Gabbay's Restart Rule in Natural Deduction and Goal-Directed Reasoning.Michael Gabbay & Murdoch J. Gabbay - 2005 - In We Will Show Them! Essays in Honour of Dov Gabbay, volume 1. pp. 701-null.
    In this paper we make some observations about Natural Deduction derivations [Prawitz, 1965, van Dalen, 1986, Bell and Machover, 1977]. We assume the reader is familiar with it and with proof-theory in general. Our development will be simple, even simple-minded, and concrete. However, it will also be evident that general ideas motivate our examples, and we think both our specific examples and the ideas behind them are interesting and may be useful to some readers. In a sentence, the bare technical (...)
     
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  11.  12
    Logic with Added Reasoning.Michael Gabbay - 2002 - Peterborough, Ont. and Orchard Park, NY: Broadview Press.
    This concise text treats logic as a tool, “generated so that half the work involved in thinking is done for you by somebody else (the rules and laws of the logic).” Gabbay explains in a clear and careful manner how formal features of, and formal relations between, ordinary declarative sentences are captured by the systems of propositional and predicate logic.
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