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William R. Stirton [7]William Stirton [2]
  1. William Stirton, Ontological Commitment by Singular Terms.
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  2. William R. Stirton (2013). A Decidable Theory of Type Assignment. Archive for Mathematical Logic 52 (5-6):631-658.
    This article investigates a theory of type assignment (assigning types to lambda terms) called ETA which is intermediate in strength between the simple theory of type assignment and strong polymorphic theories like Girard’s F (Proofs and types. Cambridge University Press, Cambridge, 1989). It is like the simple theory and unlike F in that the typability and type-checking problems are solvable with respect to ETA. This is proved in the article along with three other main results: (1) all primitive recursive functionals (...)
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  3. William R. Stirton (2012). How to Assign Ordinal Numbers to Combinatory Terms with Polymorphic Types. Archive for Mathematical Logic 51 (5-6):475-501.
    The article investigates a system of polymorphically typed combinatory logic which is equivalent to Gödel’s T. A notion of (strong) reduction is defined over terms of this system and it is proved that the class of well-formed terms is closed under both bracket abstraction and reduction. The main new result is that the number of contractions needed to reduce a term to normal form is computed by an ε 0-recursive function. The ordinal assignments used to obtain this result are also (...)
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  4. William R. Stirton (2008). Some Problems for Proof-Theoretic Semantics. Philosophical Quarterly 58 (231):278–298.
    Proof-theoretic semantics is an approach to logical semantics based on two ideas, of which the first is that the meaning of a logical connective can be explained by stipulating that some mode of inference, e.g., a natural deduction introduction or elimination rule, is permissible. The second idea is that the soundness of rules which are not stipulated outright may be deduced by some proof-theoretic argument from properties of the rules which are stipulated outright. I examine the first idea. My main (...)
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  5. William Stirton (2003). Caesar Invictus. Philosophia Mathematica 11 (3):285-304.
    The main purpose of this article is to argue that Crispin Wright and Bob Hale have not succeeded in overcoming the well-known ‘Julius Caesar objection’ to their proposed definition of the phrase ‘the number of’. It is hoped that the article will also help to clarify what would actually be needed in order to overcome this objection.
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  6. William R. Stirton (2000). Hale's 'Weak Sense' is Just Too Weak. Proceedings of the Aristotelian Society 100 (2):209–213.
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  7. William R. Stirton (2000). Singular Term, Subject and Predicate. Philosophical Quarterly 50 (199):191-207.
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  8. William R. Stirton (1995). The Logical Status of 'Exists'. Proceedings of the Aristotelian Society 95:37-50.
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  9. William R. Stirton (1994). A Problem Concerning the Definition of `Proper Name'. Philosophical Quarterly 44 (174):83-89.
    By "proper name" I mean a proper name in Frege's sense, i.e., a singular term. The "problem" mentioned in the title is whether the subject-term of an existential statement can be a proper name. I concentrate on examining some of the existing attempts to define "proper name" and conclude that, whatever answer is given to the question just posed, the authors of these attempts (Dummett, C Wright and B Hale) will have to modify some of their beliefs. My own favored (...)
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