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  1. I. L. Humberstone (forthcoming). An Alternative Account of Bringing About. Bulletin of the Section of Logic.
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  2. I. L. Humberstone (1998). Choice of Primitives: A Note on Axiomatizing Intuitionistic Logic. History and Philosophy of Logic 19 (1):31-40.
    A purported axiomatization, by P. Gärdenfors, of intuitionistic propositional logic is shown to be incomplete, and that the mistaken claim to completeness is seen to result from carelessness in the choice of primitive logical vocabulary. This leads to a consideration of various ways of conceiving the distinction between primitive and defined vocabularies, along with the bearing of these differences on such matters as are discussed in connection with Gärdenfors.
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  3. I. L. Humberstone (1997). Singulary Extensional Connectives: A Closer Look. [REVIEW] Journal of Philosophical Logic 26 (3):341-356.
    The totality of extensional 1-ary connectives distinguishable in a logical framework allowing sequents with multiple or empty (alongside singleton) succedents form a lattice under a natural partial ordering relating one connective to another if all the inferential properties of the former are possessed by the latter. Here we give a complete description of that lattice; its Hasse diagram appears as Figure 1 in §2. Simple syntactic descriptions of the lattice elements are provided in §3; §§4 and 5 give some additional (...)
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  4. I. L. Humberstone (1997). Two Types of Circularity. Philosophy and Phenomenological Research 57 (2):249-280.
    For the claim that the satisfaction of certain conditions is sufficient for the application of some concept to serve as part of the (`reductive') analysis of that concept, we require the conditions to be specified without employing that very concept. An account of the application conditions of a concept not meeting this requirement, we call analytically circular. For such a claim to be usable in determining the extension of the concept, however, such circularity may not matter, since if the concept (...)
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  5. I. L. Humberstone (1996). A Study in Philosophical Taxonomy. Philosophical Studies 83 (2):121 - 169.
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  6. I. L. Humberstone (1996). Intrinsic/Extrinsic. Synthese 108 (2):205-267.
    Several intrinsic/extrinsic distinctions amongst properties, current in the literature, are discussed and contrasted. The proponents of such distinctions tend to present them as competing, but it is suggested here that at least three of the relevant distinctions (including here that between non-relational and relational properties) arise out of separate perfectly legitimate intuitive considerations: though of course different proposed explications of the informal distinctions involved in any one case may well conflict. Special attention is paid to the question of whether a (...)
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  7. I. L. Humberstone (1996). A Basic System of Congruential-to-Monotone Bimodal Logic and Two of Its Extensions. Notre Dame Journal of Formal Logic 37 (4):602-612.
    If what is known need not be closed under logical consequence, then a distinction arises between something's being known to be the case (by a specific agent) and its following from something known (to that subject). When each of these notions is represented by a sentence operator, we get a bimodal logic in which to explore the relations between the two notions.
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  8. I. L. Humberstone (1995). Comparatives and the Reducibility of Relations. Pacific Philosophical Quarterly 76 (2):117-141.
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  9. I. L. Humberstone (1995). Negation by Iteration. Theoria 61 (1):1-24.
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  10. I. L. Humberstone (1995). The Logic of Non-Contingency. Notre Dame Journal of Formal Logic 36 (2):214-229.
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  11. I. L. Humberstone (1994). Hempel Meets Wason. Erkenntnis 41 (3):391 - 402.
    The adverse reaction to Hempel's ravens paradox embodied in giving it that description is compared with the usual reaction (universally regarded as incorrect) of experimental subjects to the Wason selection task.
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  12. I. L. Humberstone (1993). Functional Dependencies, Supervenience, and Consequence Relations. Journal of Logic, Language and Information 2 (4):309-336.
    An analogy between functional dependencies and implicational formulas of sentential logic has been discussed in the literature. We feel that a somewhat different connexion between dependency theory and sentential logic is suggested by the similarity between Armstrong's axioms for functional dependencies and Tarski's defining conditions for consequence relations, and we pursue aspects of this other analogy here for their theoretical interest. The analogy suggests, for example, a different semantic interpretation of consequence relations: instead of thinking ofB as a consequence of (...)
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  13. I. L. Humberstone (1993). Review: Keith Devlin, Logic and Information. [REVIEW] Journal of Symbolic Logic 58 (3):1082-1084.
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  14. I. L. Humberstone (1993). Zero-Place Operations and Functional Completeness, and the Definition of New Connectives. History and Philosophy of Logic 14 (1):39-66.
    Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around (...)
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  15. I. L. Humberstone (1992). Direction of Fit. Mind 101 (401):59-83.
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  16. I. L. Humberstone (1992). Some Structural and Logical Aspects of the Notion of Supervenience. Logical Analysis 35 (March-June):101-37.
     
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  17. I. L. Humberstone (1991). A Study of Some 'Separated' Conditions on Binary Relations. Theoria 57 (1-2):1-16.
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  18. I. L. Humberstone (1991). Conditionals, by F. C. Jackson. Philosophy and Phenomenological Research 51 (1):227-234.
  19. I. L. Humberstone (1991). Review: Graeme Forbes, Languages of Possibility. An Essay in Philosophical Logic. [REVIEW] Journal of Symbolic Logic 56 (1):351-352.
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  20. I. L. Humberstone (1991). Two Kinds of Agent-Relativity. Philosophical Quarterly 41 (163):144-166.
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  21. I. L. Humberstone (1990). Expressive Power and Semantic Completeness: Boolean Connectives in Modal Logic. Studia Logica 49 (2):197 - 214.
    We illustrate, with three examples, the interaction between boolean and modal connectives by looking at the role of truth-functional reasoning in the provision of completeness proofs for normal modal logics. The first example (§ 1) is of a logic (more accurately: range of logics) which is incomplete in the sense of being determined by no class of Kripke frames, where the incompleteness is entirely due to the lack of boolean negation amongst the underlying non-modal connectives. The second example (§ 2) (...)
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  22. I. L. Humberstone (1990). Wanting, Getting, Having. Philosophical Papers 99 (August):99-118.
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  23. I. L. Humberstone (1988). Heterogeneous Logic. Erkenntnis 29 (3):395 - 435.
    This paper considers the question: what becomes of the notion of a logic as a way of codifying valid arguments when the customary assumption is dropped that the premisses and conclusions of these arguments are statements from some single language? An elegant treatment of the notion of a logic, when this assumption is in force, is that provided by Dana Scott's theory of consequence relations; this treatment is appropriately generalized in the present paper to the case where we do not (...)
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  24. I. L. Humberstone (1988). Some Epistemic Capacities. Dialectica 42 (3):183-200.
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  25. J. A. Burgess & I. L. Humberstone (1987). Natural Deduction Rules for a Logic of Vagueness. Erkenntnis 27 (2):197-229.
    Extant semantic theories for languages containing vague expressions violate intuition by delivering the same verdict on two principles of classical propositional logic: the law of noncontradiction and the law of excluded middle. Supervaluational treatments render both valid; many-Valued treatments, Neither. The core of this paper presents a natural deduction system, Sound and complete with respect to a 'mixed' semantics which validates the law of noncontradiction but not the law of excluded middle.
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  26. I. L. Humberstone (1987). Critical Notice. Mind 96 (381):99 - 107.
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  27. I. L. Humberstone (1987). Wanting as Believing. Canadian Journal of Philosophy 17 (March):49-62.
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  28. I. L. Humberstone (1987). Operational Semantics for Positive ${Rm R}$. Notre Dame Journal of Formal Logic 29 (1):61-80.
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  29. I. L. Humberstone (1987). The Modal Logic of `All and Only'. Notre Dame Journal of Formal Logic 28 (2):177-188.
  30. I. L. Humberstone & A. J. Lock (1986). Semicomplemented Lattices and the Finite Model Property. Mathematical Logic Quarterly 32 (25‐30):431-437.
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  31. I. L. Humberstone (1985). The Formalities of Collective Omniscience. Philosophical Studies 48 (3):401 - 423.
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  32. I. L. Humberstone (1983). Karmo on Contingent Non-Identity. Australasian Journal of Philosophy 61 (2):188 – 191.
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  33. I. L. Humberstone (1983). Inaccessible Worlds. Notre Dame Journal of Formal Logic 24 (3):346-352.
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  34. J. F. A. K. van Benthem & I. L. Humberstone (1983). Halldén-Completeness by Gluing of Kripke Frames. Notre Dame Journal of Formal Logic 24 (4):426-430.
    We give in this paper a sufficient condition, cast in semantic terms, for Hallden-completeness in normal modal logics, a modal logic being said to be Hallden-complete (or Ήallden-reasonable') just in case for any disjunctive formula provable in the logic, where the disjuncts have no propositional variables in common, one or other of those disjuncts is provable in the logic.
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  35. I. L. Humberstone (1982). First Steps in a Philosophical Taxonomy. Canadian Journal of Philosophy 12 (3):476-478.
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  36. I. L. Humberstone (1982). Necessary Conclusions. Philosophical Studies 41 (3):321 - 335.
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  37. I. L. Humberstone (1982). Scope and Subjunctivity. Philosophia 12 (1-2):99-126.
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  38. I. L. Humberstone (1981). A Note on Two Remarks of Wigging Concerning Restricted Quantification. Australasian Journal of Philosophy 59 (4):432 – 437.
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  39. I. L. Humberstone (1981). From Worlds to Possibilities. Journal of Philosophical Logic 10 (3):313 - 339.
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  40. I. L. Humberstone (1980). You'll Regret It. Analysis 40 (3):175 - 176.
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  41. I. L. Humberstone (1979). Interval Semantics for Tense Logic: Some Remarks. [REVIEW] Journal of Philosophical Logic 8 (1):171 - 196.
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  42. I. L. Humberstone (1978). Two Merits of the Circumstantial Operator Language for Conditional Logics. Australasian Journal of Philosophy 56 (1):21 – 24.
  43. I. L. Humberstone (1971). Two Sorts of 'Ought's. Analysis 32 (1):8 - 11.
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