•  7
    The topic of fictional objects is a familiar one, the topic of fictional properties less so. But it deserves its own place in the philosophy of fiction, if only because fictional properties have such a prominent role to play in science fiction and fantasy. What, then, are fictional properties and how does their apparent unreality relate to the unreality of fictional objects? The present paper explores these questions in the light of familiar debates about the nature of fictional objects.
  •  9
    A Computationally-Discovered Simplification of the Ontological Argument
    Australasian Journal of Philosophy 89 (2): 333-349. 2011.
    The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise br…Read more
  •  22
    On Anselm’s Ontological Argument in Proslogion II
    History of Philosophy & Logical Analysis 25 (2): 327-351. 2021.
    Formulations of Anselm’s ontological argument have been the subject of a number of recent studies. We examine these studies in light of Anselm’s text and (a) respond to criticisms that have surfaced in reaction to our earlier representations of the argument, (b) identify and defend a more refined representation of Anselm’s argument on the basis of new research, and (c) compare our representation of the argument, which analyzes that than which none greater can be conceived as a definite descripti…Read more
  •  324
    Standpoint Semantics for Polysemy in Spatial Prepositions
    with Edilson J. Rodrigues, Paulo E. Santos, Marcos Lopes, and Brandon Bennett
    Journal of Logic and Computation 30 (2): 635-661. 2020.
    In this paper, we present a formalism for handling polysemy in spatial expressions based on supervaluation semantics called standpoint semantics for polysemy (SSP). The goal of this formalism is, given a prepositional phrase, to define its possible spatial interpretations. For this, we propose to characterize spatial prepositions by means of a triplet ⟨ image schema, semantic feature, spatial axis⟩⁠. The core of SSP is predicate grounding theories, which are formulas of a first-order language th…Read more
  •  2
    Property Identity and Reification
    Australasian Philosophical Review 4 (4): 367-372. 2020.
    ABSTRACT The target article uses the metaphysics of properties to make its meta-ethical claims. This comment discusses two general points in the metaphysics of properties. The first point has to do with the conditions for property identity. Philosophers who accept the existence of properties have proposed a variety of criteria for their identity. The standard Broome applies is medium coarse. Other standards for property identity could be evaluated for their appropriateness for addressing questio…Read more
  •  570
    Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components o…Read more
  •  19
    Reflections on the Logic of the Ontological Argument
    Studia Neoaristotelica 4 (1): 28-35. 2007.
    The authors evaluate the soundness of the ontological argument they developed in their 1991 paper. They focus on Anselm’s first premise, which asserts that there is a conceivable thing than which nothing greater can be conceived. After casting doubt on the argument Anselm uses in support of this premise, the authors show that there is a formal reading on which it is true. Such a reading can be used in a sound reconstruction of the argument. After this reconstruction is developed in precise detai…Read more
  •  115
    Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to funct…Read more
  •  1667
    On the logic of the ontological argument
    Philosophical Perspectives 5 509-529. 1991.
    In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordin…Read more
  •  52
    Reflections on the Logic of the Ontological Argument
    Studia Neoaristotelica 4 (1): 28-35. 2007.
    The authors evaluate the soundness of the ontological argument they developed in their 1991 paper. They focus on Anselm’s first premise, which asserts that there is a conceivable thing than which nothing greater can be conceived. After casting doubt on the argument Anselm uses in support of this premise, the authors show that there is a formal reading on which it is true. Such a reading can be used in a sound reconstruction of the argument. After this reconstruction is developed in precise detai…Read more
  •  22
    The Certainty of Skepticism
    with Ralf Meerbote
    Grazer Philosophische Studien 11 (1): 125-128. 1980.
    Carrier in a recent paper urges for consideration an argument for skepticism which is based on premises one of which in turn is to be defended by yet another principle (the "Janus Principle" of the text). We feel that the latter principle and the way Carrier wants to use it to defend his skeptical argument will find adherents, but we show that this argument rests on an interesting equivocation quite beyond repair even if we accept the "Janus Principle".
  •  338
    A computationally-discovered simplification of the ontological argument
    Australasian Journal of Philosophy 89 (2). 2011.
    The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise br…Read more