•  301
    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
  •  10
    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
  •  276
    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
  •  94
    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
  •  1186
    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
  •  37
    O logice ontologického důkazu
    Studia Neoaristotelica 4 (1): 5-27. 2007.
    De argumenti ontologici forma logicaTractatione proposita auctores manifestant, „Argumentum Ontologicum“ St. Anselmi in 2° capitulo eius Proslogii inscriptum ut validum exponi posse (i. e. consequentiam bonam servando). Hac in interpretatione vis et notio descriptionis illae „id quo maius cogitari nequit“, qua Anselmus usus est, rite agnoscitur. Datis enim lingua formali „primi ordinis“, ut aiunt, et systemati deductivo logicae huiusmodi, in quo descriptiones definitae genuini sunt termini et ub…Read more
  •  17
    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".