•  184
    We show that infinitesimal probabilities are much too small for modeling the individual outcome of a countably infinite fair lottery
  •  66
    Popper Functions, Uniform Distributions and Infinite Sequences of Heads
    Journal of Philosophical Logic 44 (3): 259-271. 2015.
    Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P=P/P. A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence …Read more
  •  172
    The Eucharist : real presence and real absence
    In Thomas P. Flint & Michael Rea (eds.), The Oxford handbook of philosophical theology, Oxford University Press. 2008.
    This article focuses on the question of whether the doctrine of the real presence of Christ's body and blood, and likewise the doctrine of the real absence of bread and wine, can be defended philosophically. It argues for an affirmative answer, and does so by considering a variety of metaphysical models, including that of Aquinas. It will appear, thus, that transubstantiation is a philosophical possibility. If it is possible for two substances to be in the same place at the same time, consubstan…Read more
  •  30
    Let Mm k be the simply connected constant curvature space form of dimension m. • Mm 0 is Rm with euclidean metric • Mm k for k > 0 is an m-sphere of radius k−1/2 • Mm k for k < 0 is m dimensional hyperbolic space modelled on the m-ball of radius (−k)−1/2.
  •  538
    On Two Problems of Divine Simplicity
    Oxford Studies in Philosophy of Religion 1 150-167. 2008.
  •  29
    Much of the discussion had focussed on the question of whether religious experiences are veridical, but then Richard M. Gale asked a more fundamental question: Are they even cognitive? An experience is cognitive if it takes an intentional accusative, such as “red cube” in “I see a red cube,” as opposed to the cognate accusative exemplified by the use of the word “waltz” in “I am dancing a waltz” which is synonymous with “I am dancing waltzily.” Cognitive experiences are objective in the sense th…Read more
  •  135
    The A-theory of time and induction
    Philosophical Studies 152 (3). 2011.
    The A-theory of time says that it is an objective, non-perspectival fact about the world that some events are present, while others were present or will be present. I shall argue that the A-theory has some implausible consequences for inductive reasoning. In particular, the presentist version of the A-theory, which holds that the difference between the present and the non-present consists in the present events being the only ones that exist, is very much in trouble
  •  7
    Animalism is the view that we are animals and, thus, satisfy the criteria of identity proper to animals. This is highly plausible, for instance because it accepts at face value what appears to be the obvious facts that we are mammals—after all, we have the hair, the inner ear bones and the milk that mammals do—and that being a mammal is a way of being an animal. On the main opposing view, one has to hold that associated with each of us there are two entities: a person and an animal, of which we …Read more
  •  8
    Not Out of Lust but in Accordance with Truth
    Logos: A Journal of Catholic Thought and Culture 6 (4): 51-80. 2003.
  •  106
    Artificial Intelligence and Personal Identity
    Faith and Philosophy 26 (5): 487-500. 2009.
    Persons have objective, not socially defined, identity conditions. I shall argue that robots do not, unless they have souls. Hence, robots without souls are not persons. And by parallel reasoning, neither are we persons if we do not have souls.
  •  164
    Review of Graham Oppy, Arguing About Gods (review)
    Notre Dame Philosophical Reviews 2007 (5). 2007.
  •  1
              The production of a number of vaccines involves the use of cell-lines originally derived from fetuses directly aborted in the 1960s and 1970s. Such cell-lines, indeed sometimes the very same ones, are important to on-going research, including at Catholic institutions. The cells currently used are removed by a number of decades and by a significant number of cellular generations from the original cells. Moreover, the original cells extracted from the bodies of the aborted f…Read more
  •  6
    Lying and speaking your interlocutor's language
    The Thomist 63 (3): 439-453. 1999.
  •  54
    The Existence of God (edited book)
    with Richard M. Gale
    Ashgate Pub Limited. 2003.
    The latter third of the 20th century has seen the philosophical defence of theism - many philosophers were caught off-guard because they assumed that metaphysics and theology had been dealt with. Moreover, the leaders of this renaissance were analytically-rooted philosophers. Upon examination however, it is clear that significant developments in philosophical theism historically have come upon the heels of breakthroughs in the core areas of philosophy concerning meaning, logic and scientific met…Read more