•  2639
    Cantor on Infinity in Nature, Number, and the Divine Mind
    American Catholic Philosophical Quarterly 83 (4): 533-553. 2009.
    The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessi…Read more
  •  1506
    Aristotle and modern mathematical theories of the continuum
    In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science, Peter Lang. 2001.
    This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open versus closed inte…Read more
  •  980
    Interpreting Anscombe’s Intention §32FF
    Journal of Philosophical Research 34 157-176. 2009.
    G. E. M. Anscombe’s view that agents know what they are doing “without observation” has been met with skepticism and the charge of confusion and falsehood. Simultaneously, some commentators think that Anscombe has captured an important truth about the first-personal character of an agent’s awareness of her actions. This paper attempts an explanation and vindication of Anscombe’s view. The key to the vindication lies in focusing on the role of practical knowledge in an agent’s knowledge of her ac…Read more
  •  760
    The Epistemology of Geometry I: the Problem of Exactness
    Proceedings of the Australasian Society for Cognitive Science 2009. 2010.
    We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing th…Read more
  •  731
    Knowledge by Intention? On the Possibility of Agent's Knowledge
    In Stephen Hetherington (ed.), Aspects of Knowing, Elsevier Science. pp. 183. 2006.
    A fallibilist theory of knowledge is employed to make sense of the idea that agents know what they are doing 'without observation' (as on Anscombe's theory of practical knowledge).
  •  554
    In chapter 7 of The Varieties of Reference, Gareth Evans claimed to have an argument that would present "an antidote" to the Cartesian conception of the self as a purely mental entity. On the basis of considerations drawn from philosophy of language and thought, Evans claimed to be able to show that bodily awareness is a form of self-awareness. The apparent basis for this claim is the datum that sometimes judgements about one’s position based on body sense are immune to errors of misidentificat…Read more
  •  490
    Thought, Reference, and Experience: Themes from the Philosophy of Gareth Evans (review)
    Australasian Journal of Philosophy 84 (1): 5. 2006.
    This is a very short book review of a recent volume on the philosophy of Gareth Evans with special attention to work on first-person reference.
  •  469
    This is a copy of the presentation given at the Workshop on Agency and Distributed Cognition at Macquarie University, March 2012.
  •  462
    This thesis proposes that an account of first-person reference and first-person thinking requires an account of practical knowledge. At a minimum, first-person reference requires at least a capacity for knowledge of the intentional act of reference. More typically, first-person reasoning requires deliberation and the ability to draw inferences while entertaining different 'I' thoughts. Other accounts of first-person reference--such as the perceptual account and the rule-based account--are critic…Read more
  •  458
    It is argued that there are ways of individuating the objects of perception without using sortal concepts. The result is an moderate anti-sortalist position on which one can single out objects using demonstrative expressions without knowing exactly what sort of thing those objects are.
  •  387
    Review of Oppy's Philosophical Perspectives on Infinity (review)
    Australasian Journal of Philosophy 85 (4): 679-695. 2007.
    This is a book review of Oppy's "Philosophical Perspectives on Infinity", which is of interest to those in metaphysics, epistemology, philosophy of science, mathematics, and philosophy of religion.
  •  342
    Collaborative Virtual Worlds and Productive Failure
    with Michael J. Jacobson, Charlotte Taylor, Wai Yat Wong, Deborah Richards, Meredith Taylor, Porte John, Kartiko Iwan, Kapur Manu, and Hu Chun
    This paper reports on an ongoing ARC Discovery Project that is conducting design research into learning in collaborative virtual worlds (CVW).The paper will describe three design components of the project: (a) pedagogical design, (b)technical and graphics design, and (c) learning research design. The perspectives of each design team will be discussed and how the three teams worked together to produce the CVW. The development of productive failure learning activities for the CVW will be discussed…Read more
  •  260
    Indispensability Without Platonism
    In Alexander Bird, Brian Ellis & Howard Sankey (eds.), Properties, Powers, and Structures: Issues in the Metaphysics of Realism, Routledge. pp. 81-97. 2012.
    According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this …Read more
  •  181
    This paper discusses an argument for the reality of the classical mathematical continuum. An inference to the best explanation type of argument is used to defend the idea that real numbers exist even when they cannot be constructively specified as with the "indefinable numbers"
  •  149
    In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In pr…Read more
  •  79
    Evaluating the models and behaviour of 3D intelligent virtual animals in a predator-prey relationship. AAMAS 2012: 79-86
    with Deborah Richards, Jacobson Michael, Taylor Charlotte, Taylor Meredith, Porte John, and Hanna Nader
    Proceedings of the Eleventh International Conference on Agent and Multiagent Systems (AAMAS). 2012.
    This paper presents the intelligent virtual animals that inhabit Omosa, a virtual learning environment to help secondary school students learn how to conduct scientific inquiry and gain concepts from biology. Omosa supports multiple agents, including animals, plants, and human hunters, which live in groups of varying sizes and in a predator-prey relationship with other agent types (species). In this paper we present our generic agent architecture and the algorithms that drive all animals. We con…Read more
  •  79
    How are Australian higher education institutions contributing to innovative teaching and learning through virtual worlds?
    with Brent Gregory, Sue Gregory, Bogdanovych A., Jacobson Michael, and Simeon Simoff and Many Others
    Over the past decade, teaching and learning in virtual worlds has been at the forefront of many higher education institutions around the world. The DEHub Virtual Worlds Working Group (VWWG) consisting of Australian and New Zealand higher education academics was formed in 2009. These educators are investigating the role that virtual worlds play in the future of education and actively changing the direction of their own teaching practice and curricula. 47 academics reporting on 28 Australian highe…Read more
  •  19
    Knowledge Beyond Reason in Spinoza’s Epistemology: Scientia Intuitiva and Amor Dei Intellectualis in Spinoza’s Epistemology
    Australasian Philosophical Review 4 (Revisiting Spinoza's Rationalism). forthcoming.
    Genevieve Lloyd’s Spinoza is quite a different thinker from the arch rationalist caricature of some undergraduate philosophy courses devoted to “The Continental Rationalists”. Lloyd’s Spinoza does not see reason as a complete source of knowledge, nor is deductive rational thought productive of the highest grade of knowledge. Instead, that honour goes to a third kind of knowledge—intuitive knowledge (scientia intuitiva), which provides an immediate, non-discursive knowledge of its singular object…Read more
  •  12
    Interpreting Anscombe’s Intention §32FF
    Journal of Philosophical Research 34 157-176. 2009.
    G. E. M. Anscombe’s view that agents know what they are doing “without observation” has been met with skepticism and the charge of confusion and falsehood. Simultaneously, some commentators think that Anscombe has captured an important truth about the first-personal character of an agent’s awareness of her actions. This paper attempts an explanation and vindication of Anscombe’s view. The key to the vindication lies in focusing on the role of practical knowledge in an agent’s knowledge of her ac…Read more
  •  3
    Actual versus Potential Infinity (BPhil manuscript.)
    Dissertation, University of Oxford. 1997.
    Do actual infinities exist or are they impossible? Does mathematical practice require the existence of actual infinities, or are potential infinities enough? Contrasting points of view are examined in depth, concentrating on Aristotle’s ancient arguments against actual infinities. In the long 19th century, we consider Cantor’s successful rehabilitation of the actual infinite within his set theory, his views on the continuum, Zeno's paradoxes, and the domain principle, criticisms by Frege, and t…Read more