The following papers have been made available for download, either as full-text, and/or as abstracts with permission requests/subscription for full access available from the journals' websites, links to which are also provided below.
Logic or Reason?
This paper explores the question of what logic is not. It argues against the wide spread assumptions that logic is: a model of reason; a model of correct reason; the laws of thought, or indeed is related to reason at all such that the essential nature of the two are crucially or essentially coillustrative. I note that due to such assumptions, our current understanding of the nature of logic itself is thoroughly entangled with the nature of reason. I show that most arguments for the presence of any sort of essential relationship between logic and reason face intractable problems and demands, and fall well short of addressing them. These arguments include those for the notion that logic is normative for reason (or that logic and correct reason are in some way the same thing), that logic is some sort of description of correct reason and that logic is an abstracted or idealised version of correct reason. A strong version of logical realism is put forward as an alternative view, and is briefly explored.
Download the free full text from the journal's webpage for this article: Logic and Logical Philosophy, Volume 21 (2012), pp. 127-163.
Four Basic Logical Issues
(with Ross Brady)
The paper addresses what we see as the four major issues in logic. The overriding issue is that of the choice of logic. We start with some discussion of the preliminary issue of whether there is such a 'one true logic', but we reserve the main discussion for the first issue of 'classical logic versus non-classical logic'. Here, we discuss the role of meaning and truth, the relation between classical logic and classical negation, and whether and, if so, how classical logic should reside at the base world. Given the argument in favor of an overall use of non-classical logic, the second issue is that of the choice of non-classical logic. Brady's logic MC of meaning containment is argued for, with some comparison made with other relevant logics. For the remaining two issues, we make a case for relevant deduction, in comparison with classical deduction, and we explore possibilities for the appropriate meta-logic, comparing classical and non-classical approaches.
Visit the journal's webpage for this article: Review of Symbolic Logic, Vol.2 (2009), pp.488-508.
Where Meaning is
In an attempt to find some new ways of tackling old problems about meaning, I explore some possible models in which meaning may be conceptually situated. I take a close look at a traditional realist conception of meaning and give some reasons as to why we may have more room to move within this than is immediately apparent. Alternative frameworks are explored along the way. The approach of thus situating meaning is an ontological one, but it is also an epistemological, as well as a hermeneutical one; in that the models put forward illuminate central issues and offer potential solutions to outstanding puzzles ranging across (at least) all of these broad realms of enquiry. Such solutions give a set of initial conceptualizations of the potential role meaning can play across broader frameworks of enquiry. As such they offer fresh inroads into otherwise deadlocked debates over the nature and place of meaning across philosophical enquiry in general.
Download my PDF copy of
Where Meaning Is, South African Journal of Philosophy, Vol. 29, No. 4 (2010), pp. 391-403. Also freely available from the journal's webpage for the article.
I argue that one in particular of Crispin Wright's attempts to capture our common or intuitive concepts of objectivity, warrant, and other associated notions, relies on an ambiguity between a given constructivist reading of the concepts and at least one other, arguably more 'ordinary', version of the notions he tries to accommodate. I do this by focusing on one case in point, and concluding with a brief argument showing how this case generalises. I demonstrate why this ambiguity is unacceptable and also that its resolution undermines the aim it serves: to account for and accommodate our ordinary conception of (at least) objectivity, warrant (or justification) and truth.
Download my PDF copy of
Objectivities, Studia Philosophica Estonica, 5.1, (2012), pp. 1-16. Also freely available from the journal's webpage for the article.
What is Wrong with Cantor's Diagonal Argument?
(with Ross Brady)
We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the LEM is instrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our
Four Basic Logical Issues
paper would provide useful background, the current paper being an application of the some of the ideas in it.
Download my PDF photocopy (2.6MB) of
What is Wrong with Cantor's Diagonal Argument?, Logique et Analyse, Vol.51 (2008), pp.185-219. Visit the journal's webpage for this issue.
Chapters in books
The Metaphysics of Logic
© Cambridge University Press 2014, expected publication date October 2014.
Download the PDF proof of my chapter 'Logical Realism' forthcoming in this book, pp. 13-31 (note that the proof is subject to copy-editing - there will be differences in the final publication).
Recent refereed conference proceedings
Social Media and the Abstract Self
Download my PDF copy of the paper presented at the Australian Institute of Computer Ethics Conference 2013.
- Review of The Applicability of Mathematics in Science: Indispensability and Ontology for International Studies in the Philosophy of Science. View my review on the journal's web page for Vol 27, Iss 2, 2013, pp. 219-222.
- Review of Reasoning in Science and Mathematics: Essays on Logic as The Art of Reasoning Well for Logic and Logical Philosophy. View or download my review on the journal's web page for Vol 22, 2013, pp. 365-371.
- Review of Critical Thinking for Logic and Logical Philosophy. View or download my review on the journal's web page for Vol 23, 2014, pp. 111-115.
- Reviews of Philosophy of Mathematics: Structure and Ontology for Philosophical Books and The Applicability of Mathematics as a Philosophical Problem for The Philosophical Quarterly. Download my PDF copy of the reviews.