•  47
    Reasoning in Science and Mathematics: Essays on Logic as The Art of Reasoning Well (review)
    Logic and Logical Philosophy 22 (3): 365-371. 2013.
    Richard L. Epstein, Reasoning in Science and Mathematics: Essayson Logic as The Art of Reasoning Well, Advanced Reasoning Forum,2011, 134 pp., ISBN-13: 978-0983452126, ISBN-10: 0983452121
  • Metaphysical Optimism
    In Anthony O'Hear (ed.), Metaphysics, Cambridge University Press. 2018.
  • This Element looks at the problem of inter-translation between mathematical realism and anti-realism and argues that so far as realism is inter-translatable with anti-realism, there is a burden on the realist to show how her posited reality differs from that of the anti-realist. It also argues that an effective defence of just such a difference needs a commitment to the independence of mathematical reality, which in turn involves a commitment to the ontological access problem – the problem of ho…Read more
  •  41
    Metaphysical Optimism
    Royal Institute of Philosophy Supplement 82 365-393. 2018.
    This paper seeks to identify and defend an approach to inquiry dubbed ‘metaphysical optimism’, particularly as it is evidenced at crisis points in the fields of physics, mathematics and logic. That the practice of metaphysical optimism at such moments, wherein it has appeared that there is no clear way to proceed or understand where we have arrived, is both reasonable and useful suggests it is to be taken seriously as capable of progressing fields and increasing knowledge. Given this, the paper …Read more
  •  49
    Myriad Philosophical Methodologies
    Metaphilosophy 47 (4-5): 679-695. 2016.
    This article offers an overview of philosophical methodologies. In an attempt to avoid a certain circularity, the article itself tries to avoid consciously or solely deploying and engaging with any current standard notion of what constitutes a philosophical method or philosophy itself. It hopes to find some of the possible places in which philosophy occurs, and this turns out to include such endeavours as literature, art, poetry, and linguistics. From here it considers how almost anything—for ex…Read more
  •  10
    Book Reviews (review)
    Logic and Logical Philosophy 22 (3): 365-371. 2013.
    Richard L. Epstein with Carolyn Kerbrger, Critical Thinking, 3rd Edition, Advanced Reasoning Forum, 2012, 464 pp., ISBN-10: 1938421000, ISBN-13: 978-1938421006.Richard L. Epstein, The Pocket Guide to Critical Thinking, 4th Edition, Advanced Reasoning Forum, 2011, 162 pp., paperback ISBN-13: 9780981550770, ISBN-10: 0981550770, ebook ISBN-13: 9780981550787
  •  139
    The Metaphysics of Logic (edited book)
    Cambridge University Press. 2014.
    Featuring fourteen new essays from an international team of renowned contributors, this volume explores the key issues, debates and questions in the metaphysics of logic. The book is structured in three parts, looking first at the main positions in the nature of logic, such as realism, pluralism, relativism, objectivity, nihilism, conceptualism, and conventionalism, then focusing on historical topics such as the medieval Aristotelian view of logic, the problem of universals, and Bolzano's logica…Read more
  •  299
    Objectivities
    Studia Philosophica Estonica 5 (1): 1-16. 2012.
    I argue that one in particular of CrispinWright’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, arguablymore ‘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 an…Read more
  •  9
    Book Reviews (review)
    Logic and Logical Philosophy 23 (1): 111-115. 2014.
    Richard L. Epstein with Carolyn Kerbrger, Critical Thinking, 3rd Edition, Advanced Reasoning Forum, 2012, 464 pp., ISBN-10: 1938421000, ISBN-13: 978-1938421006.Richard L. Epstein, The Pocket Guide to Critical Thinking, 4th Edition, Advanced Reasoning Forum, 2011, 162 pp., paperback ISBN-13: 9780981550770, ISBN-10: 0981550770, ebook ISBN-13: 9780981550787.
  •  44
    Where Meaning Is
    South African Journal of Philosophy 29 (4): 391-403. 2010.
    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 …Read more
  •  1
    Shapiro, S.-Philosophy of Mathematics
    Philosophical Books 40 283-283. 1999.
  •  98
    What is Wrong with Cantor's Diagonal Argument?
    with R. T. Brady
    Logique Et Analyse 51 (1). 2008.
    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 intrumental in the proof of Cantor'…Read more
  •  108
    Four basic logical issues
    with Ross Brady
    Review of Symbolic Logic 2 (3): 488-508. 2009.
    Four Basic Logical Issues: 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 nonclassical 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 log…Read more
  •  1030
    Logic or Reason?
    Logic and Logical Philosophy 21 (2): 127-163. 2012.
    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 co-illustrative. 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 …Read more
  •  87
    Factivity, consistency and knowability
    Synthese 195 (2): 899-918. 2018.
    One diagnosis of Fitch’s paradox of knowability is that it hinges on the factivity of knowledge: that which is known is true. Yet the apparent role of factivity and non-factive analogues in related paradoxes of justified belief can be shown to depend on familiar consistency and positive introspection principles. Rejecting arguments that the paradox hangs on an implausible consistency principle, this paper argues instead that the Fitch phenomenon is generated both in epistemic logic and logics of…Read more