Now showing 1 - 10 of 13
  • Publication
    Levels and sublevels of composition algebras
    (Elsevier, 2007)
    Lewis' and Leep's bounds on the level and sublevel of quaternion algebras are extended to the class of composition algebras. Some simple constructions of composition algebras of known level values are given. In addition, octonion algebras of sublevel 3 are presented.
      273Scopus© Citations 4
  • Publication
    Kant's Theoretical Philosophy: The 'Analytic' Tradition
    (Routledge, 2023-07-20)
    In a previous article (O’Shea 2006) I provided a concise overview of the reception of Kant’s philosophy among analytic philosophers during the periods from the ‘early analytic’ reactions to Kant in Frege, Russell, Carnap and others, to the systematic Kant-inspired works in epistemology and metaphysics of C. I. Lewis and P. F. Strawson, in particular. In this chapter I use the recently reinvigorated work of Wilfrid Sellars (1912-1989) in the second half of the twentieth century as the basis for presenting some of the most familiar ‘analytic Kantian’ themes that continue to animate current debates. I also argue that the complex relationships between Sellars’ philosophy and Kant’s thought are often misunderstood. Overall the chapter examines Sellars’ analytic appropriations of Kant in three topic-areas of significant current philosophical debate: (1) conceptual analysis and the structure of human knowledge; (2) laws of nature, the causal modalities, and the pragmatic or relative a priori; and (3) the disputes concerning Kant and nonconceptual content.
  • Publication
    Kantian Reflections on the Givenness of Zahavi’s Minimal Experiential Self
    (Taylor & Francis, 2015-10-14)
    At the core of Kant’s Critique of Pure Reason was a decisive break with certain fundamental Cartesian assumptions or claims about consciousness and self-consciousness, claims that have nonetheless remained perennially tempting, from a phenomenological perspective, independently of any further questions concerning the metaphysics of mind and its place in nature. The core of this philosophical problem has recently been helpfully exposed and insightfully probed in Dan Zahavi’s book, Self and Other: Exploring Subjectivity, Empathy, and Shame (OUP, 2014). In these remarks I suggest that Zahavi’s view of what he calls "The Experiential Self" defends precisely the sorts of claims to which a Kantian account of consciousness is fundamentally opposed, and while assessing the overall merits of the two contrasting outlooks is no easy matter, I side with the Kantian view.
      125Scopus© Citations 2
  • Publication
    Sums of squares in certain quaternion and octonion algebras
    (Elsevier Masson SAS, 2011-03)
    Formulae for the levels and sublevels of certain quaternion and octonion algebras are established. Corollaries concerning the equality of levels and sublevels of quaternion algebras with those of associated octonion algebras are presented.
      407Scopus© Citations 2
  • Publication
    Concepts of Objects as Involving Laws: A Kantian and Pragmatist Line of Thought
    (Routledge, 2017-11-28)
    This paper traces a Kantian and pragmatist line of thinking that connects the ideas of conceptual content, object cognition, and modal constraints in the form of counterfactual sustaining causal laws. It is an idea that extends from Kant’s Critique of Pure Reason through C. I. Lewis’s Mind and the World-Order to the Kantian naturalism of Wilfrid Sellars and the analytic pragmatism of Robert Brandom. Kant put forward what I characterize as a modal conception of objectivity, which he developed as an extended argument stretching from the transcendental deduction through the analogies of experience to the regulative maxims of reason and reflective judgment. In related ways in Lewis and Sellars, the very idea of an object of knowledge (and of intentionality more generally) is connected with a certain lawfulness or modal constraint the necessary representation of which, they argue, is an achievement of conceptualization. While Sellars agreed with the spirit of Lewis’s famous pragmatic conception of the a priori, Sellars’s conception of meaning and conceptual content differed in crucial ways with important consequences for this issue. I argue furthermore that a certain phenomenalist temptation threatens to spoil this insight both among some of Kant’s interpreters and in Lewis’s thought. Finally, I point out that Brandom’s "Kant-Sellars thesis" provides new support for this line of thought. Although questions concerning idealism continue to raise controversies for neo-Kantians and pragmatists, the line of thought itself represents a distinctive and still promising approach to questions concerning intentionality and conceptual content.
  • Publication
    On Sellars’s Analytic-Kantian Conception of Categories as Classifying Conceptual Roles
    (Routledge, 2022)
    I argue that Sellars’s metaconceptual theory of the categories exemplifies and extends a long line of nominalistic thinking about the nature of the categories from Ockham and Kant to the Tractatus and Carnap, and that this theory is far more central than has generally been realized to each of Sellars’s most famous and enduring philosophical conceptions: the myth of the given, the logical space of reasons, and resolving the ostensible clash between the manifest and scientific images of the human being in the world. Sellars’s distinctive contribution to this longstanding (if currently on the defensive) metaconceptual approach to the nature of ontological categories was to interpret and reconstruct it in terms of his own ‘meaning as use’ or norm-governed inferential role semantics. With these resources Sellars sought to preserve the genuine insights in the ‘realist’ or broadly platonic traditions while simultaneously defending the idea that in the end, as he puts it, “a naturalistic ontology must be a nominalistic ontology” (1980a NAO IV §129).
  • Publication
    Bounds on the levels of composition algebras
    (Royal Irish Academy, 2010)
    Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted. Alternative constructions of quaternion and octonion algebras are introduced and justified in the case where n is a multiple of a two power.
  • Publication
    Comments on Robert Brandom's 'From Empiricism to Expressivism: Brandom Reads Sellars'
    (Routledge, 2020-06-30)
    I am in agreement with most of what is contained in this powerful book. In particular, I find Brandom’s extended defense of his "Kant-Sellars thesis about modality," which is elaborated throughout the central chapters 3 to 6, the constructive heart of the book, to be both innovative and yet interpretively compelling with respect to the real semantic heart of Sellars’ philosophy. I myself agree that one of the deepest of insights elaborated in different ways by Kant, C. I. Lewis, Sellars, and now Brandom is that the objective purport of any empirical concept presupposes the prescription of lawful modal constraints governing the objects themselves, as systematically reflected in our inferential practices. This is Kant’s idea of the categories as concepts that prescribe laws to appearances, and Sellars’ idea of concepts as involving laws, and C.I. Lewis defends this, too-and now I think that Bob has really developed that in a nice way. And I also agree that these sort of normative presuppositional relationships, in general, constitute a key strand running throughout Sellars’ philosophy: Sellars’ idea, for example, that the normative espousal of principles is reflected in uniformities of practice and in certain natural regularities. (I tried to make that the center of my 2007 book on Sellars as well, in not nearly as sophisticated a way, however.) This highlights the pervasive Janus-faced interplay between what is explicitly asserted on the one hand, and the various normative practices and natural regularities that are thereby, Sellars will say, presupposed or conveyed or prescribed on the other.
  • Publication
    What to Take Away from Sellars’s Kantian Naturalism
    (Oxford University Press, 2016-06-09) ;
    I contend that Sellars defends a uniquely Kantian naturalist outlook both in general and more particularly in relation to the nature and status of what he calls ‘epistemic principles’; and I attempt to show that this remains a plausible and distinctive position even when detached from Sellars’s quasi-Kantian transcendental idealist contention that the perceptible objects of the manifest image strictly speaking do not exist, i.e., as conceived within that common sense framework. I first explain the complex Kant-inspired sense in which Sellars did not take the latter thesis concerning the objects of the manifest image to apply, at least in certain fundamental respects, to persons. In this primary Kantian sense, I suggest, persons as thinkers and agents exist univocally across both the manifest and scientific images, and this in principle would enable an integration of persons within a multi-leveled naturalistic ontology, one that is independent of Sellars’s quasi-Kantian transcendental idealist thesis. Finally, I examine in some detail how this defensible blend of Kantian and naturalist themes turns out to be what is fundamental in Sellars’s complex and controversial views on the nature and status of epistemic principles.
  • Publication
    Thought, Freedom, and Embodiment in Kant and Sellars
    (Routledge, 2016-12-02)
    Sellars once remarked on the "astonishing extent to which in ethics as well as in epistemology and metaphysics the fundamental themes of Kant’s philosophy contain the truth of the variations we now hear on every side" (SMx). Also astonishing was Sellars’ 1970 Presidential Address to the American Philosophical Association (APA), which borrowed its title from the phrase in Kant’s Paralogisms, "...this I or he or it (the thing) which thinks..." (B404). In its compact twenty-five pages Sellars managed to sketch novel yet plausible reconstructions of central aspects of Kant’s views on self-knowledge, persons, freedom, and morality, along the way suggesting how all of those Kantian views could plausibly be rendered consistent with a naturalistic ontology. In this chapter I focus on Sellars’ APA address as an occasion for reflection on how both Kant and Sellars offer insights into how we ought best to conceive the nature of and the relationships between our thinking selves, our practical agency, and our entirely natural, material embodiment.