Multiples of Pfister forms

The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the values of their first Witt indices is obtained. A number of corollaries of this result are outlined. An investigation of generic Pfister multiples is also undertaken. These results are applied to distinguish between properties preserved by Pfister products.Comment: 14 page

Group and round quadratic forms

We offer some elementary characterisations of group and round quadratic forms. These characterisations are applied to establish new (and recover existing) characterisations of Pfister forms. We establish "going-up" results for group and anisotropic round forms with respect to iterated Laurent series fields, which contrast with the established results with respect to rational function field extensions. For forms of two-power dimension, we determine when there exists a field extension over which the form becomes an anisotropic group form that is not round.Comment: 12 page

‘Psychological Nominalism’ and the Given, from Abstract Entities to Animal Minds

ABSTRACT: Sellars formulated his thesis of 'psychological nominalism' in two very different ways: (1) most famously as the thesis that 'all awareness of sorts…is a linguistic affair', but also (2) as a certain thesis about the 'psychology of the higher processes'. The latter thesis denies the standard view that relations to abstract entities are required in order to explain human thought and intentionality, and asserts to the contrary that all such mental phenomena can in principle ‘be accounted for causally' without any use of normative terms in the explanation. Recent 'Hegelian Sellarsians' such as Rorty, McDowell, and Brandom have argued that the holistic, normative themes in (1) support various non-realist or rather (German) 'idealist but common-sense realist' outlooks. By contrast, Sellars' own defenses of (2) reveal psychological nominalism itself to be a naturalistic empiricism intended to sustain the normative-holistic themes in (1) within an exhaustively scientific naturalist conception of reality

Concepts of Objects as Prescribing Laws: A Kantian and Pragmatist Line of Thought

Abstract: 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

After Kant, Sellars, and Meillassoux: Back to Empirical Realism?

ABSTRACT: I examine how Meillassoux’s conception of correlationism in After Finitude, as I understand it, relates firstly to Kant’s transcendental idealist philosophy, and secondly to the analytic Kantianism of Wilfrid Sellars. I argue that central to the views of both Kant and Sellars is what might be called, with an ambivalent nod to Meillassoux, an objective correlationism. What emerges in the end as the recommended upshot of these analyses is a naturalistic Kantianism that takes the form of an empirical realism in roughly Kant’s sense, but one that is happily wed with Sellars’ scientific realism, once the latter is disentangled from two implausible commitments that made such a reconciliation seem impossible to Sellars himself

The Web of Addiction An Exploration of the Complex Physiological, Psychological, Social and Political Forces Involved in the Development of Addictive Behaviours.

This study aimed to critically evaluate contemporary theory on the development of addictive behaviours. It acknowledged the complex dynamic relationships between five key variables including; individual, family, society, "stakeholders" and "addictive" substances in developing an interactive model of addiction. The hypothesis suggested that unitary definitions were inadequate, and that addiction was best understood as a complex phenomenon intimately linked to the prevailing social and political climate. The research employed three complimentary methods of inquiry including; a comprehensive review of relevant literature, a questionnaire administered to a group of adult students (to "reality check" theoretical frameworks) and a semi-structured groupwork session. The principle findings included; that there was a perceived preoccupation with pathological models of addiction, that addictive behaviours may be seen as functional at several levels of society and that drug and alcohol use were seen to be treated dichotomously in Ireland. It was also suggested that the role of gender issues in substance misuse were poorly understood, that the clear link between social disadvantage and problem use was largely ignored by policy makers and that key stakeholders were seen to create the reality of addiction by defining its parameters, diagnosing it and determining appropriate responses

Inferentialism, Naturalism, and the Ought-To-Bes of Perceptual Cognition

Abstract: Any normative inferentialist view confronts a set of challenges in the form of how to account for the sort of ordinary empirical descriptive vocabulary that is involved, paradigmatically, in our noninferential perceptual responses and knowledge claims. This chapter lays out that challenge, and then argues that Sellars’ original multilayered account of such noninferential responses in the context of his normative inferentialist semantics and epistemology shows how the inferentialist can plausibly handle those sorts of cases without stretching the notion of inference beyond its standard uses. Finally, it is suggested that for Sellars there were deeply naturalistic motivations for his own normative inferentialism, though the latter raises further questions as to whether this really represents, as Sellars thought, a genuinely scientific naturalist outlook on meaning and conceptual cognition

The Analytic Pragmatist Conception of the A Priori: C. I. Lewis and Wilfrid Sellars

ABSTRACT: It is a familiar story that Kant’s defence of our synthetic a priori cognition in the Critique of Pure Reason suffered sharp criticism throughout the extended philosophical revolutions that established analytic philosophy, the pragmatist tradition, and the phenomenological tradition as dominant philosophical movements in the first half of the twentieth century. One of the most important positive adaptations of Kant’s outlook, however, was the combined analytic and pragmatist conceptions of the a priori that were developed by the American philosophers C. I. Lewis (1883–1964) and Wilfrid Sellars (1912–1989), most notably in Lewis’s 1929 classic, Mind and the World Order, followed by Sellars’ critical reworking of Lewis’s outlook in ‘Is There a Synthetic A Priori?’ (1953) and other mid-century articles. Both Lewis and Sellars defended central aspects of Kant’s analysis of our a priori knowledge of mind-independent physical objects and necessary causal connections. But both also radically transformed Kant’s view by defending the idea that there are alternative a priori conceptual frameworks that are subject to an ongoing process of reassessment and replacement on overall pragmatic and explanatory grounds. Furthermore, while Sellars’ answer to his question, ‘Is There a Synthetic A Priori?’ thus represented a partial endorsement of Lewis’s pragmatic relativization of the a priori, I argue that Sellars’ account of meaning diverged from Lewis in ways that constituted a significant improvement upon the previous ‘analytic’ defenses of the a priori, not only in Lewis but in general. This arguably has implications for wider disputes concerning the nature and possibility of a priori knowledge in non-formal domains