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38
Normal science, pathological science and psychometrics
 Theory & Psychology
, 2000
"... Abstract. A pathology of science is defined as a twolevel breakdown in processes of critical inquiry: first, a hypothesis is accepted without serious attempts being made to test it; and, second, this firstlevel failure is ignored. Implications of this concept of pathology of science for the Kuhnia ..."
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Abstract. A pathology of science is defined as a twolevel breakdown in processes of critical inquiry: first, a hypothesis is accepted without serious attempts being made to test it; and, second, this firstlevel failure is ignored. Implications of this concept of pathology of science for the Kuhnian concept of normal science are explored. It is then shown that the hypothesis upon which psychometrics stands, the hypothesis that some psychological attributes are quantitative, has never been critically tested. Furthermore, it is shown that psychometrics has avoided investigating this hypothesis through endorsing an anomalous definition of measurement. In this way, the failure to test this key hypothesis is not only ignored but disguised. It is concluded that psychometrics is a pathology of science, and an explanation of this fact is found in the influence of Pythagoreanism upon the development of quantitative psychology. KEY WORDS: measurement, normal science, pathology of science, psychometrics, quantification There is no safety in numbers, or in anything else. (James Thurber) I argued (Michell, 1997a, 1997b) that quantitative psychology manifests methodological thought disorder, eliciting from Lovie (1997) criticisms quite unlike those offered by others invited to comment on my argument (Kline, 1997; Laming, 1997; Luce, 1997; Morgan, 1997). Lovie follows the postpositivist tradition stemming from Kuhn (1970a) and, from that perspective, saw my approach as a ‘hardnosed (and very outdated) positivist and empiricist/realist line ’ (Lovie, 1997, p. 393). The view that positivism is a form of empirical realism remains widespread, despite Passmore’s (1943, 1944, 1948) early critique and recent analyses (e.g. Friedman, 1991). Hence, there may be value in clarifying my argument regarding pathological forms of science and highlighting my reasons for so categorizing psychometrics. My thesis is that psychometricians are not only uncritical of an issue basic to their discipline but that, in addition, they have constructed a conception of quantification that disguises this. If science is a cognitive enterprise, then I
Genetic Measurement Theory of Epistatic Effects
, 1997
"... Epistasis is defined as the influence of the genotype at one locus on the effect of a mutation at another locus. As such it plays a crucial role in a variety of evolutionary phenomena such as speciation, population bottle necks and the evolution of genetic architecture (i.e. the evolution of dominan ..."
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Epistasis is defined as the influence of the genotype at one locus on the effect of a mutation at another locus. As such it plays a crucial role in a variety of evolutionary phenomena such as speciation, population bottle necks and the evolution of genetic architecture (i.e. the evolution of dominance, canalization and genetic correlations). In mathematical population genetics, however, epistasis is often represented as a mere noise term in an additive model of gene effects. In this paper it is argued that epistasis needs to be scaled in a way that is more directly related to the mechanisms of evolutionary change. A review of general measurement theory shows that the scaling of a quantitative concepts has to reflect the empirical relationships among the objects. To apply these ideas to epistatic mutation effects it is proposed to scale AxA epistatic effects as the change in the magnitude of the additive effect of a mutation at one locus due to a mutation at a second locus. It is shown ...
An ordering for groups of pure braids and fibretype hyperplane arrangements
 Canad. J. Math
"... This paper concerns the Artin braid groups Bn and especially the subgroups Pn of pure braids. Our main result is the explicit construction of a strict total ordering, <, of pure braids which is invariant under multiplication on both sides (for ; ; γ 2 Pn; < implies γ < γ and γ < γ) a ..."
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This paper concerns the Artin braid groups Bn and especially the subgroups Pn of pure braids. Our main result is the explicit construction of a strict total ordering, <, of pure braids which is invariant under multiplication on both sides (for ; ; γ 2 Pn; < implies γ < γ and γ < γ) and has the following
MeasurementTheoretic Justification of Connectives in Fuzzy Set Theory
, 1995
"... The problem of representing intersection and union in fuzzy set theory is considered. There are various proposals in the literature to model these concepts. The possibility of using continuous triangular norms and conorms (including min and max) are taken up in a measurementtheoretic setting. T ..."
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The problem of representing intersection and union in fuzzy set theory is considered. There are various proposals in the literature to model these concepts. The possibility of using continuous triangular norms and conorms (including min and max) are taken up in a measurementtheoretic setting. The conditions are laid out to arrive at cardinal scales on which addition and multiplication are meaningful and critically discussed. These conditions must either be accepted on normative grounds or must be empirically verified before the modeling process in order to see which operations are meaningful. It is emphasized that the Archimedean axiom and the existence of natural bounds are crucial in arriving at ratio and absolute scale representations. Keywords: Membership functions, measurement theory, operators, relations. 1 Introduction and Preview When Zadeh [45] introduced the concept of a fuzzy set he suggested to use the functions min and max to model set theoretic intersection an...
FILTRATIONS IN SEMISIMPLE LIE ALGEBRAS, I
"... Abstract. In this paper, we study the maximal bounded Zfiltrations of a complex semisimple Lie algebra L. Specifically, we show that if L is simple of classical type An, Bn, Cn or Dn, then these filtrations correspond uniquely to a precise set of linear functionals on its root space. We obtain part ..."
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Abstract. In this paper, we study the maximal bounded Zfiltrations of a complex semisimple Lie algebra L. Specifically, we show that if L is simple of classical type An, Bn, Cn or Dn, then these filtrations correspond uniquely to a precise set of linear functionals on its root space. We obtain partial, but not definitive, results in this direction for the remaining exceptional algebras. Maximal bounded filtrations were first introduced in the context of classifying the maximal graded subalgebras of affine KacMoody algebras, and the maximal graded subalgebras of loop toroidal Lie algebras. Indeed, our main results complete this classification in most cases. Finally, we briefly discuss the analogous question for bounded filtrations with respect to other Archimedean ordered groups. 1.
Group actions on onemanifolds, II: Extensions of Hölder’s Theorem
, 2001
"... This selfcontained paper is part of a series [FF1] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. In this paper we consider groups which act on R with restrictions on the fixed point set of each element. One result ..."
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This selfcontained paper is part of a series [FF1] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. In this paper we consider groups which act on R with restrictions on the fixed point set of each element. One result is a topological characterization of affine groups in Diff 2 (R) as those groups whose elements have at most one fixed point. 1
On spaces of Conradian group orderings
 J. of Group Theory
"... We classify Corderable groups admitting only finitely many Corderings. We show that if a Corderable group has infinitely many Corderings, then it actually has uncountably many Corderings, and none of these is isolated in the space of Corderings. As a relevant example, we carefully study the ca ..."
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We classify Corderable groups admitting only finitely many Corderings. We show that if a Corderable group has infinitely many Corderings, then it actually has uncountably many Corderings, and none of these is isolated in the space of Corderings. As a relevant example, we carefully study the case of BaumslagSolitar’s group B(1,2). We show that B(1,2) has four Corderings, each of which is biinvariant, but its space of leftorderings is homeomorphic to the Cantor set.
Nilpotent pseudogroups of functions on an interval
, 2008
"... A nearidentity nilpotent pseudogroup of order m ≥ 1 is a family f1,...,fn: (−1,1) → R of C 2 functions for which: fi − id  C 1 < ǫ for some small positive real number ǫ < 1/10 m+1 and commutators of the functions fi of order at least m equal the identity. We present a classification of nea ..."
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A nearidentity nilpotent pseudogroup of order m ≥ 1 is a family f1,...,fn: (−1,1) → R of C 2 functions for which: fi − id  C 1 < ǫ for some small positive real number ǫ < 1/10 m+1 and commutators of the functions fi of order at least m equal the identity. We present a classification of nearidentity nilpotent pseudogroups: our results are similar to those of Plante, Thurston, Farb and Franks. As an application, we classify certain foliations of nilpotent manifolds.
Contents
, 2007
"... 1 Thanks must go to Katherine Butterfield without whom I would never have embarked on this, and to Ian Chivers who rekindled my interest. ..."
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1 Thanks must go to Katherine Butterfield without whom I would never have embarked on this, and to Ian Chivers who rekindled my interest.