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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tradition stemming from Kuhn (1970a) and, from that perspective, saw my approach as a ‘hardnosed (and very outdated) positivist and empiricist/realist line ’ (Lovie, 1997, p. 393).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
Frege versus Cantor and Dedekind: On the Concept of Number
, 1997
"... This paper is in honor of my colleague and friend, Leonard Linsky, on the occasion of his retirement. I presented the earliest version in the Spring of 1992 to a reading group, the other members of which were Leonard Linsky, Steve Awodey, Andre Carus and Mike Price. I presented later versions in the ..."
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This paper is in honor of my colleague and friend, Leonard Linsky, on the occasion of his retirement. I presented the earliest version in the Spring of 1992 to a reading group, the other members of which were Leonard Linsky, Steve Awodey, Andre Carus and Mike Price. I presented later versions in the autumn of 1992 to the philosophy colloquium at McGill University and in the autumn of 1993 to the philosophy colloquium at CarnegieMellon University. The discussions following these presentations were valuable to me and I would especially like to acknowledge Emily Carson (for comments on the earliest draft), Michael Hallett, Kenneth Manders, Stephen Menn, G.E. Reyes, Teddy Seidenfeld, and Wilfrid Sieg and the members of the reading group for helpful comments. But, most of all, I would like to thank Howard Stein and Richard Heck, who read the penultimate draft of the paper and made extensive comments and corrections. Naturally, none of these scholars, except possibly Howard Stein, is respon
Challenges to Predicative Foundations of Arithmetic
 in Between Logic and Intuition Essays in Honor of Charles Parsons
, 1996
"... This paper was written while the first author was a Fellow at the Center for Advanced Study in the Behavioral Sciences (Stanford, CA) whose facilities and support, under grants from the Andrew W. Mellon Foundation and the National Science Foundation, have been greatly appreciated. ..."
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This paper was written while the first author was a Fellow at the Center for Advanced Study in the Behavioral Sciences (Stanford, CA) whose facilities and support, under grants from the Andrew W. Mellon Foundation and the National Science Foundation, have been greatly appreciated.
Reflections on Skolem's Paradox
"... In 1922, Thoraf Skolem published a paper titled "Some remarks on Axiomatized Set Theory". The paper presents a new proof of... This dissertation focuses almost exclusively on the first half of this project  i.e., the half which tries to expose an initial tension between Cantor's theorem and the Lö ..."
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In 1922, Thoraf Skolem published a paper titled "Some remarks on Axiomatized Set Theory". The paper presents a new proof of... This dissertation focuses almost exclusively on the first half of this project  i.e., the half which tries to expose an initial tension between Cantor's theorem and the LöwenheimSkolem theorem. I argue that, even on quite naive understandings of set theory and model theory, there is no such tension. Hence, Skolem's Paradox is not a genuine paradox, and there is very little reason to worry about (or even to investigate) the more extreme consequences that are supposed to follow from this paradox. The heart of my...
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Only up to isomorphism? Category theory and the . . .
"... Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can ..."
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Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in other branches of contemporary mathematics. If such a specification suffices, then a categorytheoretical approach will be highly appropriate. But if sets have a richer ‘nature ’ than is preserved under isomorphism, then such an approach will be inadequate.
Philos Stud DOI 10.1007/s1109801301604 Mathematical representation: playing a role
"... Abstract The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Noneliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the feature ..."
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Abstract The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Noneliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which instead explains the attributes them to the mathematical practice of representing numbers using more concrete tokens, such as sets, strokes and so on.