The measurement of factor indeterminacy

Results obtained by Guttman [1955] on the determinacy of common factors have been thought to have disturbing consequences for the common factor model. It is argued that factors must be thought of as unobservable, and uniquely defined but numerically indeterminate. It follows that Guttman's measure of indeterminacy is inconsistent with the foundations of the factor model in probability theory, and the traditional measures of factor indeterminacy used by earlier writers should be reinstated. These yield no disturbing conclusions about the model.     

Some notes on the nature of methodological indeterminacy

This paper is an attempt to extend the meaning of the concept of indeterminacy for the human sciences. The authors do this by coining the term methodological indeterminacy and arguing that indeterminacy is better understood when linked to specific methodological techniques. Paradoxically, while specific research techniques demonstrate that the issue of indeterminacy is complex, yielding the possibility of types and degrees, it does not eliminate the problem of translation first raised by Quine. However, the authors go on to argue that, from a research perspective, indeterminacy can and must be approached in such a way that it is possible to reduce cases of it, even though never completely eliminating it in the human sciences.     

The effect of additional variables on factor indeterminacy in models with a single common factor

Determinate solutions for the indeterminate common factor ofp variables satisfying the single common factor model are not unique. Therefore an infinite sequence of additional variables that conform jointly with the originalp variables to the original single common factor model does not determine a unique solution for the indeterminate factor of thep variables (although the solution is unique for the factor of the infinite sequence). Other infinite sequences may be found to determine different solutions for the factor of the originalp variables. The paper discusses a number of theorems about the effects of additional variables on factor indeterminacy in a model with a single common factor and draws conclusions from them for factor theory in general.     

Quantum metaphysical indeterminacy

Philosophical Studies - On a wide variety of presently live interpretations, quantum mechanics violates the classical supposition of ‘value definiteness’, according to which the...     

Some results on random utility models

This paper extends earlier work on the properties of Thurstone choice models to the general random utility model (RUM), in which the components of the random utility vector are not necessarily independent and identically distributed, even apart from location shifts. The condition for two RUMs to be equivalent is established, and relationships between the choice axiom, decomposition, and other conditions are explored. In the special case of the Thurstone model, the conditions considered are all equivalent to the double exponential distribution.     

Standard errors for the class of orthomax-rotated factor loadings: Some matrix results

The partial derivative matrices of the class of orthomax-rotated factor loadings with respect to the unrotated maximum likelihood factor loadings are derived. The reported results are useful for obtaining standard errors of the orthomax-rotated factor loadings, with or without row normalization (standardization) of the initial factor loading matrix for rotation. Using a numerical example, we verify our analytic formulas by comparing the obtained standard error estimates with that from some existing methods. Some advantages of the current approach are discussed.Authorship is determined by alphabetical order. The authors contributed equally to the research. Kentaro Hayashi is now at the Department of Mathematics, Bucknell University, Lewisburg, PA 17837 (email: khayashi@Bucknell.edu). Yiu-Fai Yung is now at the SAS Institute, Inc., SAS Campus Drive, Cary, NC 27513 (email: yiyung@wnt.sas.com).Part of the research was completed while Yiu-Fai Yung was a visiting scholar at the Department of Psychology, the Ohio State University. The visit was supported in part by grant N4856118101 from the NIMH and the Mason and Linda Stephenson Travel Award from the Department of Psychology, University of North Carolina at Chapel Hill. The authors are grateful to Michael Browne who suggested some relevant references and provided valuable comments on the research, and to Robert Cudeck who provided the FAS program for the numerical comparison. The expert comments by the reviewers are deeply appreciated.     

The indeterminacy of computation

Synthese - Do the dynamics of a physical system determine what function the system computes? Except in special cases, the answer is no: it is often indeterminate what function a given physical...     

Carnap and translational indeterminacy

InWord and Object W. V. Quine argues that there is no uniquely correct way to assign referents to the terms of a language; any claim about the reference of a term is implicitly relative to a manual of translation. To Rudolf Carnap this must have seemed familiar. BeforeWord and Object was written Carnap had been saying the same thing inMeaning and Necessity: under the assumption of the method of the name-relation, any claim about the reference of a term is implicitly relative to what Carnap calls a conception of the name-relation. Yet Carnap is often taken to be a victim of Quine's relativistic notion of reference. Drawing on Carnap's discussion of the name-relation inMeaning and Necessity, it is argued that Carnap's and Quine's views on reference are not so far apart as is usually perceived.I would like to thank the referees who reviewed this paper for their helpful and insightful comments. In addition, I would like to thank Dr. Richard Creath both for his comments on earlier drafts of this paper as well as for conversations (beyond number) on these and many other issues related to the Quine-Carnap debate. Creath's own discussion of this topic entitled Functionalist Theories of Meaning and the Defense of Analyticity, appears in the volumeLanguage, Logic, and the Structure of Scientific Theories: The Carnap-Reichenbach Centennial, edited by W. Salmon and G. Wolters (Pittsburgh: University of Pittsburgh Press, and Konstanz, Germany: University of Konstanz Press, 1994).     

Some puzzling results on the Poggendorff illusion

Results obtained by Weintraub and Krantz on the Poggendorff illusion were critically evaluated. It was also shown that the assimilation theory of the Poggendorff illusion adequately predicted the form of the function that results from rotating one of the oblique arms.     

Epistemic dilemmas and rational indeterminacy

Philosophical Studies - This paper is about epistemic dilemmas, i.e., cases in which one is doomed to have a doxastic attitude that is rationally impermissible no matter what. My aim is to develop...     

Kirk on Quine's reasons for indeterminacy of translation

Philosophical Studies -     

The indeterminacy of color vision

A critical survey of recent work on the ontological status of colors supports the conclusion that, while some accounts of color can plausibly be dismissed, no single account can yet be endorsed. Among the remaining options are certain forms of color realism according which familiar colors are instantiated by objects in our extra-cranial visual environment. Also still an option is color anti-realism, the view that familiar colors are, at best, biologically adaptive fictions, instantiated nowhere.I argue that there is simply no fact of the matter as to which of these remaining options is correct. I blame this indeterminacy on the fact that color vision exhibits several of the hallmarks of a modular input system, as described by Jerry Fodor in The Modularity of Mind.Finally, I speculate that the range of live options falling within the scope of the indeterminacy may be even broader than initially indicated.     

Extensionality, underdetermination and indeterminacy

I am grateful to Burton Dreben, Warren Goldfarb, Don Gustafson, Jim Higginbotham, Jerrold Katz, Joe Levine, Ted Morris, Nick Pappas, Hilary Putnam, Georges Rey and Bob Richardson for helpful discussions and comments on the issues discussed in this paper. Also I thank an anonymous reviewer for Erkenntnis for helpful comments.