IMAGINATION'S GRIP ON SCIENCE

Abstract: In part because “imagination” is a slippery notion, its exact role in the production of scientific knowledge remains unclear. There is, however, one often explicit and deliberate use of imagination by scientists that can be (and has been) studied intensively by epistemologists and historians of science: thought experiments. The main goal of this article is to document the varieties of thought experimentation, not so much in terms of the different sciences in which they occur but rather in terms of the different functions they fulfil. I argue that thought experimentation (and hence imagination) plays a role not only in theory choice but in singular causal analysis and scientific discovery as well. I pinpoint, moreover, some of the rules governing the use of thought experiments in theory choice and in singular causal analysis, that is, some of the criteria they should meet in order to fulfil those functions successfully.     

Taxicab Correspondence Analysis

Taxicab correspondence analysis is based on the taxicab singular value decomposition of a contingency table, and it shares some similar properties with correspondence analysis. It is more robust than the ordinary correspondence analysis, because it gives uniform weights to all the points. The visual map constructed by taxicab correspondence analysis has a larger sweep and clearer perspective than the map obtained by correspondence analysis. Two examples are provided. This research was financed by the Natural Sciences and Engineering Research Council of Canada. The author thanks Serge Vienneau for his help regarding the graphical displays, and also thanks the editor, associate editor, and two reviewers for their constructive comments.     

On Consistent Subsets of Large Sets of Satisfiable Sentences

We extend some results of Adam Kolany to show that large sets of satisfiable sentences generally contain equally large subsets of mutually consistent sentences. In particular, this is always true for sets of uncountable cofinality, and remains true for sets of denumerable cofinality if we put appropriate bounding conditions on the sentences. The results apply to both the propositional and the predicate calculus. To obtain these results, we use delta sets for regular cardinals, and, for singular cardinals, a generalization of delta sets. All of our results are theorems in ZFC.     

Referential Intentions: A Response to Buchanan and Peet

Buchanan [2014] argues for a Gricean solution to well-known counterexamples to direct reference theories of content. Peet [2016] develops a way to change the counterexample so that it seems to speak against Buchanan's own proposal. I argue that both theorists fail to notice a significant distinction between the kinds of cases at issue. Those appearing to count against direct reference theory must be described such that speakers have false beliefs about the identity of the object to which they intend to refer, beliefs that appear relevant to the determination of what constitutes communicative success. This suggests, further, that cases of this sort do not provide a basis for robust generalizations about singular reference.     

The Goldilocks Problem of the specificity of visual phenomenal content

Existentialist accounts maintain that visual phenomenal content takes the logical form of an existentially quantified sentence. These accounts do not make phenomenal content specific enough. Singularist accounts posit a singular content in which the seen object is a constituent. These accounts make phenomenal content too specific. My account gets the specificity of visual phenomenal content just right. My account begins with John Searle's suggestion that visual experience represents an object as seen, moves this relation outside the scope of the existential quantifier and then replaces it with the relation of objects being ‘present as accessible’, as described by Alva Noë.     

Idealizations and Concretizations in Laws and Explanations in Physics

The paper tries to provide an alternative to Hempel’s approach to scientific laws and scientific explanation as given in his D-N model. It starts with a brief exposition of the main characteristics of Hempel’s approach to deductive explanations based on universal scientific laws and analyzes the problems and paradoxes inherent in this approach. By way of solution, it analyzes the scientific laws and explanations in classical mechanics and then reconstructs the corresponding models of explanation, as well as the types of scientific laws appearing in it. Finally, it compares this reconstruction with the approaches of J. Woodward and C. Hitchcock, C. Liu and with the views of M. Thalos on analytic mechanics.

Regularized Partial and/or Constrained Redundancy Analysis

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in multiple regression analysis for some time, especially when predictor variables are nearly collinear, and the ordinary least squares estimator is poorly determined. The ridge estimation method was extended to PRA, CRA, and PCRA, where the reduced rank ridge estimates of regression coefficients were obtained by minimizing the ridge least squares criterion. It was shown that in all cases they could be obtained in closed form for a fixed value of ridge parameter. An optimal value of the ridge parameter is found by G-fold cross validation. Illustrative examples were given to demonstrate the usefulness of the method in practical data analysis situations. We thank Jim Ramsay for his insightful comments on an earlier draft of this paper. The work reported in this paper is supported by Grants 10630 from the Natural Sciences and Engineering Research Council of Canada to the first author.     

Principal component analysis with external information on both subjects and variables

A method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis. In this method, the original data are first decomposed into several components according to external information. The components are then subjected to principal component analysis to explore structures within the components. It is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices. The numerical method based on the QR decomposition is described, which simplifies the computation considerably. The proposed method includes a number of interesting special cases, whose relations to existing methods are discussed. Examples are given to demonstrate practical uses of the method.The work reported in this paper was supported by grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the first author. Thanks are due to Jim Ramsay, Haruo Yanai, Henk Kiers, and Shizuhiko Nishisato for their insightful comments on earlier versions of this paper. Jim Ramsay, in particular, suggested the use of the QR decomposition, which simplified the presentation of the paper considerably.     

The Logic and Meaning of Plurals. Part II

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages.