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.     

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.     

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.     

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.