Remarks on counterpossibles

Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another justification derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds.     

Remarks on aggression

This paper attempts to draw attention to the difference between the states of mind and inner worlds of neurotic, borderline and psychopathic patients, with reference to different types of destructiveness: anger in the neurotic patient; desperate vengeful hatred in the borderline paranoid; and a cold addiction to violence in the psychopath. Discussion focuses on technical issues and the need to meet the psychopathic patient where he really is, in the inner bleak emotional cemetery he may be inhabiting. Although most patients refuse to stay put in the neat schematic categories outlined, they do seem to appreciate and to need the therapist's recognition of the specific quality of these vastly different states of mind.     

Remarks on an Avoidable Error in a Posteriori Testing

This article discusses a widespread error that occurs with a posteriori testing in factorial analyses of variance. Frequently, an incorrect sample size is used under the radical in the formula for computing a critical difference such as the Fisher least significance difference. This usually leads to an inappropriately large critical difference; thus, few if any significant differences are uncovered between the means. An interesting example of this error, from a journal article by Van Berschot (1979), is examined. Researchers are urged always to use under the radical the number of observations on which each mean being compared is based.     

On a theorem of Feferman

Summary In this paper I have argued that Feferman's theorem does not signify the existence of skeptic-satisfying consistency proofs. However, my argument for this is much different than other arguments (most particularly Resnik's) for the same claim. The argument that I give arises form an analysis of the notion of expression, according to which the specific character of that notion is seen as varying from one context of application (of a result of arithmetic metamathematics) to another.I want to thank Dale Gottlieb, Mike Resnik, John Corcoran, Nicolas Goodman and Stewart Shapiro for careful and helpful commentary on an ancestor of this paper that was delivered at the Western Division Meetings of the APA in 1977.     

Remarks about a paired comparison model

A generalization of the customary model underlying the Law of Comparative Judgment is established. Methods for estimating location parameters and testing a certain hypothesis are discussed. The problem of the influence of the shape of the curve used to grade responses is raised and a possible approach to its solution is indicated. Two examples are provided.The author is obliged to F. Mosteller for helpful discussions.