Constructive mathematics and unbounded operators — A reply to Hellman

It is argued that Hellman's arguments purporting to demonstrate that constructive mathematics cannot cope with unbounded operators on a Hilbert space are seriously flawed, and that there is no evidence that his thesis is correct.     

The contingency argument—A reply

Conclusion Brian Medlin has excluded the possibility of something being self-explanatory in anything but a logical sense. Hence any non-logical necessity has always to be in terms of something other than the explicand. In this context, the principle of sufficient reason cannot escape contraction to a form so patently useless that no proponent of the contingency argument would want to employ it. Many of the objections in Section 4 have point, however, only against an argument which uses such an unacceptable form of the principle. The objections in Section 5 are directed against an argument framed in the only other way allowable under Medlin’s dichotomy, but which is of no use to the theist, for the simple-reason that its conclusion is not existential in the required (present actuality) sense. Objections against such an argument would concern the theist only if their validity were so wide as to embrace a truly existential argument as well. As we have-seen it is in just that case that they break down. In neither Section 4 nor 5, therefore, does the article come to grips with the contingency argument. The objections leave it untouched, because neither of Medlin’s notions of contingency and necessity corresponds to that which is operative in the argument.     

The conjunction fallacy? A reply to Bar-Hillel

In her commentary on our article, Bar-Hillel (1991) argues that our normative interpretation of the Lindaproblem is inaccurate and that the representativeness heuristic can account for all of the relevant data. I argue that the normative interpretation of the Linda problem remains slippery and that representativeness fails to account for much of the data. Furthermore, substantial evidence supports our suggestion that subjects use different underlying models in estimating likelihoods in different con problems.     

One concept or two? A reply to Raine

It is suggested that Raine's criticisms of the paper by Barbour-McMullen, Coid and Howard rest on misconceptions, particularly regarding the nature of the supposed conceptual dichotomy between “North American” and “European” concepts of psychopathy. Several points of clarification are offered. It is maintained that psychopathy is indeed a dual, rather than a unitary, concept.     

Platonism and laws: A reply to Demetra Sfendoni‐Mentzou

This paper is a reply to Demetra Sfendoni‐Mentzou; it defends a realist—indeed a platonist—account of laws of nature.