Working within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call RCA+ 0 and WKL+ 0, and show that RCA+ 0 suffices to prove B.C.T.II. Some model theory of WKL+ 0 and its importance in view of (...) Hilbert's program is discussed, as well as applications of our results to functional analysis. (shrink)

Continuing the investigations of X. Yu and others, we study the role of set existence axioms in classical Lebesgue measure theory. We show that pairwise disjoint countable additivity for open sets of reals is provable in RCA0. We show that several well-known measure-theoretic propositions including the Vitali Covering Theorem are equivalent to WWKL over RCA0.

Substantial medical evidence shows that about half of ovarian cancers originate in the fallopian tube. Some medical organizations and clinical articles have suggested opportunistic salpingectomy to reduce the risk of ovarian cancer in patients at average risk of developing it. This entails removing the fallopian tubes at the same time as another procedure that would occur anyway. The authors argue that the principles of totality and double effect can justify such salpingectomies, even though there is a low incidence of ovarian (...) cancer. Since screening tools for ovarian cancer are ineffective and treatment options are poor, the good effect of reducing the risk of death from this type of ovarian cancer can be proportionate to the bad effects of the minor increase in surgical risk over the other procedure, the unintended side effect of infertility, and the removal of normally functioning tissue. The authors conclude that it is within the purview of a patient and physician to determine whether the benefits are proportionate to the risks in a particular case. (shrink)

Surgical ethics has to do with the determination of what ought to be done, all things considered. This chapter prompts reflection on eight analytical questions:What does it mean for a practicing surgeon to be “ethical”?Where is “ethics” in the complexities of patient care?Why do well-intentioned individuals come to conflicting judgments about what should be done?What are patients and their families invited to trust?When/why does trust break down in patient care?When/how should patients and their families be involved in decision-making?Why is it (...) so hard to keep sense in care at life’s end?Is concern for justice relevant at the bedside? (shrink)