Wilfried Sieg and John Byrnes. AnModel for Parallel Computation: Gandy's Thesis.

Wilfred Sieg and John Byrnes. K-Graph Machines: Generalizing Turing's Machines and Arguments.

Mark Wicclair’s defense of conscientious objection is grounded in an effort to respect the core moral beliefs of health care providers. While such a theoretical schema has merit, this paper argues that core moral beliefs should not serve as the basis of conscientious objection in health care because we, as a community, lack reliable access to a person’s core moral beliefs and because individuals are prone to be confused about the scope and extent of their core moral beliefs. Furthermore, a (...) person’s confusion over their core moral beliefs is likely to be exacerbated when they lack time to investigate those beliefs and are under heightened external pressure to do so—both conditions frequently encountered by health care providers. Finally, the paper considers whether grounding conscientious objection in core moral beliefs might have the unintended consequence of further entrenching the practical problems that the move is aiming to solve. (shrink)

Natural deduction (for short: nd-) calculi have not been used systematically as a basis for automated theorem proving in classical logic. To remove objective obstacles to their use we describe (1) a method that allows to give semantic proofs of normal form theorems for nd-calculi and (2) a framework that allows to search directly for normal nd-proofs. Thus, one can try to answer the question: How do we bridge the gap between claims and assumptions in heuristically motivated ways? This informal (...) question motivates the formulation of intercalation calculi. Ic-calculi are the technical underpinnings for (1) and (2), and our paper focuses on their detailed presentation and meta-mathematical investigation in the case of classical predicate logic. As a central theme emerges the connection between restricted forms of nd-proofs and (strategies for) proof search: normal forms are not obtained by removing local "detours", but rather by constructing proofs that directly reflect proof-strategic considerations. That theme warrants further investigation. (shrink)

Natural deduction (for short: nd-) calculi have not been used systematically as a basis for automated theorem proving in classical logic. To remove objective obstacles to their use we describe (1) a method that allows to give semantic proofs of normal form theorems for nd-calculi and (2) a framework that allows to search directly for normal nd-proofs. Thus, one can try to answer the question: How do we bridge the gap between claims and assumptions in heuristically motivated ways? This informal (...) question motivates the formulation of intercalation calculi. Ic-calculi are the technical underpinnings for (1) and (2), and our paper focuses on their detailed presentation and meta-mathematical investigation in the case of classical predicate logic. As a central theme emerges the connection between restricted forms of nd-proofs and (strategies for) proof search: normal forms are not obtained by removing local "detours", but rather by constructing proofs that directly reflect proof-strategic considerations. That theme warrants further investigation. (shrink)

In a recent issue of this journal, Gamble and Saad offer a taxonomy of conscientious objection in health care with the aim of increasing the common ground in the debate over conscientious objection to prevent parties from talking past each other and help facilitate greater progress on this issue. Although we agree that this is an important and worthwhile project, Gamble and Saad's proposal suffers from several serious weaknesses that limit its ability to do the work set out for it. (...) In this paper, we identify some of the major problems with this particular attempt in order to highlight some desiderata for a taxonomy of conscientious objection in health care that can serve as a guide for developing improved taxonomies of this kind in the future. (shrink)

Wilfried Sieg and John Byrnes. Gödel, Turing, and K-Graph Machines.

Wilfred Sieg and John Byrnes. Generalizing Turing's Machine and Arguments.