Reviewed Works:Andrew Hodges, Rolf Herken, Alan Turing and the Turing Machine.Stephen C. Kleene, Turing's Analysis of Computability, and Major Applications of it.Robin Gandy, The Confluence of Ideas in 1936.Solomon Feferman, Turing in the Land of O.Martin Davis, Esther R. Phillips, Mathematical Logic and the Origin of Modern Computers.

This lively introduction to mathematical logic, easily accessible to non-mathematicians, offers an historical survey, coverage of predicate calculus, model theory, Godel’s theorems, computability and recursivefunctions, consistency and independence in axiomatic set theory, and much more. Suggestions for Further Reading. Diagrams.

In this paper we 1. provide a natural deduction system for full first-order linear logic, 2. introduce Curry-Howard-style terms for this version of linear logic, 3. extend the notion of substitution of Curry-Howard terms for term variables, 4. define the reduction rules for the Curry-Howard terms and 5. outline a proof of the strong normalization for the full system of linear logic using a development of Girard's candidates for reducibility, thereby providing an alternative to Girard's proof using proof-nets.

A universal Horn sentence in the language of polynomial-time computable combinatorial functions of natural numbers is true for the natural numbers if, and only if, it is true for PETs of p-time p-isolated sets with functions induced by fully p-time combinatorial operators.

The paper argues that while Schleiermacher intends to base Christian ethics on the Christian principle of a supra-rational knowledge of God's will communicated solely through Christ, and not available to human reason, Schleiermacher nevertheless borrows for his Christian ethics from his philosophical ethics. He is able to do this because his philosophical ethics, as distinct from Kant's, incorporates insights from religious feeling. Schleiermacher's Christian ethics, therefore, is more a theory of Christian, reformative action in the church and the state than (...) a full-blown religious ethics. (shrink)

Theological ethics is vulnerable to the charge made by some philosophical ethicists that it frequently commits the "naturalistic fallacy," i.e., that it fallaciously derives duties and obligations from purely descriptive theological premises. Some theological ethicists, acceding to the charge, have contented themselves with an examination of how theological ethics might "influence" or "enrich" ethical propositions based on non-theological foundations. This essay analyzes the current scene in theological ethics and argues that the "naturalistic fallacy" is not the real danger. The real (...) danger is the failure of theological ethics to work out both its theological and ethical propositions in close relationship to human experience and to each other. (shrink)

MAX WEBER FURNISHES THE ANALOGY ON WHICH THIS ESSAY IS BASED: "This-worldly Protestant asceticism... acted powerfully against the spontaneous enjoyment of possessions; it restricted consumption, especially of luxuries. On the other hand, it had the psychological effect of freeing the acquisition of goods from the inhibitions of traditionalistic ethics. It broke the bonds of the impulse of acquisition in that it not only legalized it, but... looked upon it as directly willed by God.".

The paper presents a brief survey of recent work by Metakides, Nerode and others in the area of effective algebra and makes some comments on the relation between formal presentations, characterizations, etc. of sets and of algebraic structures and their practical presentations.

There is a religious ethics implicit in Schleiermacher's doctrine of creation based on the universal feeling of absolute dependence "prior to" its being informed by any historical tradition. The "highest good" which fundamentally characterizes his religious ethics is found at the intersection of God and the World. The "original perfection of man" and the "original perfection of the world" come together when human life in the world is fully informed by the feeling of absolute dependence. Although Schleiermacher did not develop (...) his religious ethics to the same extent as his philosophical and Christian ethics, it should still be of interest to ethicists in many religious traditions, as it establishes contours and sets limits for the ethics of any monotheistic religious tradition. (shrink)

Reviewed Works:Andrew Hodges, Rolf Herken, Alan Turing and the Turing Machine.Stephen C. Kleene, Turing's Analysis of Computability, and Major Applications of it.Robin Gandy, The Confluence of Ideas in 1936.Solomon Feferman, Turing in the Land of O.Martin Davis, Esther R. Phillips, Mathematical Logic and the Origin of Modern Computers.

Review of Eckart Menzler-Trott’s book, Logic’s Lost Genius: The Life of Gerhard Gentzen.