This book, the author tells us, is "about some of the ways in which the techniques of modal logic may be used to study concepts of proof theory first studied in Gödel's famous paper on the incompleteness of arithmetic." Those who, with Quine and others, think that modal logic was conceived in sin, may well doubt that its techniques will throw anything but more Dunkel on proof theory. The author attempts to show otherwise and construes "☐A", where " ☐" is (...) the symbol for modal necessity, in terms of Gödel's arithmetical predicate "Bew" for provability. The formulae in which this latter occurs are perfectly well-defined, we are told, and thus no sin can be attached to this identification. But are such formulae perfectly well-defined? Syntactically, yes; but semantically? It is usually assumed that they are, but the full array of semantical principles needed to carry out Gödel's arithmetization seems never to have been given in full detail. And it is just possible that a fallacy of ambiguity lies concealed in such formulae, as F. Rivetti-Barbò has contended and Lesniewski appears to have hinted at. In any case, not all is happy philosophically and to everyone's satisfaction, at the very foundation of Gödel's method. Although the author purports to have proved here a number of seemingly interesting and sophisticated theorems, the real semantical issues involved seem to have been skirted.--R.M.M. (shrink)

This is the collection of essays presented to Bochenski on his 60th birthday, and it contains, as a mirror of Bochenski's own work, a broad spectrum of studies ranging from formal logic and history of logic, to the philosophy of logic and language, and to the methodology of explanation in Greek philosophy. Of the seventeen articles, these are some of the more important to the reviewer: "Betrachtungen zum Sequenzen Kalkül" by Paul Bernays, which is an extensive study of Gentzen-type formulations (...) of logic; "Remarks on Formal Deduction," H. B. Curry, a further discussion of sequenzen-logics; "Marginalia on Gentzen's Sequenzen Kalkül" by Hughes Leblanc; "Method and Logic in Presocratic Explanation," Jerry Stannard; "On the Logic of Preference and Choice," H. S. Houthakker, a suggestive presentation of decision and utility theory in logical form; "Leibniz's Law in Belief Contexts," Chisholm; "On Ontology and the Province of Logic," R. M. Martin; and "N. A. Vasilev and the Development of Many-valued Logics," G. L. Kline, an important addition to the history of logic. Other contributors are: Storrs McCall, Albert Menne, E. W. Beth, Benson Mates, Ivo Thomas, J. F. Staal, F. R. Barbò, A.-T. Tymieniecka, and N. M. Luyten. There is a bibliography of Bochenski's writings through 1962.—P. J. M. (shrink)

Upshot: In this response, I address the points raised in the commentaries, in particular those related to the scalability and robustness of the mechanism CALM, to its relation with the CAES architecture, and to the transition from sensorimotor to symbolic.