Three indexes have been compiled: authors of main articles (including our special departments such as ‘Projects in progress’ and ‘Notes and discussions’); essay reviews; and book reviews. Co-author...

The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC.

A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type (...) semantics are provided for each one of the resulting systems (the positive systems plus the semiclassical negation). (shrink)

LCo with the Converse Ackermann Property is defined as the result of restricting Contraction in LC. Intuitionistic and Superintuitionistic Negation is shown to be compatible with the CAP.

The aim of this paper is to provide a Routley-Meyer semantics for Ackermann’s logics of “strenge Implikation” Π ′ and Π ′′ . Besides the Disjunctive Syllogism, this semantics validates the rules Necessitation and Assertion. Strong completeness theorems for Π ′ and Π ′′ are proved. A brief discussion on Π ′ , Π ′′ and paraconsistency is included.

A system S has the “converse Ackermann property” if -> C is unprovable in S whenever C is a propositional variable. In this paper we define the fragments with the C.A.P. of some well-know propositional systems in the spectrum between the minimal and classical logic. In the first part we succesively study the implicative and positive fragments and the full calculi. In the second, we prove by a matrix method that each one of the systems has the C.A.P. Thus, (...) we think the problem proposed in Anderson & Belnap § 8.12 has been solved. (shrink)

Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.

The origin of paraconsistent logic is closely related with the argument, ‘from the assertion of two mutually contradictory statements any other statement can be deduced’; this can be referred to as ex contradictione sequitur quodlibet (ECSQ). Despite its medieval origin, only by the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this article is to study what happened earlier: from Principia Mathematica to that time, when it became well (...) established. The two main historical claims that I am going to advance are the following: (1) the first explicit use of ECSQ as the main argument for supporting the necessity of excluding any contradiction from deductive systems is to be found in the first edition of the book Grundzüge der Theoretischen Logik (Hilbert, D. and Ackermann, W. 1928. Grundzüge der Theoretischen Logik. Berlin: Julius Springer Verlag); (2) Łukasiewicz's position regarding the logical constraints against contradictions varies considerably from his studies on the principle of (non-) contradiction in Aristotle, published in 1910 and what is stated in his `authorized lectured notes' on mathematical logic that appeared in 1929. The two texts are: 1) a paper in German (Łukasiewicz, J. 1910. `Über den Satz des Widerspruchs bei Aristotles'. Bulletin International de l'Académie des sciences de Cracovie, Classe d'Histoire et de Philosophie, pp. 15–38) [English translation: Łukasiewicz, J. 1971. ‘On the principle of contradiction in Aristotle’, Review of Metaphysics, XXIV, 485–509]; and 2) a book in Polish. Łukasiewicz, J. 1910. O zasadzie sprzecznosci u Aristotelesa Studium krytyczne, Warsaw: Panstwowe Wydawnictwo Naukowe [German translation: Łukasiewicz, J. 1993. Über den Satz des Widerspruchs bei Aristotles. Hildesheim: Georg Olms Verlag]. The lecture notes were then published as a book (Łukasiewicz, J. 1958. Elementy Logiki Matematycznej. Warszawa: Panstwowe Wydawnictwo Naukowe [PWN] and then translated into English (Łukasiewicz, J. 1963. Elements of Mathematical Logic. Oxford, New York: Pergamon Press/the Macmillan Company). The second half of this article will concentrate on Łukasiewicz's position on ECSQ. This will lead me to propose that to regard him as a forerunner of paraconsistent logic by virtue of those early writings is accurate only if his book published in Polish is considered but not if the analysis is restricted to the paper originally published in German (as has been the case for the principal reconstructions of the history of paraconsistent logic). Furthermore, I will stress that in the 1929 book he presented one formalization of ECSQ as an axiom for sentential calculus and, also, he used ECSQ to defend the necessity of consistency, apparently independently of Hilbert and Ackermann's book. At the end, I will suggest that the aim of twentieth century usage of ECSQ was to change from the centuries-long philosophical discussion about contradictions to a more ‘technical’ one. But with paraconsistent logic viewed as a technical solution to this restriction, then, the philosophical problem revives but having now at one's disposal an improved understanding of it. Finally, Łukasiewicz's two different positions about ECSQ open an interesting question about the history of paraconsistent logic: do we have to attempt a consistent reconstruction of it, or are we prepared to admit inconsistencies within it? (shrink)

Throughout the Old Testament, the stories, laws, and songs not only teach a way of life that requires individuals to be moral, but they demonstrate how. In biblical studies, character ethics has been one of the fastest-growing areas of interest. Whereas ethics usually studies rules of behavior, character ethics focuses on how people are formed to be moral agents in the world. This book presents the most up-to-date academic work in Old Testament character ethics, covering topics throughout the Torah, the (...) Prophets, and the Writings, in addition to the use of the Bible in the modern world. In addition to Carroll and Lapsley, contributors are Denise M. Ackermann, Cheryl B. Anderson, Samuel E. Balentine, William P. Brown, Walter Brueggemann, Thomas B. Dozeman, Bob Ekblad, Jose Rafael Escobar R., Theodore Hiebert, Kathleen O'Connor, Dennis T. Olson, J. David Pleins, Luis R. Rivera Rodriguez, J. J. M. Roberts, and Daniel L. Smith-Christopher. (shrink)

A restriction of R-Mingle with the variable-sharing property and the Ackermann properties is defined. From an intuitive semantical point of view, this restriction is an alternative to Anderson and Belnap’s logic of entailment E.

We provide Routley-Meyer type semantics for relevant logics including Contractionless Ticket Entailment TW (without the truth constant t and o) plus reductio R and Ackermann’s rule γ (i.e., disjunctive syllogism). These logics have the following properties. (i) All have the variable sharing property; some of them have, in addition, the Ackermann Property. (ii) They are stable. (iii) Inconsistent theories built upon these logics are not necessarily trivial.

The body of this book contains four original papers, comments, and author's replies, from a conference on the Logic of Decision and Action held at the University of Pittsburgh in March 1966. The principal authors are Herbert Simon, N. Rescher, Donald Davidson, and G. H. von Wright. Commentators are R. Ackermann, A. R. Anderson, N. D. Belnap, R. Binkley, H. N. Castañeda, R. Chisholm, J. Robison, and the late E. J. Lemmon. As appendices, there are articles by A. R. (...) Anderson "The Formal Analysis of Normative Systems," and Rescher's very brief scheme for the classifications of "actions" according to five key generic elements. Problems of decision and action are important for all philosophical critique of norms; in ethics, philosophy of science, of the social sciences, and so forth. The task of a comprehensive logic of action is to describe or prescribe the rules that govern reasoning about the occasions for action, the discovery of action alternatives, and the choice of action. In "The Logic of Heuristic Decision Making," Herbert Simon continues to support the view presented in his earlier work, that "ordinary mathematical reasoning, hence the ordinary logic of declarative statements, is all that is required," as relevant imperatives can be brought into normative systems via correspondence rules for conversion of existential statements. In "Semantic Foundations for the Logic of Preference," Rescher starts from the familiar semantical notion of a "possible world," offering the valuation-measure for such worlds as a determinant of preferabilities, and hoping to show that divergent approaches to problems of preference may be reconciled in this way. Davidson's article, "The Logical Form of Action Sentences" analyzes concepts of agency and intentionality. G. H. von Wright sees a logic of change to be necessary in order to formulate a logic of action. His essay elaborates some of the ideas in his book Norms and Action, but also gives essential modifications of his earlier views.--M. B. M. (shrink)

This is a diligent and competent account of Popper’s philosophy of natural science primarily, and secondarily of his philosophy of the social sciences. There are discussions of such topics as the anti-positivistic origin of Popper’s views, his interpretation of probability, his theory of corroboration, his critique of Carnap, his elaboration of indeterminism, and his interpretation of quantum theory. In a chapter dealing with subjectivism, Ackermann develops Popperian arguments against the views of Paul Feyerabend and Thomas Kuhn and gives an (...) insightful elaboration of Popper’s evolutionary epistemology. (shrink)

We define two extensions of Lewis’ S3 with two versions of Peirce’s Law. We prove that both of them have the Ackermann Property.

We define two extensions of Lewis’ S3 with two versions of Peirce’s Law. We prove that both of them have the Ackermann Property.

S3o and S4o are the restrictions with the Converse Ackermann Property of the implicative fragments of Lewis' S3 and S4 respectively. The aim of this paper is to provide all possible axiomatizations with independent axioms of S3o and S40 that can be formulated with a modification of Anderson and Belnap's list of valid entailments.

S3o and S4o are the restrictions with the Converse Ackermann Property of the implicative fragments of Lewis' S3 and S4 respectively. The aim of this paper is to provide all possible axiomatizations with independent axioms of S3o and S4o that can be formulated with a modification of Anderson and Belnap's list of valid entailments.

The Pythagorean Life is the most extensive surviving source on Pythagoreanism, and has wider interest as an account of the religious aspirations of late antiquity. "...admirably clear translation and sensible introduction"--The Classical...

Robert John Ackermann deals decisively with the problem of relativism that has plagued post-empiricist philosophy of science. Recognizing that theory and data are mediated by data domains (bordered data sets produced by scientific instruments), he argues that the use of instruments breaks the dependency of observation on theory and thus creates a reasoned basis for scientific objectivity. Originally published in 1985. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished (...) backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

A selection from the correspondence of the logician Wilhelm Ackermann (1896?1962) is presented in this article. The most significant letters were exchanged with Bernays, Scholz and Lorenzen, from which extensive passages are transcribed. Some remarks from other letters, with quotations, are also included.

Die Gründe, die C. I. Lewis [5], [6] bewogen haben, neben der gewöhnlichen Implikation eine strikte Implikation einzuführen, sind bekannt. In der vorliegenden Arbeit wird aus ähnlichen Gründen eine strenge Implikation eingeführt, die jedoch einen engeren Begriff darstellt als die strikte Implikation. Mit einer Arbeit von Arnold Schmidt [7] hat meine nur geringe Berührungspunkte, da der Verfasser sich mit der strikten Implikation beschäftigt. Für diese wird ein relativ einfaches Axiomensystem angegeben und gezeigt, wie man durch geeignete Definitionen von Notwendigkeit und (...) Möglichkeit bei eventueller Hinzufügung von Zusatzaxiomen die bekannten Systeme des Modalitätenkalküls erhält. Den Hauptteil meiner Arbeit bildet die Einführung meines Implikationsbegriffs; im zweiten Teil der Arbeit komme ich dann auf dieser Basis auch zu einer Einführung der Modalitäten.Um die Art der Einführung des Kalküls zu motivieren, wollen wir kurz auf das eingehen, das uns mehr oder weniger deutlich vorschwebt, wenn wir von der strengen Implikation sprechen. Die strenge Implikation, die wir durchA → Bwiedergeben, soll ausdrücken, daß zwischenAundBein logischer Zusammenhang besteht, daß der Inhalt vonBein Teil des Inhaltes vonAist, oder wie wir es sonst ausdrücken wollen. Das hat mit der Richtigkeit oder Falschheit vonAundBnichts zu tun. So würde man die Allgemeingültigkeit einer FormelA→ (B → A) ablehnen, da sie den Schluß vonAaufB → Aeinschließt und da die Richtigkeit vonAnichts damit zu tun hat, ob zwischenBundAein logischer Zusammenhang besteht. (shrink)