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...

ZusammenfassungDer Verfasser geht auf Beziehungen zwischen dem von C. I. Lewis eingeführten Begriff der « strikten » Implikation und dem von ihm selbst eingeführten Begriff der « strengen » Implikation ein. Er zeigt, dass sich innerhalb des Systems der strengen Implikation ein weiterer Folgebegriff definieren lässt, der alle Eigenschaften hat, die von der strikten Implikation verlangt werden. Als dieser Folgebegriff wird genommen, dass die Konjunktion von A und dem Gegenteil von B unmöglich ist, was in dem System der strengen Implikation (...) keineswegs damit identisch ist, dass A in strenger Weise B impliziert. Das System der strikten Implikation wird dabei in einer von Arnold Schmidt gegebenen Form zugrunde gelegt.RésuméIl s'agit des relations entre la conception d'implication stricte introduite par C. I. Lewis et la conception de « strenge » implication introduite par l'auteur. L'auteur indique qu'une conception d'implication se laisse définir dans le système de « strenge » implication qui a toutes les qualités d'implication stricte. La définition est la suivante: A implique B a ce sens si la conjonction de A et non B est impossible ce qui n'équivaut pas à la proposition qu'il y a de « strenge » implication de A à B. Le système d'implication stricte est considéré sous la forme qui lui a été donnée par Arnold Schmidt.In this paper the author enters into the particulars of the relations of the concept of « strict » implication introduced by C. I. Lewis with the concept of « strenge » implication introduced by himself. He points out that within the system of « strenge »implication a further concept of implication may be defined which has all the qualities of strictimplication. The definition is the following: A implies B in this sense if the conjunction of A and non‐B is impossible, which is not the same as the « strenge » implication between A and B. The system of strict implication is taken in the form as formerly given by Arnold Schmidt. (shrink)

Ackermann’s function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive formulation—and therefore its totality—has a simple proof in Isabelle/HOL. This is a small example of formalising mathematics using a proof assistant, with a focus on the treatment of difficult recursions.

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)

Open peer commentary on the article “Amusement, Delight, and Whimsy: Humor Has Its Reasons that Reason Cannot Ignore” by Edith K. Ackermann. Upshot: Ackermann tackles “humor” as an agentive participant in the process of knowledge construction. Performing her thesis in her writing, she give a reflective account of how oblique ways of knowing have always been present in debates concerning epistemology, albeit not given equal status as rational ones. As such, her endeavors in this text are geared towards (...) lifting up the position of “humor” to a much deserved higher level in educational and learning practices. Consequently, our endeavors in this commentary are targeted towards a little more in this direction by focusing on how “humor” becomes a way of accessing the process of knowledge construction and of unraveling its significance. (shrink)

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)

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)

The purpose of this paper is to formulate first-order Peano arithmetic within the resources of relevant logic, and to demonstrate certain properties of the system thus formulated. Striking among these properties are the facts that it is trivial that relevant arithmetic is absolutely consistent, but classical first-order Peano arithmetic is straightforwardly contained in relevant arithmetic. Under, I shall show in particular that 0 = 1 is a non-theorem of relevant arithmetic; this, of course, is exactly the formula whose unprovability was (...) sought in the Hilbert program for proving arithmetic consistent. Under, I shall exhibit the requisite translation, drawing some Goedelian conclusions therefrom. Left open, however, is the critical problem whether Ackermann’s rule γ is admissible for theories of relevant arithmetic. The particular system of relevant Peano arithmetic featured in this paper shall be called R♯. Its logical base shall be the system R of relevant implication, taken in its first-order form RQ. Among other Peano arithmetics we shall consider here in particular the systems C♯, J♯, and RM3♯; these are based respectively on the classical logic C, the intuitionistic logic J, and the Sobocinski-Dunn semi-relevant logic RM3. And another feature of the paper will be the presentation of a system of natural deduction for R♯, along lines valid for first-order relevant theories in general. This formulation of R♯ makes it possible to construct relevantly valid arithmetical deductions in an easy and natural way; it is based on, but is in some respects more convenient than, the natural deduction formulations for relevant logics developed by Anderson and Belnap in Entailment. (shrink)

Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...) The reason is interesting: if PA is slightly weakened to a subtheory P+, it admits the complex ring C as a model; thus QRF is chosen to be a theorem of PA but false in C. Inasmuch as all strictly positive theorems of R# are already theorems of P+, this nonconservativity result shows that QRF is also a nontheorem of R#. As a consequence, Ackermann's rule γ is inadmissible in R#. Accordingly, an extension of R# which retains its good features is desired. The system R##, got by adding an omega-rule, is such an extension. Central question: is there an effectively axiomatizable system intermediate between R# and R##, which does formalize arithmetic on relevant principles, but also admits γ in a natural way? (shrink)

Scholars have long been captivated by the parallels between birdsong and human speech and language. In this book, leading scholars draw on the latest research to explore what birdsong can tell us about the biology of human speech and language and the consequences for evolutionary biology. They examine the cognitive and neural similarities between birdsong learning and speech and language acquisition, considering vocal imitation, auditory learning, an early vocalization phase, the structural properties of birdsong and human language, and the striking (...) similarities between the neural organization of learning and vocal production in birdsong and human speech. After outlining the basic issues involved in the study of both language and evolution, the contributors compare birdsong and language in terms of acquisition, recursion, and core structural properties, and then examine the neurobiology of song and speech, genomic factors, and the emergence and evolution of language. Contributors: Hermann Ackermann, Gabriël J.L. Beckers, Robert C. Berwick, Johan J. Bolhuis, Noam Chomsky, Frank Eisner, Martin Everaert, Michale S. Fee, Olga Fehér, Simon E. Fisher, W. Tecumseh Fitch, Jonathan B. Fritz, Sharon M.H. Gobes, Riny Huijbregts, Eric Jarvis, Robert Lachlan, Ann Law, Michael A. Long, Gary F. Marcus, Carolyn McGettigan, Daniel Mietchen, Richard Mooney, Sanne Moorman, Kazuo Okanoya, Christophe Pallier, Irene M. Pepperberg, Jonathan F. Prather, Franck Ramus, Eric Reuland, Constance Scharff, Sophie K. Scott, Neil Smith, Ofer Tchernichovski, Carel ten Cate, Christopher K. Thompson, Frank Wijnen, Moira Yip, Wolfram Ziegler, Willem Zuidema. (shrink)

In this article, we study the prehistory of type theory up to 1910 and its development between Russell and Whitehead's Principia Mathematica ([71], 1910-1912) and Church's simply typed λ-calculus of 1940. We first argue that the concept of types has always been present in mathematics, though nobody was incorporating them explicitly as such, before the end of the 19th century. Then we proceed by describing how the logical paradoxes entered the formal systems of Frege, Cantor and Peano concentrating on Frege's (...) Grundgesetze der Arithmetik for which Russell applied his famous paradox and this led him to introduce the first theory of types, the Ramified Type Theory (RTT). We present RTT formally using the modern notation for type theory and we discuss how Ramsey, Hilbert and Ackermann removed the orders from RTT leading to the simple theory of types STT. We present STT and Church's own simply typed λ-calculus (λ → C) and we finish by comparing RTT, STT and λ → C. (shrink)

The volume includes the proceedings from the conference FOL75 -- 75 Years of First-Order Logic held at Humboldt University, Berlin, September 18 - 21, 2003 on the occasion of the anniversary of the publication of Hilbert's and Ackermann's Grundzuge der theoretischen Logik. The papers provide analyses of the historical conditions of the shaping of FOL, discuss several modern rivals to it, and show the importance of FOL for interdisciplinary research. While there is no doubt that the celebrated book marks (...) a most important step in the development of logic, the volume in hand proves the actuality of the question "Which logic is the right logic." The volume contains articles by: H. Andreka, J. X. Madarasz, I. Nemeti, A. Avron, K. Brunnler, A. Guglielmi, G. Englebretsen, W. Ewald, P. Hajek, J. Hintikka, W. Hodges, M. Kracht, R. Lanzet, H. Ben-Yami, C. Toke, S. P. Odintsov, H. Wansing, J. A. Robinson, M. Rossberg, M. Thielscher, D. E. Willard, andJ. Wole 'nski. (shrink)

This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. (...) An overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

This article discusses two complementary themes that play an important role in contemporary South African political philosophy: (1) the racist tradition in Western philosophy; and (2) the role of ubuntu in regaining an authentic African identity, which was systematically suppressed during the colonial past and apartheid. These are also leading themes in Mogobe Ramose’s African Philosophy Through Ubuntu. The first part concentrates on John Locke. It discusses the thesis that the reprehensible racism of many founders of liberal political philosophy has (...) lethally infected liberal theory. This view neglects the distinction between genesis and justification. Political liberalism has since cleansed itself of the prejudices of its spiritual ancestors. Liberal human rights exclude racism as a matter of principle. The second part discusses the claim that the ubuntu philosophy provides a better basis for a constitution in a modern society than political liberalism. A major problem is that ubuntu is an essentially contested concept. Some philosophers consider ubuntu to be a moribund notion (Matolino); others see it as a vital concept par excellence. In the latter case, it is elaborated from sundry incompatible political views, ranging from African nationalism (Ramose) via humanist communitarianism (Metz) to liberalism (Mboti). Conclusion: as an essentially contested ideological concept, ubuntu should not be a decisive constitutional standard for the application of state force. In contrast, the constitutional model of political liberalism provides a reasonable alternative, as it is designed precisely to solve the problem of social plurality and ideological contest. (shrink)

Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x 2x but fails to preserve the contraction property xx 2. The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) (...) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem-) decidability of the negation-free axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t. (shrink)

This paper considers whether a divine-command theory of moral obligation could justify morally horrible acts, partly by examining Kierkegaard’s writings. It argues that only the commands of a God who is essentially good could be morally justified, and thus no defensible version of a DCT could actually justify horrible acts. In Works of Love Kierkegaard defends such a DCT, and thus is committed to the claim that any actual commands of God must be aimed at the good. This is consistent (...) with the claim that if we knew that a command that is alleged to be from God is directed at what is bad, the command must not be authentic. The issue raised by Fear and Trembling, where Kierkegaard’s pseudonym Johannes de Silentio considers the “binding of Isaac” story, thus raises crucial epistemic issues, which cannot be settled without considering how one might come to know that a purported revelation from God is authentic, as well as how one might come to believe that some particular moral belief is wrong. The paper defends the view that if one knew that a revelation from God was authentic, then one could be justified in holding a moral view on some particular issue, such as veganism, that clashes with the dominant views of one’s contemporaries. (shrink)

A widely accepted view in epistemology is that we do not have direct control over our beliefs. And we surely do not have as much control over our beliefs as we have over simple actions. For instance, you can, if offered $500, immediately throw your steak in the trash, but a meat-eater cannot, at will, start believing that eating animals is wrong to secure a $500 reward. Yet, even though we have more control over our behavior than we have over (...) our beliefs, some of our behavior, especially moral behavior, is heavily influenced by our beliefs. Meat-eating is one example. So, if we do not have direct control over our beliefs and our beliefs influence our moral behavior, it’s no wonder meat-eaters aren’t immediately boycotting Burger King and lining up for the Beyond Burger after hearing about the mistreatment of farmed animals. So, how, or can we, inspire meat-eaters to change their beliefs regarding the moral significance of meat-eating and, consequently, their animal-eating behavior? I propose an answer to this difficult question. (shrink)

Анотація. У статті проаналізовані досягнення Соціального Вчительства Католицької Церкви, репрезентовані працями Лева ХІІІ, Пія ХІ, Пія ХІІ, Івана Павла ІІ, що розкривають змістовні характеристики поняття «принцип субсидіарності», його роль і значення в системі християнських цінностей. Принцип субсидіарності робить можливими такі взаємовідносини в соціальному житті, коли спільнота вищого порядку не втручається у внутрішнє життя спільноти нижчого порядку, перебираючи на себе належні тій функції; заради спільного добра, спільного блага вона надає їй у разі потреби підтримку й допомогу, узгоджуючи у такий спосіб її (...) взаємодію з іншими соціальними структурами. Принцип субсидіарності скеровує соціальну практику на утвердження спільного блага в людському співтоваристві. Поширення і застосування принципу субсидіарності протистоїть небезпеці «одержавлення» суспільства та найзагрозливіших проявів колективізму, обмежує абсолютизацію влади, бюрократизацію державних і соціокультурних структур, стає одним із гарантів дотримання прав і свобод громадян своєї країни. (shrink)

There is the world of ideas and the world of practice; the French are often for sup pressing the one and the English the other; but neither is to be suppressed. -Matthew Arnold The Function of Criticism at the Present Time From its inception, bioethics has confronted the need to reconcile theory and practice. At first the confrontation was purely intellectual, as writers on ethical theory (within phi losophy, theology, or other humanistic disciplines) turned their attention to topics from the (...) world of medical practice. Recently the confrontation has grown more intense. The ap pointment of clinical ethicists in hospitals and other health care settings is an accelerating trend in North America. Concomitantly, those institutions involved in training peo ple in clinical ethics have added organized exposure to the world of practice, in the form of placement requirements, to the normal academic course load. In common with other dis ciplines, bioethics has begun to see clinical training as a con dition of didactic theory and apprenticeship. (shrink)

In [15], [16] G. Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peano arithmetic. In particular he proved, using a complicated ε-substitution method (due to W. Ackermann), that for every theorem A (A prenex) of first-order Peano arithmetic PA one can find ordinal recursive functionals Φ A of order type 0 which realize the Herbrand normal form A H of A. Subsequently more perspicuous proofs of this fact via functional interpretation (combined with normalization) and cut-elimination were found. These proofs however (...) do not carry out the no-counterexample interpretation as a local proof interpretation and don't respect the modus ponens on the level of the no-counterexample interpretation of formulas A and A → B. Closely related to this phenomenon is the fact that both proofs do not establish the condition (δ) and--at least not constructively-- (γ) which are part of the definition of an 'interpretation of a formal system' as formulated in [15]. In this paper we determine the complexity of the no-counterexample interpretation of the modus ponens rule for (i) PA-provable sentences, (ii) for arbitrary sentences A, B ∈ L(PA) uniformly in functionals satisfying the no-counterexample interpretation of (prenex normal forms of) A and A → B, and (iii) for arbitrary A, B ∈ L(PA) pointwise in given α( 0 ) -recursive functionals satisfying the no-counterexample interpretation of A and A → B. This yields in particular perspicuous proofs of new uniform versions of the conditions (γ), (δ). Finally we discuss a variant of the concept of an interpretation presented in [17] and show that it is incomparable with the concept studied in [15], [16]. In particular we show that the no-counterexample interpretation of PA n by α( n (ω))-recursive functionals (n ≥ 1) is an interpretation in the sense of [17] but not in the sense of [15] since it violates the condition (δ). (shrink)

In this article I connect two concepts that played central roles in the School of Meinong: the notion of impossible objects and that of Gestalt. Ehrenfels claims that Widerspruch or incompatibility would be a temporal Gestalt quality, specifically the trying and failing to build an intuitive presentation. Where, when, and how does this process break down exactly? Meinong’s Graz students developed a more detailed production theory for the presentation of Gestalten (Vorstellungsproduktion) which can help to determine how the failure to (...) produce one Gestalt can generate another, which moreover is typical of impossible objects. There are three contributions to Meinong’s 1904 volume Untersuchungen zur Gegenstandstheorie und Psychologie, the ones by Mally, Benussi, and Ameseder, that provide helpful analyses to clarify the incompatibility Gestalt. These suggest three options to refine the analysis of the Gestalt of impossible objects. The conclusion is that the failure of the Vorstellungsproduktion itself is not enough, the incompatibility relation between the foundations must also play a role. (shrink)

Maps and territory suggest problems which have to do with the opening of pathways in some poorly explored domain.