It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. This essay, however, shows that a range of relevant logics with the Ackermann constant cannot be conservatively extended by a Boolean negation.

It is shown that there are exactly six normal DeMorgan monoids generated by the identity element alone. The free DeMorgan monoid with no generators but the identity is characterised and shown to have exactly three thousand and eighty-eight elements. This result solves the "Ackerman constant problem" of describing the structure of sentential constants in the logic R.

The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant (...) logics. (shrink)

An Ackermann constant is a formula of sentential logic built up from the sentential constant t by closing under connectives. It is known that there are only finitely many non-equivalent Ackermann constants in the relevant logic R. In this paper it is shown that the most natural systems close to R but weaker than it-in particular the non-distributive system LR and the modalised system NR-allow infinitely many Ackermann constants to be distinguished. The argument in each (...) case proceeds by construction of an algebraic model, infinite in the case of LR and of arbitrary finite size in the case of NR. The search for these models was aided by the computer program MaGIC (Matrix Generator for Implication Connectives) developed by the author at the Australian National University. (shrink)

Here we study two connexive logics based on one of the conditionals introduced by Church in [4] and on some negations defined through falsity constants in the sense of Ackermann in [1].

Sentential constants have been part of the R environment since Church [1]. They have had diverse uses in explicating relevant ideas and in sim- plifying them technically. Of most interest have been the Ackermann pair of constants t; f, functioning conceptually as a least truth, and as a greatest , under the ordering of propositions under true impli- cation. Also interesting have been the Church constants F; T, functioning similarly as least greatest propositions.

This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics (...) which satisfy all of Anderson and Belnap’s selection criteria, provided the truth-constant known as the Ackermann constant is available. One of the selection criteria related to expressive strength is having an “enthymematic” conditional for which a deduction theorem holds. I argue that this allows for a new interpretation of Anderson and Belnap’s take on logical consequence, namely as committing them to pluralism about logical consequence. (shrink)

The main object of this article is to give two novel proofs of the admissibility of Ackermann’s rule (γ) for the propositional relevant logic R. The results are established as corollaries of cut elimination for systems of tableaux for R. Cut elimination, in turn, is established both nonconstructively (as a corollary of completeness) and constructively (using Gentzen-like methods). The extensibility of the techniques is demonstrated by showing that (γ) is admissible for RQ* (R with constant domain quantifiers). The (...) status of the admissibility of (γ) for RQ* was, to the best of the author’s knowledge, an open problem. Further extensions of these results will be explored in the sequel(s). (shrink)

Six objects associated with the magic practices of John Dee have been held within the collections of the British Museum for many decades. These objects include three wax seals, an obsidian mirror, a gold disc and a crystal ball. In this paper we review the provenance and possible association of these artefacts with Dee by comparing their features to the descriptions and diagrams set out in Dee’s manuscripts. Although we come to the conclusion that a direct link between these objects (...) and Dee remains to be proven, we also uncover a complex world of collectors whose avid interest in Dee contributed to the collection of objects assembled today, which continue to reinforce Dee’s reputation as a magician. (shrink)

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)

Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der fonnalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet fUr die Logik eine ahnliche Fonnel­ sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebrauchlich ist. In der Mathematik wurde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewohnlichen Sprache bedienen. Die groBen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum (...) wesentlichen Teil mit dadurch bedingt, daB es gelang, einen brauchbaren und leistungsfahigen Fonnalismus zu finden. - Was durch die Formel­ sprache in der Mathematik erreicht wird, das solI auch in der theoretischen Logik durch diese erzielt werden, namlich eine exakte, wissenschaftliche Behandlung ihres Gegenstandes. Die logischen Sachverhalte, die zwischen Urteilen, Begriffen usw. bestehen, finden ihre Darstellung durch Formeln, deren Interpretation frei ist von den Unklarheiten, die beim sprachlichen Ausdruck leicht auftreten konnen. Der Dbergang zu logischen Folgerungen, wie er durch das SchlieBen geschieht, wird in seine letzten Elemente zerlegt und erscheint als fonnale Umgestaltung der Ausgangsfonneln nach gewissen Regeln, die den Rechenregeln in der Algebra analog sind; das logische Denken findet sein Abbild in einem LogikkalkUl. Dieser Kalkiil macht die erfolgreiche Inangriffnahme von Problemen moglich, bei denen das rein inhaltliche Denken prinzipiell versagt. Zu diesen gehort z. B. (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.

Cognitive niche construction is the process whereby organisms create and maintain cause–effect models of their niche as guides for fitness influencing behavior. Extended mind theory claims that cognitive processes extend beyond the brain to include predictable states of the world. Active inference and predictive processing in cognitive science assume that organisms embody predictive (i.e., generative) models of the world optimized by standard cognitive functions (e.g., perception, action, learning). This paper presents an active inference formulation that views cognitive niche construction as (...) a cognitive function aimed at optimizing organisms' generative models. We call that process of optimization extended active inference. (shrink)

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)

Together, the code and inferential models of communication are often thought to range over all cases of communication. However, their prevailing versions seem unable to fully explain what I call underdeterminacy without ostension. The latter is constituted by communication where stimuli that are not (nor appear to be) produced with communicative or informative intentions nevertheless communicate information underdetermined by the relevant codes. Though the prevailing accounts of communication cannot fully explain how communication works in such cases, I suggest that some (...) version of the inferential model can—if we allow it to extend to non‐ostensive, non‐intentional behaviors. (shrink)

Context: The idea to write this paper sprang up in a casual conversation that led to the question of how the word “experience” would be translated into German. Distinctions between the German “Erleben” and “Erfahren,” and their intricacies with “Erkennen” and “Anerkennen,” soon led to the conviction that this was a thread worth pursuing. Problem: Much has been written about the nature of experience, but there is little consensus, to this day, regarding the role of consciousness in the process of (...) experiencing. Although RC acknowledges the significance of tacit or sensorimotor knowledge in the individual’s practical operating, it cannot admit it as a basis to the formation of conceptual structures that, by definition, are conscious. Method: Drawing from our backgrounds in epistemology and psychology, and a shared interest in Piaget’s psychogenetic approach, we investigate the origins and development of human experience, in this case the mastery of space, time, causation, and object-permanency. We focus on how “noticeable encounters” are gauged, reflected upon, and ultimately worked through, consciously or unconsciously, by the “experiencer.” Results: A child’s abilities to enact a certain action pattern in a given situation no more demonstrates a re-presentation of the pattern than does recognition in the case of objects. In his studies with children, Piaget has shown that the Kantian categories of space, time object, and “causality” are co-constitutive of the child’s own motion – and its felt impact – as a means to make the world cohere. Of importance here are the concepts of “effective causality,” felicitous encounters, and agency. Implications: Understanding the circumstances under which some “lived” events, whether self-initiated or striking as if out of nowhere, become noticeable and able affect a person’s life is a daunting task. This joint essay is no more than a conversation-starter and an invitation to further explore the intricacies between agency and causation, sensation and cognition, and, yes, motions and emotions in the making of consciousness itself. (shrink)

Any account of “what is special about the human brain” (Passingham 2008) must specify the neural basis of our unique ability to produce speech and delineate how these remarkable motor capabilities could have emerged in our hominin ancestors. Clinical data suggest that the basal ganglia provide a platform for the integration of primate-general mechanisms of acoustic communication with the faculty of articulate speech in humans. Furthermore, neurobiological and paleoanthropological data point at a two-stage model of the phylogenetic evolution of this (...) crucial prerequisite of spoken language: (i) monosynaptic refinement of the projections of motor cortex to the brainstem nuclei that steer laryngeal muscles, presumably, as part of a “phylogenetic trend” associated with increasing brain size during hominin evolution; (ii) subsequent vocal-laryngeal elaboration of cortico-basal ganglia circuitries, driven by human-specificFOXP2mutations.;>This concept implies vocal continuity of spoken language evolution at the motor level, elucidating the deep entrenchment of articulate speech into a “nonverbal matrix” (Ingold 1994), which is not accounted for by gestural-origin theories. Moreover, it provides a solution to the question for the adaptive value of the “first word” (Bickerton 2009) since even the earliest and most simple verbal utterances must have increased the versatility of vocal displays afforded by the preceding elaboration of monosynaptic corticobulbar tracts, giving rise to enhanced social cooperation and prestige. At the ontogenetic level, the proposed model assumes age-dependent interactions between the basal ganglia and their cortical targets, similar to vocal learning in some songbirds. In this view, the emergence of articulate speech builds on the “renaissance” of an ancient organizational principle and, hence, may represent an example of “evolutionary tinkering” (Jacob 1977). (shrink)

Over the last 30 years, representationalist and dynamicist positions in the philosophy of cognitive science have argued over whether neurocognitive processes should be viewed as representational or not. Major scientific and technological developments over the years have furnished both parties with ever more sophisticated conceptual weaponry. In recent years, an enactive generalization of predictive processing – known as active inference – has been proposed as a unifying theory of brain functions. Since then, active inference has fueled both representationalist and dynamicist (...) campaigns. However, we believe that when diving into the formal details of active inference, one should be able to find a solution to the war; if not a peace treaty, surely an armistice of a sort. Based on an analysis of these formal details, this paper shows how both representationalist and dynamicist sensibilities can peacefully coexist within the new territory of active inference. (shrink)

In evolutionary biology, niche construction is sometimes described as a genuine evolutionary process whereby organisms, through their activities and regulatory mechanisms, modify their environment such as to steer their own evolutionary trajectory, and that of other species. There is ongoing debate, however, on the extent to which niche construction ought to be considered a bona fide evolutionary force, on a par with natural selection. Recent formulations of the variational free-energy principle as applied to the life sciences describe the properties of (...) living systems, and their selection in evolution, in terms of variational inference. We argue that niche construction can be described using a variational approach. We propose new arguments to support the niche construction perspective, and to extend the variational approach to niche construction to current perspectives in various scientific fields. (shrink)

When we see or hear a spontaneous emotional expression, we usually immediately, effortlessly, and often correctly interpret it to mean happiness, sadness, or some other emotion as well as what this emotion is about. How do we do that? In this article, I evaluate how useful the concepts of natural meaning and probabilistic meaning are when it comes to explaining how we and other animals interpret emotional signs displayed without communicative intentions. I argue that Grice’s notion of natural meaning, because (...) it is a factive relation, is too restrictive for this purpose. I then present the notion of probabilistic meaning. The latter seems adequate for analyzing our ability to interpret non-communicative emotional signs, but it faces several difficulties when it comes to analyzing how we and other animals interpret emotional _signals_, i.e. signs that have the function to communicate emotional information. I present three of these difficulties. En passant, I suggest that a teleosemantic notion may be better suited for these challenges. (shrink)

Alle kulturellen Praktiken sind verkörpert: Ihnen ist die Spannungseinheit von leiblichem Erleben, physischem Tun und kulturellem Sinn eingeschrieben. Von den Kognitions- bis zu den Kulturwissenschaften ist Verkörperung daher mittlerweile ein zentrales Forschungsthema. Der vorgelegte Band widmet sich in interdisziplinärer Perspektive exemplarischen Praktiken und Ritualen des Körpers und will einem drohenden neuen Dualismus zwischen leiblicher und kultureller Verkörperung entgegenwirken. Biologischer Organismus, bewusstes Erleben und kulturelle Traditionen sollen in ihrer Wechselbezüglichkeit hervortreten und damit sichtbar machen, dass „Sinn“ ein Phänomen ist, das die (...) cartesianische Trennung von Geist und Körper unterläuft. (shrink)

In this paper, I am going to cast doubt on an idea that is shared, explicitly or implicitly, by most contemporary pragmatic theories: that the inferential interpretation procedure described by Grice, neo-Griceans, or post-Griceans applies only to the interpretation of ostensive stimuli. For this special issue, I will concentrate on the relevance theory (RT) version of this idea. I will proceed by putting forward a dilemma for RT and argue that the best way out of it is to accept that (...) the relevance-theoretic comprehension procedure ap- plies to certain non-ostensive stimuli, contrary to what is generally claimed within RT. In particular, I will argue that relevance theorists should accept that (ceteris paribus) non- ostensive emotional expressions in interactions guarantee a presumption of relevance such that they are interpreted through the relevance-theoretic comprehension procedure. This leads me to propose what I call 'the expressive principle of relevance'. (shrink)

This dissertation may be divided into two parts. The first part is about the Extended Gricean Model of information transmission. This model, introduced here, is meant to better explain how humans communicate and understand each other. It has been developed to apply to cases that were left unexplained by the two main models of communication found in contemporary philosophy and linguistics, i.e. the Gricean (pragmatic) model and the code (semantic) model. In particular, I show that these latter two models cannot (...) apply to cases where one communicate through spontaneous emotional expressions and how the Extended Gricean Model of information transmission does. The second part of the dissertation is about what emotional signs mean, in various senses of the term ‘mean'. I review existing theories of meaning and see how they apply to emotional signs, i.e. signs which give us information about the affective state of the sign producer. (shrink)

In this chapter, we start by spelling out three important features that distinguish expressives—utterances that express emotions and other affects—from descriptives, including those that describe emotions (Section 1). Drawing on recent insights from the philosophy of emotion and value (2), we show how these three features derive from the nature of affects, concentrating on emotions (3). We then spell out how theories of non-natural meaning and communication in the philosophy of language allow claims that expressives inherit their meaning from specificities (...) of emotions—namely, from being felt, evaluative attitudes toward propositional or non-propositional contents (4). (shrink)