This article outlines the motivations and main findings of Favela and Machery's “Investigating the concept of representation in the neural and psychological sciences”, and discusses what to do with the concept of representation in the brain sciences moving forward.

Cognitive Science, Volume 45, Issue 11, November 2021.

Although there is a substantial philosophical literature on dynamical systems theory in the cognitive sciences, the same is not the case for neuroscience. This paper attempts to motivate increased discussion via a set of overlapping issues. The first aim is primarily historical and is to demonstrate that dynamical systems theory is currently experiencing a renaissance in neuroscience. Although dynamical concepts and methods are becoming increasingly popular in contemporary neuroscience, the general approach should not be viewed as something entirely new to (...) neuroscience. Instead, it is more appropriate to view the current developments as making central again approaches that facilitated some of neuroscience’s most significant early achievements, namely, the Hodgkin–Huxley and FitzHugh–Nagumo models. The second aim is primarily critical and defends a version of the “dynamical hypothesis” in neuroscience. Whereas the original version centered on defending a noncomputational and nonrepresentational account of cognition, the version I have in mind is broader and includes both cognition and the neural systems that realize it as well. In view of that, I discuss research on motor control as a paradigmatic example demonstrating that the concepts and methods of dynamical systems theory are increasingly and successfully being applied to neural systems in contemporary neuroscience. More significantly, such applications are motivating a stronger metaphysical claim, that is, understanding neural systems as being dynamical systems, which includes not requiring appeal to representations to explain or understand those phenomena. Taken together, the historical claim and the critical claim demonstrate that the dynamical hypothesis is undergoing a renaissance in contemporary neuroscience. (shrink)

Dynamical systems theory (DST) is a branch of mathematics that assesses abstract or physical systems that change over time. It has a quantitative part (mathematical equations) and a related qualitative part (plotting equations in a state space). Nonlinear dynamical systems theory applies the same tools in research involving phenomena such as chaos and hysteresis. These approaches have provided different ways of investigating and understanding cognitive systems in cognitive science and neuroscience. The ‘dynamical hypothesis’ claims that cognition is and can be (...) understood as dynamical systems. Common consequences for such an approach include rejecting understanding cognition as information processing in nature, including eschewing explanatory roles for computation or representation. Contemporary applications of DST include mouse‐tracking studies in cognitive science and nonrepresentational perspectives on motor control in neuroscience. Such work has philosophical implications concerning the boundaries of cognition, explanation, and representations. DST offers powerful methodology and theories that raise many topics of philosophical significance. (shrink)

Embodied cognition is a well-established and increasingly influential branch of the cognitive, neural, and psychological sciences. Unlike embodied cognition, extended cognition is not as well-established or influential. Our goal is to defend the idea that if cognition is truly embodied, then it is embodied in systems, and if it is embodied in systems, then it extends beyond animal boundaries. In order to demonstrate this, we situate the idea of extended cognitive systems in a historical context. Then, we present a theoretical (...) and methodological framework for investigating extended cognitive systems. Finally, we discuss some potential experimental work that could adjudicate the existence of extended cognitive systems. (shrink)

Direct realism in one form or another is gaining traction as an approach to perception. With the hope of bolstering such positions, we offer a framework upon which to base an argument for direct realism in matters of perception. Better yet, we offer an empirically supported framework. The framework on offer is that of ecological psychology. With the framework in place, we then discuss how it can address visual illusions, one of the major challenges facing proponents of direct realism.

Several philosophers have expressed concerns with some recent uses of the term ‘cognition’. Underlying a number of these concerns are claims that cognition is only located in the brain and that no compelling case has been made to use ‘cognition’ in any way other than as a cause of behavior that is representational in nature. These concerns center on two primary misapprehensions: First, that some adherents of dynamical cognitive science think DCS implies the thesis of extended cognition and the rejection (...) of representation, and second, that cognition is mistakenly equated with behavior. We make three points in response to these claims: First, there is no thoroughly entrenched conception of cognition as distinct from behavior that is being illegitimately disregarded. Second, we present Shapiro’s exposition of dynamical systems theory as revealing a misunderstanding of the way that dynamical models are used in explanations of cognition and related phenomena. Accordingly, a proper conception of DCS’s methods facilitates an appreciation of extended cognition as a legitimate phenomenon of scientific investigation. Finally, we demonstrate that practicing cognitive scientists and psychologists are far more pluralistic in the phenomena they apply ‘cognition’ to than is suggested by some. At the heart of our disagreement with these concerned folks is that although we think it likely that some cognitive phenomena are representational, non-extended, and only in-between the ears, we also think there are good conceptual and empirical reasons to believe that many cognitive phenomena are non-representational, extended, and not confined to the brain. (shrink)

Complexity science is an investigative framework that stems from a number of tried and tested disciplines—including systems theory, nonlinear dynamical systems theory, and synergetics—and extends a common set of concepts, methods, and principles to understand how natural systems operate. By quantitatively employing concepts, such as emergence, nonlinearity, and self‐organization, complexity science offers a way to understand the structures and operations of natural cognitive systems in a manner that is conceptually compelling and mathematically rigorous. Thus, complexity science both transforms understandings of (...) cognition and reframes more traditional approaches. Consequently, if cognitive systems are indeed complex systems, then cognitive science ought to consider complexity science as a centerpiece of the discipline. (shrink)

In this article, we respond to Rosa Cao's, Frances Egan's, and John Krakauer's comments, defending our interpretation of our experimental results and the significance of an epistemology of the imprecise.

It is becoming ever more accepted that investigations of mind span the brain, body, and environment. To broaden the scope of what is relevant in such investigations is to increase the amount of data scientists must reckon with. Thus, a major challenge facing scientists who study the mind is how to make big data intelligible both within and between fields. One way to face this challenge is to structure the data within a framework and to make it intelligible by means (...) of a common theory. Radical embodied cognitive neuroscience can function as such a framework, with dynamical systems theory as its methodology, and self-organized criticality as its theory. (shrink)

Mechanistic frameworks of investigation and explanation dominate the cognitive, neural, and psychological sciences. In this dissertation, I argue that mechanistic frameworks cannot, in principle, explain some kinds of cognition. In its place, I argue that complexity science has methods and theories more appropriate for investigating and explaining some cognitive phenomena. -/- I begin with an examination of the term 'cognition.' I defend the idea that "cognition" has been a moving target of investigation in the relevant sciences. As such it is (...) not historically true that there has been a thoroughly entrenched and agreed upon conception of "cognition." Next, I take up mechanistic frameworks. Although 'mechanism' is an umbrella term for a set of loosely related characteristics, there are common features: linearity, localization, and component dominance. I then describe complexity science, with emphasis on its utilization of dynamical systems modeling. Next, I discuss two phenomena that typically fall under the purview of complexity science: nonlinearity and interaction dominance. -/- A complexity science framework guided by the theory of self-organized criticality and utilizing the methods of dynamical systems modeling can surmount a number of challenges that face mechanistic frameworks when investigating some kinds of cognition. The first challenge is epistemic and concerns the inadequacy of mechanistic frameworks to facilitate the comprehensibility of massive amounts of data across various scales and areas of inquiry. I argue that complexity science is more appropriate for making big data comprehensible when investigating cognition, particularly across disciplines. I demonstrate this via an approach called nested dynamical modeling (NDM). NDM can facilitate comprehensibility of large amounts of data obtained from various scales of investigation by eliminating irrelevant degrees of freedom of that system as relates to the target of investigation. -/- The second shortcoming concerns ontological blind spots within mechanistic frameworks. Cognitive phenomena like extended cognition often fail to meet most, if not all, of the criteria assumed by many mechanistic approaches, especially component dominance. I argue that research guided by the notion of interaction dominance allows for extended cognition to be a real, empirically supported phenomenon within complex systems frameworks. In this chapter I discuss some of my experimental work on extended cognitive systems. -/- The search for mechanisms can be a reasonable starting position when attempting to explain natural phenomena in the life sciences. However, too strict of an adherence to theoretical and methodological commitments such as linearity, localization, and component dominance can result in intractable epistemic challenges and ontological blind spots. Complexity science has theories and methods to overcome such challenges in the investigation of cognition. (shrink)

El escrito, adentrándose en la teoría allagmática de Gilbert Simondon, tiene como objetivo provocarle al concepto de cosmopolitismo variantes ontológicas, epistemológicas y éticas. Se piensa, dichas variantes, al romper con los primados sustancialitas que sitúan el principio de individuación como algo consumado, idean un horizonte de sentido que se muestra capaz de expresar al cosmopolitismo, no como un ideal regulativo, sino como un proceso. De este modo, pensar al cosmopolitismo como un proceso, reclama asumir los movimientos ontológicos, epistemológicos y éticos, (...) no como abstracciones, sino como devenires-límite que reclaman examinar cómo es que nos creamos. Por lo anterior, en el escrito se afirma junto a Simondon: el cosmopolitismo pensado a la luz de la allagmática involucra la producción de movimientos capaces de afirmar disímiles modos de existencia. El cosmopolitismo es un proceso siempre por hacer y por afirmar en el que nos jugamos la posibilidad de expresar una vida digna. (shrink)

I defend the claim that emergence is always a kind of interaction dominance. I utilize Francescotti’s definition of emergence, which captures five features typically thought crucial for emergence: downward causal influence, novelty, relationality, supervenience, and unpredictability. I then explicate interaction dominance, a concept from complexity science. In short, a system is interaction dominant when the interactions of the parts give rise to features that override the features of the parts in isolation or linked via additive and linear dynamics. Locust swarms (...) are presented as an illustrative case of a natural phenomenon that meets the definition for emergent properties. Moreover, locust swarms provide a case of an emergent property arising via interaction-dominant dynamics. I conclude by discussing the relationship of emergence and interaction dominance, with emphasis on the claim that all emergent properties occur due to interaction dominance, but not all systems that exhibit interaction-dominant dynamics have emergent properties. (shrink)

As with much contemporary philosophical and scientific research, the predominant metaphysics of situatedness is monism, particularly, physicalism. Here, we claim that while monism is the proper metaphysical thesis, empirically-supported theories of situated phenomena require ontological pluralism as well. We defend this position via the example of bird flocks, which are situated systems that exhibit ontologically plural features, namely, component dominance and interaction dominance. The description of these features will illustrate that understanding these phenomena requires a coevolution of conceptual and methodological (...) development. Specifically, ontological features are partially identified and evaluated by way of the analyses applied to them. Both descriptive and normative lessons are drawn. Descriptively, research on bird flocks demonstrate that natural phenomena may not be readily cast via a monistic ontology (e.g., component dominant), even at the same scale of investigation. The normative consequence is that while research on situated systems need not reject metaphysical monism, it ought to begin from a pluralistic position concerning ontology. (shrink)

According to Gibson's ecological theory of perception-action, the proper objects of perception are affordances. Affordances are directly perceivable, environmental opportunities for behavior. The current study assessed affordance judgments, and the confidence ratings corresponding to those judgments, of aperture pass-through-ability based on three modes of perceiving. The modes were vision and two blindfolded conditions involving haptic perception via technological aids: A cane and the Enactive Torch (ET). The first hypothesis, that vision would provide judgments of the critical boundary most similar to (...) the actual boundary, was not supported. The second hypothesis, that participants would perform better on pass-through-ability judgments using the ET than when using the cane, was supported. The third hypothesis, that across all three modalities participants’ ratings of confidence in the accuracy of their yes/no judgments would be lowest near the perceptual category boundary, was supported. Results suggest that in terms of making affordance judgments of aperture pass-through-ability, participants were more accurate with the haptic modalities than with vision. Results also suggest that participants were least confident with their more accurate modality, and most confident with their least accurate modality. (shrink)

Ecological psychology (see Gibson, 1979) is generally thought of as comprising two main claims. The first is that perception is direct insofar as it is not the result of information added to sensory representations. The second is that perception is comprised of affordances (at least most of the time) or opportunities for action that exist in the environment. Barrett explores the possibility of giving an objective account of perceiving religious meaning and value by means of ecological psychology. The attempt to (...) utilize ecological psychology to account for values is not without precedent, however. Jayawickreme and Chemero (2008), for instance, used the ecological concept of ‘‘affordance’’ to sketch an account of both virtues and morally relevant situations. Surprisingly, Barrett never mentions this central ecological concept, choosing instead to focus solely on the directness of perception. We believe that this constricts his ecological account of religious value. While we agree with Barrett that the cognitive science of religion treats presence as an insider’s experience, such that religious experience is a ‘‘black box’’ phenomenon, intractable, and mysterious, and that ecological theory might provide an account of values, we are not convinced by his particular attempt at an ecological account of religious meaning. (shrink)

Consciousness has traditionally been the subject matter of philosophy. However, especially in recent years, various branches of science have attempted to develop theories of consciousness. I evaluate the biological theories of Francis Crick, Gerald Edelman, and Antti Revonsuo in order to gauge the current state of biological accounts of consciousness. I begin with an explication of the easy and hard problems of consciousness as defined by David Chalmers. Next, I summarize how each theory defines ‘consciousness’ and then I evaluate each (...) theoretical model. Finally, I evaluate the models in terms of the easy problems and, especially, the hard problem. My aim in this work is to demonstrate that the current biological theories of consciousness are inadequate. This claim is not tantamount to one that claims that the theories are ineffective. On the contrary, these theories tend to be more useful than not. However, these biological models do not address the most essential component of consciousness that is subjective phenomenological experience. (shrink)

Al situar como problemática nodal la relación entre mito y soberanía, este es- crito pretende: a) cuestionar el modo en que dichas nociones se vinculan para constituir una idea de democracia ávida de un principio teleológico y b) reflexionar sobre la manera en que tal idea ciega la constitución misma de la política yacente en la στάσις. Así pues, al usar una forma controlada del ana- cronismo, traemos al presente dos problemas del pasado: 1) el agotamiento del mito insinuado por (...) Gorgias y la retórica en el siglo v a. C.; 2) el problema de la obcecación de la στάσις estudiado por Nicole Loraux, Michel Foucault y Dimitris Vardoulakis, con el fin de posicionarse frente a los procesos contemporá- neos, en los cuales la inhospitalidad, la xenofobia y las sombras de los crímenes de odio se alimentan bajo el halo de una democracia atrapada por algún tipo de mito soberano. (shrink)

Este escrito pretende repensar la paradoja de hablar en nombre propio por medio de una inmersión en la filosofía del lenguaje de Vilém Flusser, con el objetivo de esbozar otra manera de hacer frente al nihilismo contemporáneo, a través de una conceptualización no abstracta del intelecto y del lenguaje. El nihilismo que nos acecha, al capturar la diferencia por medio de una axiomática que parte de los principios de identidad, de no contradicción y de tercero excluido, condiciona a la mayoría (...) de las voces en resistencia (que pretenden hablar en nombre propio) a un binarismo que las introduce en una asimilación ciega de la realización de nuestra cultura asentada en la mathesis universalis. Para el filósofo nacido en Praga, esto se hace ostensible en la figura de los campos de concentración como expresión singular de una realización de nuestra cultura. (shrink)

Karl Popper (2002) once instructed a group of physics students to carefully write down what they observed. Popper relates that the students asked what he wanted them to observe and said that the sole instruction to “observe” was absurd. This story motivated Popper’s claim that, especially in science: Observation is always selective. It needs a chosen object, a definite task, an interest, a point of view, a problem. And its description presupposes a descriptive language . . . , which in (...) its turn presupposes interests, points of view, and problems. (2002, p. 62) In Discovering the Human Connectome, the problem is how the brain works, and from Olaf Sporns’ point of view, the brain can be understood as a network (p. ix). One of Sporns’ main goals in his previous book (2011) was to introduce neuroscientists to the theory and methods of network science. That book was Sporns’ attempt to answer the “how?” questions of integrating the methods of network science with neuroscience. The current book builds on the previous one and attempts to answer more theoretical questions such as why network science is an appropriate framework for investigating the brain. (shrink)

Network theory arguably has its origins in Euler’s (1741) graph theory, which was first developed in the mid-1700s to solve the Königsberg bridge problem. Since then, the basic units of graph theory—vertices and edges—have been utilized by a number of scientific disciplines to describe and analyze a wide variety of phenomena. Mark Newman begins his clear and comprehensive introduction to networks with a sampling of various kinds that have been studied: information networks such as the World Wide Web, biological networks (...) such as neural connections, and social networks such as friendships among members of a club. As Newman highlights, network theory and methods are utilized not only within but also across scientific disciplines. The interdisciplinary nature of the scientific study of networks is a double-edged sword. On the one hand, it fosters the cross-pollination of ideas and methods across fields—for example, applying methods used to study computer networks to the investigation of brain networks (cf., Sporns, 2011). On the other hand, such interdisciplinarity can result in confusion and misapplication of theory and methods. Accordingly, Newman’s goal in “Networks: An Introduction” is to synthesize the current state of network theory into a “consistent language and notation” (2010, p. x, Preface). This is no easy task, but Newman gives an admirable attempt that is successful in many ways. (shrink)

The importance of touch to mammalian survival and well-being cannot be overstated. The capacity for action depends on the sense of touch, which is a necessary feature of an animal’s being-in-the-world (O’Shaughnessy, 1989, pp. 38–39). Interpersonal touch has been shown to be an important part of human welfare, including disease prevention and treatment (see Field, 2001 for review). Throughout a mammal’s lifespan, social relation- ships are also mediated by touch behavior (see Thayer, 1986 for review). Given these facts, the sense (...) of touch is relevant to a variety of topics in psychology, including but not limited to: perception, action, nonverbal behavior, relationships, development, emotion, and health. (shrink)

Individuals make decisions under uncertainty every day. Decisions are based on in- complete information concerning the potential outcome or the predicted likelihood with which events occur. In addition, individuals’ choices often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision making are difficult to capture using conventional, linear mathematical models. Here, we present data from a 2-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can (...) be employed to capture the dynamics of human decision making under uncertainty (i.e., multistability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlin- ear complexities of human decision making are discussed as well as the degree to which the theory of nonlinear dynamical systems might offer an alternative framework for understanding human decision making processes. (shrink)

Individuals make decisions under uncertainty every day based on incomplete information concerning the potential outcome of the choice or chance levels. The choices individuals make often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision-making are difficult to capture using conventional, linear mathematical models. Here, we present data from a two-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can be employed to capture the dynamics (...) of human decision-making under uncertainty (i.e., multi-stability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlinear complexities of human decision-making are discussed, as well as the degree to which nonlinear dynamical systems theory might offer an alternative framework for understanding human decision-making processes. (shrink)

Mi propuesta versa sobre ciertas condiciones de posibilidad cognitivas y antropológicas que tratan de las ciencias naturales. En este sentido, la imaginación desempeña un papel fundamental en el origen de las ciencias. Sin embargo, el debate filosófico acerca de este tópico es insuficiente. Defino "imaginación científica" como una ensoñación sofisticada, controlada por la razón y la experiencia (o los experimentos), cuyo papel es producir nuevos objetos científicos. Hay tres tipos de imaginación científica: vaga, operacional y exacta. La primera concierne las (...) metáforas y las analogías. La segunda versa sobre los modelos en el sentido de representaciones imaginarias que simplifican e idealizan la realidad. La tercera es acerca de los modelos en el sentido matemático estricto. Finalmente, la imaginación científica está conectada con el mundo de la vida cotidiana. Así, el observador científico es un observador encarnado y, en consecuencia, su corporalidad provee las percepciones que son necesarias para la imaginación. (shrink)

Synthetic biology, as a research field, brings together molecular life scientists, computational biologists, and social scientists to engineer biological systems toward societally desired goals. Given the field’s broad multidisciplinarity and relatively young age, innovative educational methods are required to provide students with the needed background knowledge to push the field forward in the future. The international Genetically Engineered Machine competition is such an example where education and high-level research merge, providing the synthetic biology field with trained students, new ideas, and (...) novel results. In the 2021 edition alone, 343 teams from across the world completed the competition to tackle societal problems with synthetic biology. As Wageningen University & Research celebrates 10 years of participation in iGEM, we share our thoughts and experiences on supervising iGEM teams, which is especially relevant to organizers of current and new teams, and also others interested in the iGEM competition. (shrink)

A. Newell and H. A. Simon were two of the most influential scientists in the emerging field of artificial intelligence (AI) in the late 1950s through to the early 1990s. This paper reviews their crucial contribution to this field, namely to symbolic AI. This contribution was constituted mostly by their quest for the implementation of general intelligence and (commonsense) knowledge in artificial thinking or reasoning artifacts, a project they shared with many other scientists but that in their case was theoretically (...) based on the idiosyncratic notions of symbol systems and the representational abilities they give rise to, in particular with respect to knowledge. While focusing on the period 1956-1982, this review cites both earlier and later literature and it attempts to make visible their potential relevance to today's greatest unifying AI challenge, to wit, the design of wholly autonomous artificial agents (a.k.a. robots) that are not only rational and ethical, but also self-conscious. (shrink)

Este texto é uma leitura do conceito de comunicação proposto por Charles H. Cooley em seu livro “Social Organization”, publicado originalmente em 1909. Ao que tudo indica, trata-se de uma das primeiras abordagens teóricas da Comunicação enquanto objeto específico de conhecimento. Embora escrito há mais de um século, em um contexto diferente do atual, suas proposições antecipam algumas ideias em circulação na área. São destacadas três de suas proposições: (1) a diferenciação dos fenômenos comunicacionais em relação a outros processos individuais (...) e sociais; (2) a comunicação como relação humana primeira, vínculo mediador na formação dos sujeitos em articulação com o social e (3) cada mídia, da palavra ao impresso, atua com outros elementos na configuração de um ambiente sócio-cognitivo específico. Esses pontos são discutidos no contexto do debate epistemológico da Comunicação. (shrink)

Polypeptide growth factors (mitogens) which stimulate proliferation of fibroblasts and epithelial cells also rapidly activate transmembrane ion transport systems. The mitogen‐induced Na+ influx is due to the activation of a Na+/H+ antiport. Recent methodological developments allow, for the first time, precise measurements of the factors that control activation of the Na+/H+ antiport by these agents, and provide the tools needed to assess the physiological significance of this exchange mechanism.

Dislocations are constituents in the periphery of the clause—or, depending on the analysis, outside the structure of the clause proper. In the canonical cases, they are doubled by a functional bundle and they are separated from the core clause by an intonational phrase boundary. In many languages we find that dislocations come in two classes: a class of dislocations that are syntactically linked to a position in the core structure and a second class of dislocations that are connected only in (...) the process of interpretation. This grammatical distinction maps onto a difference in the information structure properties: D-type dislocations are given, H-type dislocations signal topic promotion. Some languages seem to have only H-type dislocations, which take over the functions of both D-type and H-type dislocations. (shrink)

Estudio bibliográfico / A bibliographical study of: Ernesto Grassi, Retorica come filosofia. La tradizione umanistica, trad. di Roberta Moroni, a. c. di Massimo Marassi, La Città del Sole, Napoli, 1999, pp. 198 . E.H. Gombrich, Imágenes Simbólicas. Estudios sobre el arte del Renacimiento, 2, versión castellana de Remigio Gómez Díaz, Editorial Debate, Madrid, 2000, pp. 244.

In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...) in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed. (shrink)

This paper discusses the first incarnation of what came to be known as the “Frege-Geach” point. The point was made by Peter Geach in his 1960 essay “Ascriptivism”, and developed in “Assertion”, a 1965 piece. Geach’s articles launch a wholesale attack on theories of non-descriptive performances advanced by “some Oxford philosophers” whom he accuses of ignoring “the distinction between calling a thing ‘P’ and predicating ‘P’ of a thing”. One view that Geach specifically targets is H. L. A. Hart’s claim (...) that sentences of the form “X φ-ed” are not primarily descriptive but ascriptive of responsibility for actions. Hart explicitly accepted Geach’s criticism, and disowned his essay. I argue that he was wrong to do so. Perhaps the essay was worth retracting, but not because of Geach’s objections. I begin by restating and refining Geach’s arguments, in order to bring out the flaw he claimed to have detected in the “pattern of philosophising” that he took Hart’s essay to exemplify. I go on to argue that Geach’s original point poses no obstacle either to non-descriptivism in general, or to Hart’s sui generis non-descriptivist claim in particular. (shrink)

Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0, 1] and a basic hoop H. We present a geometrical characterization of elements in the finitely generated free algebra of each of these subvarieties. In this characterization there is a clear insight of the role of the regular and dense elements of the generating chain. As an application, we analyze maximal and prime filters in the free algebra.