The article is devoted to the nature of the topological intuition and disclosure of the specifics of topological heuristics in the framework of philosophical theory of knowledge. As we know, intuition is a one of the support categories of the theory of knowledge, the driving force of scientific research. Great importance is mathematical intuition for the solution of non-standard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the so-called heuristics, built on (...) the basis of guesswork, obtained by intuition. The author substantiates the conclusion that topological intuition significantly specific compared to a traditional mathematical intuitions of Euclidean geometry. Today topology is a rapidly developing field of modern mathematics, integrates nicely with other sections of mathematical science. In its most general form of the topology can be defined as the branch of mathematics that studies the properties of spatial figures, does not change under deformations. The topological intuition is an instrument for development of topology on the basis of typological heuristics, which is the result of applying topological intuition to the objects topology. The author demonstrates in detail providing with the examples the specificity of topological heuristics and establishes its interconnection with Euclidean geometry. The author draws the conclusion about the fundamentality of topological intuition, and that it, perhaps, is primary in relation to traditionally understood mathematical intuition. (shrink)

The [lambda]-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from category theory, the usual calculus of [lambda]-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a ‘minimal’ topological model in which every continuous function is [lambda]-definable. These results subsume earlier ones using cartesian closed categories, as (...) well as those employing so-called Henkin and Kripke [lambda]-models. (shrink)

The present paper gives a topological solution to representability problems related to multi-utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of a semicontinuous and finite Richter–Peleg multi-utility for a preorder are studied. It is well known that, given a preorder on a topological space, if there is a lower semicontinuous Richter–Peleg multi-utility, then the topology of the space must be finer than the Upper topology. However, this condition fails to be sufficient. Instead (...) of search for properties that must be satisfied by the preorder, we study finer topologies which are necessary or/and sufficient for the existence of semicontinuous representations. We prove that Scott topology must be contained in the topology of the space in case there exists a finite lower semicontinuous Richter–Peleg multi-utility. However, the existence of this representation cannot be guaranteed. A sufficient condition is given by means of Alexandroff’s topology, for that, we prove that more order implies less Alexandroff’s topology, as well as the converse. Finally, the paper is implemented with a topological study of the maximal elements. (shrink)

Can we deploy creative practices to critically address the fatal interlocking of global surveillance technologies, neo-colonial expansionism, environmental degradation and the lethal threat of drone warfare? Throughout the following conversation, Shona Illingworth and Anthony Downey examine these and other questions in relation to the recent publication of Topologies of Air (Sternberg Press and The Power Plant, 2022). Edited by Downey, the book includes discussion and documentation of two major bodies of work by Illingworth, including Topologies of Air (2021) and Lesions (...) in the Landscape (2015), alongside an extended series of essays that analyse the psychological and environmental impact of military, industrial and corporate transformations of airspace and outer space. Employing interdisciplinary research and collaborative processes, Illingworth’s practice, as detailed in the discussion below, uses creative methodologies to visualize and interrogate this proliferating exploitation of airspace. The conversation between Illingworth and Downey also outlines the work of the Airspace Tribunal, an ongoing series of public hearings that brings together diverse disciplines, methodologies, knowledge and lived experiences to propose a new human right that will counter the colonization of the sky and, in time, protect individuals, communities and ecologies from ever-increasing threats from above. (shrink)

SummaryThe Gricean maxims of conversation are regulated by a supermaxim which determines what is relevant or not for a particular conversation. This maxim, involving a pragmatical knowledge, imposes specific restrictions on conversational strategy. It is called the “maxim of conversation topology” because it fixes the topos of a conversation.RésuméDans cet article nous démontrons que les maximes de la conversation, établies par H.P. Grice, sont dominées par une supermaxime qui détermine ce qui est pertinent et ce qui n'est pas pertinent (...) pour une certaine conversation. Cette maxime, qui implique une connaissance ?on;ordre pragmatique, impose des restrictions spécifiques sur la stratégie de conversation. Cette supermaxime, axiomatiquement premiére, est appelée ici la maxime de la topologie de la conversation, puisque c'est elle qui fixe le topos?on;une conversation.ZusammenfassungDie Maximen, die Grice für die Durchführung einer Konversation aufstellt, werden ihrerseits durch eine Obermaxime geregelt, die bestimmt, was für eine gegebene Konversation relevant ist oder nicht. Die Maxime involviert pralctisches Wissen und legt der angewendeten Strategie spezifi‐sche Einschränkungen auf. Sie wird die Maxime der Konversationstopologie genannt, weil sie den Topos einer Konversation festlegt. (shrink)

Extant research suggests that individuals employ traditional moral heuristics to support their observed altruistic behavior; yet findings have largely been limited to inductive extrapolation and rely on relatively few traditional frames in so doing, namely, deontology in organizational behavior and virtue theory in law and economics. Given that these and competing moral frames such as utilitarianism can manifest as identical behavior, we develop a moral framing instrument—the Philosophical Moral-Framing Measure (PMFM)—to expand and distinguish traditional frames associated and disassociated with observed (...) altruistic behavior. The validation of our instrument based on 1015 subjects in 3 separate real stakes scenarios indicates that heuristic forms of deontology, virtue-theory, and utilitarianism are strongly related to such behavior, and that egoism is an inhibitor. It also suggests that deontic and virtue-theoretical frames may be commonly perceived as intertwined and opens the door for new research on self-abnegation, namely, a perceived moral obligation toward suffering and self-denial. These findings hold the potential to inform ongoing conversations regarding organizational citizenship and moral crowding out, namely, how financial incentives can undermine altruistic behavior. (shrink)

The ArgumentGravitational redshift of spectral lines as one of the three early-known experimental implications of Einstein's general theory of relativity and gravitation was intensively searched for by researchers all over the world, but around 1920 most of the contemporary evidence in the sun's Fraunhofer-spectrum conflicted with the predictions of relativity theory.In 1923 the American astrophysicist Charles Edward St. John announced that his own solar spectroscopic data would force him to retreat from his former skepticism concerning the existence of gravitational redshift. (...) This statement was at the time widely interpreted by scientists and journalists alike as the open confession of a rapid conversion of one of the few remaining serious scientific opponents of Einstein's theory.This paper demonstrates that this illusion of a sudden “Gestalt switch” in St. John's evaluation of data can be dissolved by a careful step-by-step account of St. John's research practice between 1917 and 1923. After a fine-grained diachronic report of the development of St. John's interpretation of his and others' data, the second part of the paper consists in a systematic analysis of the heuristics and arguments used by St. John pro and contra gravitational redshift. (shrink)

I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and how it guides the manipulations of the represented object in ways that restructure its components by gradually adding new pieces of information to produce a hypothesis in order to solve a problem.In addition, I defend an ‘inferential’ (...) approach to the heuristic power of representations by arguing that these representations draw on ampliative inferences such as analogies and inductions. In effect, in order to construct a representation, we have to ‘assimilate’ diverse things, and this requires identifying similarities between them. These similarities form the basis for ampliative inferences that gradually build hypotheses to solve a problem.To support my thesis, I analyse two examples. The first one is intra-field, that is, the construction of an algebraic representation of 3-manifolds; the second is inter-fields, that is, the construction of a topological representation of DNA supercoiling. (shrink)

In order to establish patterns of materialization of the beliefs we are going to consider that these have defined mathematical structures. It will allow us to understand better processes of the textual, architectonic, normative, educative, etc., materialization of an ideology. The materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology and it is (...) any representation of the Reality represented by symbolic means. In all text T we can observe diverse topological structures: Metric Textual Space, Textual Topology and a Textual Lattice. (shrink)

In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show (...) that Grzegorczyk points are maximal contracting filters in the sense of De Vries, but the converse inclusion is not necessarily true. We also compare the notions of a Grzegorczyk point and an ultrafilter, and establish several properties of topological spaces based on Grzegorczyk structures. The main results of the paper are representation and completion theorems for G-structures. We prove both set-theoretical and topological representation theorems for various classes of G-structures. We also present topological object duality theorem for the class of complete G-structures and the class of concentric spaces, both restricted to structures which satisfy countable chain condition. We conclude the paper with proving equivalence of the original Grzegorczyk axiom with the one accepted by us as axiom. (shrink)

The paper points out that Adam Smith’s famous argument about the “invisible hand” (IH) of markets can be inverted. While the IH argument suggests that the baker and butcher do what is in their costumers’ interests not because they care for their costumers, but out of their own self-interest, one can also defend the converse claim: if one cares for other people and finds a way to satisfy their needs, one can expect that those others will be willing to pay (...) for the satisfaction of their needs. The paper argues that the IH argument has a strong link to the view that the ultimate goal of management should be “profit maximization” and to neo-liberalism’s tenet that in a market economy where companies attempt to maximize profits, a “socially optimal” allocation will be achieved. It is argued, however, that profit maximization is well-defined only within a mathematical model, while real-world decision-making requires one to choose the “relevant set” of options before any assessment of associated profits can be attempted. “Profit maximization” is therefore characterized as a heuristic for managerial decision-making, and it is pointed out that it is by no means essential for management to be successful and sustainable. The inverse IH argument supports natural alternatives, such as Prahalad and Hart’s “bottom-of-the-pyramid” and Yunus’s “social entrepreneurship” approach. Both require the manager to focus on people’s needs first, and regard the “money-making” aspect as secondary. (shrink)

The notion of ecological rationality implies that the accuracy of a decision strategy depends on features of the information environment in which it is tested. We demonstrate that the performance of a group may be strongly affected by the decision strategies used by its individual members and specify how this effect is moderated by environmental features. Specifically, in a set of simulation studies, we systematically compared four decision strategies used by the individual group members: two linear, compensatory decision strategies and (...) two simple, noncompensatory heuristics. Individual decisions were aggregated by using a majority rule. To assess the ecological rationality of the strategies, we varied (a) the distribution of cue validities, (b) the quantity, and (c) the quality of shared information. Group performance strongly depended on the distribution of cue validities. When validities were linearly distributed, groups using a compensatory strategy achieved the highest accuracy. Conversely, when cue validities followed a J-shaped distribution, groups using a simple lexicographic heuristic performed best. While these effects were robust across different quantities of shared information, the quality of shared information exerted stronger effects on group performance. Consequences for prescriptive theories on group decision making are discussed. (shrink)

The pages that follow offer a critical survey of the motivic pursuit of a sober and wakeful way of life in old and late Stoicism (esp. Seneca’s Letters, Epictetus’ Discourses, and Marcus Aurelius’ Meditations). The aim is to show the key role that this motif plays in the Stoic conceptualization of conversion to philosophy and the school’s protreptic or rhetoric of conversion, that is to say, the forms of speech and literary strategies employed to instruct their addressees about (...) what they understood by conversion to philosophy and exhort them to change in their way of life. Wakefulness and soberness (and their counterparts, sleep and drunkenness) have been brought up occasionally in studies on Stoic ethics or moral philosophy. Yet, scholarship in the field has, to date, failed to identify the unique light this motif sheds on the Stoic pedagogical heuristics and conversion experience. T. Bénatouïl 2006, however, has already pointed out, in a study on the practical dimension of Stoicism, that despite its apparent triviality, the Stoic discussion on the sage’s use of wine and drunkenness unveils significant insights into the principles which govern the sage’s whole way of life. With a similar conviction, I hope that what follows may also elucidate the unparalleled lens that wakefulness and soberness as a motif for conversion provides for our understanding of the Stoic pursuit of a way of life in wisdom and virtue and its distinctiveness in the interaction process between traditions that characterized the ancient Mediterranean context. (shrink)

Counterpossibles are counterfactuals with an impossible antecedent. According to the orthodox view of counterfactuals, all counterpossibles are vacuously true. This is puzzling because some counterpossible statements seem to be false. The paper analyzes two approaches to explaining why certain counterpossibles, though perhaps true, may appear to be false. The first, which appeals to the Gricean mechanism of conversational implicatures, asserts that some counterpossibles appear to be false because their assertion carries with it a false conversational implicature. However, I argue that, (...) under a closer scrutiny, this approach collapses. I therefore turn to a second approach, proposed by Timothy Williamson. It appeals to a heuristic according to which speakers may regard a counterpossible to be false if they have previously accepted its opposite. Since the applicability of Williamson’s solution is limited, I suggest a more general account. Its underlining idea is that a counterpossible is rejected if the speaker cannot find what they regard as a universally true conditional function derivable from the counterpossible by substitutions and syntactic transformations. (shrink)

Tilley argues that since religions are not summaries of bloodless beliefs but embodied communal practices, the heuristic for the justification of beliefs must shift. Although some of the lines of this shift to practical wisdom remain vague, Tilley has taken philosophy of religion in an excellent direction. Attention to these questions would sharpen his sketch: Why abandon linguistic philosophy with no attention to the help one might receive from the embodied linguistic practice of the later Wittgenstein? What grounds the (...) wisdom we seek to practice? Can community outsiders argue with insiders? Do these embodied philosophical arguments differ from theological arguments? (shrink)

Music is an abstract art form that uses sound as its means of expression. It has deeply affected our lives. This paper proposes a method for extracting segment features from nonmultiple cluster music files. We divide each piece of music into multiple segments and extract the features of each segment. The specific process includes nonmultiple cluster music file note extraction, main melody extraction, segment division, and segment feature extraction. The segment feature is extracted from a segment of a piece of (...) music, contains the main melody and accompaniment information of the segment, and can reflect the sequence relationship of the notes. This paper proposes a performance style conversion network based on recurrent neural network and convolutional neural network. The bidirectional recurrent neural network based on Gated Recurrent Unit is used to extract different styles of note feature vector sequences, and the extracted note feature vector sequence is used to predict the intensity of a specific style, and the intensity changes of different styles of nonmultiple cluster music are better learned. Through the comparison, the multiclassification strategy of “one-to-the-rest” is selected, and the fuzzy recurrent neural network is applied to the shortcomings of the unrecognizable area. Finally, according to the feature extraction method and the principle of the classifier algorithm studied in this paper, a music style classification system is implemented in the MATLAB environment. Experimental simulation shows that this system can effectively classify music performance styles. (shrink)

What is the philosophical significance of Heidegger’s interpretation of the Japanese notion of kotoba (言葉) for Japanese philosophy? Was his conversation with Tezuka Tomio a real dialogue or not? To answer to these correlated questions, I elucidate Heidegger’s 1954 essay “A Dialogue on Language” by following a topological mode of thinking, and I inquire into the way-making of a “thinking conversation”. First, I problematize whether Heidegger engaged in a genuine dialogue with Tezuka. To that end, I distinguish the hermeneutic horizon (...) of the actual encounter between Tezuka and Heidegger from Heidegger’s essay which places Tezuka (the Japanese) and Heidegger (the Inquirer) in a fictional philosophical conversation. Second, I argue that Heidegger’s topological method of interpretating kotoba can be read as a poetic means of thematizing East-West dialogue. Third and finally, exploring the topological sense of kotoba, I engage with third generation Kyoto School thinker Ueda Shizuteru’sideaof“hollow words” of language, situated in a twofold view of the world. I conclude that the true character of Heidegger’s conversation with Tezuka can be identified neither in Heidegger’s “actual” encounter with Tezuka, nor merely in Heidegger’s “hollow” essay. Departing from Ueda’s account of kotoba, it appears that a genuine conversation with language can be located in the dialogue of actuality and hollowness, which finds it expression in poetic language. (shrink)

Tilley argues that since religions are not summaries of bloodless beliefs but embodied communal practices, the heuristic for the justification of beliefs must shift. Although some of the lines of this shift to practical wisdom remain vague, Tilley has taken philosophy of religion in an excellent direction. Attention to these questions would sharpen his sketch: Why abandon linguistic philosophy with no attention to the help one might receive from the embodied linguistic practice of the later Wittgenstein? What grounds the (...) wisdom we seek to practice? Can community outsiders argue with insiders? Do these embodied philosophical arguments differ from theological arguments? (shrink)

The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the application of a term/function to any other term/function, including itself. The calculus can be seen as a formal theory with certain pre-established axioms and inference rules, which can be interpreted by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, (...) known as $ D_{\infty }$, to represent the $\lambda $-terms as the typical functions of set theory, where it is not allowed to apply a function to itself. Here we propose a construction of an $\infty $-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case $D_{\infty }$, and we see that the Scott topology does not provide enough information about the relationship between higher homotopies. This motivates a new line of research focused on the exploration of $\lambda $-models with the structure of a non-trivial $\infty $-groupoid to generalize the proofs of term conversion to higher-proofs in $\lambda $-calculus. (shrink)

In this essay I seek to critically evaluate some forms of holism and organicism in biological thought, as a more deflationary echo to Gilbert and Sarkar's reflection on the need for an 'umbrella' concept to convey the new vitality of holistic concepts in biology (Gilbert and Sarkar 2000). Given that some recent discussions in theoretical biology call for an organism concept (from Moreno and Mossio’s work on organization to Kirschner et al.’s research paper in Cell, 2000, building on chemistry to (...) articulate what they called “molecular vitalism,” studying the “vitalistic” properties of molecular, cellular, and organismal function, and Pepper and Herron’s suggestion in their 2008 paper that organisms define a category that evolutionary biology cannot do without), the question, what concept of organicism are they calling for? To what extent are such claims philosophically committed to a non-naturalistic concept of organism as organizing centre, as a foundational rather than heuristic concept – or possibly a “biochauvinism,” to use Di Paolo’s term (Di Paolo 2009)? My aim in this paper is to conceptually clarify the forms of holism and organicism that are involved in these cases (and I acknowledge that the study of early 20th-century holisms [Peterson 2010] indicates that not all of them were in fact ‘organicist’ or ‘biologistic’). I suggest that contemporary holists are still potentially beholden to a certain kind of vitalism or “biochauvinism”; but that when they reduce their claims to mere heuristics, conversely, they risk losing sight of a certain kind of organizational “thickness”, a “vital materiality” (Wheeler 2010) which is characteristic of biological systems (Bechtel 2007). And I ask if it is possible to articulate a concept of biological holism or organicism which is neither an empirical ‘biochauvinism’ nor a metaphysical ‘vitalism’? (shrink)

The present work is centered in the understanding of the conversation like typically human phenomenon and explores the possibility to claim its heuristic paper in the investigation processes in human sciences. The day-to-day of its use has made of the conversation an instrument, a mean, forgettin..

How can one discover the ethical issues associated with nanotechnologies? One heuristic is to tend closely to the ethical reflections of lay publics and the ways in which these are informed by experience with technological innovation, technology governance, and the (broken) promises of visionary science and technology. A close collaboration between social scientists and philosophers took this heuristic to its limits: On the one hand, it achieved remarkably fine–grained insights into public reflection about nanotechnologies. On the other hand, (...) a philosophical analysis of these reflections makes apparent that there is a profound disconnect between the lay ethics rooted in public talk and the ethical and normative commitments that are embedded in nanotechnological research programs and practices. Accordingly, critical engagement with the ways in which ordinary people try to make sense of nanotechnologies constitutes a novel heuristic for the discovery of ethical issues. This introduction and the subsequent four papers show this heuristic at work. (shrink)

Psychologists' work on conversational pragmatics and judgment suggests a refreshing approach to charitable interpretation and theorizing. This charitable approach—what I call Gricean charity —recognizes the role of conversational assumptions and norms in subject-experimenter communication. In this paper, I outline the methodological lessons Gricean charity gleans from psychologists' work in conversational pragmatics. In particular, Gricean charity imposes specific evidential standards requiring that researchers collect empirical information about (1) the conditions of successful and unsuccessful communication for specific experimental contexts, and (2) the (...) conversational norms governing communication in experimental contexts. More generally, the Gricean turn in psychological research shifts focus from attributional to reflexive, situational explanations. Gricean charity does not primarily seek to rationalize subject responses. Rather, it imposes evidential requirements on psychological studies for the purpose of gaining a more accurate picture of the surprising and muddled ways in which we weigh evidence and draw. Key Words: Gricean charity • methodological rationalism • interpretation • principle of charity • cognitive psychology • conversational pragmatics • heuristics and biases • reflexive analysis. (shrink)

In this paper, I outline a heuristic for thinking about the relation between explanation and understanding that can be used to capture various levels of “intimacy”, between them. I argue that the level of complexity in the structure of explanation is inversely proportional to the level of intimacy between explanation and understanding, i.e. the more complexity the less intimacy. I further argue that the level of complexity in the structure of explanation also affects the explanatory depth in a similar (...) way to intimacy between explanation and understanding, i.e. the less complexity the greater explanatory depth and vice versa. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a (...) taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

The history of productivity of the κ-chain condition in partial orders, topological spaces, or Boolean algebras is surveyed, and its connection to the set-theoretic notion of a weakly compact cardinal is highlighted. Then, it is proved that for every regular cardinal κ > א1, the principle □ is equivalent to the existence of a certain strong coloring c : [κ]2 → κ for which the family of fibers T is a nonspecial κ-Aronszajn tree. The theorem follows from an analysis of (...) a new characteristic function for walks on ordinals, and implies in particular that if the κ-chain condition is productive for a given regular cardinal κ > א1, then κ is weakly compact in some inner model of ZFC. This provides a partial converse to the fact that if κ is a weakly compact cardinal, then the κ-chain condition is productive. (shrink)

Emotion, Sense, Experience calls on historians of emotions and the senses to come together in serious and sustained dialogue. The Element outlines the deep if largely unacknowledged genealogy of historical writing insisting on a braided history of emotions and the senses; explains why recent historical treatments have sometimes profitably but nonetheless unhelpfully segregated the emotions from the senses; and makes a compelling case for the heuristic and interpretive dividends of bringing emotions and sensory history into conversation. Ultimately, we envisage (...) a new way of understanding historical lived experience generally, as a mutable product of a situated world-brain-body dynamic. Such a project necessarily points us towards new interdisciplinary engagement and collaboration, especially with social neuroscience. Unpicking some commonly held assumptions about affective and sensory experience, we re-imagine the human being as both biocultural and historical, reclaiming the analysis of human experience from biology and psychology and seeking new collaborative efforts. (shrink)

This paper presents a theoretical framework of the circular shift network coding system through the study of nonmultiple clustered interval music performance style conversion and the analysis of music conversion by using circular shift topology, and a series of basic research results of circular shift network coding is obtained under this framework. It reveals the essential connection between scalar network coding based on finite domain and cyclic shift network coding, designs a solution construction algorithm for cyclic shift (...) network coding under multicast network, and portrays the multicast capacity of cyclic shift network coding. It overcomes the problem that the piano roll-curtain representation cannot distinguish between a single long note and multiple consecutive notes of the same pitch, describes musical information more comprehensively, extracts musical implicit style from the note matrix based on autoencoder, and better eliminates the potential influence of musical content on musical performance style. A two-way recurrent neural network based on the gated recurrent unit is used to extract a sequence of note feature vectors of different styles, and a one-dimensional convolutional neural network is used to predict the intensity of the extracted note feature vector sequence for a specific style, which better learns the intensity variation of different styles of MIDI music. (shrink)

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π12 comprehension. An MF space is defined to be a topological space of the form MF with the topology generated by {Np ∣ p ϵ P}. Here P is a poset, MF is the set of maximal filters on P, and Np = {F ϵ MF ∣ p ϵ F }. If the poset P is countable, the space MF is (...) said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, “every countably based MF space which is regular is homeomorphic to a complete separable metric space,” is equivalent to. The equivalence is proved in the weaker system. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π12 comprehension. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π2 1 comprehension. An MF space is defined to be a topological space of the form MF(P) with the topology generated by $\lbrace N_p \mid p \in P \rbrace$ . Here P is a poset, MF(P) is the set of maximal filters on P, and $N_p = \lbrace F \in MF(P) \mid p \in F \rbrace$ . If the poset P (...) is countable, the space MF(P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, "every countably based MF space which is regular is homeomorphic to a complete separable metric space," is equivalent to Π2 1-CA0. The equivalence is proved in the weaker system Π1 1-CA0. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π2 1 comprehension. (shrink)

We discuss conceptual change and progress within mathematics, in particular how tools, structural concepts and representations are transferred between fields that appear to be unconnected or remote from each other. The theoretical background is provided by the frame concept, which is used in linguistics, cognitive science and artificial intelligence to model how explicitly given information is combined with expectations deriving from background knowledge. In mathematical proofs, we distinguish two kinds of frames, namely structural frames and ontological frames. The interaction between (...) both kinds of frames can drive mathematical interpretation. We first discuss two examples where structural frames (formulaic notation) drive ontological development (the discovery or exploration of mathematical objects). The development of Boole’s Boolean algebra may at first appear as a metaphorical treatment of the (then) new area of logic. In the analysis, we discuss how different (aspects of) certain algebraic frames change in the transfer, how arising difficulties are solved and overall argue that Boole uses the numerical algebra frame as a research template for the discovery of a system for calculations in logic. Following Ifrah, we analyse the discovery of zero as an extension to the number ontology as driven by the development of notation. Both structural and ontological frames are extended and simplified as notation progresses. Finally, we discuss two examples from infinite combinatorics, viz. topological graph theory, and one foundational issue. In both examples, the two simultaneous frames about one object are maintained independently. They motivate different research questions, but may also fruitfully interact: shifting between multiple synchronously maintained perspectives acts as a motor of innovation. The analysis shows how a frame-based approach allows to model how different perspectives drive mathematical innovation because they highlight different aspects, questions and heuristics. (shrink)

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

In this interview, Boris Groys discusses his key cultural-theoretical ideas, positions his thought in relation to debates on the cultural economy and clarifies questions emerging from his work. The conversation focuses on his untranslated cultural-theoretical contributions, notably Über das Neue [On the New] and Topologie der Kunst [Topology of Art], but also touches on his writings available in English, for example Art Power. The interview contains three sections. The first revisits Groys’s challenge to the postmodern claim about the end (...) of cultural innovation. He problematizes this claim with reference to the current rise of digital archives and the loss of individual and collective memory. Groys goes on to elucidate the centrality of the ready-made method to cultural innovation. Cultural activity, he argues, constitutes a ritual which promises immortality in a world of perpetual change. Finally, Groys clarifies and illustrates the questions guiding his phenomenological investigation of the ‘scene of evidence’ and the ‘mode of suspicion’. The second section is dedicated to the topology of culture in 21st-century capitalism. Groys sets out from his observation of the privatization and fragmentation of archival space. Humanity is entering a ‘new virtual Middle Age’, where individuals are engaged in a series of self-installations, travelling through a string of heterogeneous valorizing spaces. The ‘chance’ of genuine art in these conditions lies in its withdrawal from exchange. As inexchangeable ‘commodity corpses’ demanding eternal preservation, artworks can provocatively indicate the possibility of a ‘life after capitalism’. His considerations also lead Groys to discuss his notion of Soviet Communism as an installation in pursuit of the wish to ‘step out of time’. The third section centres on the problems of politics and critique. Responding to a question about the political potential of art, Groys proposes consideration of the increasing intensity — presently illustrated by the conflict in the Middle East — with which politics acts in the realm of aesthetics. The interview closes with reflections on the possibility of intellectual resistance. Referring to Nietzsche and Adorno, Groys locates the potential of opposition in a resentful critique of time: a ‘rejection of everything’ and the insistence upon the possibility that what is will vanish. (shrink)

The organism is neither a discovery like the circulation of the blood or the glycogenic function of the liver, nor a particular biological theory like epigenesis or preformationism. It is rather a concept which plays a series of roles – sometimes overt, sometimes masked – throughout the history of biology, and frequently in very normative ways, also shifting between the biological and the social. Indeed, it has often been presented as a key-concept in life science and the ‘theorization’ of Life, (...) but conversely has also been the target of influential rejections: as just an instrument of transmission for the selfish gene, but also, historiographically, as part of an outdated ‘vitalism’. Indeed, the organism, perhaps because it is experientially closer to the ‘body’ than to the ‘molecule’, is often the object of quasi-affective theoretical investments presenting it as essential, sometimes even as the pivot of a science or a particular approach to nature, while other approaches reject or attack it with equal force, assimilating it to a mysterious ‘vitalist’ ontology of extra-causal forces, or other pseudo-scientific doctrines. This paper does not seek to adjudicate between these debates, either in terms of scientific validity or historical coherence; nor does it return to the well-studied issue of the organism-mechanism tension in biology. Recent scholarship has begun to focus on the emergence and transformation of the concept of organism, but has not emphasized so much the way in which organism is a shifting, ‘go-between’ concept – invoked as ‘natural’ by some thinkers to justify their metaphysics, but then presented as value-laden by others, over and against the natural world. The organism as go-between concept is also a hybrid, a boundary concept or an epistemic limit case, all of which partly overlap with the idea of ‘nomadic concepts’. Thereby the concept of organism continues to function in different contexts – as a heuristic, an explanatory challenge, a model of order, of regulation, etc. – despite having frequently been pronounced irrelevant and reduced to molecules or genes. Yet this perpetuation is far removed from any ‘metaphysics of organism’, or organismic biology. (shrink)

Context: The idea for this article sprang from a desire to revive a conversation with the late Ernst von Glasersfeld on the heuristic function - and epistemological status - of forms of ideations that resist linguistic or empirical scrutiny. A close look into the uses of humor seemed a thread worth pursuing, albeit tenuous, to further explore some of the controversies surrounding the evocative power of the imaginal and other oblique forms of knowing characteristic of creative individuals. Problem: People (...) generally respond to humor, i.e., they are inclined to smile at things they find funny. People like to crack jokes, make puns, and, starting at age two, human infants engage in pretense or fantasy play. Research on creativity, on the other hand, has mostly scorned the trickster within. Cognitivists in particular are quick to relegate wit, whimsy, and even playfulness to the ranks of artful or poetic frivolities. Method: We use the emblems of the craftsman, the trickster, and the poet to highlight some of the oblique ways of knowing by which creative thinkers bring forth new insights. Each epitomizes dimensions intrinsic to the art of “possibilizing.” Taken together, they help us better understand what it means to be playful beyond curious, rigorous beyond reasonable, and why this should matter, even to constructivists! Results: The musings characteristic of creative individuals speak to intelligent beings’ ability to use glitches intentionally or serendipitously as a means to open up possibilities; to hold on to a thought before spelling it out; and to resist treating words or images as conventional and arbitrary signs regardless of their evocative power. To fall into nominalism, Bachelard insisted, is a poet’s nightmare! Implications: Psyche is image, said Jung, and when we feel alive we rely on the imaginal to guide our reason. Note that image is not here to be understood as a picture in the head or a photographic snapshot of the world. The imaginal does not represent, it brings forth what we understand beyond words. It does not lock us into a single mode. Instead, it is a call to be mindful, in Ellen Langer’s sense: in the present, mentally alert, and on the outlook for our psyche’s own surprising wisdom (sagacity. Constructivist content: Debates on the heuristic function and epistemological status of oblique ways of knowing have long occupied constructivist scholars. I can only guess whether my uses of Jung’s imaginal or Bachelard’s anti-nominalism would have amused or exasperated Ernst! I do know that, on occasion, Ernst the connoisseur, bricoleur, and translator allowed the rationalist-within to include the poet’s power to evoke as a legitimate form of rationality. He himself has written about oblique knowing as legit! (shrink)

Upshot: In view of Kenny’s clinical insights, Hug’s notes on the intricacies of rational vs. a-rational “knowing” in the design sciences, and Chronaki & Kynigos’s notice of mathematics teachers’ meta-communication on experiences of change, this response reframes the heuristic power of bisociation and suspension of disbelief in the light of Kelly’s notion of “as-if-ism” (constructive alternativism. Doing as-if and playing what-if, I reiterate, are critical to mitigating intra-and inter-personal relations, or meta-communicating. Their epistemic status within the radical constructivist framework (...) is cast in the context of mutually enriching conversational techniques, or language-games, inspired by Maturana’s concepts of “objectivity in parenthesis” and the multiverse. (shrink)

Why is there so much distortion in ordinary, political, social, and ethical argument? Since we have a pervasive interest in reasoning well and corresponding abilities, the extent of distortion invites explanation. The leading candidates are the need to economize, widespread, fallacious heuristics or assumptions, and self-defensive biases. I argue that these are not sufficient. An additional force is the intellectual pressure generated by acceptance of norms of conversation and argument, which exclude ‘middles’ of, prominently, neither accept nor reject. I conjecture (...) that the distortion we find is due to intellectual and normative pressures generated by our commitment to these excluded-middle norms and if, or when, their force is lessened, there is likely to be less distortion. (shrink)

The organism is neither a discovery like the circulation of the blood or the glycogenic function of the liver, nor a particular biological theory like epigenesis or preformationism. It is rather a concept which plays a series of roles, sometimes masked, often normative, throughout the history of biology. Indeed, it has often been presented as a key-concept in life science and its ‘theorization’, but conversely has also been the target of influential rejections: as just an instrument of transmission for the (...) selfish gene, but also, historiographically, as part of an outdated ‘vitalism’. Indeed, the organism, perhaps because it is experientially closer to the ‘body’ than to the ‘molecule’, is often the object of quasi-affective theoretical investments presenting it as essential, as the pivot of a science or a particular approach to nature, while other approaches reject or attack it with equal force, assimilating it to a mysterious ‘vitalist’ ontology of extra-causal forces, or other pseudo-scientific doctrines. I do not seek to adjudicate between these debates, either regarding scientific validity or historical coherence; nor do I return to the well-studied issue of the organism-mechanism tension in biology. Recent scholarship has begun to discuss the emergence and transformation of the organism concept, but has not emphasized the way the latter is a shifting, ‘go-between’ concept – invoked as ‘natural’ by some thinkers to justify their metaphysics, but then presented as value-laden by others, over and against the natural world. The organism as go-between concept is also a hybrid, a boundary concept or a limit case, which continues to function in different contexts – as a heuristic, an explanatory challenge, a model of order, of regulation, etc. – despite having frequently been pronounced irrelevant and reduced to molecules or genes. Yet this perpetuation is far removed from any ‘metaphysics of organism’, or organismic biology. (shrink)

In the first part of this essay, I develop the argument that Michel Foucault's work should be read with geographical and topological ideas in mind. I argue that Foucault's archeology and genealogy are fundamentally determined by spatial, topological, geographical, and geometrical metaphors and concepts. This spatial dimension of genealogy is explicitly related to racism and the regimes that domesticate agents through the practices, institutions and ideologies of racialization. The second part offers a genealogical reading of US history and spatiality in (...) terms of its racial institutions. I suggest that if we want to read the US geographies of topographies and cartographies of racism in a Foucauldian manner, then we must focus on plantations, ghettos, and prisons as the spaces‐institutions‐geographies that consolidated the racial matrix of US polity. My goal is to acculturate Foucauldian racial genealogy to the US racial matrix, and, conversely, to read US geo‐history in terms of racializing spatialities. (shrink)

The Article analyzes the notion of legal “thinghood” in the context of the person–thing bifurcation. In legal scholarship, there are numerous assumptions pertaining to this definition that are often not spelled out. In addition, one’s chosen definition of “thing” is often simply taken to be the correct one. The Article scrutinizes these assumptions and definitions. First, a brief history of the bifurcation is offered. Second, three possible definitions of “legal thing” are examined: Things as nonpersons, things as rights and duties, (...) and things as property. The first two definitions are rejected as not being very interesting or serving any heuristic function. Conversely, understanding legal things as property is meaningful, useful, and helps to understand what it means to say that animals are legally things. Defining things as property has certain rather important implications, which are analyzed at the end of the Article. For instance, not everything needs to be either a person or a thing: The historical institution of outlawry involved treating individuals neither as legal persons nor as legal things. One must conclude that the person–thing bifurcation is less fundamental than is often assumed. (shrink)

A central diagnostic and anecdotal feature ofautismis difficulty with socialcommunication. We take the position that communication is a two-way,intersubjectivephenomenon—as described by thedouble empathy problem—and offer uprelevance theory(a cognitive account of utterance interpretation) as a means of explaining such communication difficulties. Based on a set of proposed heuristics for successful and rapid interpretation of intended meaning, relevance theory positions communication as contingent on shared—and, importantly,mutuallyrecognized—“relevance.” Given that autistic and non-autistic people may have sometimes markedly different embodied experiences of the world, we (...) argue that what is most salient to each interlocutor may be mismatched. Relevance theory would predict that where this salient information is not (mutually) recognized or adjusted for, mutual understanding may be more effortful to achieve. This paper presents the findings from a small-scale, linguistic ethnographic study of autistic communication featuring eight core autistic participants. Each core autistic participant engaged in three naturalistic conversations around the topic of loneliness with: (1) a familiar, chosen conversation partner; (2) a non-autistic stranger and (3) an autistic stranger. Relevance theory is utilized as a frame for the linguistic analysis of the interactions. Mutual understanding was unexpectedly high across all types of conversation pairings. In conversations involving two autistic participants, flow, rapport and intersubjective attunement were significantly increased and in three instances, autistic interlocutors appeared to experience improvements in their individual communicative competence contrasted with their other conversations. The findings have the potential to guide future thinking about how, in practical terms, communication between autistic and non-autistic people in both personal and public settings might be improved. (shrink)

We here report the findings of our investigation into the validity of the conjunction fallacy (Tversky & Kahneman, 1983), bearing in mind the role of conversational rules. Our first experiment showed that subjects found a logically correct answer unacceptable when it implied a violation of the conversational rules. We argue that tautological questions, such as those which concern the relationship of inclusion between a class and its sub-class, violate conversational rules because they are not informative. In this sense, it is (...) not understood that the question in a Linda-type problem involves a comparison between an inclusive and included class, but presumed that a different type of comparison is intended. Tautological questions (and, consequently, also their answers) do not become a matter of discussion except under certain specific conditions. Our second experiment showed that, providing the context was adequately marked (such as in the case of a rhetorical question), the conjunction fallacy disappears. In two further experiments, the implications of our view were compared with those of the other critical approaches to the heuristic programme: the classical pragmatic view (which we call logical complementarity) and the frequentist view. (shrink)

The ill?named debate between postmodernists and postlibertarians should be transcended; this requires the abandonment of both foundationalism and its converse, without abandoning common sense as well (which is no mean trick). Similarly, the debate over ?minimal statism? versus the planned economy is outdated. Instead of claiming to be in possession of foundations of our scientific?cum?political knowledge in broad terms, and instead of severely limiting our knowledge to given proofs, we offer the putative heuristics of critique in general and the critical (...) evaluations of contexts in particular. (shrink)

When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call such (...) games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically. (shrink)

This dissertation is a study of the images of the soul in the Gorgias. I analyze the relationship between power and omnipotence in the conceptions of the soul defended and/or exemplified by the characters of the dialogue. ;In chapter 1 I focus on the dramatic setting of the Gorgias, which lacks clear temporal and spatial indications. I show that the three conversations are dramatically linked to the last myth of judgment. My hypothesis is that Gorgias and his followers are seen (...) by Socrates as the representatives of the age of Kronos. As opposed to the age of Zeus, which allows for correct judgment of the soul, the age of Kronos is characterized by deception and manipulation. ;Chapter 2 analyzes in detail the myth of last judgment, which presents the problem of correct and incorrect knowledge of the soul. I focus on the relationship between surface and depth involved in judging the soul of another. I show that the passage from the age of Kronos to the age of Zeus represents the passage from a primitive condition of the soul to a condition which allows for thinking and power. The concept of separation is central in my analysis. ;While Chapter 3 shows how Gorgias' claim for rhetoric's omnipotence is first brought to light and then refuted by Socrates, Chapter 4 examines Gorgias' legacy in Callicles' theory of the law of nature. The interplay between Callicles' theory and the examples used to support it brings me to consider the master/slave relationship involved in Callicles' theory and his ambiguous stance towards omnipotence and rhetoric. ;The Appendix is mainly devoted to an analysis of Socrates' Palinode in the Phaedrus. I maintain that the Palinode reveals what is implicit in Socrates' and Callicles' discussion of pleasure in the Gorgias, namely that thinking is possible only when transcendence is acknowledged. ;I conclude that the Gorgias gives us not only a topology of the human soul, but also a rich and deep understanding of the genealogy of thinking. (shrink)

It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.

Context: The thoroughly second-order cybernetic underpinnings of naturalist theatre have gone almost entirely unremarked in the literature of both theatre studies and cybernetics itself. As a result, rich opportunities for the two fields to draw mutual benefit and break new ground through both theoretical and empirical investigations of these underpinnings have, thus far, gone untapped. Problem: The field of cybernetics continues to remain academically marginalized for, among other things, its alleged lack of experimental rigor. At the same time, the field (...) of theatre studies finds itself at an impasse between post-structuralist semioticians and embodied cognitivists regarding key onto-epistemological issues. A program of research framing and utilizing naturalist theatre as a second-order cybernetic/cybersemiotic laboratory holds much promise in addressing both matters and lending credence to Ross Ashby’s assertion that “the discovery that two fields are related leads to each branch helping in the development of the other.” Method: After establishing the nature of the onto-epistemological deadlock within theatre studies, this article examines the application of cybernetic heuristics within naturalistic theatre, leading to a second-order cybernetic analysis of its processes of production and reception and the outline of an experimental program for exploring these processes further. Results: Foundations for a model of naturalist theatre as a cybersemiotic laboratory grounded in a novel operationalization of Gordon Pask’s conversation theory. Implications: The proposed laboratory could result in the generation of quantitative and qualitative research pertaining to several dimensions of second-order cybernetics; particularly cybersemiotics, which, as a result, may end up better positioned to help dissolve onto-epistemological deadlocks between constructivists and realists of all stripes across the academy and beyond. Constructivist content: I argue that an analysis of naturalistic theatre’s processes of meaning-making filtered through the constructivist ontological agnosticism of second-order cybernetics offers a productive middle way forward for those on both sides of the social constructivist/embodied cognitive realist divide, within and beyond theatre studies. The article draws upon the works of Gregory Bateson, Søren Brier, Ranulph Glanville, Heinz von Foerster, and Niklas Luhmann. (shrink)

How should we conceive of policymakers for the purposes of political analysis? In particular, if we wish to explain and predict political decisions and their consequences, if we wish to ensure that political action is as effective as it can be, how should we think of policymakers? Should we think of them as they are commonly conceived in traditional political analysis, i.e., as uniquely knowledgeable and as either altruistic (i.e., as motivated to realize goals associated with their constituents’ interests) or (...) knavish (i.e., as motivated to realize goals associated with their own personal interests), or should we treat them as possibly ignorant with respect to their political tasks? -/- It is always an open question whether policymakers possess the knowledge required to realize some policy objective. It should never be assumed a priori that policymaker knowledge is adequate to the policy tasks with which policymakers are charged. Politicians need knowledge concerning the causes of social phenomena adequate to control events sufficiently well to ensure the success of their policies. No argument has ever been offered for the standard, if only implicit, assumption that policymakers, somehow automatically, possess this knowledge. In many contexts, there is no reason to believe that policymakers possess or can acquire this knowledge. Indeed, a bit of reflection reveals how unlikely it is that and how rare the circumstances must be in which policymakers meet this condition, which political philosophers, theorists, economists, and other political thinkers have traditionally assumed as a matter of course. -/- The main purpose of the book is to encourage a conversation among scholars and students of political inquiry (in philosophy and political theory, political science, economics and political economy) concerning the best way to conceive of policymakers for the purposes of such inquiry. -/- The book defends an alternative, more realistic, method of political analysis. The book argues against the false assumption that policymakers are epistemically privileged. The book presents and defends the alternative assumption that, with respect to the knowledge required to discharge their political tasks effectively, policymakers are at least as ignorant as constituents. -/- The book further argues that whether policymakers are altruistic or knavish is, in the first instance, a function of the nature and extent of their ignorance with regard to constituent-minded policy goals. Policymakers who possess the knowledge required to be effectively altruistic are more likely to be altruistic, other things the same, than policymakers who are ignorant of the knowledge that successful altruism requires. -/- This being said, my goal is more to leave readers thinking about and inclined to debate these profound issues than to prescribe a particular methodological conclusion (even less to advocate a particular political conclusion). The book is a heuristic for spurring further conversation. It makes of readers fellow interlocutors partnered with the characters (and the author!) of the dialogue. -/- The vehicle for this analysis is a conversation between four friends, philosophy graduate students, with different interests, different levels and kinds of experience, and different political preferences. The four friends consider how politicians should be conceived for the purposes of analyzing political decision-making and its consequences. -/- In his famous Dialogues concerning Natural Religion, David Hume concluded that the assumption of an all-knowing and all-powerful God was neither necessary nor sufficient to explain natural phenomena. Dialogues concerning Natural Politics does for social science what Hume did for natural science. Both books undermine the assumption that some epistemically privileged being – God in the case of natural phenomena and God-like politicians in the case of social phenomena – must be invoked to explain relevant phenomena. (shrink)