The ability to learn complex tasks is fundamental to being human. Rahman and Gray examine this process in the context of learning to play a simple video game, using a tool called SpotLight to examine the low‐level process of skill and strategy improvements during this process. This paper was awarded the Allen Newell Best Student‐Led Paper Award at ICCM 2019.

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)

In an unusual appearance in the press room in Fall 2017 then White House Chief of Staff general John Kelly made an interesting set of observations that compared our political present to a more traditional and seemingly upright past. "You know when I was a kid growing up, a lot of things were sacred in our country. Women were sacred, looked upon with great honor. That's obviously not the case anymore, as we've seen from recent cases. Life - the dignity (...) of life - is sacred. That's gone. Religion, that seems to be gone as well", he said. In his comments Kelly seemed to be lamenting the loss of a chivalric past (which, to be clear, lounged grandly on a system of violent exclusion and deep prejudice) that is no longer available to us. In particular, he linked the idea of the sacred with the concept of honor, which in turn was linked to its close cousin, dignity. In Kelly's language, our present political moment was cast as profane and corrupt, unmoored from religion and tradition and cloaked in the shadows of moral bankruptcy. It was characterized as an age without honor and therefore without the guardrails of decency to govern behavior. It is not surprising to see the concept of honor invoked in this context in our contemporary political discourse, doused heavily in the language of remembrance of things past and often with a hyper masculine tint (look no further than Jordan Peterson and his acolytes for the most reductive examples of such thinking, or much more profoundly, to Harvey Mansfield's work on masculinity). Invoking honor in this manner seeks to restore balance and constancy to a chaotic present that in these renderings has been unmoored by radical feminists, populist movements for racial equality, and advocates of gay and trans rights. (shrink)

Negativity in Psychoanalysis examines the role of negativity in psychoanalytic theory and its application in clinical settings. While theories around negativity and death drive have become routinized within philosophical interpretations of Freudian and Lacanian psychoanalysis, they often mask an inherent positivity. This volume assembles highly esteemed psychoanalytic theorists and clinicians for an in-depth discussion on the topic. It features comprehensive introductions to Freudian and Lacanian perspectives, alongside contemporary clinical and cultural issues. The book also investigates how psychoanalytic negativity influences and (...) is influenced by social, theological, and philosophical dialogues. This work will prove invaluable for practicing psychoanalysts and those in training, while also appealing to academics and scholars in critical and cultural theory, continental and post-continental philosophy, and sociology, especially those whose research intersects clinical and theoretical traditions. (shrink)

Being a pragmatic and not a referential approach tosemantics, the dialogical formulation ofparaconsistency allows the following semantic idea tobe expressed within a semi-formal system: In anargumentation it sometimes makes sense to distinguishbetween the contradiction of one of the argumentationpartners with himself (internal contradiction) and thecontradiction between the partners (externalcontradiction). The idea is that externalcontradiction may involve different semantic contextsin which, say A and ¬A have been asserted.The dialogical approach suggests a way of studying thedynamic process of contradictions through which thetwo (...) contexts evolve for the sake of argumentation intoone system containing both contexts.More technically, we show a new, dialogical, way tobuild paraconsistent systems for propositional andfirst-order logic with classical and intuitionisticfeatures (i.e. paraconsistency both with and withouttertium non-datur) and present theircorresponding tableaux. (shrink)

What does the Kantian realm of ends look like? To partially answer that question, game theory will be used to analyse how Kantians would handle situations of strategic interaction. Starting from a thorough understanding of Kant's categorical imperative, three purportedly Kantian game theoretical models will be analysed and argued to be inconsistent with the categorical imperative. As these existing models are unfit for analysing strategic interaction in the realm of ends, a genuinely Kantian model will be constructed by adding the (...) concepts of ‘moral field’, ‘moral range’ and ‘Kantian utility function’ to the standard game‐theoretical model. Throughout the paper, the prisoner's dilemma will be used both as a case study and as a ground for argumentation. (shrink)

Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call GM+ holds. This principle implies ISP and ISP, and hence th...

The main aim of the present paper is to understand the debate between Descartes and Leibniz about eternal truths as providing the structure of several possible dialogues involving counter-logic . According to this analysis the positions of Descartes and Leibniz are understood as constituting dual and dynamic perspectives in relation to the availability of some specific choices that should provide norms of rationality. Each of these dialogues has both a universal, monological aspect (given by the winning strategy) and a contextual, (...) dialogical one (given by the play level). I conclude with the suggestion that a notion of rationality that contains both the universal and the contextual aspects does not yield a specific logic, but rather a frame of normative rationality. The conception of such a frame seems to be closely linked to the notion of a universal perfectible language discussed by Olga Pombo. The central idea is that the Leibniz’s notion of rationality is a fondateur de discursivité if we use Marcelo Dascal´s quote of Foucault. (shrink)

Jean-Luc Nancy élabore, depuis quelques années, une philosophie première où le concept d’« être-avec » occupe une place centrale. Celui-ci a suscité son lot d'interprétations. Une des critiques faite à l’encontre du concept est articulée selon l’angle éthique, plus particulièrement en ce qui a trait à la pluralité. En effet, en amalgamant « être » et « avec », Nancy annihilerait, comme Heidegger, la nécessaire pluralité de la vie en commun. C’est ce débat que nous voulons ici commenter. Nous commencerons (...) en explicitant le concept d’être-avec chez Nancy. Dans un deuxième temps, nous développerons les arguments de ceux qui reprochent à Nancy de ne pas avoir réussi à faire droit à la pluralité. Pour nous aider à y voir plus clair, nous utiliserons les travaux de Franco Volpi et de Jacques Taminiaux qui ont analysé les causes de ce déni heideggérien de la pluralité. Nous présenterons leur investigation dans la troisième section. Enfin, nous montrerons que l’être-avec nancéen, bien loin de dénier la pluralité, lui donne toute son ampleur. (shrink)

The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...) with his celebrated work on generalised side conditions, I. Neeman introduced us to a novel paradigm to iterate forcings. In particular, he could, among other things, reprove the consistency of the Proper Forcing Axiom using an iterated forcing with finite supports. In 2015, using his technology of virtual models, Veličković built up an iteration of semi-proper forcings with finite supports, hence reproving the consistency of Martin’s Maximum, an achievement leading to the notion of a virtual model.In this thesis, we are interested in constructing forcing notions with finitely many virtual models as side conditions to preserve three uncountable cardinals. The thesis constitutes six chapters and three appendices that amount to 118 pages, where Section 1 is devoted to preliminaries, and Section 2 is a warm-up about the scaffolding poset of a proper forcing. In Section 3, we present the general theory of virtual models in the context of forcing with sets of models of two types, where we, e.g., define the “meet” between two virtual models and prove its properties.The main results are joint with Boban Veličković, and partly appeared in Guessing models and the approachability ideal, J. Math. Log. 21 (2021).Pure Side Conditions. In Section 4, we use two types of virtual models (countable and large non-transitive ones induced by a supercompact cardinal, which we call Magidor models) to construct our forcing with pure side conditions. The forcing covertly uses a third type of models that are transitive. We also add decorations to the conditions to add many clubs in the generic $\omega _2$. In contrast to Neeman’s method, we do not have a single chain, but $\alpha $ -chains, for an ordinal $\alpha $ with $V_\alpha \prec V_\lambda $. Thus, starting from suitable large cardinals $\kappa <\lambda $, we construct a forcing notion whose conditions are finite sets of virtual models described earlier. The forcing is strongly proper, preserves $\kappa $, and has the $\lambda $ -Knaster property. The relevant quotients of the forcing are strongly proper, which helps us prove strong guessing model principles. The construction is generalisable to a ${<}\mu $ -closed forcing, for any given cardinal $\mu $ with $\mu ^{<\mu }=\mu <\kappa $.The Iteration Theorem. In Section 5, we use the forcing with pure side conditions to iterate a subclass of proper and $\aleph _2$ -c.c. forcings and obtain a forcing axiom at the level of $\aleph _2$. The iterable class is closely related to Asperó–Mota’s forcing axiom for finitely proper forcings.Guessing Model Principles. Section 6 encompasses the main parts of the thesis. We prove the consistency of the guessing principle $\mathrm {GMP}^+(\omega _3,\omega _1)$ that states for any cardinal ${\theta \geq \omega _3}$, the set of $\aleph _2$ -sized elementary submodels M of $H(\theta )$, which are the union of an $\omega _1$ -continuous $\in $ -chain of $\omega _1$ -guessing, I.C. models is stationary in $\mathcal P_{\omega _3}(H(\theta ))$. The consistency and consequences of this principle are demonstrated in the following diagram. We also prove that one can obtain the above guessing models in a way that the $\omega _1$ -sized $\omega _1$ -guessing models remain $\omega _1$ -guessing model in any outer transitive model with the same $\omega _1$, and we denote this principle by $\rm{SGMP}^+(\omega_3,\omega_1)$.In the following diagram, $\mathrm{TP}$ stands for the tree property; $w\mathrm{KH}$ stands for the weak Kurepa Hypothesis; $\mathrm{MP}$ stands for Mitchell property, i.e., the approachability ideal is trivial modulo the nonstationary ideal; $\mathrm{AP}$ stands for the approachability property; $\mathrm {AMTP}(\kappa ^+)$ states that if $2^\kappa <\aleph _{\kappa ^+}$, then every forcing which adds a new subset of $\kappa ^+$ whose initial segments are in the ground model, collapses some cardinal $\leq 2^{\kappa }$. The dotted arrow denotes the relative consistency, while others are logical implications.Appendices. Appendix A includes merely the above diagram. Appendix B presents a proof of the Mapping Reflection Principle with finite conditions under $\mathrm {PFA}$. Appendix C contains open problems. Finally, the thesis’s bibliography consists of 42 items.Abstract prepared by Rahman MohammadpourE-mail: [email protected]: https://theses.hal.science/tel-03209264. (shrink)

This article argues that current economic upheaval should be understood as a problem of domination, in two respects: the ‘dyadic’ domination of one actor by another, and the ‘structural’ domination of individuals by a diffuse, decentralized, but nevertheless human-made system. Such domination should be contested through specifically democratic political mobilization, through institutions and practices that expand the political agency of citizens themselves. The article advances this argument by synthesizing two traditions of political thought. It reconstructs radical democratic theory from the (...) Progressive Era. These thinkers in turn help to reinforce contemporary debates in neorepublican thought, resolving disputes over the scope of domination and the relationship between domination and democracy. This synthesis offers a novel normative framework for diagnosing and responding to the current combination of economic upheaval and political dysfunction. (shrink)

continent. 2.2 (2012): 152–154 Levi R. Bryant. The Democracy of Objects . Ann Arbor, MI: Open Humanities Press. 2011. 316 pp. | ISBN 9781607852049. | $23.99 For two decades post-anarchism has adopted an epistemological point of departure for its critique of the representative ontologies of classical anarchism. This critique focused on the classical anarchist conceptualization of power as a unitary phenomenon that operated unidirectionally to repress an otherwise creative and benign human essence. Andrew Koch may have inaugurated this trend in (...) 1993 when he wrote his influential paper entitled “Post-structuralism and the Epistemological Basis of Anarchism.” Koch’s paper certainly laid some of the important groundwork for post-anarchism’s continual subsumption of ontology beneath the a priori of an epistemological orientation, and his work continues to be cited as an early and important venture into post-anarchist philosophy. The problem is that Koch could not conceive of an anti-essentialist and autonomous ontological system, one not subject to regulation or representation by the human mind. Consequently, he was forced to assert a subjectivist claims-making ego as the foundation of a post-structuralist anarchist politics. Saul Newman was indebted to this heritage insofar as he also posited the ego (extrapolated from the writings of Max Stirner) and the subject (extrapolated from Jacques Lacan’s oeuvre ) as the paradoxical ‘outside’ to power and representation. Todd May fell into a similar trap in his book The Political Philosophy of Post-structuralist Anarchism when he wrote that “[m]etaphysics [...] partakes of the normativity inhabiting the epistemology that provides its foundations.” 1 Whereas Newman’s approach did not necessarily foreclose the possibility of metaphysics—at least to the extent that he began with the subject of the Lacanian tradition (wherein the subject is believed to be radically split between thinking and being)—May completely foreclosed the possibility of any escape from the reign of the epistemological. There laid the impasse of yesterday’s post-anarchism. This impasse at the heart of the project of post-anarchism has forced Koch, Newman, May, and many others, to come to similar conclusions about the place of ontology in post-anarchist scholarship. The post-anarchists have all formulated a response strikingly similar to Koch’s argument that any representative ontology ought to be dismantled and dethroned in favour of “a conceptualization of knowledge that is contingent on a plurality of internally consistent episteme .” 2 By dismissing all ontologies as suspiciously representative and as incessantly harbouring a dangerous form of essentialism, post-anarchists have overlooked the privilege that they have placed on the human subject, language, and discourse, at the expense of the democracy that the human subject shares with other animals, objects, and beings in the world. This epistemological characterization of post-anarchism has held sway for far too long. It is not by chance that post-anarchism, as a concept, was first formulated by Hakim Bey as an “ontological anarchism,” 3 and subsequently repressed by the canon of post-anarchist authors. Perhaps Bey’s ontological anarchism also lacked the ‘rigour’ required of today’s scholarly audience and for these two reasons (at least) he has received very little credit for his inaugurating efforts into post-anarchism. In any case, I want to challenge this reluctance and revive the roots of post-anarchism. Levi Bryant gives us a reason to believe that we can achieve the promise of Bey’s ontological anarchism without sacrificing the scholarly standard of rigour. Levi Bryant’s newest open-access book, The Democracy of Objects , is a tour de force . His book challenges post-anarchists to take their radical critique of representation a step further by questioning the “hegemony that epistemology currently enjoys in philosophy.” Bryant maintains that post-structuralism, and radical anti-humanisms, only appear to reject the subject as the locus of political agency. Their rejection is actually more of a disavowal, a replacement of the human subject with the equally human order of language or discourse. What post-structuralism attempts to elucidate is the manner in which the subject is colonized by the Other of language, discourse and social relations. What here appears as a movement away from the determining subject of humanism and existentialism is only replaced with the determining apparatuses of structures as they are conceived by astute analysts of political culture. Post-structuralism thus re-enters the anthropocentric discourse to the extent that the cultural analyst believes himself capable of conceiving the determinative structures of society. In contradistinction to the claims of post-structuralism and post-anarchism, the role of the ontologist is not to suture the gap between epistemology and the real but to de-suture it, as Bryant puts it: “[o]ntology does not tell us what objects exist, but that objects exist, that they are generative mechanisms.” Above all else, the role of ontology, for post-anarchists, ought to be a real de-centering of the subject in relation to other objects in the non-human world such that the subject becomes conceived as one object among others within a living democracy of equality. This inevitably leads to the conclusion that objects exist whether or not the subject or analyst is there to represent them: they represent themselves and are autonomous from our dictation, just as each object finds its autonomy in relation to other objects. Ontology must now be distinguished from representation. We must shift the terms of the debate and interrogate the hegemony that epistemology has been afforded within post-anarchist philosophy. At least two possibilities are now permitted. On the one hand, one could intervene into the reigning mode of philosophy, namely epistemology, by latching onto concepts from meta-ethical philosophy. Meta-ethics allows one to easily separate the ontological from the epistemological and to answer very particular questions about each in order to formulate an overarching meta-ethical position. 4 Post-anarchism is particularly adept at this task because of its resounding ability to frame itself as an ethical political philosophy in relation to the strategic political philosophy of classical Marxism. On the other hand, Bryant argues that “[p]erhaps the best way to defeat [the privilege currently held by epistemology] is to shift the terms of debate.” Shifting the terms of debate is also something that post-anarchists have been very good at doing. Thus, instead of asking the question ‘how do representative ontological systems harbour concealed epistemological orientations toward the political?’ one might ask ‘ do epistemological orientations toward the political always harbour representative and subject-centred ontological systems?” The genius of Bryant’s book rests in its ability to convincingly argue for the radical autonomy of being and of objects. This claim speaks to some of the most compelling theories of the political in anarchist and marxist political philosophy (for instance, hegemony, representation, democracy, and so on) and it re-stages the political drama of our times across a much wider terrain. The fallacy of strategic political philosophy in the Marxist tradition, as Todd May quite correctly points out, is that it remains committed to a concept of power that is unitary in its analysis, unidirectional in its influence, and utterly repressive in its effect. Similarly, Bryant’s ontology allows one to argue that there is a fallacy that occurs “whenever one type of entity is treated as the ground or explains all other entities.” Whereas May’s post-structuralist anarchism moved away from the fallacy of the unitary analysis of power, whereby subjects are constituted by the influence of a single site of power, it nonetheless remained committed to a tactical political philosophy which is monarchical in the final analysis . It remains monarchical to the extent that the human world, the world of epistemology, is treated as the yardstick of democracy. Bryant’s argument is quite instructive: “[w]hat we thus get is not a democracy of objects or actants where all objects are on equal ontological footing [...] but instead a monarchy of the human in relation to all other beings.” The real fallacy is thus not against strategic political philosophy but philosophy itself and the way it has played out over so many centuries. “The epistemic fallacy,” writes Bryant, “consists in the thesis that proper ontological questions can be fully transposed into epistemological questions.” The point that Bryant is making relates to the way ontology is today always reduced to an epistemology and thereby loses its significance as a philosophical question. This book should be applauded for its novelty and its thesis ought to be taken seriously by post-anarchists today. Because of this book, and the attendant post-continental movement that is being called ‘speculative realism,’ we can now distinguish three stages in the life of post-anarchism. First, we can deduce what Süreyya Evren has described as its ‘introductory period.’ The introductory period of post-anarchism is defined by its inability to side-step the ontological problem in the literature of classical anarchism. During this period, post-anarchism needed to distinguish itself from classical anarchism while nonetheless remaining committed to its ethical project. The second period overcomes the problem of the separation of post-anarchism from classical anarchism by re-reading the classical tradition as essentially post-anarchistic. Some of the critiques of post-anarchism—especially that from Cohn & Wilbur 5 —are included into this period insofar as post-anarchism, for them, was always already anarchism. Whereas the first and second phases have included only explicitly anarchist literature under their rubric of worthwhile investigation, in the third period this no longer holds true. To be certain, the second period permitted the incorporation of post-structuralist literature into post-anarchist discussions (but always with a certain amount of reservation). This third period, the one that is to come—the one that is already here if only we would heed its call—will not take such care with attempts at identification or canonization. Indeed, post-anarchism is already here, like a seed beneath the snow, waiting to be discovered. Levi Bryant teaches us that the third period is already here: and yet where is it? NOTES 1) Todd May. The Political Philosophy of Post-Structuralist Anarchism . University Park, PA: Pennsylvania State University Press. 1997. 2. 2) Andrew Koch. “Post-structuralism and the Epistemological Basis of Anarchism” [1993] in Post-Anarchism: A Reader . Eds. Duane Rousselle & Sureyyya Evren. London: Pluto Press. 2011. pp. 23-40. 3) Bey, Hakim. “ Post-Anarchism Anarchy .” 1987. 4) I have attempted to do this in my paper on Bataille’s post-anarchism; see Duane Rousselle. “Georges Bataille’s Post-anarchism.” Journal of Political Ideologies . 17(3): in press. 5) Jesse Cohn & Shawn Wilbur. “ What’s Wrong with Post-anarchism? ” 2010. (shrink)

The integration of digital technologies into social science has catalyzed the development of fields such as digital sociology, digital humanities, and digital social sciences more broadly. This technological shift has significant methodological implications for social science research, which are being increasingly discussed. This discussion raises critical questions about the potential and limitations of merging traditional social research methodologies with digital innovations. Digitized and digital methods have brought about promises of a new era in social science research. However, some scholars have (...) highlighted the challenges and limitations associated with this methodological transition, including data-relevant considerations, skill and expertise issues, and ethical concerns. From the vantage point of advancements in science and technology studies (STS) – a discipline that has engaged with the methods and practices of knowledge production for some decades – I will explore five additional methodological challenges posed by the digitization of social science research that has been largely overlooked or neglected in the literature of digital methods. Our analysis concludes that while digital methods can serve as valuable complementary tools, they are not sufficient to fully engage with the core practices and phenomena of social science research. Thus, digital and traditional methods can coexist, albeit not in a symmetrical manner. (shrink)

Cet article s’attache à définir la nation, en Afrique, par la notion de « révolution », c’est-à-dire d’une transformation totale de conditions anciennes – aussi bien précoloniales que coloniales – en vue de fonder des structures nationales progressistes et démocratiques. Usant de l’exemple des pays du Sahel, en particulier le Burkina Faso, le Mali et le Niger, l’article analyse cette révolution nationale comme un phénomène de cycle long, qui se déploie dans une contradiction entre un leadership politique de moins en (...) moins en adéquation avec elle, et des peuples de plus en plus conscients et exigeants quant à leurs droits civiques. Cette contradiction est par ailleurs déterminée différemment par les problèmes politiques propres au cadre urbain et au cadre rural. Elle aboutit à des luttes et contestations opposant peuples et élites qui indiquent que, si la révolution nationale est loin d’être accomplie, elle n’a pas non plus simplement avorté. (shrink)

Assuming $\mathrm{PFA}$, we shall use internally club $\omega _1$ -guessing models as side conditions to show that for every tree T of height $\omega _2$ without cofinal branches, there is a proper and $\aleph _2$ -preserving forcing notion with finite conditions which specialises T. Moreover, the forcing has the $\omega _1$ -approximation property.

The sense of agency is the experience of being the origin of a sensory consequence. This study investigates whether contextual beliefs modulate low-level sensorimotor processes which contribute to the emergence of the sense of agency. We looked at the influence of causal beliefs on ‘intentional binding’, a phenomenon which accompanies self-agency. Participants judged the onset-time of either an action or a sound which followed the action. They were induced to believe that the tone was either triggered by themselves or by (...) somebody else, although, in reality, the sound was always triggered by the participants. We found that intentional binding was stronger when participants believed that they triggered the tone, compared to when they believed that another person triggered the tone. These results suggest that high-level contextual information influences sensorimotor processes responsible for generating intentional binding. (shrink)

PREFACEProf. Göran Sundholm of Leiden University inspired the group of Logic at Lille and Valparaíso to start a fundamental review of the dialogical conception of logic by linking it to constructive type logic. One of Sundholm's insights was that inference can be seen as involving an implicit interlocutor. This led to several investigations aimed at exploring the consequences of joining winning strategies to the proof-theoretical conception of meaning. The leading idea is, roughly, that while introduction rules lay down the conditions (...) under which a winning strategy for the Proponent may be built, the elimination rules lay down those elements of the Opponent's assertions that the Proponent has the right to use for building winning strategy. It is the pragmatic and ethical features of obligations and rights that naturally lead to the dialogical interpretation of natural deduction.During the Visiting Professorship of Prof. Sundholm at Lille in (2012) the group of Lille started delving into the ways of implementing Per Martin-Löf's Constructive Type Theory with the dialogical perspective. In particular, Aarne Ranta's (1988) paper, the first publication on the subject, was read and discussed during Sundholm’s seminar. The discussions strongly suggested that the game-theoretical conception of quantifiers as deploying interdependent moves provide a natural link between CTT and dialogical logic. This idea triggered several publications by the group of Lille in collaboration with Nicolas Clerbout and Juan Redmond at the University of Valparaíso, including the publication of the book (2015) by Clerbout / Rahman that provides a systematic development of this way of linking CTT and the dialogical conception of logic. However the Clerbout / Rahman book was written from the CTT perspective on dialogical logic, rather than the other way round. The present book should provide the perspective from the other side of the dialogue between the Dialogical Framework and Constructive Type Theory. The main idea of our present study is that Sundholm's (1997) notion of epistemic assumption is closely linked to the Copy-Cat Rule or Socratic Rule that distinguishes the dialogical framework from other game-theoretical approaches. One way to read the present book is as a further development of Sundholm’s extension of Austin's (1946, p. 171) remark on acts of assertion to inference. Indeed, Sundholm (2013, p. 17) gave the following forceful formulation: When I say therefore, I give others my authority for asserting the conclusion, given theirs for asserting the premisses.Per Martin-Löf, in recent lectures, have utilized the dialogical perspective on epistemic assumptions to get out of a certain circle that threatens the explanation of the notions of inference and demonstration. A demonstration may be explained as a chain of (immediate) inferences starting from no premisses. That an inference J1... Jn—————Jis valid means that the conclusion J can be made evident on the assumption that J1, …, Jn are known. The notion of epistemic assumption thus enters in the explanation of valid inference. We cannot, however, in this explanation understand 'known' in the sense of demonstrated, for then we are explaining the notion of inference in terms of demonstration, whereas demonstration has been explained in terms of inference. Martin-Löf suggests that we here understand 'known' in the sense of asserted, so that epistemic assumptions are judgements others have made, judgements for which others have taken the responsibility; that the inference is valid then means that, given that others have taken responsbility for the premisses, I can take responsibility for the conclusion:The circularity problem is this: if you define a demonstration to be a chain of immediate inferences, then you are defining demonstration in terms of inference. Now we are considering an immediate inference and we are trying to give a proper explanation of that; but, if that begins by saying: Assume that J1, …, Jn have been demonstrated – then you are clearly in trouble, because you are about to explain demonstration in terms of the notion of immediate inference, hence when you are giving an account of the notion of immediate inference, the notion of demonstration is not yet at your disposal. So, to say: Assume that J1, …, Jn have already been demonstrated, makes you accusable of trying to explain things in a circle. The solution to this circularity problem, it seems to me now, comes naturally out of this dialogical analysis. […]The solution is that the premisses here should not be assumed to be known in the qualified sense, that is, to be demonstrated, but we should simply assume that they have been asserted, which is to say that others have taken responsibility for them, and then the question for me is whether I can take responsibility for the conclusion. So, the assumption is merely that they have been asserted, not that they have been demonstrated. That seems to me to be the appropriate definition of epistemic assumption in Sundholm's sense. One of the main tenets of the present study is that the further move of relating the Socratic Rule rule with judgemental equality provides both a simpler and more direct way to implement the constructive type theoretical approach within the dialogical framework. Such a reconsideration of the Socratic Rule, roughly speaking, amounts to the following. 1.A move from P that brings-forward a play-object in order to defend an elementary proposition A can be challenged by O. 2.The answer to such a challenge, involves P bringing forward a definitional equality that expresses the fact that the play-object chosen by P copies the one O has chosen while positing A. For short, the equality expresses at the object-languaje level that the defence of P relies on the authority given to O to be able to produce the play-objects she brings forward. More generally, according to this view, a definitional equality established by P and brought forward while defending the proposition A, expresses the equality between a play-object (introduced by O) and the instruction for building a play-object deployed by O while affirming A. So it can be read as a computation rule that indicates how to compute O's instructions. Let us recall that from the strategic point of view, O's moves correspond to elimination rules of demonstrations. Thus, the dialogical rules that prescribe how to introduce a definitional equality – correspond – at the strategic level – to the definitional equality rules for CTT as applied to the selector-functions involved in the elimination rules. So, what we are doing here is extending the dialogical interpretation of Sundholm's epistemic assumption to the rules that set up the definitional equality of a type.The present work is structured in the following way:•In the Introduction we state the main tenets that guide our book•Chapter II contains a brief overview of Constructive Type Theory penned by Ansten Klev with exercises and their solutions. •Chapter III offers a novel presentation of the dialogical conception of logic. In fact, the first two sections of the chapter provide an overview of standard dialogical logic – including solved exercises, slightly adapted to the content of the present volume. The rest of the sections develop a new dialogical approach to Constructive Type Theory. •Chapters IV and V contain the main body of our study, namely the relation between the Socratic Rule, epistemic assumptions, and equality. The chapter provides the reader with thoroughly worked out examples with comments. •After the Final Remarks the book containsa.An appendix containing a an overview of all the rules for the new formulation of dialogical approach to constructive type theory developed in the book; b.a brief outline of Per Martin-Löf's informal presentation of the demonstration of the axiom of choice.c.two examples of a tree-shaped graph of an extensive strategy. Acknowledgments: Many thanks to Mark van Atten (Paris1), Giuliano Bacigalupo (Zürich), Charles Zacharie Bowao (Univ. Ma Ngouabi de Brazzaville, Congo), Christian Berner (Lille3), Michel Crubellier (Lille3), Pierre Cardascia (Lille3), Oumar Dia (Dakar), Marcel Nguimbi ((Univ. Marien Ngouabi de Brazzaville, Congo), Adjoua Bernadette Dango (Lille3 / Alassane Ouattara de Bouaké, Côte d'Ivoire), Steephen Rossy Eckoubili (Lille3), Johan Georg Granström (Zürich), Gerhard Heinzmann (Nancy2), Muhammad Iqbal (Lille3), Matthieu Fontaine (Lille3), Radmila Jovanovic (Belgrad), Hanna Karpenko (Lille3), Laurent Keiff (Lille3), Sébastien Magnier (Saint Dennis, Réunion), Clément Lion (Lille3), Gildas Nzokou (Libreville), Fachrur Rozie (Lille3), Helge Rückert (Mannheim), Mohammad Shafiei (Paris1), and Hassan Tahiri (Lisbon), for rich interchanges, suggestions on the main claims of the present study and proof-reading of specific sections of the text. Special thanks to Gildas Nzokou (Libreville), Steephen Rossy Eckoubili (Lille3) and Clément Lion (Lille3), with whom a Pre-Graduate Textbook in French on dialogical logic and CTT is in the process of being worked out – during the visiting-professorship in 2016 of the former. Eckoubili is the author of the sections on exercises for dialogical logic, Nzokou cared of those involving the development of CTT-demonstrations out of winning-strategies. Special thanks also to Ansten Klev (Prague) for helping with technical details and conceptual issues on CTT, particularly so as author of the chapter introducing CTT. (shrink)