This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will (...) be essential reading for all those working in logic & computer science. (shrink)

We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.

ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than (...) any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent setting.

This paper presents a new modal logic for ceteris paribus preferences understood in the sense of "all other things being equal". This reading goes back to the seminal work of Von Wright in the early 1960's and has returned in computer science in the 1990' s and in more abstract "dependency logics" today. We show how it differs from ceteris paribus as "all other things being normal", which is used in contexts with preference defeaters. We provide a semantic analysis and (...) several completeness theorems. We show how our system links up with Von Wright's work, and how it applies to game-theoretic solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary modal logics. (shrink)

In _Battling to the End _René Girard engages Carl von Clausewitz, the Prussian military theoretician who wrote _On War_. Clausewitz, who has been critiqued by military strategists, political scientists, and philosophers, famously postulated that "War is the continuation of politics by other means." He also seemed to believe that governments could constrain war. Clausewitz, a firsthand witness to the Napoleonic Wars, understood the nature of modern warfare. Far from controlling violence, politics follows in war's wake: the means of war have (...) become its ends. René Girard shows us a Clausewitz who is a fascinated witness of history's acceleration. Haunted by the French-German conflict, Clausewitz clarifies more than anyone else the development that would ravage Europe. _Battling to the End _pushes aside the taboo that prevents us from seeing that the apocalypse has begun. Human violence is escaping our control; today it threatens the entire planet. (shrink)

In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We (...) also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is non-deterministic at the level of beliefs. (shrink)

This article maintains that an important class of scientific generalizations should be reinterpreted: they have typically been understood as ceteris paribus laws, but are, in fact, generics. Four arguments are presented to support this thesis. One argument is that the interpretation in terms of ceteris paribus laws is a historical accident. The other three arguments draw on similarities between these generalizations and archetypal generics: they come with similar inferential commitments, they share a syntactic form, and the existing theories to make (...) sense of them are alike. Once these generalizations are properly understood as generics, the recent cognitive approach to generics can be extended to the study of the relevant sciences. The last section indicates ways in which this extension is fruitful for the two strands of research that we combine: the philosophy of science literature on generalizations and the semantics literature on generics. (shrink)

We present a single sequent calculus common to classical, intuitionistic and linear logics. The main novelty is that classical, intuitionistic and linear logics appear as fragments, i.e. as particular classes of formulas and sequents. For instance, a proof of an intuitionistic formula A may use classical or linear lemmas without any restriction: but after cut-elimination the proof of A is wholly intuitionistic, what is superficially achieved by the subformula property and more deeply by a very careful treatment of structural rules. (...) This approach is radically different from the one that consists in “changing the rule of the game” when we want to change logic, e.g. pass from one style of sequent to another: here, there is only one logic, which—depending on its use—may appear classical, intuitionistic or linear. (shrink)

The idea of relevant logic—that irrelevant inferences are invalid—is appealing. But the standard semantics for relevant logics involve baroque metaphysics: a three-place accessibility relation, a star operator, and ‘bad’ worlds. In this article we propose that these oddities express a mismatch between non-classical object theory and classical metatheory. A uniformly relevant semantics for relevant logic is a better fit.

Le conflit des libertés constitue un problème redoutable pour toute théorie des droits fondamentaux, tant du point de vue de leur justification que de leur mise en œuvre. La théorie rawlsienne de la justice comme équité suggère une réponse originale, qui cherche à éviter tant la mise en balance des libertés que leur absolutisation rigide. Le système des libertés de base est strictement prioritaire par rapport à toute autre considération, mais les libertés elles-mêmes ne sont pas, prises individuellement, absolues : (...) elles doivent être ajustées les unes aux autres pour former un système cohérent, où les contradictions sont évitées. Elles ne sont toutefois pas négociables, car cet ajustement doit les réguler sans les restreindre. L’article reconstruit et évalue cette réponse au conflit des libertés. Il montre qu’elle n’est convaincante que si l’on renonce à l’exigence rawlsienne d’une priorité absolue du système des libertés. (shrink)

L’objection la plus ancienne et la plus redoutable à la démocratie fait valoir que le gouvernement par le peuple dessert le gouvernement pour le peuple. Les citoyens manquant pour la plupart de sagesse ou de compétence, le bien commun serait mieux assuré en confiant le pouvoir à un individu éclairé ou à une élite experte. Une réponse commune à cette objection concède la prémisse mais affirme la priorité au gouvernement par le peuple sur le gouvernement pour le peuple : le (...) droit égal à la participation devrait l’emporter sur la promotion de la compétence, même si celle-ci est requise par le bon gouvernement. La démocratie se trouve alors réduite à un ensemble de procédures équitables, traitant les citoyens en égaux ; elle ne se définit plus par la poursuite du bien commun. Il est toutefois une autre réponse à l’objection, qui évite cette dérive vers un procéduralisme étroit. Elle consiste à nier la prémisse et à affirmer la sagesse politique du peuple. Il n’est pas vrai que le gouvernement pour le peuple serait mieux assuré en confiant le pouvoir à un petit nombre de sages ou d’experts, fussent-ils les meilleurs parmi les citoyens. Cette thèse remarquable peut paraître improbable. Sa défense peut pourtant s’appuyer sur l’un des arguments les plus intrigants élaborés par la philosophie politique aristotélicienne, qui inspire et éclaire les controverses philosophiques contemporaines sur la valeur du régime démocratique : l’argument de la sagesse de la multitude. (shrink)

The COVID-19 pandemic laid bare systemic inequities shaped by social determinants of health (SDoH). Public health agencies, legislators, health systems, and community organizations took notice, and there is currently unprecedented interest in identifying and implementing programs to address SDoH. This special issue focuses on the role of medical-legal partnerships (MLPs) in addressing SDoH and racial and social inequities, as well as the need to support these efforts with evidence-based research, data, and meaningful partnerships and funding.

Standard reasoning about Kripke semantics for modal logic is almost always based on a background framework of classical logic. Can proofs for familiar definability theorems be carried out using anonclassical substructural logicas the metatheory? This article presents a semantics for positive substructural modal logic and studies the connection between frame conditions and formulas, via definability theorems. The novelty is that all the proofs are carried out with anoncontractive logicin the background. This sheds light on which modal principles are invariant under (...) changes of metalogic, and provides (further) evidence for the general viability of nonclassical mathematics. (shrink)

L’idéal démocratique est accusé d’être irréaliste. Le gouvernement du peuple par le peuple et pour le peuple serait une chimère dans les sociétés contemporaines. Il faudrait lui préférer les visées plus modestes associées à l’élection : un droit de vote égal et la satisfaction du plus grand nombre. La démocratie ne se laisse pourtant pas réduire à la compétition électorale. Les acteurs et les institutions politiques qui s’en réclament invoquent non seulement un marché, où rivalisent des intérêts privés, mais un (...) forum, où s’affrontent des visions adverses de la justice. Ils attendent de la délibération collective qu’elle serve l’autonomie politique et le bien commun, mais savent aussi qu’elle peut les menacer, lorsque la liberté, l’égalité ou la publicité lui font défaut. Cette enquête philosophique interroge la pertinence de l’idéal démocratique pour des sociétés complexes, dotées d’institutions représentatives et soumises à la communication de masse. Elle montre à quelles conditions cet idéal peut aujourd’hui orienter la critique et l’action. Les citoyens peuvent encore aspirer à se gouverner eux-mêmes, donc à délibérer en égaux. -/- The democratic ideal is accused of being unrealistic. Government of the people by the people and for the people would be a chimera in contemporary societies. The more modest aims associated with election should be preferred: equal suffrage and the satisfaction of the greatest number. But democracy cannot be reduced to electoral competition. The political actors and institutions that claim it invoke not only a market, where private interests compete, but also a forum, where opposing visions of justice confront each other. They expect collective deliberation to serve political autonomy and the common good, but they also know that it can threaten them when it lacks freedom, equality or publicity. This philosophical inquiry questions the relevance of the democratic ideal for complex societies with representative institutions and subject to mass communication. It shows under what conditions a deliberative understanding of this ideal can today orient criticism and action. Citizens can still aspire to govern themselves, hence to deliberate as equals. (shrink)

This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift (...) to non-classical logic may recast the meanings of these apparently ‘absolute’ theorems. (shrink)

Previously we reported a three-factor structure for hallucinations accompanying sleep paralysis . These earlier analyses were, however, based on retrospective accounts. In a prospective study, 383 individuals reported individual episodes online providing further evidence for the three-factor structure as well as clearer conceptually meaningful relations among factors than retrospective studies. In addition, reports of individual episodes permitted a more fine-grained analysis of the internal structure of factors to assess predictions based on the hypothesis that a sensed or felt presence is (...) a core experience affecting other SP hallucinations. Results were generally consistent with this hypothesis. In particular, associations among, and temporal stability of, sensory hallucinations were largely explained by their common association with FP. The findings are consistent with REM initiation of a threat activated vigilance system with pervasive effects on the SP experience and suggest a potential model for the thematic organization of nightmares and dreams more generally. (shrink)

These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting (...) with Godel's paradox --so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination. Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction, all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way. (shrink)

The semantics for counterfactuals due to David Lewis has been challenged by appealing to miracles. Miracles may skew a given similarity order in favour of those possible worlds which exhibit them. Lewis responded with a system of priorities that mitigates the significance of miracles when constructing similarity relations. We propose a prioritised ceteris paribus analysis of counterfactuals inspired by Lewis’ system of priorities. By analysing the couterfactuals with a ceteris paribus clause one forces out, in a natural manner, those possible (...) worlds which do not satisfy the requirements of the clause, thus excluding miracles. If no world can satisfy the ceteris paribus clause in its entirety, then prioritisation is triggered to select worlds that maximise agreement on those things which are favoured most. (shrink)

Hervaeus Natalis distinguishes two types of items that can have esse obiective in the intellect: objects of acts of intellection (man, this cat, etc.) and properties unapprehended by these acts, or background properties (being a species, being a particular, etc.), that are beings of reason. Yet, his conception of the esse obiective of objects evolved. First, he had a neutral conception of esse obiective: items presenting themselves to the intellect are cognized, transparently, without being altered in the process. Later, he (...) developed an ontologically committing conception of the objective being of objects: items presenting themselves to the intellect take on rational being (esse rationis) as such. This evolution transpires because Hervaeus introduces intentional relations as what makes the cognized item be objectively in the intellect and includes them within the class of background properties (being of reason). Both these conceptions manage to account for our access to extra-mental things. -/- . (shrink)

Go back to An-fang, the Peace Square at An-Fang, the Beginning Place at An-Fang, where all things start (… ) An-Fang was near a city, the only living city with a pre-atomic name (… ) The headquarters of the People Programmer was at An-Fang, and there the mistake happened: A ruby trembled. Two tourmaline nets failed to rectify the laser beam. A diamond noted the error. Both the error and the correction went into the general computer. Cordwainer SmithThe Dead Lady (...) of Clown Town, 1964. (shrink)

Many contemporary philosophies of democracy agree that public deliberation plays an essential role in the making of legitimate political decisions. However, this consensus masks significant disagreement concerning the exact source of its value, as it is alternatively located in its impact on participants, in its expressive value, in its fairness, or in the quality of the decisions it produces. These rival justifications of democratic deliberation have different, and sometimes contradictory, consequences for political practices and institutions. This article analyses these justifications (...) to decide between them and to clarify how they relate to each other. It develops an original justification of democratic deliberation by showing that it treats citizens fairly as listeners if not speakers. While it is not certain that democratic deliberation makes it in general more likely to reach a good decision, it makes the conditions for political judgement less unequal. (shrink)

Investigation of “out-of-body experiences” has implications for understanding both normal bodily-self integration and its vulnerabilities. Beyond reported associations between OBEs and specific brain regions, however, there have been few investigations of neurochemical systems relevant to OBEs. Ketamine, a drug used recreationally to achieve dissociative experiences, provides a real-world paradigm for investigating neurochemical effects. We investigate the strength of the association of OBEs and ketamine use relative to other common drugs of abuse. Self-report data from an online survey indicate that both (...) lifetime frequency of ketamine use and OBEs during ketamine intoxication were more strongly related to the frequency of OBEs and related phenomena than other drugs. Moreover, the apparent effects of other drugs could largely be explained by associated ketamine use. The present results, consistent with the role of NMDA receptors in OBEs, should encourage future studies of the role of neurochemical systems in OBEs. (shrink)

Ludics [1] is a novel approach to logic—especially proof-theory. The present introduction emphasises foundational issues.For ages, not a single disturbing idea in the area of “foundations”: the discussion is sort of ossified—as if everything had been said, as if all notions had taken their definite place, in a big cemetery of ideas. One can still refresh the flowers or regild the stone, e.g., prove technicalities, sometimes non-trivial; but the real debate is still: this paper begins with an autopsy, the autopsy (...) of the foundational project.Up to say 1900, the realist/dualist approach to science was dominant; during the last century some domains like physics evolved so as to become completely anti-realist; but this evolution hardly concerned logic.By the turn of the XXth century mathematics was jeopardised by paradoxes, the most famous of them being due to Russell. Hilbert's reaction was to focus on consistency. But the reduction of paradoxes—and therefore of foundations—to solely the antinomies is highly questionable: indeed, the typical paradoxical artifacts are secret sharers, objects satisfying the formal definitions but far astray from the intended meaning, typically the Peano “curve” which contradicts our perception of dimension. Fortunately, topology has been able to show that dimension m is not the same as dimension n … but just for a second, forget this and imagine consistent mathematics in which balls in any dimension are homeomorphic: what a disaster! This exclusive focus on consistency—not to speak of the strategic failure of the Programme—should explain why logic, especially foundations lost contact with other sciences during last century. (shrink)

We present a generalization of Segerberg's onion semantics for belief revision, in which the linearity of the spheres need not occur. The resulting logic is called broccoli logic. We provide a minimal relational logic, with a bi-modal neighborhood semantics. We then show that broccoli logic is a well-known conditional logic, the Burgess-Veltman minimal conditional logic.

Mill’s claim that representative government can be democratic, and as such “the ideally best form of government”, rests on the virtues of public deliberation, which he sees both as a means for pursuing just political decisions and as a means of participation for the widest citizenry. His view has been criticized, by Schmitt in particular, for assuming that free discussion can dissolve the conflict of social forces and that it leads to the discovery of the truth. But does it really (...) depend on such premises? The focus of the paper is the tension between the search for truth and the need for inclusion in Mill’s theory of representative government. An examination of the role played by freedom of discussion suggests that far from sublimating social conflict or guaranteeing the correctness of political decisions, the deliberative process regulates the conflict of opinions, understood as a violent struggle over truth, on an egalitarian basis. (shrink)

Standard modal logic for alethic modalities analyses modalities as ranging over all possible worlds. This leaves very little room in the space of worlds to entertain impossible things. My proposal is to liberate the Leibnizian universe and reinforce the relative aspect of possibility; worlds are possible with respect to some worlds, and impossible for others. The central idea is to isolate relative possibility from conditionality. To accommodate counterpossibles, I provide a dialetheic conditional modal logic, a theory that is dialetheic at (...) every level, in the logic as well as in the set theory behind it. (shrink)

Unmet legal needs contribute to housing, income, and food insecurity, along with other conditions that harm health and drive health inequity. Addressing health injustice requires new tools for the next generations of lawyers, doctors, and other healthcare professionals. An interprofessional group of co-authors argue that law and medical schools and other university partners should develop and cultivate Academic Medical-Legal Partnerships (A-MLPs), which are uniquely positioned to leverage service, education, and research resources, to advance health justice.