Although Plesu started his career as an art historian, he soon came under the influence of Constantin Noica, a major Romanian thinker who had tried to combine Platonism with a rather idiosyncratic form of existentialism. Plesu was briefly a minister for culture in the first post-revolutionary Romanian cabinet, and thereafter worked as an editor and as an educator; he is currently the president of a small private graduate international college in Bucharest. He is the author of a number of (...) books in which he draws intriguingly from material in art, religion, philosophy, and sometimes politics. The current volume, his most recent, is a case in point. (shrink)

In the period between Constantine's reunification of the Empire in 324 and the deposition of Romulus Augustulus in 476 M. Valerius Probus enjoyed a large reputation as master of all areas of the ars grammatica. The commentary on Terence attributed to Donatus and the commentary of Servius on Virgil cite him more often than they do any other ancient authority. His fame persisted through the Dark Ages. Eugenius of Toledo set him with Varius and Tucca against Aristarchus, the greatest (...) of the Alexandrian students of Homer. Modern writers on the history of Roman scholarship have estimated in widely different ways his quality as a textual critic, the level of his reputation during the century after his death and the influence which his activities had on the transmission of the Latin classics. That he ‘annotated’ at least some of these in the manner of an Aristarchus is not in dispute, but everything about the nature of his ‘annotation’ is. This paper will treat afresh a famous statement about Probus in Suetonius' De grammaticis, two lists of notae associated with Probus’ name in a late eighth-century manuscript from Monte Cassino, cod. Paris, Bibl. Nat. lat. 7530, two references to such notae which have been detected in Virgilian scholia and a number of statements in these scholia which appear to give Probus’ reasons for affixing notae. The results of my study are largely negative but may help to control general discussion of the history of a number of Latin texts. (shrink)

In this article, the author examines Romanian child protection reforms during European Union accession as a case of externally facilitated modernization aimed at solving acute social problems. The data for this case study came primarily from fifty-three unstructured interviews with civil servants, civil society representatives, and EU officials. The author finds that in a similar manner to other externally driven modernization projects, the belief according to which Western institutions constituted a universal blueprint, applicable regardless of particular contexts and historical legacies, (...) led to unintended consequences. What is more, because the reformers did not envisage that Western institutions might carry their own pathologies, they ended up replicating some of these pathologies. The study suggests that the goal of externally facilitated public policy should not be to create replicas of Western institutions but to spur local innovation that takes advantage of successful Western institutional logics. (shrink)

This article aims to investigate, from an interdisciplinary point of view, the concept of parliamentary immunity. The main objective of this inquiry is to identify the historical premises and the political, linguistic, and legal instruments that determined the conceptualization of parliamentary immunity in light of the main intellectual events in Romania and France. Embracing Reinhart Koselleck's working methods, this research will develop _in extenso_ a comparative conceptual analysis based on methodological rigor, emphasizing not only the importance of the concept after (...) its entry into national languages, but also the political usages of the concept and the present understandings of it. (shrink)

The typical approach to decoding speech from the brain (using brain-machine interfaces) is to decode low-level linguistic units (e.g. phonemes, syllables) from motor articulation areas (e.g. Premotor cortex) with the aim of assembling these low-level units into higher-level discourse. We propose that brain-to-speech decoding may benefit from adopting a functional view of language, which conceives of language as an instrumental tool for interacting with others' intentions in order to fulfil one's own intentions. This functional view of language motivates adopting usability (...) (i.e. the decoder's usefulness as a tool for achieving goals), in addition to decoding accuracy, as a criterion for assessing decoder performance. Decoders may achieve gains in usability by incorporating data about communicative situations and speaker intentions in order to generate and fill in speech act templates. We suggest that this intention-oriented, template-based, and functionally inspired view of brain-to-speech decoding may facilitate efforts to achieve naturalistic speech decoding. (shrink)

COnstantien Sandis speaks to Nassim Taleb about inductive knowledge,black swans, Hume, Popper, and Wittgenstein.

Review the Istvan Kiraly V.'s book: Death and History.

Modern societies are characterized by a division of epistemic labor between laypeople and epistemic authorities. Authorities are often far more competent than laypeople and can thus, ideally, inform their beliefs. But how should laypeople rationally respond to an authority’s beliefs if they already have beliefs and reasons of their own concerning some subject matter? According to the standard view, the beliefs of epistemic authorities are just further, albeit weighty, pieces of evidence. In contrast, the Preemption View claims that, when one (...) discovers what an authority believes, it is not permissible to rely on any of one’s own reasons concerning the subject matter. The original version of this view, as proposed by Linda Zagzebski, has recently been severely criticized for recommending blind trust and for abandoning even minimal standards for critical thinking. In our paper, we defend a new version of the Preemption View—Defeatist Preemptionism—in a way that differs radically from Zagzebski’s. We argue that our view can be derived from certain widely accepted general epistemic principles. In particular, we claim that preemption can be identified as a special case of source sensitive defeat. Moreover, we argue that Defeatist Preemptionism does not lead to the undesirable consequences that critics ascribe to the Preemption View. The paper thus articulates the foundations and refinements of the Preemption View, such that it adequately captures the phenomenon of epistemic authority and the rational requirements related to it. (shrink)

Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules for (...) the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s (2013) local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e. non-compact. Consequently, I reconsider the use of the ω-rule and I show that the addition of the ω-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement. (shrink)

The anthology contains twenty-two essays and is divided into two parts. The essays are, in the main, critical responses to aspects of what has come to be known in action theory as the ‘Standard View’ – the view that traces back to Donald Davidson's contribution to twentieth-century philosophy of action. The view under criticism treats actions as bodily movements caused in a non-deviant way by belief–desire pairs, construes these belief–desire pairs as the primary reasons for the actions that they cause, (...) and embraces event-causality.The issue of how we should conceive of action is taken up in several essays. For example: in Essay 1, Fred Dretske challenges the view that actions are external events that are the effect of the reasons for which the action is done. In Essay 16, Helen Steward, proposes that, instead of treating the availability of a reason-giving explanation as essential to action, we should construe action as ‘an exercise of the power of bodily control by an animal’. In Essay 21, Jonathan Dancy argues for a deflationary approach to actions, which forgoes treating actions ‘as individuals, with identity conditions’.Other authors – for example, Stephen Everson, Rowland Stout and Maria Alvarez – focus on the issue of what reasons for action are. Are they psychological states, or propositions, or states of affairs? Also under review is how to distinguish different kinds of reason: normative and explanatory reasons, and even explanatory and motivating reasons. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

Is knowledge-how, or “practical” knowledge, a species of knowledge-that, or “theoretical” knowledge? There is no comfortable position to take in the debate around this question. On the one hand, there are counterexamples against the anti-intellectualist thesis that practical knowledge is best analysed as an ability. They show that having an ability to ϕ is not necessary for knowing how to ϕ. On the other hand, the intellectualist analysis of practical knowledge as a subspecies of theoretical knowledge is threatened by its (...) own set of counterexamples, which convincingly establish that practical knowledge lacks many of the typical characteristics of theoretical knowledge. Most strikingly it does not even appear to require a belief. In this paper, I develop an account of practical knowledge that avoids these counterexamples. It also manages to preserve both the status of such knowledge as a cognitive achievement and its apparently close conceptual relation to abilities. I start with the counterexamples against the necessity of abilities for practical knowledge and show that they fail because they underestimate the cognitive demands of attempts. I then make use of the logic of dispositions to bridge the gap that counterexamples against the necessity of abilities for practical knowledge open. It is argued that, instead of the ability to ϕ, it is a specific disposition to have the ability to ϕ that constitutes practical knowledge about ϕ. The resulting theory is an anti-intellectualist position that preserves essential intellectualist motivations and thus should be satisfactory for proponents of both views. (shrink)

In his 1995 book Colour vision (New York: Routledge), Evan Thompson proposes a new approach to the ontology of color according to which it is tied to the ecological dispositions-affordances described by J.J. Gibson and his followers. Thompson claims that a relational account of color is necessary in order to avoid the problems that go along with the dispute between subjectivists and objectivists about color, but he claims that the received view of perception does not allow a satisfactory relational account (...) of color. Hence to avoid the problems of the subjectivist/objectivist dispute one must abandon the received view of perception. I describe an account which is similar to Thompson's, but which invokes instead the physical dispositional properties described by the received view. All of the distinguishing characteristics that Thompson claims separate his ecological dispositions from physical dispositions are in fact found in the physical dispositions appealed to by my proposed theory. Because my proposed theory is similar to subjectivism, Thompson's departure from the received view is not as radical as he claims. In a final section I describe the a posteriori manner in which a substantive departure from the received view must be carried out by describing an example of ecological experimentation. (shrink)

This paper examines the relation between the various forces which underlie human action and verbal reports about our reasons for acting as we did. I maintain that much of the psychological literature on confabulations rests on a dangerous conflation of the reasons for which people act with a variety of distinct motivational factors. In particular, I argue that subjects frequently give correct answers to questions about the considerations they acted upon while remaining largely unaware of why they take themselves to (...) have such reasons to act. Pari passu, experimental psychologists are wrong to maintain that they have shown our everyday reason talk to be systematically confused. This is significant because our everyday reason-ascriptions affect characterizations of action that are morally and legally relevant. I conclude, more positively, that far from rendering empirical research on confabulations invalid, my account helps to reveal its true insights into human nature. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

This paper seeks to develop a phenomenological account of the disorientation of grief, specifically the relationship between disorientation and the breakdown in practical self-understanding at the heart of grief. I argue that this breakdown cannot be sufficiently understood as a breakdown of formerly shared practices and habitual patterns of navigating lived-in space that leaves the bereaved individual at a loss as to how to go on. Examining the experience of losing a loved person and a loved person-to-be, I instead propose (...) that this breakdown should be understood primarily in relation to a distinctive kind of futurity operative in disorientation,irrespectiveof the extent to which there is a breakdown of formerly shared practices and habitual patterns of navigating lived-in space. Drawing on the resources afforded by Heidegger’s phenomenology, I argue that it is acore characteristicof the experience of disorientation in grief that the grieving person can no longer meaningfully press ahead into aspecific futural self. This view comes with certain advantages over existing accounts of the temporality of grief for making sense of the disorientated relationship to futurity, which the appeal to Heideggerian resources makes possible. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

Interview with Constantine Sigov, dedicated to the history of the "European Dictionary of Philosophies": from the emergence of an idea in the early 90's in France until the accomplishment of the Ukrainian edition in 2019.

The Things We Do and Why We Do Them argues against the common assumption that there is a kind of thing called "action" which all reason-giving explanation of action are geared towards. Sandis explains why all theories concerned with the form which any such explanation must take fail from the outset, and shows how various debates on the nature of so-called motivating reasons only arise because the participants all share a number of mistaken views which follow from the basic assumption (...) under attack. In so doing, he urges philosophers and psychologists alike to stop asking whether the explanation of action is causal, and to focus instead on its multifarious objects. This book will appeal to anyone interested in motivational psychology, the reasons for which we act, and the philosophy of explanation in general. (shrink)

Hinge Epistemology is rapidly becoming one of the most exciting areas of epistemology and Wittgenstein studies. In connecting these two fields it brings a revived energy to both, opening them up to fresh developments. The essays in this volume extend the subject in terms of both depth and breadth. They present new voices and challenges within hinge epistemology. They explore new applications and directions of hinge epistemology, particularly as it relates to the philosophy of mind, society, ethics, and the history (...) of ideas. (shrink)

Vann McGee has recently argued that Belnap’s criteria constrain the formal rules of classical natural deduction to uniquely determine the semantic values of the propositional logical connectives and quantifiers if the rules are taken to be open-ended, i.e., if they are truth-preserving within any mathematically possible extension of the original language. The main assumption of his argument is that for any class of models there is a mathematically possible language in which there is a sentence true in just those models. (...) I show that this assumption does not hold for the class of models of classical propositional logic. In particular, I show that the existence of non-normal models for negation undermines McGee’s argument. (shrink)

With AI permeating our lives, there is widespread concern regarding the proper framework needed to morally assess and regulate it. This has given rise to many attempts to devise ethical guidelines that infuse guidance for both AI development and deployment. Our main concern is that, instead of a genuine ethical interest for AI, we are witnessing moral diplomacies resulting in moral bureaucracies battling for moral supremacy and political domination. After providing a short overview of what we term ‘ethics washing’ in (...) the AI industry, we analyze the 2021 UNESCO Intergovernmental Meeting of Experts (Category II) tasked with drafting the Recommendation on the Ethics of Artificial Intelligence and show why the term ‘moral diplomacy’ is better suited to explain what is happening in the field of the ethics of AI. Our paper ends with some general considerations regarding the future of the ethics of AI. (shrink)

Die Untersuchung stellt die Psychologie und Psychiatrie des jungen Kant vor, die im Rahmen seiner Auseinandersetzung mit dem schwedischen Gelehrten, Mystiker und Geisterseher Emanuel von Swedenborg entstanden ist. Hieraus ging Kants Wahnkritik hervor, in der er die drei Aspekte der Schizophrenie die Projektion, die Ich-Spaltung sowie die Paranoia analysiert. Constantin Rauer zeigt, dass und wie Kant seine fruhe Wahnkritik in die spatere Vernunftkritik ubertragen hat, und wie sich durch diese Anwendung der Psychologie auf die Logik das vollzog, was spater (...) Kants kritische Wende genannt wurde. Damit vollzieht der Autor erstmals Kants Revolution der Denkungsart und mit dieser die Genese seiner Kritik der reinen Vernunft systematisch nach. So fuhrt seine Untersuchung zu einem neuen Kant-Verstandnis, indem sie zeigt, dass Kants Vernunftkritik auch als eine Anti-Wahnkritik zu verstehen ist. Mit seiner Kritik des Wahns aber zielt Kant auf die verborgene Irrationalitat der Moderne: auf den erkenntnistheoretischen Wahn des Empirismus, den ethischen Wahn des Sozialdarwinismus sowie den religiosen Wahn im Kulturrelativismus. "Die Arbeit ist klar und uberzeugend aufgebaut. Uberdies ist sie sehr gut lesbar geschrieben: klar, zupackend, argumentativ, immer wieder von erhellenden Bildern durchsetzt; und die Verbindung einer wohldurchdachten Interpretation und Argumentation mit einer neuartigen These fuhrt zu einem philosophisch geradezu spannenden Text.... Hier findet eine hochentwickelte internationale Kantforschung einen grundlegend neuen Blick." ". (shrink)

K. R. Popper distinguished between two main uses of logic, the demonstrational one, in mathematical proofs, and the derivational one, in the empirical sciences. These two uses are governed by the following methodological constraints: in mathematical proofs one ought to use minimal logical means (logical minimalism), while in the empirical sciences one ought to use the strongest available logic (logical maximalism). In this paper I discuss whether Popper’s critical rationalism is compatible with a revision of logic in the empirical sciences, (...) given the condition of logical maximalism. Apparently, if one ought to use the strongest logic in the empirical sciences, logic would remain immune to criticism and, thus, non-revisable. I will show that critical rationalism is theoretically compatible with a revision of logic in the empirical sciences. However, a question that remains to be clarified by the critical rationalists is what kind of evidence would lead them to revise the system of logic that underlies a physical theory, such as quantum mechanics? Popper’s falsificationist methodology will be compared with the recently advocated extension of the abductive methodology from the empirical sciences to logic by T. Williamson, since both of them arrive at the same conclusion concerning the status of classical logic. (shrink)

Moral particularism is often conceived as the view that there are no moral principles. However, its most fêted accounts focus almost exclusively on rules regarding actions and their features. Such action-centred particularism is, I argue, compatible with generalism at the level of character traits. The resulting view is a form of particularist virtue ethics. This endorses directives of the form ‘Be X’ but rejects any implication that the relevant X-ness must therefore always count in favour of an action.

Our technological lifeworld has become an info-computational media populated by data and algorithms, an artificial environment for life and shared experiences. In this chapter, I tried to sketch three new assumptions for bioethics – it is hardly possible to substantiate ethical guidelines or an idea of normativity in an aprioristic manner; moral status is a function of data entities, not something solely human; agency is plural and thus is shared or sometimes delegated – in order to chart a proposal for (...) a posthuman bioethics. Posthuman is perhaps not the best expression available, but it covers the idea of a shift from a world centered on self-contained and exclusively human agency to a more comprehensive and relational way of thinking. The “posthuman” label should be understood as a rebuttal of biocentrism and anthropocentrism by moving closer to conceptions we encounter in population ethics or in discourse about biosocial and technical systems. Posthuman bioethics is “environmentalist” without losing the humanistic stance. The question regarding how suitable an infocentric bioethics is in practice remains to be settled. The moral principles in bioethics could be reconceived as relying on these new assumptions, in a postindividualistic manner that accepts formal primacy of causal digital artifacts in affording actions in a world of ambient algorithmic intelligence. (shrink)

A solid cast of contributors present the first collection of essays on the Philosophy of Action.

In this paper, I present a solution to the problem that the need to accommodate the phenomenon of epistemic defeat poses for reliabilism. Defeaters are supposed to remove justification for previously justified beliefs. According to standard process reliabilism, the justification of a belief depends on the reliability of a process that is already completed when a defeater for that belief is obtained. It is hard to see, then, how a defeater can affect reliabilist justification, if that justification, from the perspective (...) of the defeater, lies wholly in the past. What is more, undercutting defeaters plausibly defeat by generating incompatibilities with higher-order propositions :105–118, 2014; Melis in Philos Stud 170:433–442, 2014). This is hard to integrate with reliabilism which explicitly denies higher-order conditions for justification. I argue that both of these phenomena can be accommodated by it via what I call the “Replacement Principle”: when a defeater is obtained, it generates either a logical incompatibility or a doxastic incompatibility. The resulting tension is registered and initiates a reasoning process that compares the epistemic support for the defeater with that for the defeated belief. This process may replace the original reliable formation process as a doxastic base for the defeated belief. If the defeater is not given its due weight in the reasoning process, that process was unreliable and if the defeated belief is retained as a result, it will be unjustified. This is intuitively the right result. Since reasoning is reliable, only if it is rational, the account manages to capture the intuition that disregarding a defeater would be irrational without having to make rationality a condition for justification. Replacement is not only plausible on causal pictures of doxastic basing, but also required in order to allow for the possibility of belief reevaluation in general and is therefore not an ad hoc addition to reliabilism, but rather part of its inherent explanatory resources. (shrink)

This essay is motivated by the thought that the things we do are to be distinguished from our acts of doing them. I defend a particular way of drawing this distinction before proceeding to demonstrate its relevance for normative ethics. Central to my argument is the conviction that certain ongoing debates in ethical theory begin to dissolve once we disambiguate the two concepts of action in question. If this is right, then the study of action should be accorded a far (...) more prominent place within moral philosophy than previously supposed. I end by considering an extension of the above to aesthetic evaluation and,mutatis mutandis, that of our lives in general. (shrink)

Deleuze and Philosophy provides an exploration of the continuing philosophical relevance of Gilles Deleuze. This collection of essays uses Deleuze to move between thinkers such as Plato, Aristotle, Husserl, Hume, Locke, Kant, Foucault, Badiou and Agamben. As such the reader is left with a comprehensive understanding not just of the philosophy of Deleuze but how he can be situated within a much broader philosophical trajectory. Constantin Boundas has gathered together recent scholarship on Deleuze's philosophy by an acclaimed line-up of (...) international contributors, all of whom seek to provide new and previously unexplored theoretical terrains that will be of interest to both the Deleuze specialist and student alike. Three of the essays are by key French Deleuzians whose work is not widely available in translation. This enticing collection is essential reading for anyone interested not just in Deleuze but in the history of philosophical ideas. Contributors include: Zsuzsa Baross, Veronique Bergen, Ronald Bogue, Bruce Baugh, Rosi Braidotti, Claire Colebrook, Bela Egyed, Philippe Mengue, Dorothea Olkowski, Davide Panagia, Daniel W. Smith, Jeremie Valentin, Arnaud Villani. (shrink)

A number of well-developed theories shed light on the question, under what circumstances our beliefs enjoy epistemic justification. Yet, comparatively little is known about epistemic defeat--when new information causes the loss of epistemic justification. This book proposes and defends a detailed account of epistemic defeaters. The main kinds of defeaters are analyzed in detail and integrated into a general framework that aims to explain how beliefs lose justification. It is argued that defeaters introduce incompatibilities into a noetic system and thereby (...) prompt a structured re-evaluation process that makes a justified reinstatement of the defeated belief impossible. The account is then applied to the topic of disagreement, where it is used in an argument for conciliationism, as well as a new explanation for higher-order defeat. Throughout the book, the notion of defeat is the center of attention, while a number of new issues are discussed at the intersections of defeat and justification. Specifically, new problems are raised for broadly internalist accounts of defeat, a fully descriptive reliabilist account of defeat is provided, and the case for normative defeat is revisited. (shrink)

This chapter contains sections titled: Basic Actions Action Individuation References Further reading.

Gilles Deleuze: The Intensive Reduction brings together eighteen essays written by an internationally acclaimed team of scholars to provide a comprehensive overview of the work of Gilles Deleuze, one of the most important and influential European thinkers of the twentieth century. Each essay addresses a central issue in Deleuzeʹs philosophy (and that of his regular co-author, Félix Guattari) that remains to this day controversial and unsettled. Since Deleuzeʹs death in 1994, the technical aspects of his philosophy have been largely neglected. (...) These essays address that gap in the existing scholarship by focusing on his contribution to philosophy. Each contributor advances the discussion of a contested point in the philosophy of Deleuze to shed new light on as yet poorly-understood problems and to stimulate new and vigorous exchanges regarding his relationship to philosophy, schizoanlysis, his aesthetic, ethical and political thought. (shrink)

We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated lattice.