Husserl: Philosophy of Logic

Translator's Preface LA LOGIQUE DE HUSSERL, etude sur "Logique for- melle et logique transcendentale" the original of the present translation, was published ...

This paper analyzes and compares the attempts at solving the paradox of non-existence put forward by Alexius Meinong and Edmund Husserl. It will be argued that Meinong’s solution is not convincing since he retreats from the field of predicate logic, in which the paradox arises, to a version of propositional logic. On the other hand, Husserl´s approach is more promising since he moves forward to an extension of predicate logic, in which judgments may be evaluated in relation to different contexts (...) or, in Husserl´s terminology, “spheres”. More precisely, to Husserl, existential judgments have to be interpreted as a kind of cross-sphere judgments, and thus existence fulfills a function loosely analogous to that of modal operators in possible-worlds semantics. (shrink)

Husserl and the Logic of Experience includes both detailed work on particular aspects of logical theory (such as an inquiry into the status of the principle of excluded middle) and also detailed investigations into the nature of the logic of temporal conceptions. Demonstrating the cultural import of Husserl's work while also showing its continuing significance for logical theory, this collection is a milestone in the study of transcendental phenomenology.

Husserl war wie die meisten Logiker seiner Zeit vor allem am apophantischen Sprachgebrauch, an der logischen Problematik des Urteils, interessiert : mehr als seine Vorgänger und Zeitgenossen jedoch hat er sich auch eingehend mit der Problematik des nicht-apophantischen Sprachgebrauchs, im besonderen mit Logik und Genealogie der Frage beschäftigt. Im ersten Teil dieses Beitrags wird ein Uebersicht über die Positionen seiner Zeitgenossen und Vorgänger in diesem Bereich gegeben : implizit oder explizit hat Husserl gegen diese Auffassungen, in der Weise einer mittelalterlichen (...) „quaestio”, polemisiert. Im zweiten Teil wird Husserls frühe Theorie (Logische Untersuchungen), im dritten Teil seine spätere Theorie (Ideen, Analyses zur passiven Synthesis und „Erfahrung und Urteil”) analysiert. Die erste Theorie gibt eine reinlogische Analyse des Frageverhaltens, wobei ihre sprachliche und kommunikative Bedeutung auf den Hintergrund bleibt. Die späteren Darlegungen befassen psychologische Betrachtungen über die Genese von Fragen im Bewustsein und über ihre Bedeutung im Erkenntnisprozess. Im letzten Teil wird versucht sowohl der primären phänomenale Gegebenheit von Fragen u. dgl. als Sprechakt Rechnung zu tragen, wie auch den Elementen einer „erotetischen Logik”, die in der Denkwelt Husserl und seiner Vorgänger und Zeitgenossen nicht oder nur ungenügend figurieren. Eine vollständige Phänomenologie des Fragens umfasst nicht nur logisch- und psychologischphänomenologische Betrachtungen, sondern auch „pragmatische” : ihre sprachliche und kommunikative Aspekte sind nicht von neben sächlicher, sondern von essentieller Bedeutung. Will man vollständig verstehen was Fragen „bedeutet”, so muss man sich jedoch dem Problem des Fragenden und In-Frage-gestelten Menschen zuwenden. Das wird, am Leitfaden der Phänomenologie von Heidegger und Levinas, von Sartre und Merleau-Ponty, aber auch von Gadamer, Jaspers und anderen zeitgenössischen Autoren, in einen Beitrag auseinandergesetzt welche im Anschluss an diesem erscheinen wird. (shrink)

This dissertation deals with the ways in which Husserl and Heidegger as phenomenologists are guided by the commitment to a logical theory of science. It considers the internal relationship between, respectively, Husserlian and Heideggerian phenomenology and a conception of logic that would link phenomenological philosophy of logic to the contemporary definition of this discipline. The dramatic transition in the modern history of logic is played out explicitly in Husserl's conception of formal theory of science, which hinges on his idea of (...) formal ontology, and implicitly in Heidegger's conception of a fundamental ontology that would ultimately engender a new idea of logic. Their respective conceptions of formal and fundamental ontology intersect in the way they both understand "world" as phenomenological pre-condition for any higher level meaning constitution. The synthetic structure of worldly experience serves as protological basis for any formal- or natural-linguistic interpretation of scientific activity. In short, it is the way that Husserl and Heidegger understand the relationship between logic and ontology that allows them to work within the philosophical presuppositions of modern logic and eventually to generate a critique that points beyond phenomenology to this tradition---the contemporary history of logic from meta-mathematics to philosophy of language. ;Beginning with a methodological discussion of phenomenological meaning-investigation, i.e. Besinnung, the dissertation then proceeds from Husserl's initial engagement with formal logic and mathematics up to a conception of logic that would eventually make possible a dialogue between Heidegger and more recent philosophy of language. Between Husserl and Heidegger, it is the very object of logic that is at stake, i.e. whether logic is concerned primarily with the interpretation of formal-theoretical systems or with the analysis of discourse understood in terms of natural language. Yet reading Husserl and Heidegger through the phenomenology of logic also sketches a possibility for reading them together that has gone largely unexplored. Despite the ways in which their respective projects in phenomenology are often viewed as incommensurable, their phenomenology of logic leads back to a common commitment to a proto-logical conception of meaning based in principles of passive constitution. (shrink)

This explorative article is organized around a set of questions concerning the concept of a function. First, a summary of certain general facts about functions that are a common coin in contemporary logic is given. Then Frege's attempt at clarifying the nature of functions in his famous paper Function and Concept and in his Grundgesetze is discussed along with some questions which Freges' approach gave rise to in the literature. Finally, some characteristic uses of functional notions to be found in (...) the work of Bernard Bolzano and in Edmund Husserl's early work are presented and elucidated. (shrink)

"Husserl's work include lengthy treatment of universals, categories, meanings, numbers, manifolds, etc. from an ontological perspective. Here, however, we shall concentrate almost exclusively on the Logical Investigations, which contain in a clear form the ontological ideas which provided the terminological and theoretical basis both for much of the detailed phenomenological description and for many of the metaphysical theses presented in Husserl's later works.

In this piece of work we considerer mathematical logic as a whole. The three steps distinguished by Husserl, to wit, pure logic grammar, logic of the non-contradiction and logic of the truth, are analysed. They are applied to the logistics by distinguishing different levels and layers. In each level the logistics methods and its correspondence with the formal ontology inside the philosophical phenomenology are taken into account. The subject is completed explaining the axiomatic as well as the Greek life in (...) Euclides and in comparison with Hilbert. Finally, we intend to interpret the Greek logic, Leibniz logic and logistics from the viewpoint of different types of life related to them. In all these cases we presuppose, as a source, the apofantic aristotelian form of the proposition. (shrink)

Résumé — Dans cet article, je postule qu’il y a plusieurs variétés d’antipsychologisme logique, auxquelles correspondent différents concepts de « logique pure ». Deux conceptions sont ici confrontées : la « logique de l’idéalité » de Husserl et la « logique de la validité » de Rickert. Contrairement à l’emploi équivoque des termes « validité » et « idéalité » chez Heidegger, je montre d’abord que ces deux conceptions, bien que très proches, ne sont pas parfaitement superposables, car Rickert partage (...) l’antipsychologisme de Husserl mais rejette sa théorie des significations. Il apparaît ensuite que cette divergence – particulièrement visible dans la recension inédite, par Rickert, du livre très controversé de Palágyi – touche en réalité un « point faible » des Recherches logiques de Husserl : la confusion entre les objets logiques et les idéalités mathématiques. L’alternative « axiologique » proposée par Rickert évite d’emblée cette confusion en soutenant que le sens logique des propositions, fondé sur de pures « valeurs théoriques », est irréductible à un objet idéal.— In this article, I postulate that there are several varieties of logical antipsychologism, to which correspond various concepts of “pure logic”. Two conceptions are here under discussion : Husserl’s “logic of ideality” and Rickert ’s “logic of validity”. Against the equivocal use of “validity” and “ideality” by Heidegger, I first show that none of those conceptions can be exactly superimposed on the other one, because Rickert agrees with Husserl’s antipsychologism but rejects his theory of significations. It then appears that this difference – which is particularly obvious in Rickert ’s unpublished review of Palágyi’s very controversial book –, reveals in fact a “weak point” in Husserl’s Logical Investigations : the confusion between logical and mathematical objects. Rickert ’s “axiological” alternative avoids directly this confusion by asserting the irreducibility of the propositional sense – which is grounded on pure “theoretical values” – to an ideal object. (shrink)

Quel est le chemin qui, chez Husserl, nous mène de la logique formelle à celle transcendantale? S’agit-il de la voie kantienne qui va de la “logique générale” à celle “transcendantale” ou le caractère mathématique de la logique moderne interdit que celle-ci puisse jouer le rôle de “fil conducteur transcendantal”? Dans cet article, à la lumière de ce que l’on pourrait appeler la réciprocité entre passivité et logique, on avance la thèse selon laquelle c’est justement la logique mathématique qui pour Husserl (...) peut jouer un tel rôle. Chez Husserl, il y a en effet aussi bien une logique de la passivité qu’une passivité de la logique : non seulement ce qui est passif est synthétique et, en tant que tel, formellement déterminé, mais la logique, en tant que corpus de connaissances, est à son tour saturée par une passivité qui en assure le sens et la validité en tant que logique. C’est au point de croisement entre les deux, où l’une gouverne la force constitutive de l’autre et vice-versa, que l’on peut trouver le fil conducteur d’une enquête sur la possibilité d’une logique transcendantale à partir d’une réflexion sur la logique mathématique formelle. (shrink)

In his fifth Logical Investigation, Husserl intensely scrutinizes three possible significations of the concept of consciousness. In these analyses, he also strives to clearly delineate between two types of consciousness: psychological and phenomenological. The goal of this paper is to show that the way in which the (psychical) act is conceived and defined, according to the Husserlian approach, as a lived, intentional experience plays an essential role in clarifying the distinction between the empirical-psychological level of consciousness (where the act as (...) a lived experience manifests itself) and its eidetic or ideal level (wherein any type of objectivity is constituted as such). Moreover, I shall try to argue that the notion of act conceived in this manner had influenced and decisively determined the development of the entire Husserlian phenomenology and theory of knowledge exactly because it explains how knowledge in general is constituted from an objective point of view. Another highly relevant distinction that needs to be dealt with in this context is the difference that Husserl establishes between the descriptive and intentional contents of the act. I shall try to show that this distinction presupposes in fact a previous conceptual determination of the noema (undertaken jointly with the analysis of the noetical components of consciousness at this level), and that the way in which the relationship between these two strands of consciousness is described determines further and in a fundamental manner the development of the idea of intentionality itself. (shrink)

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

According to Edmund Husserl in the Prolegomena to Pure Logic, which constitutes the preliminary rational foundation for – and also the entire first volume of – his Logical Investigations, pure logic is the a priori theoretical, nomological science of „demonstration“.1 For him, demonstration includes both consequence and provability. Consequence is the defining property of all and only formally valid arguments, i. e., arguments that cannot lead from true premises to false conclusions. And provability is the property of a logical system (...) such that, for every truth of logic in that system, there is, at least in principle, a rigorous step-by-step logically valid procedure demonstrating its validity according to strictly universal, ideal, and necessary logical laws. In this way, the laws of pure logic completely determine its internal structure. Moreover, these laws and these proofs are all knowable a priori, with selfevident insight. So not only is pure logic independent of any other theoretical science, in that it requires no other science in order to ground its core notion of demonstration, it also provides both epistemic and semantic foundations for every other theoretical science, as well as every practical discipline or „technology. “ To the extent that pure logic is the foundation of every other. (shrink)

(No abstract is available for this citation).

In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic –Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively logical (...) inferences are viewed as analogical to arithmetical calculation. The paper ends with an examination of Husserl’s involvement with the key characters of the algebra of logic tradition. It is concluded that Ernst Schröder, but presumably also Hermann and Robert Grassmann influenced Husserl most in his turn away from psychologism. (shrink)

This paper discusses Jean van Heijenoort’s (1967) and Jaakko and Merrill B. Hintikka’s (1986, 1997) distinction between logic as auniversal language and logic as a calculus, and its applicability to Edmund Husserl’s phenomenology. Although it is argued that Husserl’s phenomenology shares characteristics with both sides, his view of logic is closer to the model-theoretical, logic-as-calculus view. However, Husserl’s philosophy as transcendental philosophy is closer to the universalist view. This paper suggests that Husserl’s position shows that holding a model-theoretical view of (...) logic does not necessarily imply a calculus view about the relations between language and the world. The situation calls for reflection about the distinction: It will be suggested that the applicability of the van Heijenoort and the Hintikkas distinction either has to be restricted to a particular philosopher’s views about logic, in which case no implications about his or her more general philosophical views should be inferred from it; or the distinction turns into a question of whether our human predicament is inescapable or whether it is possible, presumably by means of model theory, to obtain neutral answers to philosophical questions. Thus the distinction ultimately turns into a question about the correct method for doing philosophy. (shrink)

According to the leading commentators and the author himself, Edmund Husserl's Formal and transcendental Logic is the most important work on phenomenological logic ever written. Nonetheless, it has, in general, gained far less attention than theLogical Investigations and the Ideas on a Pure Phenomenology and Phenomenological Philosophy. In particular, the argument of § 1 of the Logic, namely, that it is fruitful to start with the meanings of the expression “logos” in order to develop a genuinely transcendental logic, has received (...) virtually no consideration. This paper takes a step towards filling this empty space by analyzing and criticizing the argument of § 1 as a problem to which (a) solution(s) must be found: First, it offers an introduction to the problem per se, which is one of the relationship between speech and reason; second, it tries to bring the given senses of “logos” to a higher grade of conceptual clarity and distinctness than that in the text; third, it attempts to decide whether and how far these senses of the word can be documented according to principles of Classical philology; fourth, it endeavors to determine exactly the relationship between the meanings of “logos” in § 1 and the senses of “logic” in §§ 1–107; finally, it strives to show that, with respect to the account of the relationship between speech and reason provided by Husserl in the Logic, there is, at best, a conflict and, at worst, a contradiction between the strategy outlined in § 1 and the tactics adopted in § 2ff. Throughout, the paper reads Husserl's “descriptions” as ‘arguments’ for his positions, thereby avoiding any of the obscurity sometimes infecting work in “Continental philosophy”. (shrink)

This book makes available to the English reader nearly all of the shorter philosophical works, published or unpublished, that Husserl produced on the way to the phenomenological breakthrough recorded in his Logical Investigations of 1900-1901. Here one sees Husserl's method emerging step by step, and such crucial substantive conclusions as that concerning the nature of Ideal entities and the status the intentional `relation' and its `objects'. Husserl's literary encounters with many of the leading thinkers of his day illuminates both the (...) context and the content of his thought. Many of the groundbreaking analyses provided in these texts were never again to be given the thorough expositions found in these early writings. Early Writings in the Philosophy of Logic and Mathematics is essential reading for students of Husserl and all those who enquire into the nature of mathematical and logical knowledge. (shrink)

The article introduces and discusses an unpublished manuscript by Edmund Husserl, conserved at the Husserl-Archives Leuven with signature K I 26, pp. 73a–73b. The article is followed by the text of the manuscript in German and in an English translation. The manuscript, titled “The Transition through the Impossible” ( Der Durchgang durch das Unmögliche ), was part of the material Husserl used for his 1901 Doppelvortrag in Göttingen. In the manuscript, the impossible is characterized as the “sphere of objectlessness” ( (...) Sphäre der Gegenstandslosigkeit ) and Husserl addresses the question whether and when it is warranted to perform a transition through the impossible to obtain valid results for the sphere of objectivity. (shrink)

This paper deals with Husserl’s idea of pure logic as it is coined in the Logical Investigations. First, it exposes the formation of pure logic around a conception of completeness ; then, it presents intentionality as the keystone of such a structuring ; and finally, it provides a systematic reconstruction of pure logic from the semiotic standpoint of intentionality. In this way, it establishes Husserlian pure logic as a phenomenological epistemology of mathematical logic.

The purpose of this paper is to provide a unitary typology for the incompatibilities of meanings at stake on different levels of Husserlian pure logic—namely, between systems of axioms and pure morphology of meanings; I show that they perfectly match by converging on the notion of Widersinn.

Au terme des Prolégomènes, Husserl formule son idée de la logique pure en la structurant sur deux niveaux: l'un, supérieur, de la logique formelle fondé transcendantalement et d'un point de vue épistémologique par l'autre, inférieur, d'une morphologie des catégories. Seul le second de ces deux niveaux est traité dans les Recherches logiques, tandis que les travaux théoriques en logique formelle menés par Husserl à la même époque en paraissent plutôt indépendants. Cet article est consacré à ces travaux tels que recueillis (...) dans les appendices VI-X du volume 12 des Husserliana. Mettant en évidence la théorie de la signification qui les sous-tend par le biais d'une analyse de la question dite de l'extension des systèmes d'axiomes et de sa résolution au moyen d'une notion de complétude, son objectif est d'expliciter les modalités de l'intégration de la logique formelle dans l'idée husserlienne de la logique pure au tournant du xx siècle.When formulating his idea of pure logic in the Prole.. (shrink)

The centerpiece of the Analyses is a translation from the German of notes for a series of lectures given by phenomenologist Edmund Husserl in the early twenties, which is to say some eighty years ago. Husserl designated the topic of the lectures 'transcendental logic'. In this context, the term, 'transcendental', is not to be understood in some mystical sense, but rather in a Kantian sense: pertaining to the conditions of possibility of experience. Likewise, the term, 'logic', is not to be (...) taken in the narrow sense of formal logic, but rather in the very general sense it had for Platonic dialectic: a concern with normative guidelines and critical assessment of the possibility of truth. The topic of the lectures is succinctly characterized by Husserl as 'a universal theory of science, and at the same time, a theory of science in principle,' where the latter means 'the science of the a priori of all sciences as such' (p. 1). (shrink)

A Husserlian phenomenological approach to logic treats concepts in terms of their experiential meaning rather than in terms of reference, sets of individuals, and sentences. The present article applies such an approach in turn to the reasoning operative in various paradoxes: the simple Liar, the complex Liar paradoxes, the Grelling-type paradoxes, and Gödel’s Theorem. It finds that in each case a meaningless statement, one generated by circular definition, is treated as if were meaningful, and consequently as either true or false, (...) although in fact it is neither. The situation is further complicated by the fact that the sentence used to express the meaningless statement is ambiguous, and may also be used to express a meaningful statement. The paradoxes result from a failure to distinguish between the two meanings the sentence may have. (shrink)

There are two main objections against epistemological foundation of logical principles: 1. Every argument for them must necessarily make use of them. 2. Logical principles cannot be abstracted from experience because they imply elements of meaning that exceed in principle our finite experience (like universality & necessity). In opposition to these objections I argue for Husserl's thesis that logic needs a theory of experience as a foundation. To show the practicability of his attempt I argue that he is able to (...) avoid the two circles mentioned. Motivated by this investigation the Appendix presents some mathematical doubts concerning the proofs by Cantor of the transfiniteness of the set of real numbers. (shrink)

This work brings together three themes whose relationship has gone unexplored in the recent literature of philosophy: the transcendental phenomenology of Edmund Husserl, the phenomenological ontology of Martin Heidegger and the discipline of logic, especially formal logic. Part One and Two of the work present a detailed explication of Husserl's and Heidegger's philosophy of logic which are respectively characterized as an archeology of logic based upon transcendental phenomenological criticism and a radical phenomenology of logic based upon phenomenological criticism which issues (...) from a concern with the question of the meaning of Being. Part Three, then, offers a comparative analysis combined with a critical appraisal of these two philosophies of logic in order to achieve a more penetrating understanding of the relationship between Husserl and Heidegger. Thus, in one sense, this work takes the domain of logic and the varying approaches to it by Husserl and Heidegger as a clue to the similarities and dissimilarities within the thinking of these two phenomenologists, especially with regard to the understanding each has of the goal and method of phenomenology, and the results proper to phenomenological reflection. (shrink)

Psychologism in logic holds that logic is a branch of psychology. This view has been vigorously defended by John Stuart Mill and by a number of German philosophers of logic, notably Erdmann. Its chief critics have been Husserl and Frege and, to a lesser extent, Russell. Husserl set forth a profound and detailed critique of psychologism in Logical Investigations. This paper examines this critique. First, I explain why the psychologistic theory is attractive. Then I show that Husserl's critique is not (...) convincing, partly because he does not take the theory in its most plausible form and partly because he ignores certain important distinctions (for example, between what a statement is about and what it is true in virtue of). Then I raise two new objections to the psychologistic theory. The purpose of this paper is to suggest that the psychologistic theory remains an important and serious position from which we can learn much about the status of logic. (shrink)

"La Lógica pura, la idea de la Gramática pura y el problema de una filosofí­a del lenguaje en las Investigaciones Lógicas" Una de las cuestiones centrales que hasta hoy en dí­a se siguen debatiendo en torno a la recepción de las Investigaciones Lógicas, se refiere a la relación entre pensamiento y lenguaje, entre significado y expresión lingí¼í­stica, entre percepción y juicio, entre Lógica y Gramática que estableció en el debate con G. Frege y A. Marty, entre otros. El autor se (...) ocupa de las influencias -en parte directas o indirectas- que ha dejado la obra de Husserl sobre la lingí¼í­stica moderna, la filosofí­a del lenguaje del siglo XX y la filosofí­a analí­tica del lenguaje. "The pure Logic, the pure Grammar's idea and the problem of a philosophy of the language in the Logical Investigations". One of the central questions that until today is continued debating around the reception of the Logical Investigations, it refers to the relationship between thought and language. between meaning and linguistic expression, between perception and judgement, between Logic and Grammar that Husserl settled down in the debate with G. Frege and A. Marty, among others. The author is in charge of the influences -direct or indirectly- that has left the work of Husserl on the modern linguistics, the philosophy of the language of the XX century and the analytic philosophy of the language. (shrink)

French translation of "Truth-Makers" (1984). A realist theory of truth for a class of sentence holds that there are entities in virtue of which these sentences are true or false. We call such entities ‘truthmakers’ and contend that those for a wide range of sentences about the real world are moments (dependent particulars). Since moments are unfamiliar we provide a definition and a brief philosophical history, anchoring them in our ontology by showing that they are objects of perception. The core (...) of our theory is the account of truthmaking for atomic sentences, in which we expose a pervasive ‘dogma of logical form’, which says that atomic sentences cannot have more than one truthmaker. The authors uphold the mutual independence of logical and ontological complexity. The theory is compared with that of Wittgenstein’s Tractatus, and the authors outline formal principles of truthmaking taking account of both kinds of complexity and suggesting how to overcome Wittgenstein’s problem of negation. (shrink)

German translation of Mulligan, Simons and Smith, "Truth-Makers" (1984) A realist theory of truth for a class of sentence holds that there are entities in virtue of which these sentences are true or false. We call such entities ‘truthmakers’ and contend that those for a wide range of sentences about the real world are moments (dependent particulars). Since moments are unfamiliar we provide a definition and a brief philosophical history, anchoring them in our ontology by showing that they are objects (...) of perception. The core of our theory is the account of truthmaking for atomic sentences, in which we expose a pervasive ‘dogma of logical form’, which says that atomic sentences cannot have more than one truthmaker. The authors uphold the mutual independence of logical and ontological complexity. The theory is compared with that of Wittgenstein’s Tractatus, and the authors outline formal principles of truthmaking taking account of both kinds of complexity and suggesting how to overcome Wittgenstein’s problem of negation. (shrink)

In this piece of work we considerer mathematical logic as a whole. The three steps distinguished by Husserl, to wit, pure logic grammar, logic of the non-contradiction and logic of the truth, are analysed. They are applied to the logistics by distinguishing different levels and layers. In each level the logistics methods and its correspondence with the formal ontology inside the philosophical phenomenology are taken into account. The subject is completed explaining the axiomatic as well as the Greek life in (...) Euclides and in comparison with Hilbert. Finally, we intend to interpret the Greek logic, Leibniz logic and logistics from the viewpoint of different types of life related to them. In all these cases we presuppose, as a source, the apofantic aristotelian form of the proposition. (shrink)