Aristotle: Logic and Philosophy of Language, Misc

The list of katēgoriai presented at the start of Top. I 9 was traditionally interpreted as a version of the canonical Aristotelian list of categories, and as largely equivalent to the list we find in Categories 4. Accordingly, its first item, the ‘what it is’, was identified with the category of substance. This interpretation has been challenged by several scholars, all sharing the view that the ‘what it is’ in Top. I 9 cannot be substance, since it collects items belonging (...) to all Aristotelian categories (e. g. human being, colour, length). Rather, they say, it is a manner of predication – i. e. essential predication – and can only determine an ontologically miscellaneous class of items. Against this family of proposals, I argue afresh that the traditional interpretation is almost entirely correct. To this purpose, I take advantage of the distinction between kinds of predicate and kinds of predication. (shrink)

In the Posterior Analytics Aristotle contrasts demonstrations with syllogisms through signs. In the Prior Analytics he defines a sign as a demonstrative premise. One is thus led to ask: is a sign a demonstration? This book reconstructs the history of the notion of "demonstration through signs" from roughly the third through to the thirteenth century. It examines the work of Aristotle's Greek, Arabic, and Latin commentators, both within and outside the tradition of the Posterior Analytics.

The translation of Aristotle's "Rhetoric" from Ancient Greek was developed over many years by classical philologists at the University of Latvia, together with specialists in Baltic philology and ancient philosophy. The translation is innovative: it does not use internationalisms, only Latvian vocabulary. Helpful for the reader is the glossary of key terms. The translation is supplemented by academic commentaries and articles.

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of (...) opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts. (shrink)

I discuss the argument Aristotle ascribes to Parmenides at Physics 186a23-32. I discuss (i) the reasons why Aristotle considers it as eristic and inconclusive and (i) the solution (lusis) Aristotle proposes against it.

Even though Aristotle speaks often about language, his remarks do not fall within the province of any given discipline, let alone belong to the same subject matter or amount to a πραγματεία of their own. Rather, they are somewhat scattered across the Aristotelian corpus and are to be gleaned from a vast array of texts, including ethical and political writings (where language plays a remarkable role in shaping human sociability), treatises on natural history (where Aristotle outlines the physiology of phonation (...) in some animals such as birds and human beings), books on the soul (where Aristotle describes how language is intertwined with perception, imagination and thought) and works on dialectics, poetics and rhetoric (where linguistic expression is described as a powerful means of both persuasion and deception). Accordingly, «Le langage. Lectures d’Aristote» elects to study Aristotle’s understanding of language and its workings by asking relevant Aristotelian texts only those questions these texts answer – either by themselves or in conjunction with one another. -/- Quelque nombreuses et quelque influentes qu'elles soient par ailleurs, les vues d'Aristote sur le langage se caractérisent à la fois par leur hétérogénéité et par leur marginalité. Sans faire nulle part du langage et de la signification l'objet d'une investigation autonome et méthodique, Aristote multiplie les remarques et les digressions à leur sujet, que ce soit dans ses écrits d'éthique et de politique ou dans ses traités d'histoire et de philosophie naturelle, ou encore dans ses manuels de dialectique, de poétique et de rhétorique. Face à l'abondance de ces matériaux et aux difficultés qu'ils présentent du fait de s'offrir au lecteur en ordre quelque peu dispersé, «Le langage. Lectures d'Aristote» fait le choix d'indexer l'étude du langage chez Aristote sur des passages précis du corpus en ne posant aux textes aristotéliciens d'intérêt linguistique que les questions auxquelles ces mêmes textes - tantôt pris isolément, tantôt mis en relation les uns avec les autres - apportent une réponse. (shrink)

This paper addresses a difficult passage from Aristotle’s Metaphysics (V. 4, 1015a11-13) in which he identifies a metaphorical use of the term “nature” (phusis) to refer to the entities which he calls “substances” (ousiai). I claim that the passage at stake deploys the very notion of metaphor on the basis of an analogy (as defined in the Poetics and in the Rhetorics), which is grounded on a weak (and, sometimes, very weak) similarity between two relations (each involving two relata). The (...) sentences found in 1015a11-13 belong to those kind of metalinguistic sentences which we usually employ to shed some light on the metaphorical use of a term. The similarity Aristotle is presupposing is this: both nature and substance are, in their respective fields, some kind of principle that guarantees (besides other things) certain persistence conditions for what they are the principles of. And this weak similarity is enough for the term “nature” to refer metaphorically to substances. (shrink)

The overall purpose of this paper is to contribute to the debate over a possibility to reconstruct such theories which are not explicitly formulated in the preserved texts of ancient authors. Aristotle is one of those who did not write a single treatise on language, though language – both, as an instrument, as well as an object of the study – was still focal point of his philosophy. In his writings, Aristotle rigorously distinguishes several ways of methodologically examining same phenomenon. (...) He is aware of the fact that every phenomenon can be examined from various perspectives and that different goals of the study lead us towards different answers. Aristotle’s views on language are scattered through his entire oeuvre. The main aim of this paper is to offer and justify a new way of reconstructing Aristotle’s theory of language. In the first part, the paper justifies the very existence of Aristotle’s theory of language and outlines a plan how to proceed with reconstruction of such theory. In the second part, the preliminary plan is situated into the current state of Aristotelian scholarship. Finally, in the third part, the plan of reconstruction is elaborated using an integrationist approach. Integrationism (the idea that our language is a very complex phenomenon which has to be studied from different perspectives and the results of those studies cannot be reduced to each other and cannot be merged into a single atemporal model, instead those results should be understood as an integral part of the very temporal nature of our language) allows me to explain how various different dimensions of language are uncovered in Aristotle’s works and how they gradually arise from each other. (shrink)

This book investigates what change is, according to Aristotle, and how it affects his conception of being. Mark Sentesy argues that change leads Aristotle to develop first-order metaphysical concepts such as matter, potency, actuality, sources of being, and the teleology of emerging things. He shows that Aristotle’s distinctive ontological claim—that being is inescapably diverse in kind—is anchored in his argument for the existence of change. -/- Aristotle may be the only thinker to have given a noncircular definition of change. When (...) he gave this definition, arguing that change is real was a losing proposition. To show that it exists, he had to rework the way philosophers understood reality. His groundbreaking analysis of change has long been interpreted through a Platonist lens, however, in which being is conceived as unchanging. Offering a comprehensive reexamination of the relationship between change and being in Aristotle, Sentesy makes an important contribution to scholarship on Aristotle, ancient philosophy, the history and philosophy of science, and metaphysics. (shrink)

These are the commentaries (or notes) for Aristotle's Metaphysics V (Delta) 18-30. This file must be read together with the translation into Portuguese, which has been published as a different item, with a different DOI. In the Introduction, I discuss many issues about Aristotle's jargon, Aristotle's style and Aristotle's awareness of many philosophical problems that nowadays we locate within the branch Philosophy of Language.

The expression tode ti, commonly translated as ‘a this’, plays a key role in Aristotle’s metaphysics. Drawing lightly on theories of demonstratives in contemporary linguistics, I discuss the expres...

My aim is to show that, in Posterior Analytics B 8, the conception of lunar eclipse brought about by pre-demonstrative knowledge (hoti) is deeply vague and radically different from the one obtained by demonstrative knowledge (dioti).

Aristotle‘s categories are presented as a system relying on logic and syntax instead of on meanings. His square of oppositions is found to be of crucial importance.

My aim in this paper is twofold: I will try to clarify what the conditions developed in EN I a discipline or an argument must meet to be assumed as precise are, and, then, try to present evidence that the exam of akrasia in EN VII 3 meets these conditions. In the first part of this paper, I will select passages in which such conditions are displayed, and also distinguish between practical precision and theoretical precision. In the second part, where (...) the analysis of the senses of having but not using knowledge in EN VII 3 is carried on, I will claim that Aristotle’s objective is reaching the adequate statement of the explanandum that will be the subject of causal enquiry of akrasia. My concluding remarks will claim that the conditions displayed in this paper’s first part are met by Aristotelian procedure in EN VII 3. (shrink)

The work of this dissertation, in a broad sense, seeks to rescue what may be in the original project or nucleus of philosophy, from its Socratic arising: the idea of elucidative rationality. This rationality is aimed at expressing our practices in a way that can be confronted with objections and alternatives. The notion of expression is central to this rationality. This centrality is elucidated by the contemporary philosopher Brandom (1994, 2000, 2008a, 2013), from his view of the semantic inferentialism. With (...) this view, this dissertation, in a strict sense, investigates evidences that leads to the distinction of the inferentially expressivist tradition of syllogistic. In this semantic inferentialism, logic is the “organ of semantic self-consciousness”. In this sense, logic does not define the rational, in the most basic sense, but allows us to be aware, through inferential articulation, of the conceptual contents, which govern all our thoughts. Evidences presented in the work of this dissertation seek to show that the syllogism is marked by the logical-elucidative character of this semantic self-consciousness, because of its expressive role as inseparable from the notion of inference. In the first part of this dissertation, then, the tradition of syllogistics is examined, in which the expression is the main notion. This study is based on the tradition of syllogistics, composed of the Aristotelian school of Campinas, organized by Angioni (2014a), the logical economist Keynes (1906), and the “formalist” schools, represented mainly by the logician Łukasiewicz (1957, 1929/1963) and by Corcoran (1972, 1974, 2009, 2015). The main claims of the Campinas school are analyzed: the non-epistemological, but explanatory, exposition of (scientific) knowledge, in the syllogism, the secondary role of the notion of truth, the priority of the predicative structure, and the suggestion of approaching of the syllogistic to the relevant system of logic. In this analysis, we add the discussion about the reasoning of the epagogic type, important to the practical understanding of the “first principles”. The key points of Keynes are also discussed: the semantic priority of propositional judgment and the explanatory role of deductive inference. The second part of this dissertation discusses the relation between expression, inference and the expressive role of logic, based on the semantic inferentialism of Brandom. In order to discuss this relationship, propaedeutic questions are raised, related to the semantic role of sentences and subsentences (terms and predicates) in language, to different conceptions of logical validity, beyond the truth-functional aspect, to the logical demarcation of symbolic rules, to demarcation of logic, the idea of “formal logic”, and the removal of formal semantics from natural language concern. Next, the theoretical framework of Brandom's semantic inferentialism is presented. In this framework, the idea of philosophical semantics, pragmatisms of the semantic and conceptual type, expressivisms of the rationalist, logical and propositional conceptual type, and the semantically primitive notion of incompatibility come into play. Thus, to those who are interested in the correspondence between ancient logic and modern logic, the work of this dissertation offers a useful contribution, especially to projects of formalization of the syllogistics, which need not appeal against or in favor of a strictly formal approach to logic. (shrink)

In their pioneering, masterly research and survey on Bartolomeo Fonzio’s manuscripts, published in 1974, Stefano Caroti and Stefano Zamponi informed the reader that the Ms. Ricc. 152 of the Riccardiana Library in Florence was a huge amount of notebooks with notes taken by Fonzio while attending the Studium in Florence. Among them Caroti and Zamponi called the reader’s attention to the notes Fonzio took when he went to Argyropoulos’ lessons on the Posterior Analytics. In this essay the reader finds a (...) transcription of those notes, preceded by some comments on the sources from which the outstanding commentator is likely to have drawn and which can be picked out from the fragmentary notes, that is John Philoponus and Paul of Venice. (shrink)

Aux prises avec une archive en pleine expansion et une littérature secondaire dont la masse a atteint et, notamment depuis son tournant numérique, largement dépassé un seuil critique, l’archéologie philosophique a fait le deuil du rêve micrologique de « tout lire, tout étudier » que Michel Foucault s’était pourtant donné pour idéal régulateur en s’interdisant d’effectuer un tri en amont des « choses dites dans une culture, conservées, valorisées, réutilisées, répétées et transformées ». Il importe désormais moins de décrire la (...) totalité d’un champ que de tracer et de croiser des itinéraires. En gros, il s’agit de « raconter des intrigues », selon la formule bien connue de Paul Veyne. Arrimée à la philologie et à l’histoire des corpus, cette théâtralisation du travail philosophique n’est cependant pas arbitraire. Comme l’explique Alain de Libera dans l’un des rares propos métarchéologiques qu’il a livrés en marge de son œuvre canonique, face à l’« accumulation folle de connaissances et d’informations » qui caractérise l’environnement actuel de la recherche, « le rôle de l’historien-archéologue est d’identifier les bonnes structures ». Comment s’y prend-il ? « Il y a pour ce faire – poursuit Alain de Libera au cours du même « Grand entretien d’Actu-Philosophia » – un critère d’identification heuristique : la simplicité. La force d’une hypothèse de travail se mesure au nombre d’éléments qu’elle est capable d’intégrer et d’unifier, en un mot : de “simplifier” ». Parmi les intrigues qui ont marqué l’histoire récente de l’archéologie à vocation philosophique il y a sans doute l’« ἐπιστήμη alexandrinienne » qu’Alain de Libera a identifiée en étudiant les doctrines anciennes et médiévales de l’abstraction et qu’il a baptisée de la sorte pour souligner le rôle qu’Alexandre d’Aphrodise a joué dans sa genèse. Pour peu qu’il soit convaincu de son intérêt intrinsèque, le lecteur, surtout s’il se trouve être un antiquisant ou un médiéviste, résistera difficilement à la tentation de se demander s’il est possible de procéder à une extension – même ponctuelle – du « réseau aphrodisien » : peut-on élargir avec le même succès son domaine d’application en testant son pouvoir d’inclusion dans d’autres cas que celui de la filière qu’il était initialement destiné à synchroniser ? C’est une ébauche de simplification de cet ordre que mon hommage voudrait esquisser à partit de quelques textes qu’Alain de Libera a lui-même étudiés et selon une trajectoire parallèle à celle qu’il a lui-même tracée. (shrink)

The main aim of my paper is to analyse Aristotle’s theory of language in the context of his Physics I.1 and via an analysis and an interpretation of this part of his Physics I try to show that (i) the study of human language (logos) significantly falls within the competence of Aristotle’s physics (i.e. natural philosophy), (ii) we can find the results of such (physical) inquiry in Aristotle’s zoological writings, stated in the forms of the first principles, causes and elements (...) of the human speech (logos) and (iii) the analogies (Phys. 184b13-14) made by Aristotle at the very end of the first chapter make better sense if we consider them in the broader context in which Aristotle recognizes language as a complex natural phenomenon we are born into and which has to be not only biologically, but also socially developed through our lives. Hence, I aim towards a more naturalistic reading of Aristotle’s views on language. (shrink)

This book is both a history of philosophy of logic told from the Kantian viewpoint and a reconstruction of Kant’s theory of logic from a historical perspective. Kant’s theory represents a turning point in a history of philosophical debates over the following questions. (1) Is logic a science, instrument, standard of assessment, or mixture of these? (2) If logic is a science, what is the subject matter that differentiates it from other sciences, particularly metaphysics? (3) If logic is a necessary (...) instrument to all philosophical inquiries, how is it so entitled? (4) If logic is both a science and an instrument, how are these two roles related? Kant’s official answer to these questions centers on three distinctions: general versus particular logic; pure versus applied logic; pure general logic versus transcendental logic. The true meaning and significance of each distinction becomes clear, I argue, only if we consider two factors. First, Kant was mindful of various historical views on how logic relates to other branches of philosophy (viz. metaphysics and physics) and to the workings of common human understanding. Second, he first coined ‘transcendental logic’ while struggling to secure metaphysics as a proper “science,” and this conceptual innovation would in turn have profound implications for his mature theory of logic. Against this backdrop, I reassess the place of Kant’s theory in the history of philosophy of logic and highlight certain issues that are still debated today, such as normativity of logic and the challenges posed by logical pluralism. In Chapter 1, “Kant and a Philosophical History of Logic – Methodological Reflections,” I discuss certain exegetical challenges posed by Kant’s logic corpus and argue for a “history of philosophical problems” method by which to reconstruct a Kantian theory of logic. In Chapter 2, “The Nature and Place of Logic – A History of Controversies,” I construct a partial history of philosophy of logic that revolves around the (supposedly) scientific status of logic on the one hand and its value or utility on the other. In Chapter 3, “The Making of a Scientific Logic from Bacon to Wolff,” I examine how four representative early modern philosophers – Francis Bacon, John Locke, G.W. Leibniz, and Christian Wolff – approached the four questions mentioned above. In Chapter 4, “Kant on the Way to His Own Philosophy of Logic,” I consider how Kant, in the decade between around mid-1760s and mid-1770s, navigated between existing accounts of logic until he finally found his own voice. I highlight the breakthroughs that would mark his critical departures from previous views and pave the way for the final articulation of his own view. In Chapter 5, “Logic and the Demands of Kantian ‘Science’,” I zero in on Kant’s official theory of logic in his monumental publication, Critique of Pure Reason. I foreground both what makes the theory original and what leaves it vulnerable to criticisms from post-Kantian thinkers. (shrink)

In the tradition stemming from Aristotle through Aquinas, rational decision making is seen as a complex structure of distinct phases in which reasoning and will are interconnected. Intention, deliberation, and decision are regarded as the fundamental steps of the decision-making process, in which an end is chosen, the means are specified, and a decision to act is made. Based on this Aristotelian theoretical background, we show how the decision-making process can be modeled as a net of several patterns of reasoning, (...) involving the classification of an action or state of affairs, its evaluation, the deliberation about the means to carry it out, and the decision. It is shown how argumentation theory can contribute to our understanding of the mechanisms involved by formalizing the steps of reasoning using argumentation schemes, and setting out the value-based criteria underlying the evaluation of an action. Representing each phase of the decision-making process as a separate scheme allows one to identify implicit premises and bring the roots of ethical dilemma to light along with the means to resolve them. In particular, we will show the role of framing and classification in triggering value-based reasoning, and how argumentation theory can be used to represent and uproot the grounds of possible manipulations. (shrink)

Tradução anotada do Grego para o Português.

Aristotle, in Chapter 7 of his Categories, classifies habits and dispositions, as well as knowledge, among relatives. However, in Chapter 8 of the Categories, he affirms that habits, including knowledge, and dispositions, including unstable knowledge, are qualities. Thus, habits and dispositions in general, and knowledge in particular, seem to be subject to a ‘dual categorization’. At the end of Chapter 8 of the treatise, the issue of the dual categorization is explicitly raised. How can one and the same thing be (...) a quality and a relative? Aristotle gives two distinct solutions to this problem. Both have been criticized by some modern commentators : these solutions would amount to a rejection of the basic principles of the categorial system and, as such, to a sort of philosophical suicide. However, Aristotle’s early commentators, notably the Greek Neoplatonists and Boethius, made attempts to render both solutions plausible and compatible with the rest of the doctrine. Their attempts are not only of exegetical interest, they also contain some significant philosophical analyses concerning the categories. In what follows, I will present the abovementioned problem of dual categorization in Aristotle and the two solutions offered to it in Categories, 8, 11a20-38. I will then turn to the early reception of this text, and focus on the way the Greek Neoplatonists and Boethius tried to make Aristotle’s solutions more plausible. Throughout, I will try to establish in what sense habits and dispositions in general, and knowledge in particular, are relative. I will conclude with some remarks on the later reception of Categories, 8, 11a20-38 and on the problem of the ontological status of mental acts and states. (shrink)

This book presents an exhaustive study of the three 13-century discussions explicitly dealing with the notion of Significatio. The study aims to show that the three discussions emerge because of apparently opposite claims about the signification of words in the authoritative literature of the period. It also shows that the three discussions develop in the same direction - towards a unified use of the notion of signification, which keeps its explanatory role in semiotics, but loses its role in grammar and (...) logic. (shrink)

This article is intended to examine the structure and scope of the argumentation drawn in Metaphysics Γ 4, 1006a18-b34. As we shall see, though this passage does not bring a complete proof of the Principle of Non-Contradiction, it corresponds to its first step, which consists in determining the conditions of meaning necessary for discourse. That passage encloses in nuce the reasons which underlie Aristotelian conviction con- cerning the conventional nature of names and also brings to light the way this conven- (...) tional nature of names must be understood according to Aristotle. (shrink)

My aim is to figure out whether Aristotle’s response to the argument for fatalism in De Interpretatione 9 is successful. By “response” here I mean not simply the reasons he offers to highlight why fatalism does not accord with how we conduct our lives, but also the solution he devises to block the argument he provides for it. Achieving my aim hence demands that I figure out what exactly is the argument for fatalism he voices, what exactly is his solution, (...) whether his solution is coherent, and whether it does indeed succeed. I find that the argument is essentially bivalence plus that the truth of a proposition stating that an event will happen in the future entails that this event will necessarily happen, that Aristotle’s solution is to restrict bivalence when it comes to propositions about contingent future events, that this solution is coherent, and that while it does not rule out the possibility of fatalism, it does succeed in blocking the argument for fatalism offered within chapter 9. (shrink)

This paper attempts to clarify the nature and the importance of a third kind of sophistic argument that is not always found in the classification of those arguments in the secondary literature. An argument of the third kind not only is a valid one, but is also constituted of true propositions. What makes it a sophistic argument is the fact that it produces a false semblance of scientific explanation: its explanation seems to be appropriate to the explanandum without being so. (...) Evidence from this kind of argument comes from Sophistic Refutations 11, and Brison’s attempt to square the circle should be counted as one of its instances. (shrink)

Meontology of Gorgias vs. Nihilism. The purpose of this paper is to challenge Gorgias’ image of a “nihilist existentialist”. The original thesis ouden estin, too frequently rendered as „nothing exists”, thus reducing the verb “to be” to denote “bare” existence, and ouden to denote “nothingness”. On close inspection, it turns out that, in Gorgias, neither do we have a negation of reality nor an affirmative treatment of the word “nothingness”.Therefore, ouden” should not be understood as a negation of all reality (...) or a kind of affirmative “nothingness”, whereas “estin” should not be reduced to “bare” existence. (When existence is negated what we obtain is annihilation). Such practices still affect the various translations of Gorgias’ treaty On the non-being or on Nature. Gorgias’ “sophist” thought is typically interpreted as a joke or a parody of dialectical thinking of the Eleatics. In fact, as it turns out, he made no parody of dialectic but applied the elenctic, apagogic method in Zeno’s masterly manner. He did so not for an artificial purpose but to prove the absurdity of the hypothesis of absolute, transcendent (hence incognizable) one Truth-Being, which eliminates the non-being of becoming as absolute non-being. Gorgias argued in earnest in favour of relative being as such, Becoming as the only reality, which from the point of view of absolute being is after all non-being, but not-this-being, or relative non-being but not non-relative non-being, as the Eleatics had claimed. Gorgias’ positions appears to be an apologia of non-being which is, that is of Becoming. We do not transform the “nothing” into a “no thing”. The main question of the treaty is: what is predicated by the word “nothing”? Gorgias’ position can be recapitulated as “nothing is sc. true, there is no criterion because, after all, everything is opinion. It is reinforced further by meontological, i.e. anti-eleatic Gorgias’ emphasis: “No thing is Being (substance)”, because everything is Becoming. Thus the title if Gorgias’ treaty can thus be treated as as an antithesis to that of Melissos’, which – in our opinion – is to emphasize the “non-beingness” of nature, the non-substantiality of things. Therefore, if Gorgias’ text was polemical, and it questioned (while at the same time maintaining the positivity of Becoming as non-being) only the immutability of things, and thus we cannot speak of the existence or the cognizability of natures or of essences of things. In sum, the reasoning of Zeno and Melissos was of a kind that is apt to cut both ways, and that is what Gorgias showed. The argument given as peculiar to himself was to this effect. “What is not” is not, so, it is just as much as “what is”. It is as if the onset of the issues that Plato will take up in The Sophist as the problem of non-being understood as difference. The axis of Gorgias’s anti-eleatic critique, in our view, is his polemic with Parmenides’ famous thesis B3 regarding the relationship of identity or equality between noein and einai. It is an additional and perhaps the most important point of his critique that aims at demonstrating that such relationship is impossible. In brief, things are not words just as thoughts are not words. (shrink)

This book reconstructs the theory of signification implicit in Aristotle's De Interpretatione and its psychological background in his writing De Anima, a project often envisioned by scholars but never systematically undertaken.