Definition Of Notion Research Articles

Solving a puzzle of definition

ABSTRACT This paper concerns the question of which logical principles hold for real definitions. Recently, Samuel Elgin has presented five principles concerning real definitions that seem initially plausible. He has shown them to be jointly inconsistent. This gives rise to a puzzle that can only be solved by denying one of the principles. In this paper, I argue against Elgin's principle of expansion, which concerns substituting a definiens for its definiendum within the definiens of a further definition. I show that this principle fails for every irreflexive notion of definition and proposes a replacement that allows to restore consistency and solve the puzzle.

Operating with Names: Operational Definitions in the Analects and Beyond

The philosophy of Confucius has often been accused of lacking classical definitions of its core concepts. However, as I shall argue, Confucius systematically used nonclassical definitions—to be precise, operational ones. The notion of operational definition comes from Percy Bridgman’s The Logic of Modern Physics (Bridgman 1927) and means that the definiendum is defined by a set of operations that results in determining the meaning of the term in question. In the case of Confucian argumentation, operational definitions are mostly nominal and, in contrast to unambiguous methods of measurement, also context-dependent. This results in there being various yet not mutually inconsistent definitions of one term, and in “paradigmatic examples” playing a crucial role. As I show, this mode of defining things had major implications for the content of Confucius’ thought. In fact, many of its forms could be traced back to other Chinese philosophers, including those of non-Confucian provenance.

LEXICAL DEFINITION: ITS SCOPE AND SIGNIFICANCE

Understanding the notion of definition is a central issue in such scientific disciplines as Philosophy, Semantics, and Lexicography. The paper considers different types of definitions focusing on lexical definition, which is the main component of a dictionary entry. An attempt is made to designate lexical definition and stipulative definition as subcategories of word-thing definition.

Frege on the Fruitfulness of Definitions

What, in Frege’s view, makes definitions fruitful? In Grundlagen §70, Frege offers an answer: Unfruitful definitions are definitions that “could just as well be omitted and leave no link missing in the chain of our proofs”. The §70 passage, however, poses an interpretive puzzle as its characterization of fruitfulness appears to conflict with other conditions that Frege imposes on definitions, namely, eliminability and conservativeness. It appears that the only way to resolve this conflict is to attribute to Frege a notion of fruitfulness that is trivially satisfied and, hence, poorly motivated. I argue that this worry is misplaced. This is because Frege distinguishes between two roles of definitions, namely, between definitions qua explanations of concepts (analytic definitions), and definitions qua resources of a proof system (logical definitions). I use this distinction to argue that a fruitful definition, for Frege, is a definition that plays both roles, and that to play both roles, the definition has to be used in the proof of sentences containing the term so defined. Starting from §70, I develop and defend this reading of Frege’s notion of fruitful definition.

Analytical Sociology and Symbolic Interactionism: Bridging the Intra-disciplinary Divide

The aim of the present article is to contribute to the development of the Desire-Belief-Opportunity-model from a symbolic interactionist perspective. The main argument is that this model needs to incorporate the classical notion of definition of the situation to be able to account for the formative impact of interaction on the formation of actor’s beliefs, as well as the complex interdependency between two of its key components, namely the beliefs and the action opportunities of the actor. It is argued that the theoretical advancement of the DBO-model in this particular direction is not only feasible but also brings it considerably closer to the analytical refinement and the empirical validation it currently lacks.

Definitions more geometrarum and Newton's scholium on space and time

Newton's Principia begins with eight formal definitions and a scholium, the so-called scholium on space and time. Despite a history of misinterpretation, scholars now largely agree that the purpose of the scholium is to establish and defend the definitions of key concepts. There is no consensus, however, on how those definitions differ in kind from the Principia's formal definitions and why they are set-off in a scholium. The purpose of the present essay is to shed light on the scholium by focusing on Newton's notion and use of definition. The resulting view is developmental. I argue that when Newton first wrote the Principia, he viewed the scholium's definitions as items of “natural philosophy.” By the time of the third edition, however, he came to view their methodological status differently; he viewed them as belonging to the more qualified “manner of geometers.” I explicate the two methods of natural inquiry and draw out their implications for Newton's account of space.

Pre-Service Mathematics Teachers’ Concept Definitions and Examples Regarding Sets

The purpose of this study is to reveal the concept definitions and examples of pre-service elementary mathematics teachers regarding sets. In this context, students’ formal definitions, personal definitions and examples in sets were investigated. Concept of equal sets, subsets, union, intersection, compliment, and difference were considered as basic concepts of sets in this study. The participants of the study consisted of 79 freshmen studying in the department of elementary mathematics teacher training at a state university of Turkey. The study adopted qualitative research approach and is a sample of a case study. The data of the study was collected from DKFS form and unstructured interviews. The results of the study indicated that most of the pre-service teachers had difficulty in giving notational definitions and daily-life examples while they gave successfully verbal definitions of the basic concepts in sets. It was revealed that verbal definitions, notational, prototype examples with schema, symbols and operational properties were parts of some pre-service teachers’ concept images. Furthermore, some pre-service teachers confused equal sets with equivalent sets and difference with symmetric difference. They also did not consider the universal set in defining the compliment. It was found that most of the pre-service teachers had difficulty in expressing their thoughts using mathematical language throughout the study.

Substance, Accidents and Definition in Giles of Rome’s Quaestiones metaphisicales

Scholars paid scant attention to Giles of Rome’s Quaestiones methaphisicales. This is due to many reasons. The Quaestiones are likely the first of the Aristotelian commentaries written by Giles and all XVI-century printed editions conserve but a reportatio of the course on Metaphysics that Giles probably gave in Paris between 1268/1269 and 1271. Since Giles never edited the text of his lectures, we cannot be sure that Giles approved the list and the contents of the questions we may read today. Moreover, the current list is also incomplete because a study of cross-references in Giles’ Aristotelian commentaries (Donati 1990) showed that Giles wrote other questions, not included in the list we have today. Despite of these features, Giles’ Quaestiones are import both historically and philosophically. They contribute to fixing the chronology of Giles’ first works and to illustrating the metaphysics of the early Giles. In particular, a close examination of the questions on Books VII and VIII of Aristotle’s Metaphysics, devoted to substance and accidents, shows various things. For example, the influence exerted by Averroes’s Commentary on Giles’s teaching and, accordingly, the pivotal role played by the notion of definition in the explanation of the essence of substance and accidents. More generally, such an examination permits us bringing to light the exegetical devices Giles used in order to reconcile Thomas Aquinas’s view of the primacy and unicity of substantial form (a thesis that Giles, albeit with some hesitations, maintains across his career) with his idiomatic position that indeterminate dimensions must precede in some way substantial form. If this were not the case, Giles argues, we could not explain the process of particularization and multiplication of a form that is in itself ‘unparticular’ (imparticularis).

What are Implicit Definitions?

The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely (1) as specifications of the meaning of the primitive terms of a theory and (2) as definitions of higher-order mathematical concepts or structures. We analyze these two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning.

Syntactic Interference: A Study of Ígálá and English Noun Phrases in Malachai 1:6 and Mathew 2:1

Ígálá native speakers face some challenges in their attempt to acquire the English language and one of these challenges is encountered in their attempt to use English Noun Phrases. Learning English Noun Phrases by speakers whose mother-tongue is Ígálá is one of the most frequent and significant areas of difficulties at syntactic level which Ígálá learners of English come across due to the differences between the NP systems in both languages. The Ígálá language has an NP system that functions differently, for instance, the notion of definiteness and indefiniteness of articles are encoded differently than in that of the English language. Given the fact that articles are one of the most frequent words occurring in the English language Noun Phrase, this study pinned down such an important issue by describing how the differences between the Ígálá and English languages in concern to the Noun Phrase system cause Ígálá learners of English to commit errors (Mother-Tongue interference) in their English learning process as a result of Mother-Tongue illiteracy, incompetence in both L1 and L2, and inconsistencies in Ígálá articles. This work was anchored on PSG and labelled brackets as a model of syntactic analysis. The paper made use of bilingual text approach. The work observed that there is direct transfer of the grammatical features of Ígálá to English language and that there is positive transfer of linguistic features from Ígálá to English where there are linguistic similarities between the two languages. The paper also observed that possessive adjectives (his, my, your, her) pose no problem for Ígálá learners of English. The paper concluded by saying that the problems Ígálá L1 speakers encounter while attempting to use English Noun Phrases are based not only on the degree of differences between the Ígálá and English Noun Phrase systems, but inconsistencies in Ígálá articles. Keywords : Second Language, Noun Phrase, Interference. DOI : 10.7176/JLLL/60-06 Publication date :September 30 th 2019

Induction and explanatory definitions in mathematics

In this paper, I argue that there are cases of explanatory induction in mathematics. To do so, I first introduce the notion of explanatory definition in the context of mathematical explanation. A large part of the paper is dedicated to introducing and analyzing this notion of explanatory definition and the role it plays in mathematics. After doing so, I discuss a particular inductive definition in advanced mathematics— $${ CW}$$ -complexes—and argue that it is explanatory. With this, we see that there are cases of explanatory induction.

Determiners and quantifiers in Spanish: types, tests and theories

This article provides an overview about the main facts and analytical options in the domain of determiners and quantifiers in Spanish. It covers the main classification of determiners and their basic syntactic and semantic properties (§1), the differences in behaviour between quantifiers and determiners in the strict sense (§2), the notion of definiteness and the contrasts in the use of the definite and indefinite articles (§3), the notion of specificity (§4) and the main types of quantifiers and how they can be identified (§5). In terms of analytical problems, it discusses whether determiners should be considered heads or not (§6), the areas within the determiner and quantifier domain (§7), the nature of the indefinite article as an element that shares properties with existential quantifiers (§8), the problems posed by proper names (§9) and the possible existence of phonologically null determiners in Spanish (§10). Conclusions are presented in §11.

Theory and Practice of Lexicographic Definition

The paper offers a rigorous characterization of the notion of lexicographic definition: a minimal paraphrase formulated in the same language as the word defined and satisfying six lexicographic principles, which are formulated and discussed. The major types of semantic components in a lexicographic definition are identified and described: firstly, central vs. peripheral components, semantic-class marking components, presuppositional components, actant-specification components, weak components, and metaphor-marking components; secondly, conjunctive and disjunctive components. Three additional topics are introduced: the roles that the definition plays in a lexical entry (accounting for the semantic, syntactic and lexically restricted cooccurrence of the headword); lexical units whose definition is problematic; lexical connotations and semantic labels. Though the perspective offered on lexicographic definition is theory-oriented-within the framework of Explanatory Combinatorial Lexicology (ECL)-, a strong emphasis is put on the writing of actual definitions, a couple dozen of which is proposed and analyzed.

Frege’s Unification

What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature.

Queer in Your Ear: Connecting Space, Community, and Identity in LGBT BBC Radio Programs, 1992–2000

This article analyses two long-running gay and lesbian radio programs from the BBC from the 1990s to highlight different approaches to notions of identity and definition, based on items that focused on interactions with physical space, both public and private. The weekly program Gay and Lesbian London broadcast in London on BBC GLR94.9 contained items that constructed a different relationship between gay identity and locations, compared to Gaytalk on BBC GMR, and its relationship with Manchester. By exploring the significance of gay and lesbian radio in relation to ideas around community, and its relationship with the editorial narrative, the paper argues there is fluidity between community and identity. The subsequent analysis of the radio output in the two programs focuses on the intersection between spatial relationships and sexuality. Content from the Manchester program foregrounded the prominence of the city’s commercial area, the Gay Village, in queer lives, while in London, domesticity and dispersed community apart from the gay scene dominated the narrative. The way these two programs mediated the relationship between communities of listeners and their locations throws light on gay and lesbian experiences during an important period of social and political change.

ABSTRACT INDUCTIVE AND CO-INDUCTIVE DEFINITIONS

AbstractIn [G. Curi, On Tarski’s fixed point theorem. Proc. Amer. Math. Soc., 143 (2015), pp. 4439–4455], a notion of abstract inductive definition is formulated to extend Aczel’s theory of inductive definitions to the setting of complete lattices. In this article, after discussing a further extension of the theory to structures of much larger size than complete lattices, as the class of all sets or the class of ordinals, a similar generalization is carried out for the theory of co-inductive definitions on a set. As a corollary, a constructive version of the general form of Tarski’s fixed point theorem is derived.

Engagement and practical wisdom in clinical practice: a phenomenological study.

In order to understand the lived experiences of physicians in clinical practice, we interviewed eleven expert, respected clinicians using a phenomenological interpretative methodology. We identified the essence of clinical practice as engagement. Engagement accounts for the daily routine of clinical work, as well as the necessity for the clinician to sometimes trespass common boundaries or limits. Personally engaged in the clinical situation, the clinician is able to create a space/time bubble within which the clinical encounter can unfold. Engagement provides an account of clinical practice as a unitary lived experience. This stands in stark contrast to the prevailing notion, referred to as a dual discourse, that describes medicine as the addition of humanism to science. Drawing on Aristotle's notion of phronesis and Sartre's definition of the situation, we illustrate how this novel perspective entwines clinical practice, the person of the clinician, and the clinician's situation.

John Buridan on the Possibility of Defining Definition

The study of the medieval reception of Aristotle’s Topics has largely been oriented toward debates on dialectical argumentation. And this is surely right. Nonetheless, I wish to approach John Buridan’s commentary on the Topics from another perspective, which highlights some semantic features of the set of predicates around which the work is organized. Thus, in my paper I will first reconstruct Buridan’s account of the identification of the predicates discussed in the Topics. I will argue that, for him, they are different in that they reflect one or more features of the way in which definiens and definiendum relate. By doing this, I will shed light on the role the notion of definition plays in Buridan’s commentary, so that an interpretation of it as a work on definition becomes promising. In the second part of the paper, I will offer an analysis of Buridan’s first move in his commentary toward a theory of definition. It concerns the problem of whether there is a definition of definition. In examining Buridan’s answer, I will argue for the close connection between his treatment of definitions and his theory of supposition, so that distinctions among the different modes of supposition help him to disambiguate statements in their possible meanings, and thus to clarify the difficulty related to the definability of definition.

Conceptual Analysis and Analytical Definitions in Frege

AbstractLogical (or conceptual) analysis is in Frege primarily not an analysis of a concept but of its sense. Five Fregean philosophical principles are presented as constituting a framework for a theory of logical or conceptual analysis, which I call analytical explication. These principles, scattered and sometime latent in his writings are operative in Frege's critique of other views and in his constructive development of his own view. The proposed conception of analytical explication is partially rooted in Frege's notion of analytical definition. It may also be the basis of what is required of a reduction of one domain to another, if it is to have the philosophical significance many reductions allegedly have.

БАЗОВЫЕ ПОНЯТИЯ ЛИНГВОКУЛЬТУРОЛОГИЧЕСКОГО АНАЛИЗА

The article represents the attempt to consider and comprehend methodological and conceptual notions, the definition and selection of which faces every researcher in the process of linguistic and cultural analysis of a text. It focuses on such key concepts as language, culture, language personality, linguistic worldview, cultural specificity, cultural code, concept, conceptual sphere, mythologem, etc. Despite numerous studies devoted to these realia, some aspects still require clarification and additional theoretical reasoning. The aim of the research in the article is also the study of sociocultural and linguistic trends of the formation of the national linguistic identity in the framework of intercultural communication and the characteristic of the features of the linguistic worldview of an individual.Based on the results of the study there is a conclusion that cultural linguistics is a scientific paradigm with a developed conceptual basis and definite categorical notion.