On the definition of an infinitely-many-valued predicate calculus

1960 ◽  
Vol 25 (3) ◽  
pp. 212-216 ◽  
Author(s):  
Joseph D. Rutledge
Keyword(s):  
Predicate Calculus ◽  
Extended System ◽  
Index Set ◽  
Formal Framework ◽  
Individual Variables ◽  
Definition Of ◽  
The Individual

This paper presents a class of plausible definitions for validity of formulas in the infinitely-many-valued extension of the Łukasiewicz predicate calculus, and shows that all of them are equivalent. This extended system is discussed in some form in [3] and [4]; the questions discussed here are raised rather briefly in the latter.We first describe the formal framework for the validity definition. The symbols to be used are the following: the connectives + and ‐, which are the strong disjunction B of [2] and negation respectively; the predicate variables Pi for i ∈ I, where I may be taken as the integers; the existential quantifiers E(J), where J⊆I, and I may be thought of as the index set on the individual variables, which however do not appear explicitly in this formulation.

Completeness in the theory of types

1950 ◽  
Vol 15 (2) ◽  
pp. 81-91 ◽  
Author(s):  
Leon Henkin
Keyword(s):  
Functional Calculus ◽  
Formal System ◽  
Axiom System ◽  
Second Order ◽  
True Proposition ◽  
Arbitrary Domain ◽  
Individual Variables ◽  
Definition Of ◽  
The Individual ◽  
Positive Integers

The first order functional calculus was proved complete by Gödel in 1930. Roughly speaking, this proof demonstrates that each formula of the calculus is a formal theorem which becomes a true sentence under every one of a certain intended class of interpretations of the formal system.For the functional calculus of second order, in which predicate variables may be bound, a very different kind of result is known: no matter what (recursive) set of axioms are chosen, the system will contain a formula which is valid but not a formal theorem. This follows from results of Gödel concerning systems containing a theory of natural numbers, because a finite categorical set of axioms for the positive integers can be formulated within a second order calculus to which a functional constant has been added.By a valid formula of the second order calculus is meant one which expresses a true proposition whenever the individual variables are interpreted as ranging over an (arbitrary) domain of elements while the functional variables of degree n range over all sets of ordered n-tuples of individuals. Under this definition of validity, we must conclude from Gödel's results that the calculus is essentially incomplete.It happens, however, that there is a wider class of models which furnish an interpretation for the symbolism of the calculus consistent with the usual axioms and formal rules of inference. Roughly, these models consist of an arbitrary domain of individuals, as before, but now an arbitrary class of sets of ordered n-tuples of individuals as the range for functional variables of degree n. If we redefine the notion of valid formula to mean one which expresses a true proposition with respect to every one of these models, we can then prove that the usual axiom system for the second order calculus is complete: a formula is valid if and only if it is a formal theorem.

A model theoretic approach to Malcev conditions

1977 ◽  
Vol 42 (2) ◽  
pp. 277-288 ◽  
Author(s):  
John T. Baldwin ◽  
Joel Berman
Keyword(s):  
Extensive Study ◽  
Second Order ◽  
Theoretic Approach ◽  
Easy Consequence ◽  
First Order ◽  
Congruence Relations ◽  
Individual Variables ◽  
Definition Of ◽  
The Individual ◽  
Necessary And Sufficient

A varietyV(equational class of algebras) satisfies a strong Malcev condition ∃f1,…, ∃fnθ(f1, …,fn,x1, …,xm) where θ is a conjunction of equations in the function variablesf1, …,fnand the individual variablesx1, …,xm, if there are polynomial symbolsp1, …,pnin the language ofVsuch that ∀x1, …,xmθ(p1…,pn,x1, …,xm) is a law ofV. Thus a strong Malcev condition involves restricted second order quantification of a strange sort. The quantification is restricted to functions which are “polynomially definable”. This notion was introduced by Malcev [6] who used it to describe those varieties all of whose members have permutable congruence relations. The general formal definition of Malcev conditions is due to Grätzer [1]. Since then and especially since Jónsson's [3] characterization of varieties with distributive congruences there has been extensive study of strong Malcev conditions and the related concepts: Malcev conditions and weak Malcev conditions.In [9], Taylor gives necessary and sufficient semantic conditions for a class of varieties to be defined by a (strong) Malcev condition. A key to the proof is the translation of the restricted second order concepts into first order concepts in a certain many sorted language. In this paper we show that, given this translation, Taylor's theorem is an easy consequence of a result of Tarski [8] and the standard preservation theorems of first order logic.

Some forms of completeness

1962 ◽  
Vol 27 (3) ◽  
pp. 344-352 ◽  
Author(s):  
P. C. Gilmore
Keyword(s):  
Predicate Symbol ◽  
Constant Term ◽  
Predicate Calculus ◽  
First Order ◽  
Individual Variables ◽  
The Individual ◽  
And Function ◽  
Order Predicate Calculus

By a theory is meant an applied first-order predicate calculus with at least one predicate symbol and perhaps some individual constants and function symbols and a specified set of axioms. In addition to the terms defined by means of the individual variables, constants, and function symbols a theory may also include among its terms those constructed by means of operators such as the epsilon or iota operators; that is, expressions like (εχΡ) or (οχΡ), where P is a well formed formula (wff) of the theory, may also be terms. A constant term of a theory F is then a term in which no variable occurs free. We are interested only in theories which have at least one constant term so that if a theory doesn't have any individual constants it must necessarily admit as terms expressions constructed by means of operators. A sentence of a theory F is a closed wff.

Development of a German-Language Questionnaire to Measure Collective Orientation as an Individual Attitude

2017 ◽  
Vol 76 (3) ◽  
pp. 91-105 ◽  
Author(s):  
Vera Hagemann
Keyword(s):  
Team Performance ◽  
Reliability And Validity ◽  
Future Research ◽  
German Language ◽  
Team Members ◽  
Collective Orientation ◽  
Team Research ◽  
German Speaking ◽  
Individual Variables ◽  
The Individual

Abstract. The individual attitudes of every single team member are important for team performance. Studies show that each team member’s collective orientation – that is, propensity to work in a collective manner in team settings – enhances the team’s interdependent teamwork. In the German-speaking countries, there was previously no instrument to measure collective orientation. So, I developed and validated a German-language instrument to measure collective orientation. In three studies (N = 1028), I tested the validity of the instrument in terms of its internal structure and relationships with other variables. The results confirm the reliability and validity of the instrument. The instrument also predicts team performance in terms of interdependent teamwork. I discuss differences in established individual variables in team research and the role of collective orientation in teams. In future research, the instrument can be applied to diagnose teamwork deficiencies and evaluate interventions for developing team members’ collective orientation.

The Autobiographical Subject and the Death Penalty

2013 ◽  
Vol 35 (2) ◽  
pp. 165-187
Author(s):  
E. S. Burt
Keyword(s):  
Death Penalty ◽  
First Person ◽  
Philosophical Investigation ◽  
The Subject ◽  
Definition Of ◽  
The Individual

Why does writing of the death penalty demand the first-person treatment that it also excludes? The article investigates the role played by the autobiographical subject in Derrida's The Death Penalty, Volume I, where the confessing ‘I’ doubly supplements the philosophical investigation into what Derrida sees as a trend toward the worldwide abolition of the death penalty: first, to bring out the harmonies or discrepancies between the individual subject's beliefs, anxieties, desires and interests with respect to the death penalty and the state's exercise of its sovereignty in applying it; and second, to provide a new definition of the subject as haunted, as one that has been, but is no longer, subject to the death penalty, in the light of the worldwide abolition currently underway.

ГЕРМЕНЕВТИКА ЛИЧНОСТИ КАК МЕТОД СОВРЕМЕННОЙ ПЕРСОНОЛОГИИ

1970 ◽  
Vol 6 (1) ◽  
pp. 32-42
Author(s):  
Елена Старовойтенко
Keyword(s):  
Text Setting ◽  
Research Setting ◽  
Textual Representations ◽  
General Scientific ◽  
Definition Of ◽  
The Individual ◽  
The Continuum

Персонологическая интерпретация текстов предполагает реализацию общенаучных, а также специфических для персонологии, герменевтических установок, к которым относятся: установка на интерпретацию текста как исследование, установка на разнообразие герменевтических действий с текстом, установка на выявление неисследованных содержаний текста, установка на творческое постижение тайн текста, установка на целостное отношение к личности и "Я" автора текста, установка на выявление способности автора быть "практикующим феноменологом", установка на определение места изучаемого текста в континууме текстовых репрезентаций "личности", установка на соотнесение своего понимания текста с другими интерпретациями и их интеграцию, установка на раскрытие сущности авторской "идеи личности", возможное только в единстве интерпретаций, установка на построение и применение герменевтической модели, определяющей процедуру интерпретации как исследования и творчества, установка на определение места проделанного герменевтического поиска в культуре познания и жизни личности, установка на интерпретацию различных видов "текстов личности". Personological interpretation of texts suggests the implementation of the general scientific and also hermeneutical settings specific for Personology which include the setting of the interpretation of the text as a research, setting of a variety of hermeneutical actions with the text, setting to identify unexplored contents of the text, setting of the creative comprehension of the mysteries of the text, setting of the integrity of the attitude of the individual and the "I" of the author of the text, setting to reveal the author's ability to be "practicing phenomenologist", setting of the definition of the place in the text in the continuum of textual representations of the "personality", setting in the correlation of the understanding of the text with other interpretations and their integration, setting of the disclosure of the author's "ideas person" is possible only in the unity of interpretation, setting of the construction and usage of hermeneutical models defining the procedure for the interpretation of both studies and work, the setting to determine the place of hermeneutical research in culture and knowledge of a person's life, setting of the interpretation of various types of "texts of the individual."

¿Quién soy yo? Reflexiones teórico sistémicas acerca de la indentidad individual

2017 ◽  
Vol 1 (1) ◽  
pp. 15-31
Author(s):  
Francisco Xavier Morales
Keyword(s):  
Identity Construction ◽  
Social Systems ◽  
Social Contexts ◽  
Individual Identity ◽  
Contemporary Society ◽  
Self Identity ◽  
Moral Communication ◽  
Identity Based ◽  
Definition Of ◽  
The Individual

The problem of identity is an issue of contemporary society that is not only expressed in daily life concerns but also in discourses of politics and social movements. Nevertheless, the I and the needs of self-fulfillment usually are taken for granted. This paper offers thoughts regarding individual identity based on Niklas Luhmann’s systems theory. From this perspective, identity is not observed as a thing or as a subject, but rather as a “selfillusion” of a system of consciousness, which differentiates itself from the world, event after event, in a contingent way. As concerns the definition  of contents of self-identity, the structures of social systems define who is a person, how he or she should act, and how much esteem he or she should receive. These structures are adopted by consciousness as its own identity structures; however, some social contexts are more relevant for self-identity construction than others. Moral communication increases the probability that structure appropriation takes place, since the emotional element of identity is linked to the esteem/misesteem received by the individual from the interactions in which he or she participates.

Public Service Motivation in Buffy the Vampire Slayer

Public Voices ◽  
2016 ◽  
Vol 12 (1) ◽  
pp. 67 ◽  
Author(s):  
Sharon Mastracci
Keyword(s):  
Popular Culture ◽  
Public Service ◽  
Public Service Motivation ◽  
Public Servants ◽  
Buffy The Vampire Slayer ◽  
The Public ◽  
American Popular Culture ◽  
Public Servant ◽  
Definition Of ◽  
The Individual

In this paper, the author examines public service as depicted in the television series Buffy the Vampire Slayer (BtVS). First, she shows how slaying meets the economist’s definition of a public good, using the BtVS episode “Flooded” (6.04). Second, she discusses public service motivation (PSM) to determine whether or not Buffy, a public servant, operates from a public service ethic. Relying on established measures and evidence from shooting scripts and episode transcripts, the author concludes Buffy is a public servant motivated by a public service ethic. In this way, BtVS informs scholarship on public service by broadening the concept of PSM beyond the public sector; prompting one to wonder whether it is located in a sector, an occupation, or in the individual. These conclusions allow the author to situate Buffy alongside other idealized public servants in American popular culture.

The Concept of the Individual and Its Scope

2018 ◽  
Author(s):  
Ursula Renz
Keyword(s):  
Strict Sense ◽  
Physical Concept ◽  
Individual Group ◽  
Group Minds ◽  
Definition Of ◽  
The Individual

This chapter discusses the implications of Spinoza’s concept of individual bodies, as introduced in the definition of individuum in the physical digression. It begins by showing that this definition allows for an extremely wide application of the term; accordingly, very different sorts of physical entities can be described as Spinozistic individuals. Given the quite distinct use of the terms divisibilis and indivisibilis in his metaphysics, however, the chapter argues that the physical concept of individuality is not universally applied in the Ethics but reserved for physical or natural-philosophical considerations. The chapter concludes with a discussion of the problem of collective individuals. It is argued that, while societies or states are described as individual bodies, they do not constitute individual group minds in the strict sense of the term for Spinoza. This in turn indicates that minds are not individuated in the same way as bodies.

scholarly journals Validity of the Gender Dysphoria diagnosis and incidence trends in Sweden: a nationwide register study

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Malin Indremo ◽  
Richard White ◽  
Thomas Frisell ◽  
Sven Cnattingius ◽  
Alkistis Skalkidou ◽  
...  
Keyword(s):  
Gender Dysphoria ◽  
Age Groups ◽  
Medical Intervention ◽  
Future Research ◽  
Advantages And Disadvantages ◽  
Incidence Trends ◽  
Interaction Terms ◽  
Definition Of ◽  
The Individual ◽  
Nationwide Register Study

AbstractThe aim of this study was to examine the validity of the Gender Dysphoria (GD) diagnoses in the Swedish National Patient Register (NPR), to discuss different register-based definitions of GD and to investigate incidence trends. We collected data on all individuals with registered GD diagnoses between 2001 and 2016 as well as data on the coverage in the NPR. We regarded gender confirming medical intervention (GCMI) as one proxy for a clinically valid diagnosis and calculated the positive predictive value (PPV) for receiving GCMI for increasing number of registered GD diagnoses. We assessed crude and coverage-adjusted time trends of GD during 2004–2015 with a Poisson regression, using assigned sex and age as interaction terms. The PPV for receiving GCMI was 68% for ≥ 1 and 79% for ≥ 4 GD-diagnoses. The incidence of GD was on average 35% higher with the definition of ≥ 1 compared to the definition of ≥ 4 diagnoses. The incidence of GD, defined as ≥ 4 diagnoses increased significantly during the study period and mostly in the age categories 10–17 and 18–30 years, even after adjusting for register coverage. We concluded that the validity of a single ICD code denoting clinical GD in the Swedish NPR can be questioned. For future research, we propose to carefully weight the advantages and disadvantages of different register-based definitions according to the individual study’s needs, the time periods involved and the age-groups under study.

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