scholarly journals Model-Theoretic Accounts of Logical Consequence - Themes from Etchemendy

2021 ◽  
Author(s):  
◽  
Kasper Højbjerg Christensen
Keyword(s):  
Standard Model ◽  
Model Theory ◽  
Logical Consequence ◽  
Kripke Semantics ◽  
Logical Necessity ◽  
Representational Model ◽  
Definition Of ◽  
In Virtue Of

<p>This thesis is a discussion and continuation of a project started by John Etchemendy with his criticism of Tarski's account of logical consequence. To this end the two central concepts of the thesis are those of an interpretational and representational model-theoretic account of logical consequence, respectively.  The first chapter introduces Etchemendy's criticism of Tarski's account of logical consequence, a criticism which turns essentially on an interpretation of Tarski according to which his proposed account gives rise to a purely interpretational model-theoretic account of logical consequence. Consequently there must be a representational aspect to our model-theoretic definition of logical consequence.  The second chapter introduces Etchemendy's notion of logical consequence: that of being truth preserving in virtue of the semantics of the involved terms. While this notion is representational, we argue that Etchemendy's notion of a categorematic treatment of terms reintroduces an interpretational aspect back into the model theory. The chapter investigates the resulting notion, compares it to other notions in the literature, and presents certain results that can be proved, under certain conditions, about this notion in relation to the notion of being truth preserving in virtue of the semantics of all terms.  Chapter three of the thesis is concerned with the question of how a standard model, seen as a domain and an interpretation function, manages to capture the different notions of model-theoretic consequence. As we explain, this question is most pressing when we want our models to both represent and interpret, and we will present a theory which allows us to see the models as both representing non-actual possibilities as well as provide interpretations for the terms.  The fourth chapter applies the lessons of the preceeding chapters to argue that Kripke Semantics can be seen as capturing the notion of being truth preserving in all possibilities under all interpretations of the non-logical terminology in the case where our language is augmented with an operator, ⃞, to represent logical necessity. We will argue this point by contrasting it with, though not necessarily disagreeing with, claims made by various authors to the effect that Kripke Semantics is not the appropriate semantics when our language contains an operator for logical necessity.</p>

scholarly journals Model-Theoretic Accounts of Logical Consequence - Themes from Etchemendy

2021 ◽  
Author(s):  
◽  
Kasper Højbjerg Christensen
Keyword(s):  
Standard Model ◽  
Model Theory ◽  
Logical Consequence ◽  
Kripke Semantics ◽  
Logical Necessity ◽  
Representational Model ◽  
Definition Of ◽  
In Virtue Of

<p>This thesis is a discussion and continuation of a project started by John Etchemendy with his criticism of Tarski's account of logical consequence. To this end the two central concepts of the thesis are those of an interpretational and representational model-theoretic account of logical consequence, respectively.  The first chapter introduces Etchemendy's criticism of Tarski's account of logical consequence, a criticism which turns essentially on an interpretation of Tarski according to which his proposed account gives rise to a purely interpretational model-theoretic account of logical consequence. Consequently there must be a representational aspect to our model-theoretic definition of logical consequence.  The second chapter introduces Etchemendy's notion of logical consequence: that of being truth preserving in virtue of the semantics of the involved terms. While this notion is representational, we argue that Etchemendy's notion of a categorematic treatment of terms reintroduces an interpretational aspect back into the model theory. The chapter investigates the resulting notion, compares it to other notions in the literature, and presents certain results that can be proved, under certain conditions, about this notion in relation to the notion of being truth preserving in virtue of the semantics of all terms.  Chapter three of the thesis is concerned with the question of how a standard model, seen as a domain and an interpretation function, manages to capture the different notions of model-theoretic consequence. As we explain, this question is most pressing when we want our models to both represent and interpret, and we will present a theory which allows us to see the models as both representing non-actual possibilities as well as provide interpretations for the terms.  The fourth chapter applies the lessons of the preceeding chapters to argue that Kripke Semantics can be seen as capturing the notion of being truth preserving in all possibilities under all interpretations of the non-logical terminology in the case where our language is augmented with an operator, ⃞, to represent logical necessity. We will argue this point by contrasting it with, though not necessarily disagreeing with, claims made by various authors to the effect that Kripke Semantics is not the appropriate semantics when our language contains an operator for logical necessity.</p>

Essentialism and Logical Consequence

2018 ◽  
Author(s):  
Rosanna Keefe ◽  
Jessica Leech
Keyword(s):  
Logical Consequence ◽  
Prima Facie ◽  
Logical Pluralism ◽  
Logical Necessity ◽  
Popular View

According to an increasingly popular view, the source of logical necessity is to be found in the essences of logical entities. One might be tempted to extend the view further in using it to tackle fundamental questions surrounding logical consequence. This chapter enquires: how does a view according to which the facts about logical consequence are determined by the essences of logical entities look in detail? Are there any more or less obvious problems arising for such a view? The chapter uncovers a prima facie result in favour of logical pluralism. However, it then goes on to raise some concerns for this result. It argues that, considered generally, it is difficult to see how essence could do all of the requisite work alone. The chapter also shows how considering things from the perspective of disputes between particular rival logics makes an interesting and important difference to the picture of things presented by the essentialist account.

scholarly journals Reactivity in social scientific experiments: what is it and how is it different (and worse) than a Placebo effect?

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
María Jiménez-Buedo
Keyword(s):  
Experimental Data ◽  
Conceptual Framework ◽  
Placebo Effect ◽  
Placebo Effects ◽  
Causal Inferences ◽  
Scientific Experiments ◽  
Social Scientific ◽  
The Many ◽  
Definition Of ◽  
In Virtue Of

AbstractReactivity, or the phenomenon by which subjects tend to modify their behavior in virtue of their being studied upon, is often cited as one of the most important difficulties involved in social scientific experiments, and yet, there is to date a persistent conceptual muddle when dealing with the many dimensions of reactivity. This paper offers a conceptual framework for reactivity that draws on an interventionist approach to causality. The framework allows us to offer an unambiguous definition of reactivity and distinguishes it from placebo effects. Further, it allows us to distinguish between benign and malignant forms of the phenomenon, depending on whether reactivity constitutes a danger to the validity of the causal inferences drawn from experimental data.

scholarly journals First Order Languages: Further Syntax and Semantics

2011 ◽  
Vol 19 (3) ◽  
pp. 179-192 ◽  
Author(s):  
Marco Caminati
Keyword(s):  
Model Theory ◽  
Atomic Formula ◽  
Order Model ◽  
Logical Implication ◽  
First Order ◽  
Definition Of ◽  
Theory Interpretation

First Order Languages: Further Syntax and SemanticsThird of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are introduced. Depth of a formula. Definition of satisfaction and entailment (aka entailment or logical implication) relations, see [18] III.3.2 and III.4.1 respectively.

scholarly journals The ethics of teacher and learner at Mekdad Yalgen and its educational applications: أخلاقيات المعلم والمتعلم عند مقداد يالجن وتطبيقاتها التربوية

2017 ◽  
Vol 1 (3) ◽  
Author(s):  
Hind Mohammed bin Abdullah Al Ahmad ◽  
Afnan bin Fahad bin Abdullah Al Rashed
Keyword(s):  
Conceptual Framework ◽  
Moral Education ◽  
Educational Thought ◽  
Educational Framework ◽  
Moral System ◽  
Educational Applications ◽  
Definition Of ◽  
The Individual

This study, entitled "The Ethics of the Teacher and the Learner at Mekdad Yalgen and its Educational Applications," included four chapters in addition to the list of references. The study aimed to identify the cultural, social and educational framework that influenced educational ideas at Mekdad Yaljin, and on the first and the first principles which are the starting points of the study. And the ethics of the teacher and its educational applications at Mekdad Yalgen, the ethics of the learner and its educational applications at Mekdad Yalgen, and on the most prominent ways to promote the moral and moral learners at Mekdad Yalgen. Studying the need to conduct an educational intellectual study that shows the importance of teacher and learner ethics in educational thinkers. In the second chapter, it contains the conceptual framework and previous studies. The study covered the conceptual framework of Mekdad Yalgen, his birth, his stages, his education, his efforts and his scientific achievements, and the King Phil Award, and the most important factors influencing his educational idea. The researcher sought to follow the relevant studies in Yaljin and studies related to the ethics of the teacher and the learner. The third chapter deals with the general principles of educational thought at Mekdad Yalgen starting with the theory of knowledge of its concept and its dimensions. Then, it tackles the concept of human nature and its components, then the Islamic moral system, the definition of morality and the place of ethics. In the fourth chapter: the researcher dealt with the ethics of the teacher and learner at Mekdad Yalgen and its educational applications. Hali included the importance of moral education and the role of Islamic moral education in the building of the individual, society and human civilization, and also contained the ethics of the teacher and the learner and its educational applications at Mekdad Balgin.

The anatytic conception of truth and the foundations of arithmetic

2000 ◽  
Vol 65 (1) ◽  
pp. 33-102 ◽  
Author(s):  
Peter Apostoli
Keyword(s):  
Philosophy Of Mathematics ◽  
Logical Truth ◽  
Numerical Identity ◽  
Hume’S Principle ◽  
Contextual Definition ◽  
Definition Of ◽  
Axiomatic Set Theory ◽  
In Virtue Of ◽  
Second Order Logic ◽  
Foundations Of Arithmetic

Until very recently, it was thought that there couldn't be any current interest in logicism as a philosophy of mathematics. Indeed, there is an old argument one often finds that logicism is a simple nonstarter just in virtue of the fact that if it were a logical truth that there are infinitely many natural numbers, then this would be in conflict with the existence of finite models. It is certainly true that from the perspective of model theory, arithmetic cannot be a part of logic. However, it is equally true that model theory's reliance on a background of axiomatic set theory renders it unable to match Frege's Theorem, the derivation within second order logic of the infinity of the number series from the contextual “definition” of the cardinality operator. Called “Hume's Principle” by Boolos, the contextual definition of the cardinality operator is presented in Section 63 of Grundlagen, as the statement that, for any concepts F and G,the number of F s = the number of G sif, and only if,F is equinumerous with G.The philosophical interest in Frege's Theorem derives from the thesis, defended for example by Crispin Wright, that Hume's principle expresses our pre-analytic conception of assertions of numerical identity. However, Boolos cites the very fact that Hume's principle has only infinite models as grounds for denying that it is logically true: For Boolos, Hume's principle is simply a disguised axiom of infinity.

Tarski

Truth ◽  
2011 ◽  
Author(s):  
Alexis G. Burgess ◽  
John P. Burgess
Keyword(s):  
Mathematical Logic ◽  
Model Theory ◽  
The State ◽  
Truth Predicate ◽  
Object Language ◽  
French And English ◽  
Direct Definition ◽  
Definition Of ◽  
Basic Features ◽  
Self Reference

This chapter offers a simplified account of the most basic features of Alfred Tarski's model theory. Tarski foresaw important applications for a notion of truth in mathematics, but also saw that mathematicians were suspicious of that notion, and rightly so given the state of understanding of it circa 1930. In a series of papers in Polish, German, French, and English from the 1930s onward, Tarski attempted to rehabilitate the notion for use in mathematics, and his efforts had by the 1950s resulted in the creation of a branch of mathematical logic known as model theory. The chapter first considers Tarski's notion of truth, which he calls “semantic” truth, before discussing his views on object language and metalanguage, recursive versus direct definition of the truth predicate, and self-reference.

Material Consequence and Formal Grounding

2020 ◽  
Vol 57 (2) ◽  
pp. 79-95
Author(s):  
Elena G. Dragalina-Chernaya ◽  
Keyword(s):  
Logical Consequence ◽  
Logical Relation ◽  
Fixed Domain ◽  
Classical Definition ◽  
Modal Force ◽  
Definition Of

According to Alfred Tarski’s classical definition, logical consequence is necessary and formal. This paper focuses on the question: In what sense (if any) is material consequence a logical relation? For Tarski, material consequence has no modal force. Treating all terms (of a language with a fixed domain) as logical, he reduces logical consequence to material consequence. Thus, Tarskian material consequence seems to be a logical oxymoron designed to emphasize the importance of the distinction between logical and extra-logical terms for the definition of logical consequence. Historically, however, there have been different approaches to material consequences. This paper attempts to provide an investigation into the parallels between Tarski’s dichotomy of formal and material consequence and the modern

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