Model-Theoretic Accounts of Logical Consequence - Themes from Etchemendy

<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>

Model-Theoretic Accounts of Logical Consequence - Themes from Etchemendy

<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>

Rules, understanding and language games in mathematics

The article is devoted to the applicability of Wittgenstein’s following the rule in the context of his philosophy of mathematics to real mathematical practice. It is noted that in «Philosophical Investigations» and «Remarks on the Foundations of Mathematics» Wittgenstein resorted to the analysis of rather elementary mathematical concepts, accompanied also by the inherent ambiguity and ambiguity of his presentation. In particular, against this background, his radical conventionalism, the substitution of logical necessity with the «form of life» of the community, as well as the inadequacy of the representation of arithmetic rules by a language game are criticized. It is shown that the reconstruction of the Wittgenstein concept of understanding based on the Fregian division of meaning and referent goes beyond the conceptual framework of Wittgenstein language games.

Al-Ghazali And Hume On Natural Causal Necessity And Miracles

This paper argues that Al-Ghazali and Hume arrived at same conclusion i.e.both reject natural causality as a logical necessity however they provide very different premises for this conclusion. Moreover, Hume’s rejection of the natural causal necessity leads him to religious skepticism whereas, Al-Ghazali’s rejection of natural causal necessity leads him to have a strong faith in God and Miracles. The paper discusses the problem of causation in their philosophies focusing on the issues such as: causation as habit; uniformity in the natural order; causation is a mere sequence of observed things; whether causal relation is ontological or epistemological; issues related to miracles and diverse possibilities. Furthermore, the paper also focuses on the issue of Occasionalism and free will with special reference to Al-Ghazali and Hume.

The Principle of Excluded Middle in Kant

The principle of excluded middle is more important than is commonly believed for understanding Kant's overall philosophical project. In the article, this principle is examined in the following contexts: (i) kinds of judgments, (ii) concepts of opposition, negation, and determination, and (iii) apagogic proof. It is first explained how the principle of excluded middle is employed by Kant in distinguishing between the kinds of judgment. Also called the principle of division, it is the principle of disjunctive and apodictic judgments in Kant's famous table of judgments. Next, the Author shows which kind of opposition is related to the principle of the excluded middle. As a merely logical criterion of truth, this principle grounds the logical necessity of a cognition and plays an important role in the use of apagogical proofs. Then Kant's account of logical negation will be investigated briefly. Negative judgment with a negative copula indicates that something is not contained within the sphere of a given concept. This process occurs in accordance with the principle of excluded middle. Finally, an analysis is made of how Kant presents the metaphysical principle of thoroughgoing determination and its differences from the logical principle of excluded middle.

SOCIAL EXPRESSION IN MULTIMEDIA TEXTS

The article investigates functional techniques of extralinguistic expression in multimedia texts; the effectiveness of figurative expressions as a reaction to modern events in Ukraine and their influence on the formation of public opinion is shown. Publications of journalists, broadcasts of media resonators, experts, public figures, politicians, readers are analyzed. The language of the media plays a key role in shaping the worldview of the young political elite in the first place. The essence of each statement is a focused thought that reacts to events in the world or in one’s own country. The most popular platform for mass information and social interaction is, first of all, network journalism, which is characterized by mobility and unlimited time and space. Authors have complete freedom to express their views in direct language, including their own word formation. Phonetic, lexical, phraseological and stylistic means of speech create expression of the text. A figurative word, a good aphorism or proverb, a paraphrased expression, etc. enhance the effectiveness of a multimedia text. This is especially important for headlines that simultaneously inform and influence the views of millions of readers. Given the wide range of issues raised by the Internet as a medium, research in this area is interdisciplinary. The science of information, combining language and social communication, is at the forefront of global interactions. The Internet is an effective source of knowledge and a forum for free thought. Nonlinear texts (hypertexts) – «branching texts or texts that perform actions on request», multimedia texts change the principles of information collection, storage and dissemination, involving billions of readers in the discussion of global issues. Mastering the word is not an easy task if the author of the publication is not well-read, is not deep in the topic, does not know the psychology of the audience for which he writes. Therefore, the study of media broadcasting is an important component of the professional training of future journalists. The functions of the language of the media require the authors to make the right statements and convincing arguments in the text. Journalism education is not only knowledge of imperative and dispositive norms, but also apodictic ones. In practice, this means that there are rules in media creativity that are based on logical necessity. Apodicticity is the first sign of impressive language on the platform of print or electronic media. Social expression is a combination of creative abilities and linguistic competencies that a journalist realizes in his activity. Creative self-expression is realized in a set of many important factors in the media: the choice of topic, convincing arguments, logical presentation of ideas and deep philological education. Linguistic art, in contrast to painting, music, sculpture, accumulates all visual, auditory, tactile and empathic sensations in a universal sign – the word. The choice of the word for the reproduction of sensory and semantic meanings, its competent use in the appropriate context distinguishes the journalist-intellectual from other participants in forums, round tables, analytical or entertainment programs. Expressive speech in the media is a product of the intellect (ability to think) of all those who write on socio-political or economic topics. In the same plane with him – intelligence (awareness, prudence), the first sign of which (according to Ivan Ogienko) is a good knowledge of the language. Intellectual language is an important means of organizing a journalistic text. It, on the one hand, logically conveys the author’s thoughts, and on the other – encourages the reader to reflect and comprehend what is read. The richness of language is accumulated through continuous self-education and interesting communication. Studies of social expression as an important factor influencing the formation of public consciousness should open up new facets of rational and emotional media broadcasting; to trace physical and psychological reactions to communicative mimicry in the media. Speech mimicry as one of the methods of disguise is increasingly becoming a dangerous factor in manipulating the media. Mimicry is an unprincipled adaptation to the surrounding social conditions; one of the most famous examples of an animal characterized by mimicry (change of protective color and shape) is a chameleon. In a figurative sense, chameleons are called adaptive journalists. Observations show that mimicry in politics is to some extent a kind of game that, like every game, is always conditional and artificial.

Causal Powers and Structures

Brian Ellis provides a detailed and systemic overview of his version of dispositional essentialism. Ellis is famous for having developed and defended a mixed ontology for scientific realism. This is a robustly Aristotelian ontology that involves a mix of categorical and essentially dispositional properties inhering as universal in individualized entities. In this contribution, Ellis briefly defends this sort of ontology by arguing that it, or something very much like it, is necessary to provide an account of the system of reality discovered through modern science. It is, moreover, entirely adequate for the job of accounting for the ontology of modern science. He then turns to consider three objections to his ontology. The first is what other contributors will call the ‘directedness problem’, which is the idea that powers are directed at their manifestation in a way analogous to the directedness of intentionality. The second is what other contributors call the ‘intrinsicness problem’, which is the idea that causal powers are intrinsic to or inhering in their subject. The third is what other contributors call the ‘necessity problem’, which is the idea that there is something important and distinctive about metaphysical necessity vis-à-vis logical necessity.

Three Tensions in the Theory of Racial Capitalism

In this essay the author assesses the relevance of scholarship on racial capitalism for sociological theory. The author highlights three tensions within the existing literature: (1) whether “race” as opposed to other forms of difference is the primary mode of differentiation in capitalism, (2) whether deficiencies in existing theory warrant the new concept “racial capitalism,” and (3) whether the connection between race and capitalism is a contingent or logical necessity. Existing discussions of racial capitalism implicitly or explicitly raise these tensions, but they do not adequately resolve them. Nonetheless, they remain important for generating further theory and research.

Challenges to Open Inquiry

Knowledge grows when conventional wisdom can be challenged, extended, modified, updated, and, in some cases, proven to be completely wrong. This doesn’t mean that all of today’s socially informed beliefs are wrong. But it does mean that it would be a mistake to assume that all of them must be right. If history is any guide, some percentage of what are taken as “truths” today will in fact be understood to be wrong in the future. If that proposition is accepted, then of logical necessity, moving toward a fuller understanding of complex social issues requires viewing them with a wide aperture, and with a willingness to engage with, criticize, and either accept or reject hypotheses that may be out of step with the three beliefs.

Comments on Fabrice Correia’s “More on the Reduction of Necessity to Essence”

I have long admired Fabrice Correia’s work on the conceptual foundations of metaphysics and his present chapter is a characteristically judicious and original contribution to the subject. He is principally concerned with certain reductive theses that I propounded in “Essence and Modality” (EM; 1994). These are that a metaphysical necessity is a proposition true in virtue of the nature of all objects, that a conceptual necessity is a proposition true in virtue of the nature of all concepts, and that a logical necessity is a proposition true in virtue of the nature of all logical concepts. Given that there are different notions of what it is for a proposition to be true in virtue of the nature of some objects, Correia’s interest is in what notion or notions of this sort might underwrite these various reductive claims and, to this end, he is prepared in principle to relinquish any other desiderata one might wish to impose upon these notions....