What Do We Mean by Logical Consequence?

In the beginning of the 20th century, many prominent logicians and mathematicians, such as Frege, Russell, Hilbert, and many others, felt that mathematics needed a very rigorous foundation in logic. Many results of the time were motivated by questions about logical truth and logical consequence. The standard approach in the early part of the 20th century was to use a syntactic or proof-theoretic definition of logical consequence. This says that for one sentence to be a logical consequence of [a set of premises] is simply for that sentence to be derivable from [them] by means of some standard system of deduction (Etchemendy 1988). However, many famous results of the time, especially Gödel\u27s incompleteness theorems led to logicians such as Tarski to define logical consequence with what was eventually developed into the standard ``model-theoretic definition. This way of defining logical consequence says that a argument of a certain form is a logically valid argument if it is impossible for the premises to be true and the conclusion false (Mates 1972, Cannon 2016). Many philosophers have written about the effectiveness of this definition, but in 1990 John Etchemendy offered a fundamental criticism of Tarski\u27s definition both as to whether it is conceptually correct, and whether it captures the right set of arguments, or interpretations. This paper explores Etchemendy\u27s argument and various responses from prominent philosophers

Non-transitive counterparts of every Tarskian logic

The aim of this article is to show that, just like in recent years Cobreros, Égré, Ripley and van Rooij provided a non-transitive counterpart of classical logic (meaning by this that all classically acceptable inferences are valid, but Cut and other metainferences are not) the same can be done for every Tarskian logic, with full generality. In order to establish this fact, we take a semantic approach, by showing that appropriate structures can be devised to characterize a non-transitive counterpart of every Tarskian logic, starting from the logical matrices that are usually taken to render them

О замысле и исторических трансформациях понятия "логика"

Рассматривается ряд основных поворотов в истолковании логики; приводятся основания считать, что главной целью логики является не просто создание логических систем, а умение получать корректные логические рассуждения. Это, в свою очередь, поднимает вопрос о компьютерном и теоретическом моделировании этих процессов, главным образом, в контекстуально не проясненных смысловых средах

Truth, Meaning, and Circularity

http://philpapers.org/rec/HORTMAIt is often argued that the combination of deflationism about truth and the truth-conditional theory of meaning is impossible for reasons of circularity. I distinguish, and reject, two strains of circularity argument. Arguments of the first strain hold that the combination has a circular account of the order in which one comes to know the meaning of a sentence and comes to know its truth condition. I show that these arguments fail to identify any circularity. Arguments of the second strain hold that the combination has a circular explanation of the ideas or concepts of meaning and truth. I show that these arguments identify a genuine, but acceptable, circularity.Work on the paper was completed with a grant from the University of Missouri Research Board

Susan Stebbing’s logical interventionism

We examine a contribution L. Susan Stebbing made to the understanding of critical thinking and its relation to formal logic. Stebbing took expertise in formal logic to authorise logical intervention in public debate, specifically in assessing of the validity of everyday reasoning. She held, however, that formal logic is purely the study of logical form. Given the problems of ascertaining logical form in any particular instance, and that logical form does not always track informal validity, it is difficult to see how she could justify her belief in logical interventionism. Her answer to this problem is the contribution we explore here. It involves the view that although the logician’s expertise is not sufficient to assess arguments made in everyday contexts on its own, it nevertheless plays a unique role in giving systematicity and direction to the critique of such arguments, in particular, in public debate.PostprintPeer reviewe

The presidential address: truth: the identity theory

I want to promote what I shall call (unoriginally, and for the sake of its having a name ) ‘the identity theory of truth’. I suggest that other accounts put forward as theories of truth are genuine rivals to it, but are unacceptable. A certain conception of thinkables belongs with the identity theory’s conception of truth. I introduce these conceptions in Part I, by reference to John McDowell’s Mind and World; and I show why they have a place in an identity theory, which I introduce by reference to Frege. In Part II, I elaborate on the conception of thinkables, with a view to demonstrating that the identity theory’s conception of truth is defensible. Part III is concerned with the theory’s relation to some recent work on the concept of truth: I hope to show that the identity theorist not only has a defensible conception of truth, but also, in the present state of play, has appropriate ambitions

Definição

O presente artigo visa dar uma visão panorâmica sobre os principais tipos de definição e a sua relevância filosófica. A primeira parte con- siste numa introdução geral focada nos seguintes tópicos: definição de ‘definição’; classificação das definições; desenvolvimento histórico da teoria da definição; controvérsias no debate filosófico sobre definições; e estado de arte. A segunda parte pretende contribuir para fechar algu- mas lacunas na teoria da definição que são apontadas na primeira parteAbstract The present article aims to give an overview over the main types of definition and their philosophical relevance. The first part consists of a general introduction that focuses on the definition of ‘definition’, the classification of definitions, the historical development of the theory of definition, the controversies in the philosophical debate on definitions, and the state of the art. The second part is designed to fill some gaps in the theory of definition that are pointed out in the first part.Fundação para a Ciência e a Tecnologia, Faculdade de Letras da Universidade de Lisbo