We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...) more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)

T. J. Smiley; XII.—Entailment and Deducibility, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 233–254, https://doi.org/10.1093.

I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...) follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentenceσis false. Moreover, … we are concerned here with the concept of logical, i.e.,formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since. (shrink)

Introduction to Logic is a proven textbook that has been honed through the collaborative efforts of many scholars over the last five decades. Its scrupulous attention to detail and precision in exposition and explanation is matched by the greatest accuracy in all associated detail. In addition, it continues to capture student interest through its personalized human setting and current examples. The 14th Edition of Introduction to Logic, written by Copi, Cohen & McMahon, is dedicated to the many thousands of students (...) and their teachers - at hundreds of universities in the United States and around the world - who have used its fundamental methods and techniques of correct reasoning in their everyday lives. (shrink)

Following David Hitchcock and Stephen Toulmin, this paper takes warrants to be material inference rules. It offers an account of the form such rules should take that is designed (a) to implement the idea that an argument/inference is valid only if it is entitlement preserving and (b) to support a qualitative version of evidence proportionalism. It attempts to capture what gives warrants their normative force by elaborating a concept of reliability tailored to its account of the form such rules should (...) take. (shrink)

In many actual arguments, the conclusion seems intuitively to follow from the premisses, even though we cannot show that it follows logically. The traditional approach to evaluating such arguments is to suppose that they have an unstated premiss whose explicit addition will produce an argument where the conclusion does follow logically. But there are good reasons for doubting that people so frequently leave the premisses of their arguments unstated. The inclination to suppose that they do stems from the belief that (...) the only way in which an argument's conclusion can follow definitely from its premisses is to follow logically. I argue that this belief is mistaken. I propose a revision of the current generic conception of logical consequence, and its variant specifications, to avoid the paradoxes of strict implication. The revised conception can then be naturally extended to include also what we might call 'enthymematic consequence'. This concept is a kind of consequence, whose properties merit investigation. (shrink)

Filling the need for an accessible, carefully structured introductory text in symbolic logic, Modern Logic has many features designed to improve students' comprehension of the subject, including a proof system that is the same as the award-winning computer program MacLogic, and a special appendix that shows how to use MacLogic as a teaching aid. There are graded exercises at the end of each chapter--more than 900 in all--with selected answers at the end of the book. Unlike competing texts, Modern Logic (...) gives equal weight to semantics and proof theory and explains their relationship, and develops in detail techniques for symbolizing natural language in first-order logic. After a general introduction featuring the notion of logical form, the book offers sections on classical sentential logic, monadic predicate logic, and full first-order logic with identity. A concluding section deals with extensions of and alternatives to classical logic, including modal logic, intuitionistic logic, and fuzzy logic. For students of philosophy, mathematics, computer science, or linguistics, Modern Logic provides a thorough understanding of basic concepts and a sound basis for more advanced work. (shrink)

EDITOR'S INTRODUCTION Throughout his life Bolzano's interest was divided between ethics and mathematics, between his will to reform the religion of the ...

37 arguments were selected by random sampling methods from calls to radio and television phone-in programs. I discuss whether my general theory of inference evaluation applies to them and how frequently they exemplify a recognized argument scheme. I also compare their dependence on context, their complexity and their quality to those features of a previously studied sample of 50 scholarly arguments.