After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics (...) is the logic of Bunched Implications due to Pym and O’Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle. (shrink)

The first part of this paper presents asympathetic and critical examination of the approachof Shahid Rahman and Walter Carnielli, as presented intheir paper “The Dialogical Approach toParaconsistency”. In the second part, possibleextensions are presented and evaluated: (a) top-downanalysis of a dialogue situation versus bottom-up, (b)the specific role of ambiguities and how to deal withthem, and (c) the problem of common knowledge andbackground knowledge in dialogues. In the third part,I claim that dialogue logic is the best-suitedinstrument to analyse paradoxes of the (...) Sorites type.All these considerations lead to philosophicallyrelevant observations concerning principles of charityon the one hand, and compactness on the other. (shrink)

Being a pragmatic and not a referential approach tosemantics, the dialogical formulation ofparaconsistency allows the following semantic idea tobe expressed within a semi-formal system: In anargumentation it sometimes makes sense to distinguishbetween the contradiction of one of the argumentationpartners with himself (internal contradiction) and thecontradiction between the partners (externalcontradiction). The idea is that externalcontradiction may involve different semantic contextsin which, say A and ¬A have been asserted.The dialogical approach suggests a way of studying thedynamic process of contradictions through which thetwo (...) contexts evolve for the sake of argumentation intoone system containing both contexts.More technically, we show a new, dialogical, way tobuild paraconsistent systems for propositional andfirst-order logic with classical and intuitionisticfeatures (i.e. paraconsistency both with and withouttertium non-datur) and present theircorresponding tableaux. (shrink)

We describe a logic which is the same as first-order logic except that it allows control over the information that passes down from formulas to subformulas. For example the logic is adequate to express branching quantifiers. We describe a compositional semantics for this logic; in particular this gives a compositional meaning to formulas of the 'information-friendly' language of Hintikka and Sandu. For first-order formulas the semantics reduces to Tarski's semantics for first-order logic. We prove that two formulas have the same (...) interpretation in all structures if and only if replacing an occurrence of one by an occurrence of the other in a sentence never alters the truth-value of the sentence in any structure. (shrink)

This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous (...) impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities. (shrink)

Aristotle thought of his logic and methodology as applications of the Socratic questioning method. In particular, logic was originally a study of answers necessitated by earlier answers. For Aristotle, thought-experiments were real experiments in the sense that by realizing forms in one's mind, one can read off their properties and interrelations. Treating forms as independent entities, knowable one by one, committed Aristotle to his mode of syllogistic explanation. He did not think of existence, predication and identity as separate senses of (...) estin. Aristotle thus serves as an example of a thinker who did not rely on the distinction between the allegedly different Fregean senses, thereby shedding new light on our own conceptual presuppositions. This collection comprises several striking interpretations that Jaakko Hintikka has put forward over the years, constituting a challenge not only to Aristotelian scholars and historians of ideas, but to everyone interested in logic, epistemology or metaphysics and in their history. (shrink)

This is the companion volume to Gregory Vlastos' highly acclaimed work Socrates: Ironist and Moral Philosopher. Four ground-breaking papers which laid the basis for his understanding of Socrates are collected here, in revised form: they examine Socrates' elenctic method of investigative argument, his disavowal of knowledge, his concern for definition, and the complications of his relationship with the Athenian democracy. The fifth chapter is a new and provocative discussion of Socrates' arguments in the Protagoras and Laches. The epilogue 'Socrates and (...) Vietnam' suggests that Socrates was not, as Plato claimed, the most just man of his time. The papers have been prepared for publication by Professor Myles Burnyeat with the minimum of editorial intervention. (shrink)

Most current work in epistemology deals with the evaluation and justification of information already acquired. In this book, Jaakko Hintikka instead discusses the more important problem of how knowledge is acquired in the first place. His model of information-seeking is the old Socratic method of questioning, which has been generalized and brought up-to-date through the logical theory of questions and answers that he has developed. Hintikka also argues that philosophers' quest for a definition of knowledge is ill-conceived and that the (...) entire notion of knowledge should be replaced by the concept of information. He offers an analysis of the different meanings of the concept of information and of their interrelations. The result is a new and illuminating approach to the field of epistemology. (shrink)

particular alternative logic could be relevant to another one? The most important part of a response to this question is to remind the reader of the fact that independence friendly (IF) logic is not an alternative or “nonclassical” logic. (See here especially Hintikka, “There is only one logic”, forthcoming.) It is not calculated to capture some particular kind of reasoning that cannot be handled in the “classical” logic that should rather be called the received or conventional logic. No particular epithet (...) should be applied to it. IF logic is not an alternative to our generally used basic logic, the received first-order logic, aka quantification theory or predicate calculus. It replaces this basic logic in that it is identical with this “classical” first-order logic except that certain important flaws of the received first-order logic have been corrected. But what are those flaws and how can they be corrected? To answer these questions is to explain the basic ideas of IF logic. Since this logic is not as well known as it should be, such explanation is needed in any case. I will provide three different but not unrelated motivations for IF logic. (shrink)