Online research in philosophy

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski''s discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.

Symbolic logic is a marvelous thing. It allows for an explicit expression of existence, viz. by means of the existential quantifier, and by it only. This is the true gist in Quine’s slogan “to be is to be a value of a bound variable.” Accordingly, one can also formulate explicitly the thesis of nominalism in terms of such logic. What this thesis says is that all the values of existential quantifiers we need in our language are particular objects, not higher-order objects such as properties, relations, functions and sets. This requirement is satisfied by the first-order languages using the received first-order logic. The commonly used basic logic is therefore nominalistic. But this result does not tell anything, for the received first-order logic is far too weak to capture all we need in mathematics or science. According to conventional wisdom, we need for this purpose either higher-order logic or set theory. Now both of them deal with higher-order entities and hence violate the canons of nominalism. This does not refute nominalism, however. For I will show that both set theory and higher-order logic can be made dispensable by developing a more powerful first-order logic that can do the same job as they do. Moreover, there are very serious problems connected with both of them. This constitutes an additional reason for dispensing with them in the foundations of mathematics. I will show how we can do just that. But we obviously need a better first-order logic for the purpose. Hence my first task is to develop one. But is this a viable construal of the problem of nominalism? The very distinction between particular and higher-order entities might perhaps seem to be hard to capture in logical terms — harder than has been indicated so far. Logicians like Jouko Väänänen (2001) have emphasized the complexities involved in trying to distinguish first-order logic from higher-order logic..

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

Neutrosophic Logic was created by Florentin Smarandache (1995) and is an extension / combination of the fuzzy logic, intuitionistic logic, paraconsistent logic, ...

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

Classical logic -- Temporal logic -- Modal logic -- Conditional logic -- Relevantistic logic -- Intuitionistic logic.

In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\ -D.\ F\'evrier's 'logic of complementarity' as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed 'paraclassical logic'.

Jaakko Hintikka has argued that ordinary first-order logic should be replaced byindependence-friendly first-order logic, where essentially branching quantificationcan be represented. One recurring criticism of Hintikka has been that Hintikka''ssupposedly new logic is equivalent to a system of second-order logic, and henceis neither novel nor first-order. A standard reply to this criticism by Hintikka andhis defenders has been to show that given game-theoretic semantics, Hintikka''sbranching quantifiers receive the exact same treatment as the regular first-orderones. We develop a different reply, based around considerations concerning thenature of logic. In particular, we argue that Hintikka''s logic is the logic that bestrepresents the language fragment standard first-order logic is meantto represent. Therefore it earns its keep, and is also properly regarded as first-order.

Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka’s independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.