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MOST OFTEN READING TEXT:

Many-worlds theory of truth
author: Alexander Boldachev,
The logical world is a set of propositions, united by common principles of establishing their truth. The many-worlds theory asserting that the truth of any proposition in any given logical world is always established by comparing it with standard propositions in this world – directly or via the procedure of transferring the truth.

CURRENT ISSUE:

Judgments and Truth: Essays in Honour of Jan Woleński

author: Andrew Schumann,
It is a Preface to Volume 9:3/4 that has brought a renewed focus to the role of truth conceptions in frameworks of semantics and logic. Jan Woleński is known due to his works on epistemological aspects of logic and his systematization of semantic truth theory. He became the successor and the worthy continuer of prominent Polish logicians: Alfred Tarski and Kazimierz Ajdukiewicz. This volume is collected on the 80th anniversary of Woleński’s birth and draws together new research papers devoted to judgments and truth. These papers take measure of the scope and impact of Woleński's views on truth conceptions, and present new contributions to the field of philosophy and logic.

Proof vs Truth in Mathematics

author: Roman Murawski,
Two crucial concepts of the methodology and philosophy of mathematics
are considered: proof and truth. We distinguish between informal proofs
constructed by mathematicians in their research practice and formal
proofs as defined in the foundations of mathematics (in
metamathematics). Their role, features and interconnections are
discussed. They are confronted with the concept of truth in mathematics.
Relations between proofs and truth are analysed.

The Mystery of the Fifth Logical Notion
(Alice in the Wonderful Land of Logical Notions)

author: Jean-Yves Beziau,
We discuss a theory presented in a posthumous paper by Alfred Tarski
entitled “What are logical notions?”. Although the theory of these logical
notions is something outside of the main stream of logic, not presented in
logic textbooks, it is a very interesting theory and can easily be
understood by anybody, especially studying the simplest case of the four
basic logical notions. This is what we are doing here, as well as
introducing a challenging fifth logical notion. We first recall the context
and origin of what are here called Tarski-Lindenbaum logical notions. In
the second part, we present these notions in the simple case of a binary
relation. In the third part, we examine in which sense these are
considered as logical notions contrasting them with an example of a nonlogical
relation. In the fourth part, we discuss the formulations of the four
logical notions in natural language and in first-order logic without
equality, emphasizing the fact that two of the four logical notions cannot
be expressed in this formal language. In the fifth part, we discuss the
relations between these notions using the theory of the square of
opposition. In the sixth part, we introduce the notion of variety
corresponding to all non-logical notions and we argue that it can be
considered as a logical notion because it is invariant, always referring to
the same class of structures. In the seventh part, we present an enigma: is
variety formalizable in first-order logic without equality? There follow
recollections concerning Jan Woleński. This paper is dedicated to his 80th
birthday. We end with the bibliography, giving some precise references
for those wanting to know more about the topic.

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