Abstract
Abstract Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness.
Highlights
Suszko is known both for his eponymous acceptance of the ‘Suszko Thesis’, under which all logical systems whose consequence operator satisfies the criterion of structurality are bivalent systems, and for his rejection of the ‘Frege’s Axiom’ (FA)
In his attempt to prove one of the fundamental principles of ‘classical’ logic, i.e. Principle of Contradiction (PC), Jan Łukasiewicz [10] has shown that it is unprovable but that it rests on three distinct readings: an ‘ontological’ reading, by virtue of which PC says that it is impossible for the same object to have a property and not to have it at the same time; a ‘logical’ reading, whereby PC means that a proposition cannot be true and false at the same time; a ‘psychological’ reading, by virtue of which PC says that one cannot believe and not believe in the same judgment
We hope to have followed the general method of analysis which he has developed so far and which could be depicted as formal philosophy: the use of formal tools for the understanding and elucidation of philosophical problems
Summary
Suszko is known both for his eponymous acceptance of the ‘Suszko Thesis’, under which all logical systems whose consequence operator satisfies the criterion of structurality (or of extensionality) are bivalent systems, and for his rejection of the ‘Frege’s Axiom’ (FA). Sentences do not express truth-values but situations, and this explains why Suszko distinguishes identity from material equivalence or biconditional since the rejection of FA1 implies that two sentences may have the same truth-value without being identical There is another way to reject FA, by reasoning in reverse to Suszko and ISSN 2299-0518 accepting FA1 while rejecting FA2. It is this position that we will associate with the name of Łukasiewicz and defend in this article, while seeking to justify it through several writings of Professor Woleński. We will insist on a formal tool essential to metalogical reflection and which Woleński frequently uses in the articles treated here: the theory of opposition
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