OF MADNESS AND MANY-VALUEDNESS: AN INVESTIGATION INTO SUSZKO’S THESIS

SUSZKO’S THESIS IS A PHILOSOPHICAL CLAIM REGARDING THE NATURE OF MANY-VALUEDNESS. IT WAS FORMULATED BY THE POLISH LOGICIAN ROMAN SUSZKO DURING THE MIDDLE 70S AND STATES THE EXISTENCE OF “ONLY BUT TWO TRUTH VALUES”. THE THESIS IS A REACTION AGAINST THE NOTION OF MANY-VALUEDNESS CONCEIVED BY JAN ?UKASIEWICZ. REPUTED AS ONE OF THE MODERN FOUNDERS OF MANY-VALUED LOGICS, ?UKASIEWICZ CONSIDERED A THIRD UNDETERMINED VALUE IN ADDITION TO THE TRADITIONAL FREGEAN VALUES OF TRUTH AND FALSEHOOD. FOR ?UKASIEWICZ, HIS THIRD VALUE COULD BE SEEN AS A STEP BEYOND THE ARISTOTELIAN DICHOTOMY OF BEING AND NON-BEING. ACCORDING TO SUSZKO, ?UKASIEWICZ’S IDEAS RESTED ON A CONFUSION BETWEEN ALGEBRAIC VALUES (WHAT SENTENCES DESCRIBE/DENOTE) AND LOGICAL VALUES (TRUTH AND FALSITY). THUS, ?UKASIEWICZ’S THIRD UNDETERMINED VALUE IS NO MORE THAN AN ALGEBRAIC VALUE, A POSSIBLE DENOTATION FOR A SENTENCE, BUT NOT A GENUINE LOGICAL VALUE. SUSZKO’S THESIS IS ENDORSED BY A FORMAL RESULT BAPTIZED AS SUSZKO’S REDUCTION, A THEOREM THAT STATES EVERY TARSKIAN LOGIC MAY BE CHARACTERIZED BY A TWO-VALUED SEMANTICS. THE PRESENT STUDY IS INTENDED AS A THOROUGH INVESTIGATION OF SUSZKO’S THESIS AND ITS IMPLICATIONS. THE FIRST PART IS DEVOTED TO THE HISTORICAL ROOTS OF MANY-VALUEDNESS AND INTRODUCE SUSZKO’S MAIN MOTIVATIONS IN FORMULATING THE DOUBLE CHARACTER OF TRUTH-VALUES BY DRAWING THE DISTINCTION IN BETWEEN ALGEBRAIC AND LOGICAL VALUES. THE SECOND PART EXPLORES SUSZKO’S REDUCTION AND PRESENTS THE DEVELOPMENTS ACHIEVED FROM IT; THE PROPERTIES OF TWO-VALUED SEMANTICS IN COMPARISON TO MANY-VALUED SEMANTICS ARE ALSO EXPLORED AND DISCUSSED. LAST BUT NOT LEAST, THE THIRD PART INVESTIGATES THE NOTION OF LOGICAL VALUES IN THE CONTEXT OF NON-TARSKIAN NOTIONS OF ENTAILMENT; THE MEANING OF SUSZKO’S THESIS WITHIN SUCH FRAMEWORKS IS ALSO DISCUSSED. MOREOVER, THE PHILOSOPHICAL FOUNDATIONS FOR NON-TARSKIAN NOTIONS OF ENTAILMENT ARE EXPLORED IN THE LIGHT OF RECENT DEBATES CONCERNING LOGICAL PLURALISM.