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Fuzzy Logic and Sorites Paradox : The Problem of Missing Input



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Fakulta / Pracoviště MU

Filozofická fakulta

Popis Sorites paradoxes are a class of paradoxical arguments which arise as a result of using vague terms such as “heap”, “bald”, or “tall”. Vague terms, in contrast with precise terms, lack precise boundaries of application. There are objects to which a) the vague term applies, b) the vague term does not apply, and c) it is uncertain whether vague term applies or not (so called borderline cases). In borderline cases it is uncertain whether the vague term in question applies to them or not. Moreover, this uncertainty cannot be resolved by any enquiry. When we are asked whether some person is tall, we take only his height into consideration. When said person measures 150 centimetres, we are inclined to say that the person in not tall. When that person measures 220 centimetres, we would not hesitate calling that person tall. We, however, would not be so sure about a person measuring 184 centimetres. Yet we would be sure that a person measuring 190 centimetres is taller than a person measuring 185 centimetres. It seems that being tall is a matter of degree. At least proponents of fuzzy logic would say so. Sentences like “X is tall” can therefore have different truth value ranging from 1 – absolutely true – to 0 – absolutely false – according to X’s height. “X is tall” can have truth value of 0.48571 for X measuring 184 centimetres and truth value of 0.57143 for X measuring 190 centimetres. In the case of sorites paradox, at least one of its premises has an intermediate truth value and its consequence therefore cannot be absolutely true (or absolutely false). In my talk I am going to examine some of the problems that fuzzy logic faces when dealing with sorites paradoxes. I am going to point out that fuzzy logic can only be applied when certain class of vague terms is used to formulate sorites paradox, while it cannot be applied when the rest of vague terms is used.
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