Ten Questions and One Problem on Fuzzy Logic

Ten questions on fuzzy logic as a formal logic of consequence under vagueness are discussed; a problem of deenability of truth is formulated. Recently I had a very interesting friendly e-mail discussion with Professor Parikh on vagueness and fuzzy logic. Parikh published several papers concerning the notion of vagueness. They contain critical remarks on fuzzy logic and its ability to formalize reasoning under vagueness 10,11]. On the other hand, for some years I have tried to advocate fuzzy logic (in the narrow sense, as Zadeh says, i.e. as formal logical systems formalizing reasoning under vague-ness) and in particular to show that such systems (of many-valued logic of a certain kind) ooer a fully edged and extremely interesting logic 4,5]. But this leaves open the question of intuitive adequacy of many-valued logic as a logic of vagueness. Below I shall try to isolate eight questions Parikh asks, add two more and to comment on all of them. Finally I formulate a problem on truth (in)deenability in Lukasiewicz logic which shows, in my opinion, that fuzzy logic is not just \applied logic" but rather belongs to systems commonly called \philosophical logic" like modal logics etc. 1 Ten questions Before starting, let us quote from Parikh's 10]. He refers on a test where students assigned a numerical value to ten questions, among them the question \is President de Klerk an African?". He says: \If fuzzy logic says that there is an x such that President de Klerk is x-African, then it must tell us how to measure x and how to resolve the connict between a person who says that de Klerk is .8-African and another the he is .2-African. It must also tell us how the correct value x is related to these two connicting reports and what it means to way that x is the correct value. If fuzzy logic does not answer these