Andrzej Grzegorczyk

PSYCHOLOGISTIC SOLUTIONS OF ANTINOMIES

Semantical antinomies seem to be consequences of antipsychologistic paradigm adopted by logicians at the beginning of 20 Century. Rejecting this paradigm yields a chance of solving antinomies. Antinomies impair our whole science. Hence “solving” means: such a description of the intel- lectual situation which exhibits science as consistent. Of course, individual knowledge of some human beings may remain inconsistent, but we want to have an interpretation of individual inconsistency which shows that: if the individual knowledge of a given human being X is inconsistent, then this is because X neglects an important methodological principle. Such a solution of the antinomy of self-liar may be presented (as in the following), and shows the analogy between the antinomy of self-liar and the antinomy of barber. Barber makes an advertisement: ”I shave these and only these male inhabitants of my village who do not shave themselves”. He fails because his declaration is unfeasible since he is also inhabitant of his village. If a self-liar declares the rejection of the declaration he is just making, then he fails also because he produces for himself a task which is also unfeasible. His knowledge becomes inconsistent, because he makes an irresponsible declaration. He declares the rejection of a statement which is not yet uttered, because its utterance is not finished in the moment of his declaring. Classical presentation of the antinomy of self-liar usually is formulated in terms of truth anf untruth, but the presentation in terms of assertion and rejection better shows the declarative character of the utterance of self-liar. One can say that self-liar transgresses the moral principle of responsi- ble assertion (or rejection) , or what makes the same: responsible attribu- tion of truth or untruth. A responsible assertion (rejection) may concern only a text which is finished, and then we can concentrate on it. Alfred Tarski shared the antipsychologistic tendency of his time with other logicians. He also considered colloquial natural language as neces- sarily inconsistent. The linguistical investigations of the second half of our

66 century seem to suggest a different philosophical vision of natural languages which may be summarized as follows: natural languages are universal tools of mind. Using these tools one can utter every thinking. Hence the incon- sistency, when it emerges in an argument, does not oblige us to blame the language as such but rather to blame the thinker for his assumptions. The antypsychologistic tendency leads to consider the meaning as in- dependent on the uttering person. The antypsychologists seem to under- stand semantical conceptions as being beyond the psychological conditions of people which are using the language. Hence, for example, the meaning of a name becomes easly identified with the content of the class which is signified by the considered name, and then the antinomy of the class of all classes leads to the antinomy of heterological names. One can summerize the experience of antipsychologism as follows: Contradictions emerge when we absolutize the meaning of our uttering. If we relativize the meaning of an utterance to the experience of the uttering person, then antinomial ar- guments turn into veridical observations concerning human cognition. The experience of the paradox of Grelling and Nelson may be epitomize veridi- cally in the theorem: Theorem 1. For any properly methodologically educated human being there is a methodologically correctly defined set of expressions such that: when this human being examines the notion of this set then he/she does not use it accurately for denoting the members of this set. The experience of the paradox of self-liar implies: Theorem 2. There is a linguistically properly stated problem such that no human being sufficiently methodologically educated, which tackles this problem, thinks about it consistently, sincerely and fully consciously. (The formal proofs of these theorems rests, of course, on the formal definitions of involved terms. They are exhibited in my book: Logic - a Human Affair. Scholar. Warsaw 1997.)

Institute of Philosophy and Sociology Polish Academy of Sciences Nowy Swiat 72 00-330 Warszawa Poland

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