T he L ogical S tructure of E volution and E manation *

GOTTHARD GlfNTHER: When I decided t o accept Dr. Roland Fischer’s generous invitation to read a paper a t this conference I felt somewhat like a forger who passes on his counterfeit money to a n unsuspecting public. I t has been a time-honored tradition t o say t h a t logic and its laws are timeless a n d of eternal validity. This viewpoint has, of course, sometimes been subjected t o a sceptical scrutiny, b u t all a t tempts t o analyze time with the means of a logical calculus have come t o nothing. Consequently, since the traditional viewpoint seems t o be t h e correct one, it follows t h a t a logician at a Time Conference should be apersona nongrata, a n d the currency with which he pays for admission should not be acceptable. However, I feel t h a t m y presence has some justification. T h e logic discussed in all previous confrontations between Logic and Time was invariably the classic two-valued logic; b u t it might be proper t o raise t h e old issue again when a logician claims t h a t our traditional theory of thinking is not the only one and t h a t a trans-classic system of rationality might be able to tackle t h e problem of time if more powerful methods of investigation were available. Since the classic theory of rationality is indissolubly linked with t h e concept of value, first of all one has t o show t h a t t h e whole “value issue” covers t h e body of logic like a thin coat of paint. Scrape t h e paint off a n d you will discover a n unsuspected system of structural forms and relations suggesting methods of thinking which surpass immeasurably all classic theories. This was t h e purpose of m y paper “Time, Timeless Logic and Self-Referential Systems.” T h e trans-classic order which we discover beyond the classic theory of logic was called “kenogrammatic structure.” However, there seemed t o be some doubt a s to how I arrived a t t h a t kenogrammatic concept, and limited t ime permitted no discussion of t h e transition from value to kenogram. Consequently, the quintessence of m y procedure seems t o require some detailed explanation. Such a n explanation I have given in a n earlier publication,’ but , alas, only in strict logical terminology which may make it again difficult for a n interdisciplinary audience t o follow. In this dilemma, I turned to my colleague Heinz Von Foerster, a veteran in interdisciplinary meetings, t o help out . H e suggested t h a t I present t h e development of these concepts in a mathematical vocabulary. But since this vocabulary is not my vehicle of mental propulsion, I let Von Foerster tell his story in his own words. HEINZ VON FOERSTER: Perhaps the easiest way t o see the emergence of the concept Kenogram is to see i t through the concept of the “inverse” of a logical function. T h e inverse of a logical function is derived in precise analogy t o the inverse of a mathematical function.