Virtual Logic-Finite Language and the Imagination of Infinity

摘要

This virtual logic column concerns the relationship of the concept of infinity and the finite use of language. When I speak or write, each sentence is a finite string of words and each word is a finite string of letters. Yet language is open-ended and there is no limit to the number or variety of sentences that can be produced. In cybernetics it is a catch-phrase that "Self-reference is infinity in finite guise." The circularity of self-reference can be regarded as an infinite loop of references or an infinite regress as in Figure 1. The self-referring loop in the figure is finite. Since it is a loop it is possible to go around the loop any number of times. Thus there is an infinity associated with the self-reference and one can go back and forth between this infinity and the finiteness of the loop.