Notations and computability

Abstract

It is suggested that the notation in which an idea is expressed is not a matter of arbitrary convenient choice but may have far-reaching consequences, in particular for the design of machine intelligences. The definability of a function may depend upon the notation used. The notation therefore becomes in effect the first axiom of the axiomatic system. The implication for computing is that translation from one language to another must be expected to cause some problems, perhaps including contradiction and falsity; and efforts to create conscious machine intelligence must use the same or similar languages at the highest processing levels.

Keywords:

• Computability
• machine intelligence
• axiomatic systems
• artificial intelligence
• notations

C.R. Categories:

• F.4.1