Sociological Aspects 
MacKay: ‘There is a misunderstanding here. I am not 
disputing that what is inside my skull is a machine; but I 
doubt whether this or any machine could embody within itself 
a complete description of itself. 
Medawar: Are you saying that it is logically self-contradic- 
tory? 
MacKay: Yes, it is logically self-contradictory for the same 
general reason that a picture cannot contain a picture of itself: 
it would involve an infinite regress. 
Medawar: ‘That is a good analogy, but has the proposition 
been demonstrated rigorously, like Gédel’s theorem* ? 
MacKay: I think Gédel’s theorem can be regarded as a 
formal demonstration of this proposition as a special case. The 
situation where we try to introspect into what we are doing 
when we are judging is essentially the Gédel situation. 
Lederberg: I hope we are not confusing the issue of the 
limits to introspective analysis with the limitations on the 
possibility of a computer simulation of the human brain. We 
are not limited to introspection to find out how the brain is 
put together and we are bound to discover some organizing 
rules to take the place of a manifold description of every 
neurone and its connexions. 
I would readily agree that the storage capacity of my own 
memory could not begin to accommodate a microscopic descrip- 
tion of its own structure, and by a consistency argument, one 
might prove its inability to map that structure on itself. This 
does not prevent the mapping of that structure on another 
computer of larger capacity—my specification is then “‘copy 
39 
me”’. The aim of all this—just what the morphologists do in 
*In 1931, K. Gédel in Vienna established a theorem which has been described 
as the most decisive result in modern mathematical logic. Broadly speaking, 
Godel showed (Monatshefte fiir Mathematik und Physik, vol. 38) that any proof of 
the self-consistency of a logical deductive system—comprising definitions, axioms 
and all the theorems derived from them—would itself involve a specific contradic- 
tion within the system. That isto say, undecidable statements exist; within a given 
logical system certain assertions (which may even be known to be true) can be 
neither proved nor disproved. In particular, such a logical system can never be 
self-validating, in the sense that any discussion of its internal consistency must 
appeal to a higher context beyond the system itself. 
181 
