Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

immutable pillar of the machine's system, but could be overridden on
occasion, then:

The system will have ceased to be a formal logical system, and the machine

will barely qualify for the title of a model for the mind.lo

Now many programs which are being developed in AI research have very

little in common with programs for generating truths of number theory-

programs with inflexible rules of inference and fixed sets of axioms. Yet

they are certainly intended as "models for the mind". On their top level-

the "informal" level-there may be manipulation of images, formulation of

analogies, forgetting of ideas, confusing of concepts, blurring of distinc-

tions, and so forth. But this does not contradict the fact that they rely on the

correct functioning of their underlying hardware as much as brains rely on

the correct functioning of their neurons. So AI programs are still "concrete

instantiations of formal systems"-but they are not machines to which

Lucas' transmogrification of Codel's proof can be applied. Lucas' argument

applies merely to their bottom level, on which their intelligence-however

great or small it may be-does not lie.

There is one other way in which Lucas betrays his oversimplified vision

of how mental processes would have to be represented inside computer

programs. In discussing the matter of consistency, he writes

If we really were inconsistent machines, we should remain content with our

inconsistencies, and would happily affirm both halves of a contradiction.

Moreover, we would be prepared to say absolutely anything-which we are

not. It is easily shown that in an inconsistent formal system everything is

provable. II

This last sentence shows that Lucas assumes that the Propositional Calculus

must of necessity be built into any formal system which carries out reason-

ing'. In particular, he is thinking of the theorem «Pi\-P>:JQ> of the

Propositional Calculus; evidently he has the erroneous belief that it is an

inevitable feature of mechanized reasoning. However, it is perfectly plausi-

ble that logical thought processes, such as propositional reasoning, will

emerge as consequences of the general intelligence of an AI program, rather

than being preprogrammed. This is wl:J.at happens in humans! And there is no

particular reason to assume that the strict Propositional Calculus, with its

rigid rules and the rather silly definition of consistency that they entail,

would emerge from such a program.

An Underpinning of AI

We can summarize this excursion into level distinctions and come away

with one final, strongest version of the Church-Turing Thesis:

CHURCH-TuRING THESIS; AI VERSION: Mental processes of any sort can be

simulated by a computer program whose underlying language is of

578 Church, Turing, Tarski, and Others