Human Thinking is not Abstract Manipulation
  

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By: Dr. David Booth
When you find yourself carrying out a simple but repetitive mental task, you might ask: Could a computer do this instead? This casual comparison may give insight even if you decide that it is not worthwhile to make use of a program.

It is not useful, however to confuse human thought with a computer, as is done when you hear educators speak of children “processing” the “data” of their experience. They imagine that the soul of a child is an imperfect reproduction of some computer process. That does not give the educator any useful insight at all.


The mistaken urge to confuse human thought with computer action can easily be traced back to philosophical positions that appeared in the early twentieth century. Scientifically inclined philosophers thought that all knowledge must be patterned after the scientific theories of that time. These theories, so it was believed, rest ultimately on basic facts which can be combined using valid patterns of formal logic to obtain knowledge. The theory of computation that ultimately led to electronic computers began with the study of logical combinations needed to build complex assertions out of fundamental facts.

It seemed plausible; yet it is completely mistaken; and its critics were ignored.  The following illustration was devised by the mathematician Paul Finsler, to clarify the situation.

image shows: ( 1,2,3,  The smallest number not mentioned in this box)

What is the smallest number not mentioned in this box?  Certainly one, two and three are mentioned.  There is also a clause that might specify some number.  If it specifies four, then five would be the smallest number not mentioned.  If it does not specify four, then four would be the first number not mentioned there.

Let us see whether or not the clause specifies four.  If it did specify four then four would have to be, according to the specification, the smallest number not mentioned. But that would be absurd, because we have supposed that four is mentioned.

Actually the whole clause is meaningless, and does not name any number at all.  We have seen that it does not specify four. It cannot truthfully specify something larger than four either, since four has not been mentioned in the box. That settles the matter.  The clause is meaningless and specifies nothing at all.  Now, however, we can see that four really is the smallest number that is not specified.  The phrase “The smallest number that is not mentioned in this box” is meaningless when it is in the box but denotes the number four when we speak it.

The box is like the world of formal logic, manipulating statements without regard for their actual content. The box is not merely limited; it can affect the meaning of words it contains, as Finsler’s example shows. There is no substitute for human judgment.  Knowing how to get “information” from the internet puts more stress on our powers of judgment than we get under nature’s guidance.

Here is a puzzle that shows how the context of an assertion affects the conclusions drawn from it.  Two boys go outside to play while wearing their Sunday clothes. Their father says sternly, “Do not soil your clothes.” After a while the father comes out, scowls and says, “Someone has soiled his clothes.”

In fact, both the boys dirtied the backs of their shirts. Each of them can see that his brother has violated their father’s injunction; yet, each continues to play happily in the belief that his own clothes are clean. Suddenly, each one bursts into tears, realizing that his clothes are soiled too. How do they know?

The solution is that each boy reasons, “My brother would be crying already had he not seen that my clothes are soiled.”

This example shows how judgments can depend on the context of the situation.  Finsler’s box illustrates the fact that abstract, formal manipulation can never hope to escape from the context that structures them.


These two examples together might help give you confidence that the failure of the mind-as-computer philosophy, does not at all suggest a gloomy future for real human thought. To exceed the capacities of any possible computer, all we have to do is think.

Dr. David Booth is a mathematician and inventor who teaches the upper grades at the Austin, TX, Waldorf School.




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