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Asif Ali
The Halting Problem
Hello Cousin,
The ambition you have regarding computers is one that I admire greatly.
However, even they are incomplete. In other words their exists problems that even the
“God computer” cannot answer accurately. Gödel’s incompleteness theorem proved this
idea. To put it simply he proved that any proof that is about a system couldn’t be proved
within that system. In more descriptive words he provided evidence that “any system
which is expressive enough to be consistent and complete is also expressive enough to
contain selfreferential statements which doom it to incompleteness.” The halting
problem is just another technique of proving the same claims as the incompleteness
theorem, relating it to computer’s (which is a system) limitedness. In detail we will
explain the idea of the halting problem to show you why there cannot be a “God
computer”.
Suppose we live in a world where the “God computer” does in fact exists. In such
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This note was uploaded on 01/27/2011 for the course PHI 330 taught by Professor Mar during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 Mar

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