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Questions about algorithms

Can you program a simple calculator with an algorithm and make it so that it does at least some arithmetic problems incorrectly? (Important here is the supposition that the errors be non-random)? I suppose Yes. Can you make a program that uses an algorithm to detect whether or not the said calculator's program is set to work correctly? Let's suppose the answer is yes. But can you make that program defective so that it fails to catch some programs? If the answer to the other two is yes, then Yes to this question as well. In such a case, can a calculator, relying on algorithms in any sense be said to know that it knows when it has the right answer? No.

Comments

Leo White said…
Thanks. The issue in play is whether the computer's ability to use algorithms to solve arithmetical problems involves the knowledge that the solution is true, and in the case of abstract questions, that this truth is universally and necessarily so.
6:07 PM
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