In a very real sense, I hope that computers never get to the point that we see in the short story "A Logic Named Joe". (Thanks need to go to Erin Hamson for finding a radio version of the short story that I found really cool). It is a scary thought to think that computers would "logically" start thinking for us, and outsmart us in every way. This is the idea behind movies like I Robot with Will Smith
Or Eagle Eye, with Shia Labeouf
It's quite a scary thought. Logic and probability cannot solve everything. There needs to be feeling and emotion behind our problem solving as well. Otherwise we will be considered heartless. Which is kind of how computer logic could be considered in these stories: heartless.
And yet, we have also had shown to us that there are unsolvable problems by Alan Turing. So computers will never be able to solve ALL problems. A paradox could be considered a problem computers will never be truly able to solve. For example: Suppose you are on the moon, and a Martian flies up to you in his flying saucer, and then says, "All Martians lie all the time." Now, if this statement is true, then he is lying. But, if he is lying, then all Martians tell the truth all the time. However, if all Martians tell the truth all the time, then he must have been telling the truth, so all Martians lie all the time. And around and around we go. This is also the basis of the idea of the halting problem brought up by David Harel in his book "Computers LTD: What They REALLY Can't Do".
Problems involving the emotions and our souls I think is a type of problem that computers will never be able to solve. This also another reason why it is such a blessing to have the Holy Ghost to help us make righteous, heartfelt decisions in the world around us. I'm grateful for that help that we have been given us from Heavenly Father, to help us solve the problems and concerns in our life that are truly important.