What's wrong with the old arguments that lead us to believe that if machines could ever think at all, they'd have to think with perfect logic? We're told that by their nature, all machines must work according to rules. We're also told that they can only do exactly what they're told to do. Besides that, we also hear that machines can only handle quantities and therefore cannot deal with qualities or anything like analogies.
Most such arguments are based upon a mistake that is like confusing an agent with an agency. When we design and build a machine, we know a good deal about how it works. When our design is based on neat, logical principles, we are likely to make the mistake of expecting the machine to behave in a similarly neat and logical fashion. But that confuses what the machine does inside itself — that is, how it works — with our expectations of how it will appear to behave in the outer world. Being able to explain in logical terms how a machine's parts work does not automatically enable us to explain its subsequent activities in simple, logical terms. Edgar Allan Poe once argued that a certain chess-playing machine had to be fraudulent because it did not always win. If it were really a machine, he argued, it would be perfectly logical — and therefore could never make any mistakes! What is the fallacy in this? Simply that there is nothing to prevent us from using logical language to describe illogical reasoning. To a certain extent it's true that machines can do only what they are designed to do. But this does not preclude us, when once we know how thinking works, from designing machines that think.
When do we actually use logic in real life? We use it to simplify and summarize our thoughts. We use it to explain arguments to other people and to persuade them that those arguments are right. We use it to reformulate our own ideas. But I doubt that we often use logic actually to solve problems or to get new ideas. Instead, we formulate our arguments and conclusions in logical terms after we have constructed or discovered them in other ways; only then do we use verbal and other kinds of formal reasoning to clean things up, to separate the essential parts from the spaghettilike tangles of thoughts and ideas in which they first occurred.
To see why logic must come afterward, recall the idea of solving problems by using the generate and test method. In any such process, logic can be only a fraction of the reasoning; it can serve as a test to keep us from coming to invalid conclusions, but it cannot tell us which ideas to generate, or which processes and memories to use. Logic no more explains how we think than grammar explains how we speak; both can tell us whether our sentences are properly formed, but they cannot tell us which sentences to make. Without an intimate connection between our knowledge and our intentions, logic leads to madness, not intelligence. A logical system without a goal will merely generate an endless host of pointless truths like these:
A implies A. P or not P. A implies A or A or A. If 4 is 5, then pigs can fly.