I have a bit of a theory on the subject. I think we do have a ‘sixth sense’ but we have evolved away from it. Most animals are very aware of potential danger; dogs can show strange behaviour long before the cause of it is apparent. When we were closer to our animal ancestors, we probably had similar ‘foresight’. The ‘sixth sense’ may just be a more attuned level of our other senses of course.
I use as an example, our peripheral vision. Mankind has benefitted from having binocular vision that allows us to judge distance. But this is at the expense of having all around vision that would enable us to see danger approaching (like a hare does). But, in compensation we have a (potentially) very keen sense of motion in our peripheral vision – which is one explanation of why we can see flickering on display screens that we can’t see when looking directly at them. However, we no longer rely on peripheral motion detection to survive (unless you’re a motorcyclist!), and we’ve lost the natural use of that ‘sense’. Next time you go into the woods, stand still and concentrate on the motion in your peripheral vision – you should notice a heightened level of wildlife detection. It’s an exercise carried out by hunters and trackers to deliberately increase their sense of the environment.
In answer to TeeDee’s question, I don’t think I necessarily act directly on a ‘sixth sense’; I think it makes me more aware to look for anomalies and patterns that I do act on. Maybe it all comes back to the ‘seeing not looking’ and ‘hearing not listening’ concepts.
On the other hand, maybe it's a load of old b******s