I'm surprised there's not more replies here! or maybe I should have checked the dog post because more people are dog lovers.

To me its a simple line of thought: animals are aware/have emotions. animals have souls. animals are so in-tune with emotions (thiers and ours) that its a very plain language to them. animals being in-tune have a natural psychic ability to communicate with each other and us, if were listening. animals who are psychic also have this 6th sense of "knowing" and its just another level of awareness or sensitivity that humans sometimes have depending on how sensitive they've become.
We all have the ability, just animals are better at it than we are- just like we are better at the slower mental wave of spoken language and thought processes. A very in-tune person would also be able to sense the moment someone makes a decision in their head and it is almost like its being broad-cast loud and clear. Thats my experience anyway, when I'm feeling particularly sensitive and a person is focused on a certain thought- its like mentally they are staring intently at a picture of a red car and anyone who's paying attention mentally will automatically look at the same picture because that person is so focused. so when the owner says in their mind "gotta get fluffy now if I dont want to be late" they are usually pretty focused and fluffy gets a loud and clear "time for the vet!" and they book it for the nearest hiding place. Thats my explanation.
