I think from a scientific perspective, nobody can actually and measure a ‘soul’ so to speak. That would be very easy if we could just simply measure a certain property directly of animals but we would need to know what property we are trying to measure. However, as you might imagine, if you asked ten different people to describe a soul, you will likely get ten different answers so we are not off to the best start! So your tag of ‘theology/philosophy’ is certainly appropriate on this one
I believe this touches loosely upon some of the topics also explored in this post from the main site: