It has been said children are more 'sensitive' to things Paranormal - since they are a blank slate and aren't influenced by society's skepticism - I believe we are all born with a 'sixth sense' and it is buried in some by outside influences as we mature...
I think young aged people can see ghost better than older people.
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If you believe that there are ghosts then there's no reason for suspecting that babies do not see them. On the other hand as I don't believe that there are such beings as ghosts, I would say that neither babies nor children nor adults can see them.