There are some metaphysical questions Buddha refused to answer; whether there is a self is one of them.
"The Buddha states that it is unwise to be attached to both views of having and perceiving a self and views about not having a self. Any view which sees the self as "permanent, stable, everlasting, unchanging, remaining the same for ever and ever" is "becoming enmeshed in views, a jungle of views, a wilderness of views; scuffling in views, the agitation (struggle) of views, the fetter of views."[Douglas W. Shrader
To the Buddha these questions provoke clinging and attachment and are traps of dualistic thinking. As his teachings are all about suffering and non attachment as an end to sufferings, the views about 'self' and 'non self' incite attachment and are best not to indulge.
I touch the tree in my garden every morning to connect with the positive energy of nature. This morning an ant crawled onto my palm and gave me a little bite. Instinctively I blew it off onto the ground. I know the ant will find its way back to its intended destination.
I began to reflect the world of ants or for that matter other animals like my pet cat. Animals, I am sure can think, albeit in a limited way relative to humans. Like other animal species, humans in all probability also perceive things in a limited way. So much truths have yet to be uncovered scientifically. Just like it takes centuries for humans to discover that the earth is round and not flat, there must be so much that is unknown to us. Similarly, just like my cat's brains are not meant to fathom the 'reality' that humans live in; so too the limited capacity of a human brain may not allow them to understand larger truths.
In the end each specie just tries to live well. For us humans, we will do well not being attached to the concept of self.