Hi Dan. I should say, first, It is CS Lewis who makes this argument, not me. Just want to give credit where credit is due. Finally, if curious, I highly recommend the book. But to answer your question, Lewis defines consciousness as a soul or a "timeless" quality that sits outside our lived or sentient experience. The fact that some animals appear to be conscious such as dogs, cows, horses, pigs, cats, etc., does not in and if itself prove the presence of a "self" or a "soul" in the sense that is true of mankind. I will paste an excerpt from the book which addresses this illusion of animals having consciousness based on the fact that we humans can act as if conscious when in fact we are sometimes we are truly unconscious,  from an administered drug or a comatose state. Finally, I am not saying I wholeheartedly agree with Lewis. I prefer to take the Jordan Peterson approach. That is, I will act as if animals are conscious. That is treat them with kindness, respect and dignity. Pets or not.  
https://m.primal.net/JKsm.jpg