Further explanation:
First of all, the above argument refers to your own consciousness, not the concsiousness that you think you perceive in other entities, which could very well just be an illusion to you. And before we get on, do not think that I am trying to say that we can not be in illusion. We are probably illusioned many times every day in various ways. What I want to say is that if you experience that you are conscious, then the consciousness that you experience can not be an illusion to you. You might very well be in illusion about the real nature of your consciousness, but it is not an illusion for you that you are conscious. Because an illusion can only take place in a consciousness, and it can never happen in non-conscious things. So if an illusion would take place, then there is consciousness there already. So your own consciousness can not be an illusion.