JS: "On what basis do you claim that there is one thing, called "consciousness," which is the basis for all our emotions, our mathematical calculations, our awareness of time, and so on?  Don't you agree that one of the problems here is that the term "consciousness" is being used too irresponsibly, and that we shouldn't make these kinds of assumptions?"

If human consciousness is not at the root of all this, what could be?  Animals don't seem to be aware they are going to die one day, to be able to add 2 and 2, to sometimes want to commit suicide (lemmings aside...), to worship gods, etc etc.  If these kinds of things, and the others I mentioned, are not somehow the consequence of human consciousness, what function or meaning could the idea of human consciousness even have? Perhaps we should scrap the idea altogether? What is the point of it, after all?

JS: "If we want to understand what it means to be a human being, we have to look at human behavior,"

So, yes, let's dismiss thoughts, feelings, the notion of understanding - indeed anything at all that can't be 'observed'. This is Skinner pure and simple... Though you are not alone. Skinner is far from dead in contemporary (analytic) philosophy. He hangs around like Banquo's ghost.

JS: "The point is that in actual cases it is obvious what we mean when we say "that person is conscious."  In some cases, for example, we mean, "that person is awake and alert."

Exactly. But when we try to understand what human consciousness is, do we mean nothing more than 'being awake and alert'. I certainly don't.  If that were all that's involved I wouldn't give the topic the time of day. (And remember even a cat can be 'awake and alert')
 
JS: "It is a question of whether you want to define "consciousness" to be something which can be discovered or if you want to define it as something which must remain beyond comprehension.

But you're suggesting that science is the only way of discovering something. If you really think that, why would you have any use at all for philosophy?  Or do you think that philosophy is nothing more than science? (There again you would not be alone...)

DA