“Black’s Objection” has confused legions of readers from 1959 till nearly the present day.  Here I will try to set out the dialogue for you a little more explicitly and a little more fully than I did in class.  I'll attempt a dialogue (do not try that at home).  The dramatis personae will change when we get farther into the debate, but it will remain a dialogue between an Identity Theorist and an opponent.
 

    SMART [responding to some of the ineffectual objections]:  Place did not say the identity is a priori, or a matter of word-meaning or concepts.  (Duh.)  It’s a posteriori, empirical, something that has to be discovered through observation and experimentation and research.  Water and H₂0, genes and DNA molecules, lightning and electrical discharge, dum de dum,…  [Whistles a happy tune.]

    BLACK:  Ah.  Yes, there are empirical identities discovered by science.  But we philosophers don’t get them for free.  There’s a condition that has to be met.  In order to discover an empirical identity between Xs and Ys, where Xs are a familiar everyday sort of thing and Ys are (perhaps) technical scientific things, obviously we have to be able to recognize Xs to begin with.  And, nearly as obviously, we have to be able to recognize them or pick them out independently of anything we know about Ys, since we probably haven’t even heard of Ys before we start our research.  Now, here’s a deductive argument.
 

    1.  If Xs are (only) empirically identical with Ys, we must be able to recognize Xs independently of Ys.   [As just argued.]

    2.  To recognize Xs independently of Ys, we must identify them by reference to a property they have independently of their being Ys.

So
    3.  If Xs are (only) empirically identical with Ys, we must identify them by reference to a property they have independently of their being Ys.   [1,2]

So
    4.  If mental yellow flashes or yellow after-images are empirically identical with brain processes (say with y-fiber firings), we must identify them by reference to a property they have independently of their being y-fiber firings.   [Special case of 3.]

    5.  The  property by which we identify mental yellow flashes is not any physical property.   [Descartes showed to my satisfaction that I know my own mental contents independently of there being any physical world at all, even if in fact there couldn’t be any mental states or events without a physical world.]

    6.  Every (here relevant) property is either a physical property or a nonphysical, mental property.   [Nonphysical mental = “irreducibly psychic.”]

So
    7.  The  property by which we identify mental yellow flashes is a nonphysical, irreducibly psychic property.  [5,6]

So
    8.  Mental yellow flashes have a nonphysical, irreducibly psychic property.  [7]

    9.  Nothing that has a nonphysical, irreducibly psychic property can be simply identical with a purely physical brain process.   [For then the brain process would hardly qualify as purely physical.]
_______________________________________________________

  10.  Mental yellow flashes are not simply identical with purely physical brain processes; the Identity Theory is false.   [8,9]   QED
 

    BLACK’S GHOST<1>:  All right, yes, 7 doesn’t follow from 6.  There are topic-neutral properties in addition to physical and nonphysical-mental ones, so there’s a theoretical possibility that my mental yellow flash is picked out by reference to some topic-neutral property it has rather than by an irreducibly psychic one.  But (get real!) surely I don’t in fact identify my own mental yellow flash as “the thing that is going on in me that is like what goes on in me when I really see a lemon…,” or anything like that.  I identify it as (surprise, surprise) a yellow flash I experience.

    ARMSTRONG [bursting in at the door]:  But who says the property of being a yellow flash is an irreducibly psychic property?  Maybe it is itself a topic-neutral property, rather than a nonphysical-mental one.  In fact, here, according to (ahem) my Causal Analysis of mental concepts, is what it means to “experience a yellow flash”: it’s to be in a state that is typically caused by seeing a bright yellow object and that in turn typically causes….”   The latter description is topic-neutral; therefore, so is “experience a yellow flash” (the two being synonymous).  But, notice, even if my Causal Analysis is incorrect, no one has yet shown that experiencing a yellow flash is irreducibly psychic rather than topic-neutral.

    THE AUTHOR OF THE AFTER-IMAGE OBJECTION:  But what about the yellow flash, or the after-image, itself, considered as an individual thing rather than as embedded in an event of experiencing?  It seems to have properties that the brain process doesn’t.  So it is not identical with the brain process.

    SMART:  There is no yellow individual thing embedded in the event of experiencing.  There is only the event of experiencing.

    BLACK’S GHOST:  All right  for now  but there is yellowness.  If you deny that, you are a liar.  And where is the yellowness located, ontologically speaking?  There is (I hope for your sake) nothing yellow in your brain.  And let’s suppose there is no real yellow object in the room; the experience is illusory.  What thing, then, is yellow?  What, anyway, bears or supports the yellowness?   [Thunderclap.  Bring up ominous mood music.]

1.  So far as I know, Black himself never returned to the issue.  I am developing the rest of this dialogue on his behalf.  If he doesn’t like it, he can haunt me.