Let us distinguish strong and weak versions of the transitivity thesis as follows:
Strong Transitivity: Necessarily, when one has a conscious experience one is conscious of the experience itself.
Weak Transitivity: When one has a conscious experience one is conscious of the experience itself.
One can argue against strong transitivity by arguing that it is possible to have a conscious experience without being conscious of the experience itself. One way in which this would be possible is if “being conscious of an experience” didn’t give the meaning of “having a conscious experience” but instead was a contingent way of fixing the reference of “having a conscious experience”.
Kripke illustrates the difference between giving the meaning of a term and contingently fixing its reference in terms of the example of “meter” and the standard metal bar in Paris. For the sake of simplicity, let us call that metal bar in Paris “Frenchy”. If “meter” simply meant “the length of Frenchy” then the phrase “Frenchy might have been longer than a meter” is necessarily false. However, it is relatively obvious that there is a way of thinking about “Frenchy might have been longer than a meter” whereby it is not necessarily false. On this way of thinking, we use “the length of Frenchy at time t” to identify a length that Frenchy has contingently and then we use “meter” to refer to that length for whatever object in whatever possible world has that length. There are possible worlds in which Frenchy does not have that length. Thus there are possible worlds in which Frenchy is not a meter long.
By analogy, I suggest, we use “states we are conscious of” to fix the reference of certain kinds of brain states, but there are possible situations in which those brain states occur without their possessors being conscious of them.