Originally Posted by pdupiano
How is (b) an isomorph of (x)?
Can you further explain what you mean by isomorph aswell because I'm failing to see the connection wherein (x) is structurally identical to (b). At the moment I do not see them as being identical in any way.
I imagine you are probably more interested in why the test conditions for (b) share an isomorphic relationship of any sort with (x). (b) is isomorphic to (x) to the extent which it pertains to (x). This is just simple identity function; it's not much more than to say something is identical to itself in that case.
However, the test conditions are isomorphic to (x) because the compound proposition itself already states the conditions of its confirmation or falsification through (b). That is, with the causal component isolated, the purported phenomenon occurs (in this case, the experimental stimulus being cables, the phenomenon being differentiation). It is necessarily a part of (x) because this is precisely what (x) purports to claim about the world, as represented by its part (b). This is why one need not inquire into the truth value of (a), because while it is of course alluded to as being the other component of the compound statement, (b) and its attendant test conditions are independent as a matter of their place within the compound statement.
So, when you are thinking that the test conditions assume you have perception, in some sense this is true because (b) is contained in (x), and for (x), (a) is a component proposition. However, it is not germane because the experiment is only testing the proposition (x) to the extent of (b), and because the test conditions are isomorphic to the claim made by (x) [through (b)], to reject the test conditions is to simultaneously reject (b), and therefore falsify (x). Therefore, it is not helpful (or particularly relevant) to concern oneself with testing for (a), or generally considering the truth value of (a).