It is clearly relevant to the antecedent of case (2) of the theorem we want to prove.
At this point, it is rather self evident that, being TP53 and TP53-P two distinct entities, their interaction (or lack thereof) with MDM2 can be described by two separate expressions: where by ⊢/ we mean that the antecedent (in this case, MDM2 & TP53-P) does not imply the consequent (in this case, MDM2 * TP53-P).
This issue is also related to the identity condition, since it would appear in many cases that there is no parallel movement in the antecedent clause.
In this case, the antecedent of the PRO is the whole event-denoting matrix clause.
But in that case, the antecedent of (1.3″)—that the belief that "Things which we desire to desire are good", provides a reason for action is false, so far as Russell's analysis is concerned.
One way to understand the problem is to revise the semantics of implication, in order to eliminate the trivial cases, namely cases where the antecedent cannot be true, or the consequent cannot be false.
While Rosenberger was concerned with the rights a student has to use an extracurricular speech program already in place, todays case considers the antecedent question, acknowledged but unresolved in Rosenberger: whether a public university may require its students to pay a fee which creates the mechanism for the extracurricular speech in the first instance.
However, it would presumably still be a minimal requirement that it is never the case that the antecedent is true and the consequent false.
Lewis could say that his default metric was only meant to apply to cases where the antecedent was about the happening or non-happening of a particular event at a particular time, and it wouldn't have seriously undermined his larger project.
Philo maintained that a conditional is false when and only when its antecedent is true and its consequent false, and true in the three remaining cases: whenever the antecedent is false, and when both antecedent and consequent are true (SE, Against the Logicians 2.113-114).
In either case, a is the antecedent and b the consequent.
