It is inherent in our truth tables that we configure a statement to be either true or false, but it seems that this might have certain exceptions, especially in conditionals.
For example, the commonly held tradition when faced with a conditional in which the antecedent never occurs or is 'false' is to hold that the conditional is automatically 'true'. So for example, if we have a conditional in which we say 'If it rains tomorrow (p), I will go for a jog (q).' In the event of the nonoccurrence of it raining tomorrow (p), then the entire conditional is considered true.
But it seems that from a certain view such a conditional would neither be true nor false. This appears to be the case in that the truth or falsity of a statement can only be determined by analysis of its whole meaning, but since the antecedent never occurs, it couldn't be said whether such a conditional, taken as a whole, is true or not.
This is because the consequent depends on the antecedent for its truth-value, in that the consequent of jogging is meaningful and relevant only insofar as a precondition is met in the antecedent that it rains tomorrow. Thus, if it doesn't rain tomorrow, the very truth-value and relevance of the consequent seems to be drastically diminished. As such, the whole of the statement is no longer determined and seems to rather be cast into a 'neutral' or undetermined relation to truth.
This of course means that the principle of the excluded middle has certain exceptions (namely those regarding conditionals). However, accepting this would apparently be a big sacrifice for logicians to make. As such, have any solutions been offered to appease the common sense notion that conditionals can sometimes be a supposed exemption from the principle of the excluded middle? Furthermore, if it is recognized that there are exceptions, how has the principle been interpreted in light of this?