I hope my basic grasp of logic (first-order logic) is sufficient for the purpose of this discussion which concerns the temporal aspect of the logical conditional.

First off, some definitions:

Time: The only aspects of time that matter to this discussion is its tripartite division into past, present, and future.

Logical conditional: "IF...THEN..." statements and example of which is "if x > 3 then, x > 0". A general formulation of the logical conditional is "IF P THEN Q" where P is taken as the sufficient condition (the antecedent) for Q and Q is the necessary condition (the consequent) for P. If a proposition P is sufficient for Q, it means that P & ~Q is impossible. Conversely, if Q is necessary for P then ~Q & P is impossible.

Consider the following statements:

1. If the plant grows then the plant was watered

2.; If I decapitate you then you will die

There's nothing wrong with either of the two statements - they make complete sense. However, in the case of statement 1, the consequent "the plant was watered" temporally precedes the antecedent "the plant grows" [the plant has to be watered before it can start growing] and in the case of 2, the consequent "you will die" comes after, in a temporal sense, the antecedent "I decapitate you" [death follows decapitation].

That means, if time is removed from the equation, the following occurs:

3. If the plant grows then the plant was watered = If plant growth then water

4. If I decapitate you then you will die = If decapitate then death


If we're then to analyze statements 3 and 4, as formulated outside of time, we wouldn't know if we should water the plant to make it grow or that plant growth produces water. We also wouldn't know whether statement 4 means that you can cause death by decapitation or that death occurs before decapitation. In short, the logical conditional is temporally unbounded i.e. without some words that indicate time like "will" "was" and verb-tenses, we wouldn't know if the antecedent precedes or succeeds, time-wise, the consequent.

In essence, the logical conditional is chronologically ambiguous and cuts both ways - backward into the past and forward into the future - and which is meant needs to be made explicit using words like "was", "will", and verb-tenses.

What significance does this particular, peculiar aspect of the logical condtional have?