# What part of a universal propositions is the antecedent?

The wiki article on vacuous truth says:

a vacuous truth is a conditional or universal statement that is only true because the antecedent cannot be satisfied.

I'm familiar with identifying the antecedent and consequent in a conditional, but I'm unsure what part of a universal proposition would be the antecedent.

The article gives the following example:

For example, the statement "all cell phones in the room are turned off" will be true when there are no cell phones in the room.

Would the subject class "cell phones in the room" be the antecedent since it being empty results in the statement being true? In general, is the subject class the antecedent in a universal?

• Yes, your guess is correct. Commented Jun 25, 2021 at 20:16
• To translate "all cell phones in the room are turned off" into first order logic, you'd have to turn it into something like "for all x, cellphoneintheroom(x) -> turnedoff(x)", so the antecedent would be cellphoneintheroom(x) and this would be vacuously true if there is no x in your domain of discourse that satisfies cellphoneintheroom(x). Commented Jun 25, 2021 at 20:47
• How can a ceĺl phone be turned off if there are none to be turned off? The antecedent can be there but if it has nothing to cause a change on it becomes vacuous. Commented Jun 26, 2021 at 0:11
• So its not the subject class thats the antecedent but the cause. The turning of is the subject class and the turned off phones the belong to the consequense class. The phones themselves belong to the conditional class (a tv can be turned off also). So the subject class is "turning off", the conditional class is "phones", and the consequence class is that of " turned off phones". So without phones in the room the conclusion that all phones in the room are turned off cant be made. Commented Jun 26, 2021 at 0:28
• The antecedent is the noun or noun clause BEFORE the main verb in the alleged sentence. In this case Cell Phones would be the noun clause BEFORE the main VERB which is ARE. You can make a conditional statement from the All statement: if there are any cell phones in the room, then they must be turned off. Now your objection to the case where there are no cell phones in the room never arises.I never stated there were cell phones in the room.The statement only applies if there were a cell phone in the room.The instuctions in the scenario do not apply if there are no cell phones. No falsification. Commented Jun 26, 2021 at 15:18