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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?

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  • 1
    Yes, your guess is correct.
    – lemontree
    Jun 25 at 20:16
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    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).
    – Hypnosifl
    Jun 25 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. Jun 26 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. Jun 26 at 0:28
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    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.
    – Logikal
    Jun 26 at 15:18
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The guess is not correct. It's the turning off that is the subject class. The phones are the conditional class (you can turn off many things but we restrict to phones, ie, the turning off is conditioned). The turned off phones belong to the consequential class. If there are no phones in the room then they can't be turned off so the conclusion that if there are no phones in the room then they are tutned off is false.

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    What do you mean by "subject class" and "conditional class", have you seen these terms used in any branch of formal logic? Normally "antecedent" and "consequent" in discussions of logic refer specifically to material implication, i.e. for a statement of the form P -> Q, P is the antecedent and Q is the consequent. So in this context, if you wanted to say turning off cellphones is the antecedent, you need to show how you could do a reasonably faithful translation of the statement into a more formal version w/ the material conditional, like my "for all x, cellphoneintheroom(x) -> turnedoff(x)".
    – Hypnosifl
    Jun 26 at 23:36
  • @Hypnosifl In the quetion is asked for the subject class. The subject is the turning of itself. Turning of can be applied to many things. But we only apply it to phones. This is the condition n the turning off. So the antecedent class is automatically the phones. This means that the antecedent class (being the same as the condition class) has no need to be mentioned. It's already implied by the conditional class. The consequential class is the class containing the phones that are turned on and is a subclass of the antecedent class, depending on the subject class. Jun 27 at 1:12
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    The question uses the words "subject class" to describe the linguistic category "cell phones in the room", it's not asking if that's the subject class. It's asking if in logical terms "cell phones in the room" would be the antecedent, and whether more generally the subject class in any similar sentence would be the antecedent.
    – Hypnosifl
    Jun 27 at 1:22
  • @Hypnosifl Thats exactly what I said in my last comment. The antecedent class contains the phones (in the room) and the consequence class is a subclass of this (containing the phones that are turned on). The more general question I havent answered because I didnt see that. Jun 27 at 2:10
  • @Hypnosifl If the antecedent class is empty (no phones in the room) then the consequnce class is empyu too. So no phones in the room cant imply that they are turned off because the class of turned off phones is empty. Just as the antecedent class. Jun 27 at 2:18

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