I suppose the truth table for conditionals can be tricky to interpret. The word ‘antecedent P’ means “that which leads," (regardless if it's true or false) and the word ‘consequent Q’ means “that which follows" (regardless if it's true or false). Both P and Q is the whole constituents. And the truth table gives us four possible cases for the value of P and Q.
The Logical Conditional rules states: “A conditional P --->Q is false, if and only if, antecedent P is true and consequent Q is false, otherwise it’s all true.”
1. First row you have T, T, and T.
If P that which leads is true, then Q will immediately follow as true. It's reasonable to assume the whole constituents is true because P imply Q.
*Remember that the P is doing the leading or implying, so the second, third, and fourth rows must follow this line of reasoning too.
2. Second row you have T, F, and F.
If P that which leads is true, then Q didn't follow as true because it's false. It's reasonable to assume the whole constituents is false because P didn't imply Q.
3. Third row you have F, T, and T.
If P that which leads is false, then Q will immediately follow happens to be true. It's reasonable to assume the whole constituents is true because P imply Q.
4. Fourth row you have F, F, and T.
If P that which leads is false, then Q will immediately follow as false. It's reasonable to assume the whole constituents is true because P imply Q.
Are you calling the antecedent P, whether or not it is true, the statement including the "If", or the statement after the "If".
The word "if" in this instance is hypothetical.
“If miracles were performed in Sodom, then Sodom would have remained to this day.”
Both constituents of P and Q I've viewed this from the actual position from what we already know that has occurred in actual world. The possibilities cases for 1-3 is not applied in the actual world. If you believe P and Q is applied to one of the possibilities, then you have to demonstrate that is the case.
What happen in the actual world?
1). Jesus did not perform miracles in Sodom.
2). Sodom was judged and destroyed.
Compared to
1). “If miracles were performed in Sodom." Is false in the actual world.
2). "then Sodom would have remained to this day.” Is false in the actual world.
It's reasonable to assume the whole constituents itself is true because P imply Q. The logical form of a conditional doesn't depend on something is actually true or actually false. No matter how absurd, like "If a banana tree is planted in the air, then it doesn't require soil." We know in the real actual world that is not the case. The logical form of a conditional itself isn't invalid. No matter how ridiculous a statement might be. The idea can be absurd and irrational but the logical form itself is true.
I don't see how, "If miracles were performed in Sodom" can be true nor false, if it includes the IF.
Then you have to negate antecedent P.
~P
Or, are you negating the whole constituents of P--->Q
~(P--->Q)
Now to say "miracles were performed in Sodom" can be true or false, because it is a complete statement. So which is the antecedent that can be true or false --that is, does the antecedent include the IF, or is it merely identified by the IF?
It doesn't matter if the antecedent P is true or false in a hypothetical. If you examine the hypothetical from what we already known in the actual, then you should be able to draw your conclusion. Pick your choice.
1. P--->Q
2. P---> ~(Q)
3. ~(P)--->Q
4. ~(P--->Q)
4. Fourth row you have F, F, and T.
If P that which leads is false, then Q will immediately follow as false. It's reasonable to assume the whole constituents is true because P imply Q.
It the actual antecedent, which can be true or false, does not actually include the "If" then please rewrite this where I can follow along. If the statement including the IF can be true or false, then please explain how.
A conditional doesn't have to be written in a "if, then" statements.
If = (for, since, because, etc.)
Then = (so, it, therefore, etc.)
Again, "If miracles were performed in Sodom" is neither true nor false. I'm sorry for being picky, but I'm not following what you are saying because of (at least) this.
I think you might have a problem distinguishing between "hypothetical" and "actual."
1. Hypothetical is contrary to what we already know about the actual world. It's imagined and not real.
2. Actual is what we already know is real and is existing. We observed though things that has occurred or is occurring.