Logical analysis of John 14:15, 21

[TonyChanYT]

John 14:

15 If you love Me, you will keep My commandments.

Let statement L = you love Me.
K = you keep My commandments.

In terms of first-order logic, John 14:15 expresses the conditional statement, C1: L→K

John 14:

21a Whoever has my commands and keeps them is the one who loves me.

In terms of first-order logic, John 14:21a expresses the conditional statement, C2: K→L

C1 ∧ C2⇒ L→K ∧ K→L⇒ L⟷K

In English, you love me if and only if you keep my commandments, i.e., L and K are logically equivalent. According to first-order logic, you can't have one without the other.

 

[Binyawmene]

In terms of first-order logic, John 14:15 expresses the conditional statement, C1: L→K

Prepositional Logic is not the first order of logic.
Predicate Logic is the first order of logic.

In terms of first-order logic, John 14:21a expresses the conditional statement, C2: K→L

C1 ∧ C2⇒ L→K ∧ K→L⇒ L⟷K

And John 14:21 is not a logical conditional, but maybe a logical conjunction. I agree that both would result in the same truth value. So, they are logically equivalent.

 

[TonyChanYT]

Prepositional Logic is not the first order of logic.

Right. Check out https://christcentered.community.forum/threads/first-order-logic.1731/