It wasn't really suppose to make sense, I wasn't trying to explain it, but okay...
in prepositional logic, each letter of the alphabet stands for a sentence- so the letter A might stand for the sentence "Alice will go to the party," and the letter B might stand for "Betty is going to the party." There are various tools used to manipulate these sentence letters and one of them is ->, or the conditional. The conditional is used to mean "If such and such, then so and so"- if J stands for "Jack will go up the hill", and I stands for "Jill will go up the hill", then "J->I" means "If Jack goes up the hill, then Jill will go up the hill."
The problem I was having with it was the conditional using "Only if." We were asked to translate "Alice will go to the patry only if Betty will go to the party." I translated this as "B->A"; the lecturer translated it as "A -> B". He's right, of course; my translation would be "If Betty goes to the party, Alice goes to the party." The original statement does NOT say this; it says if Betty DOES NOT go, Alice will not go- but it does not say that Alice will ALWAYS go if Betty goes. If Betty were to go to the party and Alice were not to go, the original statement is still true, but mine is not.
Effectively, the correct translation means "If Alice is at the party, Betty must also be at the party"- ie it is necessary for Bettuy to be at the party if Alice is at the party. My translation was probably marred by my idea that the -> arrow implies cause and effect (it's not helped by the fact that the part of the logical sentence, or whatever you would call it, before the conditional is referred to as the antedecent and the part after it is referred to as the consequent.) It doesn't; only that if this is true, then that _must_ be true.
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
no subject
Date: 2005-02-24 06:44 am (UTC)in prepositional logic, each letter of the alphabet stands for a sentence- so the letter A might stand for the sentence "Alice will go to the party," and the letter B might stand for "Betty is going to the party." There are various tools used to manipulate these sentence letters and one of them is ->, or the conditional. The conditional is used to mean "If such and such, then so and so"- if J stands for "Jack will go up the hill", and I stands for "Jill will go up the hill", then "J->I" means "If Jack goes up the hill, then Jill will go up the hill."
The problem I was having with it was the conditional using "Only if." We were asked to translate "Alice will go to the patry only if Betty will go to the party." I translated this as "B->A"; the lecturer translated it as "A -> B". He's right, of course; my translation would be "If Betty goes to the party, Alice goes to the party." The original statement does NOT say this; it says if Betty DOES NOT go, Alice will not go- but it does not say that Alice will ALWAYS go if Betty goes. If Betty were to go to the party and Alice were not to go, the original statement is still true, but mine is not.
Effectively, the correct translation means "If Alice is at the party, Betty must also be at the party"- ie it is necessary for Bettuy to be at the party if Alice is at the party. My translation was probably marred by my idea that the -> arrow implies cause and effect (it's not helped by the fact that the part of the logical sentence, or whatever you would call it, before the conditional is referred to as the antedecent and the part after it is referred to as the consequent.) It doesn't; only that if this is true, then that _must_ be true.
Um, you did ask. ;) Sorry.