Basic Translation Group 3 Indicators - Clarification Needed

Number_5

I was hoping to see if someone has be able to make a concise explanation/understanding of this indicators and their respective rules. I find the them to be a bit confusing relative to #1 and #2 - especially because the rule states you can pick either idea to negate and then it becomes the suff. cond.

Hoping to see if theres something a bit more straightforward. Thanks in advance.

Logician

Hey there, so the group 3 indicators (unless, without etc..) are definitely something you're going to want to memorize- especially when you're just starting out. But eventually, the goal is that you begin to understand the function of these words so that you won't rely on the words themselves but rather on how they operate in a premise.

So with that being said, here's an example:

"Tom will not buy groceries today unless its sunny."

I think in plain english we all know what this sentence means, Tom will buy groceries only if its sunny. Which in logic would be represented: Tom buys groceries today ---> It's sunny. And you'll notice that "only if" belongs to group 2. All this to say that the differences (i.e functions) of the groups are all geared towards the same goal of representing english in logic.

Now, if you follow the group 3 translation. you can pick either term and it will work.

1) Picking the first term "not buy groceries": so we negate this term and make it the sufficient condition, while the other term "its sunny" becomes the necessary condition.

So "not buy groceries" negated becomes "will buy groceries or buy groceries".

Buy Groceries ---> It's sunny (BG --> S)

2) Picking the second term "its sunny": so again, we negate this term and make it the sufficient condition, while the other term "will not buy groceries" becomes the necessary condition.

So "its sunny" negated becomes "its not sunny"

It's not sunny ---> Tom will not buy groceries (/S --> /BG)

Notice that statement 1 and 2 are identical statements, they're just contrapositives of each other- which is precisely why you can pick either term and get the same result.

Contrapositive of statement 1: If its not sunny, Tom will not buy groceries. (/S ---> /BG)

Contrapositive of statement 2: If toms buys groceries, then its sunny (BG ---> S)

Hope this helped!

Totality Dude

The two conditions are married together and it’s a blessing. No need to identify, just take one of the two ideas and negate it. You have your SC at that point, add the NC and you’re diagrammed. I love these because it’s a hard rule and identifying can be tricky for me.