Lawgic: Group 4 indicator and double negative (or not)

Phil Ivey

Hi, I was making up statements to practice and I'm confused about how "no" works when there is a double negative (or what I think is double negative). The statement reads: "No one who fails to come to the party is David."

Based on JY's lesson, we isolate "no" as a Group 4 Necessary Condition indicator. The first idea is "Fail to Come to the Party" (FTCTP) and the second idea is "David" (D). So, I pick either of the two ideas, negate it, and make it a necessary condition. I chose the first idea.

D --> /FTCTP
which, I think, can be rewritten as D --> CTP since "Not Fail to Come to the Party" is essentially "Come To the Party"

Is this lawgic accurate? Some of my friends are suggesting that because of the "fail to", the correct lawgic would be: CTP --> D

and now im confused

thanks in advance for your input!

chrijani7

I don't think you should be changing the FTCTP to CTP, just make note in your mind that it means he went to the party. I say this because your changing the way your lawgic is represented, which makes it more difficult to interpret (in my opinion).

No one who fails to come to the party is David
Take our 2 ideas like you did. FTCTP & D.

Choosing "D" as our negate necessary, it would follow like such:
FTCTP--> /D
How it reads: If you fail to come to the party, then you are not David.

Taking the contrapositive OR choosing FTCTP as our negate necessary, it would be like this:
D--> /FTCTP
How it reads: If are you are David, then you do not fail to come to party.

Being someone who fails to come to the party, is sufficient for us to infer that the "someone" is NOT David. BUT not being David does not tell us anything about going to the party.

Now, taking the way your friends suggested and only using CTP we would end up with this:
Our 2 elements : CTP & D, BUT remember that in front of CTP is FAIL TO so if you are not going to represent by FTCTP, you still need to remember that failing to is NOT going. So actually our 2 elements are /CTP (not coming to party or failing to come to party) & D.
Choosing /CTP as our negate sufficient we get this:
D-->CTP
How it reads: If you are David, then you came to the party.

Taking the contrapositive or choosing D our negate necessary we get this:
/CTP--> /D
How it reads: If you are not coming to the party (or failing to come to the party), then you are not David.

I think what happened is that your friends forgot to include negations by excluding "FT" you need to put the negation. Hope this clears this up or I at least helped in someway.