Either/or, either/or but not both, and Double "not" not arrow

[jupiterlaw]

I always review as many of the forum posts as possible before posting questions to ensure my question has not already been answered. Through my review today, I noticed a thread about the "double-not-not" arrow (or negative sufficient and necessary condition double-not arrow) where someone was confused about why the Clarice and Cindy example would be diagrammed differently than the Gomez and Hong example.

I believe I understand this quite clearly but wanted to clarify if the following information I have gathered is correct.

Essentially, if you find it to be useful:

1. Either/or statements can be diagrammed as A <–|–> B

• e.g., Either Jack or John will attend the party.

• we know this can be diagrammed as: John –> Jack

and Jack –> John

• But can statements like this (the standard either/or) be diagrammed: John <–|–> Jack?

2. Either/or but not both can be diagrammed with the double-not AND double-not-not

• e.g., Either Cindy or Clarice will attend the party, but not both.

• we know this can be diagrammed as: Cindy –> Clarice, Clarice –> Cindy, Cindy –> Clarice, Clarice –> Cindy

• but can we also demonstrate this statement as: Cindy <–|–> Clarice and Cindy <–|–> Clarice?

[Robert Carroll]

jupiterlaw,

All of the following are identical in meaning:

Either Jack or John will attend the party.

Jack John

Jack John

They are entirely interchangeable.

The notation you provided for the Cindy and Clarice situation is perfectly acceptable. Note that, as with the conditional ways to diagram that relationship, one diagram alone doesn't give the full meaning. In order to show both parts of "Cindy or Clarice, but not both", you need both conditionals:

Cindy Clarice
Cindy Clarice


or both Double-Not Arrows:

Cindy Clarice
Cindy Clarice

Robert Carroll

[jupiterlaw]

jupiterlaw,

All of the following are identical in meaning:

Either Jack or John will attend the party.

Jack John

Jack John

They are entirely interchangeable.

The notation you provided for the Cindy and Clarice situation is perfectly acceptable. Note that, as with the conditional ways to diagram that relationship, one diagram alone doesn't give the full meaning. In order to show both parts of "Cindy or Clarice, but not both", you need both conditionals:

Cindy Clarice
Cindy Clarice


or both Double-Not Arrows:

Cindy Clarice
Cindy Clarice

Robert Carroll

Yes, this is what I thought! Thanks.