Negating negative statements

[lucia]

Hello,
I seem to have a recurring issue with my diagramming (or possibly, understanding) on conditional statements in the Powerscore LR Bible. As I work through my LR book, I find that frequently instead of negating a negative statement, I simply make it positive. It makes sense to me, but I don't know if this is logically valid.

For example: a statement from Q4 on page 142: "if the planets climate is not too extreme and unstable to support life, then it has a stable angle of rotation"

Powerscore diagrams it like this:
~PCE --> AS
(if planet climate not too extreme to support life, then stable angle)

And I would diagram it like this:
SL --> AS
(if support life, then stable angle).

Another example, from the LR Powerscore bible, page 128 #12.
Powerscore diagrams the original statement like this:
C --> ~DRV
(If citizen, then can't be denied the right to vote)

And i diagrammed it like this:
C --> RV
(If citizen, then have the right to vote).

In both examples, are the two statements logically equivalent?

[Dave Killoran]

Hi Lucia,

This is another great question As a quick and dirty method, what you are doing will typically work. The problem is that it's not exact, and there will be times where it will fails you. Because we want methods that never fail, that's why you see us using the negations of the negative.

When could it fail you? When the statements aren't binary, or limited to just two values. If you are talking about a light being on or off, you'd be fine. For example, the negation of "not off" is technically "not not off" but in this binary situation that is the same as "on," and "on" is what you'd want to use. But what about if we were talking about a business, and that business could be profitable, break even, or lose money? If the statement said that the business "did not lose money last year," then the negation is not that they were profitable, because saying so forgets about the break even option.

So, the rule here is it depends on the situation. Only two options? Go ahead and make it positive. Three or more? Negate the negative in the manner you see us use.

Please let me know if that helps. Thanks!

[lucia]

Hi Dave,

Sorry, looks like I forgot to answer. Yes, that makes a lot of sense--I've been keeping this in mind and it's been a good exercise to try and determine when statements are binary and when they're not. Thank you for your thorough reply, to both this question and the one I posted on the Games board!

[Dave Killoran]

No worries at all! Glad I could help

[avengingangel]

I came to the forum because I did the same thing when diagramming "No citizen can be denied the right to vote." Dave, your answer is helpful and makes perfect sense. My additional question is, how do you know that "denied the right to vote" is the actual term, and not a negation of the term? I read the word "denied" as a synonym for "not," etc., so that's why I turned it into a positive (bc of the double negative, no citizen can be denied the right to vote." Is it because you can only use the words "not" and "no" as modifiers? And any other word, however similar in meaning in the "real world" should not be diagrammed as a negative? (Words like "denied," "stopped" "lessen" "prevent" "quit," etc.??) I hope I'm explaining this clearly! Any insight or further explanation would be of incredible value. Thanks !!

[Jon Denning]

Hi angel,

Part of what you're seeing here is the subjectivity inherent in the English language, and the resulting ability that gives you to interpret it and diagram it in multiple ways. Let me explain.

To say "denied the right to vote" really allows for (at least) two possible representations:

1. You could say "No vote" and show Vote
2. You could say "Denied vote" and simply diagram it Denied Vote (or DV, or whatever)

So for the sentence as a whole, "No citizen can be denied the right to vote," either of those two options above would be fine:

1. Citizen Vote
2. Citizen Denied Vote

The first says "all citizens have the right to vote," and the second is entirely synonymous as "all citizens cannot be denied the right to vote" (or "no citizen can be denied the right to vote," which is, again, the same thing).

I tend to try to show things as the "positive" version when I can, so I favor #1 up there, but that's more personal preference than logical superiority. Ultimately what matters is that you recognize the interchangeability of the terms--between including the negative "denied" or representing that negative with a "/"--and know that the test makers can use either versions, too.

I hope that helps, but if you still have questions please let me know!