I actually have a rather long attention span. And although all propositions can be argued many different ways, I beg to differ on the exact quote. Statements(by definition) have exactly one truth value. True or false. It is impossible to have something that is both. Give examples of this and it may sway my opinion.

Nike, please do not EVER post sahee's face in public. You might be arrested for indecent exposure.

And for squirrel:
OMFG THIS WEBSITE HAS A WHITE BACKGROUND! THE FUCKIN RACISTS!
No one was intending to be racist here! Now stop being so oversensitive to these posts!

Well the "scripture" in Principia Discordia were meant to broaden the mind, not to have a full literal meaning. Just like the Zen teachings, koans...
anyway if we want to be challenged by your question, and try to answer, then I guess, we'd have to point to some sentences that make the recipient say "well yes... and no".

Sentences that can be subjectively interpreted both ways, by different people, or by us, being able to look at the thing from two perspectives, etc.
Like "religion is helpful"
- true: yes. it provides comfort to folks. undereducated folks can have the nice feeling of them understanding everything... (well, god did it, god wanted it... even if the term "god" is so abstract, and it relates to nothing. just an imaginary concept)
- false. it isn't. it blocks the way for proper knowledge, it shows the world not in it's true form, it brings/brought about wars, stupid bigots etc. bla bla bla etc.

Now there might come 2-3 pms right now supporting my point of view. 5-6 which doesn't. But is my point of view true? false? to some extend true and to some - false?
How can a point of view be true or false? and if we have people thinking both ways, then can we take it as your answer? that some sentences can be considered both true and false?

Besides, if you want a less subjective sentences examples that would use such a paradox, then just google "liar sentences" or something like that...

Or MAYBE just cut yourself...
It will be easier...

Still, I think, that the author just meant sentences that can be interpreted both ways, or that are to some extend true to some not, or one part of a long sentence is true, the other false, etc.

...
I changed my mind.
DEFINITELLY cut yourself... for bringing me to blabber such an abstract nonsense ;P!

In it's simplest form, it just means that there is more than 1 perspective to look at something, and the perspective that comes most easily to you might not be fully truthful. It encourages you to challenge things that you would usually believe or simply assume.

example: Do dreams exist? Or is what you assume to be a dream simply you returning to conciousness with your eyes closed?

I think the terms were mixed up. Sahee, your example was of a proposition, not an actual statement. The truth value of a proposition is determined by a statement. A statement is basically a given fact(in this case, those premises you provided.) So yes, a proposition can easily be considered true OR(not and!) false, depending on how all of the premises prove/disprove the conclusion. I hope this may clear things up.

get out of our board

huhh man chill out..he is already gone

Well quite the contrary. :P
How could stating that "religion is helpful" is a proposition?

Because the truth of it is argued multiple ways, as you already pointed out. But a statement is where the truth value is already assumed, for example, "Our sky is blue." The truth of that is already assumed and does not need to be proven. However, if you said that Pluto has a purple sky, that is unknown, can be argued, and thus is a proposition.

"Our sky is blue" actually does fit in with the scripture. It appears blue so there's some truth in it, but other times it can appear black (night) or red/orange/yellow (dusk/dawn) and it only seems to be blue (or red/orange/yellow...etc) because light refracts as it passes through it - the sky is actually colourless hence the bit o false. And the bit of meaninglessness, well who cares what colour the sky is; it makes no practical difference.

also according to wiktionary

Proposition: An assertion so formulated that it can be considered true or false. (a fact/false fact?)

Statement: A presentation of opinion or position. (can be debated, no clear right/wrong answer)