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I am lying!

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Moonfisher:
I'm not saying it's THE thing to do, I'm saying the rule he proposed would work for eliminating the paradox he mentioned... that's all.
And the rule would make sense in a lot of ways. As you say yourself "Self-referential objects that can be expanded indefinitely"... this is a gray area that allows infinate loops. So you can either accept that this also allows a paradox or proposition with a shifting state that will never setle (However you wish to look at it) or have a rule that prevents this "paradox" but also eliminates a lot of usefull propositions.

I keep saying, there's no right or wrong, and I'm not advocating any of these ideas... in the end I don't realy care where this is going, don't know much about logic and I rarely use it in this way. I just found the whole conversation interesting.
I don't know Haskell so it's hard for me to say what it allows or doesn't allow. I have no idea how it works and how bound it is to the rules of logic, so I can't say what would work well for this laguage. If I understand correctly the laguage is strictly bound to the rules of logic and uses self referential statements to create loops? It seems like most statements who end up refering to themselves would create an infinate loop... but is that the whole idea?

Anyway as said, I don't know much about this stuff, on nothing about Haskell, I just know what makes sence. And if I had to pick then I'm not sure if I would find either rule or no rule more apealing for it's uses, but I do think logic with shifting states seems to make less sence to me.
You said a valid proposition was either true or false and could not be both or it would not be a valid proposition, so it seems to me that a "Self-referential objects that can be expanded indefinitely" wouldn't be able to garantee a value of true or false and therefor wouldn't be a valid proposition...
Or maybe I misunderstood something... as mentioned, don't know all that much about logic, I just know what makes sence

abyaly:
Banning self-reference is not necessary to solve the paradox. I don't think any new rules are needed at all.

Logic doesn't have shifting states. Every statement is completely stable. I think you are making the mistake of thinking about the logical statement in steps. The trick is that no matter what angle you think of it from, the original statement (as it was written) isn't changing, so it's value can't be changing either.

Also, Haskell is really cool. It's a pure, lazy, functional language inspired by category theory. It's worth taking a look if you're interested in programming. Functional languages in general will warp your mindset a bit the first time you encounter them.

jknilinux:
Well, aby, your idea just doesn't "feel" right to me- if you think something's false, but you get a contradiction when it's false, then it must be true. But, if something's not-a-proposition, even if we get a contradiction from this, we still leave it in the not-a-proposition set, because things in that set we just ignore.
The cover story of the new york times today is "everything we'll say tomorrow is true"... this seems fine. The next day, the cover story is "everything we said yesterday was false"... Uhoh, contradiction. So, let's just leave it in the not-a-proposition set, and ignore it.


Anyway, there's one final paradox that deserves some attention here. It's closely related to the liar, but not quite...

Take the statement x:"x => y", (aka x, defined as "x implies y", aka the statement "if me, then y")
The only way implication, aka if...then, can be false, is if the "if" part is true and the "then" part is false. For example:

If it's raining, then the street is wet (AKA R => W). This can only be false if it's raining and the street is not wet. So, it can only be false if R is true and W is false.

So, back to x. If x is false, then what it means must be false, so it is false that "x => y". This can only be false if x is true and y is false. So x is true. However, we just assumed x is false! So, if x is false, then x is true and false, so x cannot be false. So, x must be true...

If x is true, then what x means must be true. So, x is true, if x then y is true, so y must be true.

Uh, one problem... What was y? Here's the awful truth: y was anything. You can put anything in y: "I exist", "I don't exist", "I both exist AND don't exist"... I can prove anything with this!

Hence, a paradox is born. Plus, you can't just cheat and call it "not a proposition" either...

BWAHaaHaaHaaaaaaa! (sry- I just had to do that...)

Peter:

--- Quote from: jknilinux ---Uh, one problem... What was y? Here's the awful truth: y was anything. You can put anything in y: "I exist", "I don't exist", "I both exist AND don't exist"... I can prove anything with this!

Hence, a paradox is born. Plus, you can't just cheat and call it "not a proposition" either...

BWAHaaHaaHaaaaaaa! (sry- I just had to do that...)
--- End quote ---
Why should it mean anything at all. What is wrong with the sentance at all.

If it is raining then the earth is round.(yes it is, the fact that it's too if it isn't raining is a detail)

abyaly:

--- Quote ---Take the statement x:"x => y", (aka x, defined as "x implies y", aka the statement "if me, then y")
The only way implication, aka if...then, can be false, is if the "if" part is true and the "then" part is false. For example:
--- End quote ---
Curry's paradox is a good one, and I'll admit that logical systems that allow its construction are broken.

PS - The programming language Haskell was named after Haskell Curry, which is the same person this paradox is attributed to.

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