1. Jun 7, 2005

Berislav

Consider some hypothetical universal rule which everything (including nothing) must satisfy. Then take that some hypothetical object that does not satisfy this axiom. What can be said about that object? Certainly it can not be said that it doesn't exist.

2. Jun 7, 2005

3. Jun 7, 2005

Berislav

Ah, yes! But the object itself is not the paradox, it's the rule. What I'm basically trying to point out is the paradox in absolute undiscriminating rules.

4. Jun 7, 2005

El Hombre Invisible

Well, both really. The rule alone cannot be paradoxical - it requires proof to the contrary. For it to be the hypothetical rule in question, it must be correct. It must also be proved incorrect by the object, so is not the rule in question. An absolute undiscriminating rule cannot, in reality, be a paradox. If it is correct, it will not be disproved. If it is disproved, it is not absolute.

5. Jun 7, 2005

honestrosewater

How do you talk sensibly about absolute things? You are using rules in determining whether the situation is paradoxical, so your determination is relative to the rules you're using. Why can't the rule be satisifed and not satisifed at the same time? How do you even determine whether the rule is satisified in the first place?
BTW, rules that are always satisfied in some system pose no problems. Rules that are never satisfied in some system also pose no problems. For instance, "P or not P" always being satisfied and "P and not P" never being satisfied, where P is any statement, are common. In fact, you used them yourselves. :)

6. Jun 7, 2005

El Hombre Invisible

"Why can't the rule be satisifed and not satisifed at the same time?"

Because part of the rule is that te rule must be satisfied all of the time.

7. Jun 7, 2005

Berislav

Yes. A rule is disproved if there is something that doesn't satisfy it within the confines of it's domain. If the domain is everything and nothing it is easy to disprove such a rule for the exception to it doesn't need to exist.

For instance the first axiom of mathematics:

x=x,

a number which doesn't satisfy it doesn't exist. This rule poses no problem as it's only defined in the realm of numbers that exist.

One can not. That's my point.

True.

It's an abstract concept. Without defining the rule in question you can not determine whether it's satisfied.

Yes, but not in all systems, as I tried to demonstrate.

Yes, but that is because with "normal" rules there is always some third possibility, which is something outside the system in which the rule is defined. In the case of the most universal true rules it is nothing.

Last edited: Jun 7, 2005
8. Jun 7, 2005

honestrosewater

Right, the only requirement was that the rule always be satisfied, so if the rule is always satisfied and always not satisfied, then the requirement is met. It never said the rule was never not satisfied; It also never said it couldn't be both at once, nor that not not being satisifed was the same as being satisfied, etc. So you don't know if the situation is contradictory (i.e. paradoxical).
Also, you need to say what a rule and everything are and what it means for a rule to be satisfied before you can even talk about a rule that is satisfied by everything. So what "the rule that is satisfied by everything" is depends on your definition of rule, everything, and satisfaction. So the idea of absolute things just doesn't make sense to me; They don't depend on how you think about them, so how do you think about them?
I agree with what you said; I was just pointing out some assumptions that were being made.

9. Jun 7, 2005

honestrosewater

What does that mean- everything and nothing?
Mathematics isn't a single theory, and a theory need not have an equality relation, but okay...
Something that doesn't exist doesn't have the property of being a number, so it doesn't make sense to talk about numbers that don't exist. If something is a number, it exists. I guess this is rather subtle, but when someone says there exists no number that has such and such properties or meets such and such conditions, it doesn't mean there exists some number that doesn't exist; It just means such and such properties or conditions are incompatible.
But this isn't a problem in logic or math, since every rule in logic and math is relative to the theory in which it is stated. Edit: And they also have a definite range of application. So what a rule means and what it applies to is determined by the theory.
I don't really know what you mean by this. Could you explain a little more?

Last edited: Jun 7, 2005
10. Jun 8, 2005

Berislav

All which exists and all which doesn't exist.

True. Things that do not exist have no property other than non-existance.

I never said that it was. What I wanted to point out is that absolute universal rules are impossible.

If a "rule" has an exception within it's domain (i.e, within it's range of application) then it isn't valid and it's not really a rule. It could have an exception outside it's range of application and still be correct.

If the range of application is all that exists and doesn't, then the rule has an exception.

11. Jun 8, 2005

honestrosewater

I don't know if letting non-existence be a property causes problems, but it is at least superfluous. You can just assume that every object exists; i.e., that existing is exactly what it means to be an object. So you either have a set with some objects or a set with none.

Imagine this. I say that if any two objects have the all the same properties, then they are equal, and if two objects are equal, then they have all the same properties. Now, if non-existence were a property and all objects having that property have only that property, then all non-existent objects are equal, i.e., there is exactly one non-existent object. But what about the property of being a round square? What can you say about an object having that property? If any object having that property must also have the property of not existing, then it isn't true that all objects having the property of not existing have only one property. So do you say the two properties are equal? What about several incompatible properties- is that combination of properties also equal to the property of not existing? Worse, how do you determine that no object can have some combination of properties? How do determine that no object can be a round square? By finding that there is NO object with those properties. But that doesn't work anymore- there is exactly ONE object that is a round square - the object that doesn't exist.
Also, do you want to be able to say things like, for all objects x, if x is greater than 2, then x is greater than 1? Well, is the object that doesn't exist greater than 2? It certainly isn't equal to 2, otherwise 2 wouldn't exist. So it must be greater than or less than 2. There's no reason to say either- which is a big problem! But let's say it's less than 2. Then it must be equal to 1 (we're in the set of natural numbers). But it can't be equal to 1. So we still have a big problem- our rules don't apply to every object anymore. Oh, wait, there is a solution: the non-existent object isn't a number, so it isn't even in the theory to begin with! So I don't see how it helps to let non-existence be a property- and I have never seen it be.
Impossible in which system?
Yes, I suppose, but how does this make absolute, universal rules impossible?
What exception?

12. Jun 8, 2005

Daminc

Hang on a minute, numbers are not real anyway, they are abstract concepts to help us define relationships. Working with your example you could have a round square that doesn't exist and is twice as big as another round square that doesn't exist.

What would be interesting to debate is whether there is and infinite amount of objects that don't exist since we have a finite amount of objects that do exist.

For example, if the sum of all possibilities objects was Infinite and the number of impossible (non-existing) objects were Infinite then we would be left with no objects that are real.

(Playing with abstract concepts and logic rarely gets you anywhere but it is fun )

13. Jun 8, 2005

honestrosewater

Who said anything about objects having to be "real"? A rule isn't "real" either.
Sure, you get to make the rules. But I was looking at the consequences of those rules. And normally, being round and being square are incompatible.
If you're talking about real objects, there really isn't anything to debate. Do you know how many objects exist? Do you know that you've observed every object? Do you know what the rules for existence are? If not, you will have to settle for a model, so you're back to logic.
If you want any two objects having all the same properties to be equal (i.e. each object equal to itself), and vice versa, and if an object that doesn't exist has only that one property of non-existence, then there is at most one object that doesn't exist.
No, you would be left an infinite number of possible objects and an infinite number of impossible objects. They wouldn't cancel each other out. Plus, knowing the number of possible objects only puts a limit on the number of actual objects; It doesn't tell you how many there are.
Perhaps it rarely gets you anywhere. Humanity wouldn't have gotten this far without it.
Meh, I don't mean to sound rude, I'm just too tired to be extra polite.

14. Jun 8, 2005

Daminc

Ok, I stand corrected. Objects can be concepts as well as 'real things' however I perceive 'real' as that which can be discerned to exist which leads to that which cannot exist does not exist.

Thats because round and square are descriptive qualities and are independent of the object. If the object is described as 'round' then nobody would describe it as square unless their word for round is square.

I think you'll find it rarely gets the vast majority of people anywhere however, after saying that, I would like to point out that if you play with abstract concepts and logic then I would estimate that a good 95% of the time you don't get anywhere hence using the term 'rarely' rather than 'never'.

15. Jun 8, 2005

honestrosewater

Okay, but if you want to know what I meant by "objects", you just have to ask me. I meant abstract or concrete (real, physical); I think the context makes clear which one.
How would discerning that which exists lead to anything about non-existence? Can you discern a real object that doesn't exist? Or is a non-existent object necessarily abstract?
It's because that's what follows logically from the rules. I've been talking about logic. In logic, if the rules say so, there cannot exist an object in that logical system that is both square and round. Period. There is nothing more certain.
Language, money, math, science, and intelligence itself all rely on our use of abstract concepts and logic. How unconstructive is your playing? :tongue2:

16. Jun 8, 2005

Daminc

I didn't take into account that your idea of what an object is would be different from mine. Sorry.
I'm not very educated when it comes to QM but doesn't the QM math work on the principle that everything has a possibility of existing therefore everything potentially exists even that we believe doesn't exist. It's only the one frame that we observe to exist = one probability.
Very . I play with space/time and light and I'm not capable of proving any of it :uhh:

17. Jun 8, 2005

honestrosewater

Sorry, am I sounding mean? I didn't really consider that your idea of an object would be different from mine. I was just saying there's one way to find out...
Heh, I actually have a thread going about this and am not qualified to comment on what QM says. But QM is still only a model of reality, and the idea here applies at the macroscopic level anyway. Say I will flip a coin and let it land on the empty table in front of me. The probability of getting heads up is 1/2, the probability of getting tails up is 1/2. But when I perform the experiment, I get only one result. Say I get heads up. Does a coin tails up exist on the table in front of me? No, there exists no coin on the table with the property of being tails up. There exists only one coin on the table and it has the property of being heads up, and heads up and tails up are mutually exclusive. Tails up was a possibility but is not an actuality.
Ah, well, that sounds like serious playing. ;) But how many people play with the concepts of spacetime and light?

18. Jun 9, 2005

Daminc

AFAIK, everything in science uses a model. It's just that the ones we use today hold up to a lot of strutiny. If QM exists it has to marry Classical physics in some way so QM theory would have to apply to the macroscopic level.
Unfortunately, not many people (none where I live & work) which is why I come here to have a chat with people.

19. Jun 9, 2005

honestrosewater

Right, that's what I mean by a model- a physical theory. I don't know what you mean- QM does exist. You don't need any theory to perform an experiment. If there's a coin laying flat on a table, only one side of the coin will be facing up. Just go look at some coins. :tongue2:
This almost certainly isn't true. Does QM say it's possible for energy to not be conserved? I doubt it. And a theory that just said anything was possible wouldn't be falsifiable. Plus, there may be parts of the theory that have nothing to do with reality. For instance, you may use a function to describe the speed of some object. The function may be infinite, but that doesn't mean objects can go arbitrarily fast or slow, or that space is infinite, or so on.
Even if you were to say that everything potentially exists, you're still only talking about potentials. The potential only puts a limit on the actual.
Yes, no one where I live either. And the crowd here at PF is ever rarer for their knowledge and generosity.

20. Jun 10, 2005

Daminc

I'm sorry, I should expand that a bit: If QM exists how we think it exists...

I've alway been a skeptic...about everything. I'm the type of guy that feels that if I drop an apple to the ground that it would probably drop straight down. If it went sideways or straight up I wouldn't be surprised, just curious.

I doubt the validity of everything of everything we see, hear, feel, know etc, etc and instead go with the balance of probability (e.g. the probability of the apple reaching the ground in a straight line is very, very high).

My friends think this is unusual but I don't understand why :)

What about you? Do you accept some things as fact? If so, how much proof do you need before you believe it's true?