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[Roc CURIOUSBEAST_EATER]

A couple days ago, I watched about the Modal ontological argument when I Started to think about the fact that axiom S5 (that is used for 3rd premise of the Modal argument) can be used to support a number of self-contradictory positions including an irresistible (or unstoppable) force and unmovable object existing in the same world (what happens if a irresistible force hits the unmovable object?). I spend a couple creating this argument, although most of it was wasted trying figure out how premise 13 should stated.

Axiom S5 states that if it exists in some possible worlds then it exists in all possible worlds. The Logic I am talking about of course is Modal logic, I don't know much about it apart from the axiom I trying to refute.

 This argument has  premises and a conclusion. it is a Reductio ad absurdum argument you will see in the argument present below.
A Reductio ad absurdum argument works by assuming what your trying to disprove to be true then push that assumption to it's logical (and absurd) conclusion to expose contradictories that the assumption creates. since everything that creates contradictories are false, it logically follows that the assumption the assumption is false.
The argument goes as follows.
1. Axiom s5 (X in some worlds = X in all worlds) is true.
2. It is possible that a unmovable objects exists.
3. If it is possible that a unmovable objects exists, then it exists in some possible worlds. (from 2)
4. If a unmovable object exists in some possible worlds, then it exists in all possible worlds. (from 1 and 3)
5. if a unmovable object exists in all possible worlds, then it exists in the real world. (from 4)
6. It is possible that a irresistible force exists.
7. If it is possible that a irresistible force exists, then it exists in some possible worlds. (from 6)
8. If a irresistible force exists in some worlds, then it exists in all possible worlds. (from 1 and 7)
9. If a irresistible force exists in all possible worlds, then it exists in the real world. (from 8)
10. The idea of a unmovable object and irresistible force existing in the same world is self-contradictory. (from 5 and 9)
11. all self-contradictory ideas are false.
12. any axiom that creates self-contradictory ideas are incoherent. (from 11)
13. Axiom S5 created this self-contradictory idea. (from 10 and 11).
Conclusion: Premise 1 cannot be true. (from 12 and 13)

I want this argument to be critiqued, since I want to see if the argument is logically valid, the logic is sound and the premises are true. The best way to do this to have other try expose the flaws in the argument. I will be surprised if the argument survives the critiquing without any changes to it.

[Sergarr]

That's a weird-as-hell axiom. Wouldn't it basically mean that all possible worlds are absolutely equivalent to each other?

[LordBucket]

1. Axiom s5 (X in some worlds = X in all worlds) is true.

I am unfamiliar with axiom S5, but as you've presented it, it does not appear to imply that any worlds besides the real one exist. They might, or they might not. 'All worlds' could be a set with only one member: {the real world}. If so, then your logic chain falls apart.

2. It is possible that a unmovable objects exists.
3. If it is possible that a unmovable objects exists, then it exists in some possible worlds. (from 2)

6. It is possible that a irresistible force exists.
7. If it is possible that a irresistible force exists, then it exists in some possible worlds

You appear to be making assertions other than the one you're attempting to disprove. 2 and 6 don't appear to follow from 1, and if they're removed, your logic chain falls apart.

10. The idea of a unmovable object and irresistible force existing in the same world is self-contradictory. (from 5 and 9)

There may be reasonable definitions for 'unmovable object' and 'irresistible force' for which 10 is not implied by 5 and 9.

[MagmaMcFry]

PTW. Modal logic makes no damn sense.

[SirQuiamus]

PTW. Modal logic makes no damn sense.

QFT

That axiom is strangely arbitrary and metaphysical: Any possible proposition is declared necessarily possible simply because the logic requires it, and a certain mystical force ensures that its terms have the same referents, come what may, in all possible worlds. "End of Discussion." Your attempt to "refute" such an axiom is admirable, although I'm not entirely sure why you would have accepted it in the first place.

Can you give us a reasonable definition of an 'unmovable object?' 

[ShadowHammer]

Can you give us a reasonable definition of an 'unmovable object?' 

Some such definitions are used in this video.

[SirQuiamus]

Yes, objects with infinite mass are very reasonable. 

[ShadowHammer]

Yes, objects with infinite mass are very reasonable. 

I didn't really think that one through.

[LordBucket]

Can you give us a reasonable definition of an 'unmovable object?'

A definition? Not going to step into that minefield.

However, it's very easy to give an example of one. For example: your frame of reference.

Some such definitions are used in this video.

Which demonstrates another flaw with the OP: the immovable object and irresistible force could be the same phenomenon, in which case step 10 is not valid.

[Leafsnail]

All you've done is shown that 2 and 6 are contradictory.  There's no reason to accept that either of them is necessarily possible anyway.

[LordBucket]

All you've done is shown that 2 and 6 are contradictory.

But they're not. We have two examples already:

1) they're the same phenomenon
2) they pass through each other without interacting

Here's a third:

3) they never come into contact with each other.

Though 2 and 3 are basically the same thing: they don't interact.

[Leafsnail]

All of those things are semantic quibbles that don't address the core argument in any meaningful way though.

[TheDarkStar]

So, my questions are these: Why do 2 and 6 follow from 1? Also, why would 1 be true? What does "world" mean?

[wierd]

All you've done is shown that 2 and 6 are contradictory.

But they're not. We have two examples already:

1) they're the same phenomenon
2) they pass through each other without interacting

Here's a third:

3) they never come into contact with each other.

Though 2 and 3 are basically the same thing: they don't interact.

I can give an example of an (apparently) unstoppable force at least-- Hubble expansion. Current projections indicate that it will overpower all other forces in the universe in the far distant future.

Black hole singularity is not an immovable object. While it has infinite density, it has finite mass, and therefore only requires finite energy to move. If these objects were unmovable, they could not be in the rotating reference frame surrounding sagitarius A, the center of our galaxy-- yet they are.  Moreover, these objects would not move in accordance with hubble expansion, yet they do. Black hole singularities are not immovable objects.  About the only immovable object I can think of would be the universe itself, but that is a contrivance; it is logically unable to move, because there is no coordinate system outside of itself in which it could move. If there is a coordinate system outside the universe, we cant know about it.

[Roc CURIOUSBEAST_EATER]

All you've done is shown that 2 and 6 are contradictory.  There's no reason to accept that either of them is necessarily possible anyway.

Since the axiom I am trying to refute requires the existence of the 2 objects since they are possible, despite the fact that the 2 things existing in the same world is self-contradictory.
The reason why I say those 2 things are possible is because the existence of either thing is not logically impossible (unlike square circles).
Anyway, The argument needs to be changed as it is currently too easy to miss the core argument.