Axiom S5

[GoodKat]

That which is possibly true is possibly necessarily true
That which is necessarily true cannot possibly be false
That which is possibly false cannot possibly be necessarily true
That which is possibly necessarily true is necessarily true
That which is possibly true is necessarily true

So basically the term "logically possible" is useless because it it's logically possible for something to be true then it must be true.

Bear in mind, this is talking about logical possibility, not epistemological possibility. If something is epistemologically possible(ie. you don't know if it's true or not), then it is unknown whether or not it's logically possible.

For instance, I don't know if God exists or not, that means that from my perspective it is epistemologically possible that God exists, however, if God does not exist, then it is logically impossible for Him to exist, thus, I don't know if it's logically possible for God to exist or not.

 

[Deleted member 1694]

For instance, I don't know if God exists or not, that means that from my perspective it is epistemologically possible that God exists, however, if God does not exist, then it is logically impossible for Him to exist, thus, I don't know if it's logically possible for God to exist or not.

Ow. Head.

However; by the logic you state, everything is possible. Like the moon is made of cheese, the earth is flat, that if you smash your hi-def TV with a 6 foot mallet, it will turn into magical elf.

 

[GoodKat]

Ow. Head.

However; by the logic you state, everything is possible. Like the moon is made of cheese, the earth is flat, that if you smash your hi-def TV with a 6 foot mallet, it will turn into magical elf.

No, this axiom proves that if something is not necessarily true then it is not logically possible. Sure, it is epistemologically possible that the moon is made out of cheese, but it's not logically possible unless it's necessarily true.

 

[Squawk]

That which is possibly necessarily true is necessarily true
That which is possibly true is necessarily true

Those two lines are fallacious I think, and so the rest falls down.

 

[GoodKat]

That which is possibly necessarily true is necessarily true
That which is possibly true is necessarily true

Those two lines are fallacious I think, and so the rest falls down.

How are they fallacious? If all that is possibly true is possibly necessarily true, and all that is possibly necessarily true is necessarily true, then all that is possibly true must be necessarily true.

 

[Squawk]

That which is possibly necessarily true is necessarily true
That which is possibly true is necessarily true

Those two lines are fallacious I think, and so the rest falls down.

How are they fallacious? If all that is possibly true is possibly necessarily true, and all that is possibly necessarily true is necessarily true, then all that is possibly true must be necessarily true.

If something is possibly true then it is possibly necessarily true - I agree with that
If something is possibly necessarily true is neccessarly true - I disagree with that.

It does not follow, because by definition something which is "necessarily true" cannot be "possibly necessary" and you end up with the statement that everything is neccessarily true, an obvious fallacy. The easiest way to see this is to replace the word true with false and see what contradictions you end up with. We can achieve this as follows

If something is possibly true then it is possibly false.

Fork 1
If something is possibly true then it is possibly necessarily true
If something is possibly necessarily true then it is neccessarily true

Fork 2
If something is possibly false then it is possibly necessarily false
If something is possibly necessarily false thaen it is necessarily false.


Therefore, if something is possibly true it is both necessarily true and neccesarily false, a paradox and a contradiction and an example of the falacious reasoning, all of which comes from the lines I highlighted.

 

[ImprobableJoe]

How are they fallacious? If all that is possibly true is possibly necessarily true, and all that is possibly necessarily true is necessarily true, then all that is possibly true must be necessarily true.

Nope. All that is possibly necessarily true is also possibly NOT necessarily true. You can't just wave away the other possibility.

 

[GoodKat]

If something is possibly true then it is possibly necessarily true - I agree with that
If something is possibly necessarily true is neccessarly true - I disagree with that.

It does not follow, because by definition something which is "necessarily true" cannot be "possibly necessary" and you end up with the statement that everything is neccessarily true, an obvious fallacy. The easiest way to see this is to replace the word true with false and see what contradictions you end up with. We can achieve this as follows

If something is possibly true then it is possibly false.

Fork 1
If something is possibly true then it is possibly necessarily true
If something is possibly necessarily true then it is neccessarily true

Fork 2
If something is possibly false then it is possibly necessarily false
If something is possibly necessarily false thaen it is necessarily false.


Therefore, if something is possibly true it is both necessarily true and neccesarily false, a paradox and a contradiction and an example of the falacious reasoning, all of which comes from the lines I highlighted.

[/quote]

Remember that we are speaking in logical absolutes, not in an epistemological sense. In pure logic, possibly true does not imply possibly false.

 

[GoodKat]

To elaborate, if statement X is necessarily true, then it is also possibly true, and not possibly false.

 

[Squawk]

Remember that we are speaking in logical absolutes, not in an epistemological sense. In pure logic, possibly true does not imply possibly false.

My formal logic is rusty (been a long time since my maths degree and we only touched on logic), but possibly true does imply possibly not true. The only thing that possibly true rules out is neccessarily not true.

I simply use "false" to refer to not true in this instance.

 

[Squawk]

To elaborate, if statement X is necessarily true, then it is also possibly true, and not possibly false.

Neccessarily true implies possibly true, but possibly true does not imply necessarily true.

Possibly necessarily true implies possibly neccesarily not not true, but does not imply necessarily not not true.

(fuck me)

 

[GoodKat]

To elaborate, if statement X is necessarily true, then it is also possibly true, and not possibly false.

Neccessarily true implies possibly true, but possibly true does not imply necessarily true.

Possibly necessarily true implies possibly neccesarily not not true, but does not imply necessarily not true.

Does necessarily true imply possibly true?

 

[Squawk]

Does necessarily true imply possibly true?

Actually in hindsight probably not, I was mid thought about the not not true stuff and skipped the thinking about that.

 

[GoodKat]

Does necessarily true imply possibly true?

Actually in hindsight probably not, I was mid thought about the not not true stuff and skipped the thinking about that.

So if something is necessarily true, it's not possible for it to be true?!

 

[Squawk]

So if something is necessarily true, it's not possible for it to be true?!

That is not the meaning of possibly, why even make that post?

 

[GoodKat]

So if something is necessarily true, it's not possible for it to be true?!

That is not the meaning of possibly, why even make that post?

My point is that if something is necessarily true, then it is also possibly true. Necessarily true by definition rules out possibly false, and thus possibly true does not imply possibly false.

BTW just to let you know, the validity of axiom S5 is almost universally agreed upon by logicians.

 

[Squawk]

BTW just to let you know, the validity of axiom S5 is almost universally agreed upon by logicians.

Interesting how I can't reference to it when I quote it in a google search.

Bah, I don't know how to set stuff out with formal logic symbols, so words will have to suffice.

Basically we have 4 options
necessarily not true
possibly not true
possibly true
necessarily true

If something is "necessarily not true" then "possibly true" and "necessarily true" are eliminated

If something is "possibly not true" then "necessarily true" is eliminated

If something is "possibly true" then "necessarily not true" is eliminated

If something is "necessarily true" then "necessarily not true" and "possibly not true" are negated.

So, if something is "necessarily true", it is also "possibly true", however it is of no consequence that it is "possibly true" since we already know it to be necessarily true. It's a bit of a tautology.

The same argument can be made for "necessarily not true" and "possibly not true".

 

[Squawk]

hmm, just searched for axiom s5 rather than quoting it and found a few references, will read.

##edit

Universally accepted? The first couple of links I read talk about the contention around this. Essentially it is a formulation issue. The idea is that

necessarily possibly true is the same as necessarily true, and it is contended.

##edit 2

And the original point still stands. We can apply this to any statement, and "not p" is the same as "p".

 

[ImprobableJoe]

To elaborate, if statement X is necessarily true, then it is also possibly true, and not possibly false.

Sure, but that doesn't mean it works in the opposite direction. If statement x is possibly true, that does NOT mean it is necessarily true.

 

[ImprobableJoe]

BTW just to let you know, the validity of axiom S5 is almost universally agreed upon by logicians.

That confirms my "logic devolves into nonsense" claim.