Earth still exists - does this fact tell us anything about LHC safety? When LHC was about to be launched there were many fears that it would destroy the world. To counter them scientists tried to carefully examine all possibilities and concluded that there is nothing dangerous. While most of their arguments sounds fine and reasonable to me there is one which I never understood. It is mentioned in many places, and here are some examples of it:

we can conclude that the existence of our solar system proves that mini black holes can not be dangerous.

http://arxiv.org/abs/0807.3349 

If we ignore these strong theoretical arguments, we could pursue another path. Huge numbers of high-energy cosmic rays have hit the earth over its lifetime. Thus, we can argue, nature has already carried out the LHC experiments many times. If we are still here, the LHC must be safe. This is a standard argument that was worked out carefully by Jaffe et al.

http://physics.aps.org/articles/v1/14

It  has  always  been reassuring that higher-energy cosmic rays have been bombarding the Earth since its creation  with no disastrous side-effects.

http://arxiv.org/abs/0806.3414

This report explains why there is nothing to fear from particles created at the LHC. In fact, collisions just like those the LHC will make have been produced by cosmic rays bombarding the earth throughout its existence. It would take about 100,000 LHC experiments to match the number of cosmic ray events that have already occurred. We can rest assured that our planet will not be affected by the four experiments about to be conducted in Geneva.

Statement by the Executive Committee of the DPF on the Safety of Collisions at the Large Hadron Collider.
So, basically, from those two facts:


*

*For billion of years events similar to those at LHC were happening on Earth.

*Earth still exists.


We are concluding that:


*If we will recreate these events at LHC Earth will still exist.


In my opinion (3) does not follow from (1) and (2).
Imagine the following scenario: out of all planets with life, 99% are destroyed by some events caused by cosmic rays before the appearance of scientists on these planets who will conduct experiments at particle accelerators. However, at 1% of lucky planets evolution will have enough time to create curious scientists who will build particle accelerators. Scientists on these planets will then argue that it is safe because their planet still exists. But on 99% of planets there is no one to argue. Sounds like survival bias.
If you are asking why conditions on our planet are comfortable for life, the answer is obvious - because there is no one to ask such questions on planets which are not comfortable for life, so if you are asking one you must be on a proper planet.
If you are asking why our planet was not destroyed by some hypothetical cosmic ray event, the answer should be - because on planets destroyed by such events there is no one to ask, it shouldn't be - because such events are impossible.
So, using billions of years of Earth existence as an argument is wrong. Instead you can use existence of other bodies (which do not affect existence of life on Earth) as an argument.
What do you think, is this correct?
 A: Just to elaborate on Chris White's point that you can use the same argument to doubt the safety of anything, here's a slight reworking of the argument you give that shows why we should avoid breathing air:

So, basically, from those two facts:
  
  
*
  
*For [hundreds of thousands] of years [humans have breathed air].
  
*[There are no recorded incidents of human spontaneous combustion].
We are concluding that:

  
*If we will recreate [human breathing] at LHC [no humans will spontaneously combust].
  
  
  In my opinion (3) does not follow from (1) and (2).
Imagine the following scenario: out of all planets with life, 99% are
  destroyed by [breathing-induced spontaneous combustion] before the appearance
  of scientists on these planets who will conduct [breathing] experiments at
  particle accelerators. However, at 1% of lucky planets evolution will
  have enough time to create curious scientists who will build particle
  accelerators. Scientists on these planets will then argue that it is
  safe because their planet still exists. But on 99% of planets there is
  no one to argue. Sounds like survival bias.

It's entirely possible that we're just one of the extremely lucky planets and by chance have never experienced spontaneous combustion. But it seems much more likely that breathing just isn't that dangerous.
A: Your reasoning demonstrates precisely why formal logic alone is insufficient to study nature. In particular, it lacks the ingredient of inductive inference that is a cornerstone of empirical science.
A cosmic ray striking the Earth is not some random act of the gods that can have any imaginable consequence whatsoever. It is a cosmic ray striking the Earth. Sure, by formal logic we cannot see 100 trillion black ravens safe cosmic rays and conclude anything about the next raven cosmic ray. But everything we know in physics indicates the collisions in the LHC should be similar to the ones in the atmosphere -- otherwise, you'd probably be forced to believe that subatomic particles care about where in the universe they are with respect to human beings and their constructs.
Note that your reasoning could be used to disprove the safety of anything whatsoever. I assure you that never before in the history of the observable universe has user number 40492 ever asked a question about particle collider safety on Stackexchange. Sure, millions of other users have asked questions, and sure billions of things have been done on the internet, and sure no electronic device has ever been known to initiate a supernova and destroy its solar system, but perhaps you asking this very question could be the trigger for such an event. And by the anthropic principle we would never know until we detonated the planet.
A: This answer is in order to clarify what the physics is behind the scares for LHC safety and to point out that your statistical analysis is on wrong premisses.
High energy cosmic rays permeate  the universe, not only planets but all the stars with their order of magnitude greater masses and crossectional areas. If cosmic rays could seed black holes there should be many black holes in our solar system neighborhood. In fact just the sun would add orders of magnitude to the statistics of safety, even if there did exist a tiny tiny probability for a micro black hole to create a large black hole. Astronomers guess that there may be a black hole in the center of our galaxy. One.
Thus the existence of the universe as we know it, which is made up of stars and not mainly black holes would extend the statistical  safety margin by many orders of magnitude.
In fact, all calculations of micro black holes  possibly generated by particle scatterings show that they have a very small lifetime and they immediately decay into many normal particles, like photons and pions etc, which is the signature by which they are sought at LHC. It is all a theoretical proposition.
After all it is only because of  high energy phenomenological models based on string theories that this scarecrow appeared in the public discourse . The human race exists because the probability to be eaten by a lion did not stop it from hunting or exploring.
A: 
Imagine the following scenario: out of all planets with life, 99% are
  destroyed by some events caused by cosmic rays before appearence of
  scientists on these planets who will conduct experiments at particle
  accelerators.

Except we still have the planets in our solar system intact, and so apparently do thousands of other solar systems. 
A: The anthropic principle will always guarantee that no universal catastrophe is ever experienced directly
Even if the universe had a probability of 99.99999999% of decaying into a false vacuum a femtosecond after the big bang, none of these universes have observers that ponder their existence and post to Physics.SE, so the fact that we are here already skews the perceived probability of false vacuum decay toward samples that have us as observers
In essence, if all it took to destroy the universe (and complex entities capable of organizing information about the universe like us) was that some magic pencil balanced on its tip falled on some of its sides, then all that the complex entities would perceive is that the the magic pencil would stay in unstable equilibrium for arbitrarily long periods of time
This is also related with the Doomsday argument, which tries to estimate the most probable number of humans that will ever live, based on current numbers, but it also implicitly assumes that there is a bounded number of humans that will ever live. But if there was such a bound, it would mean that there exists a future time where there are no humans to further reproduce. It is clear that if you don't assume that such bound exists, the most probable number of humans also becomes unbounded, and the Doomsday argument becomes a fallacy. Same happens with any 'fear' of destroying the universe in any finite experiment like the LHC
