# If something is Possible is it therefore Necessary?

Does anybody agree on this:

“Given an infinite time Y, every possible event X needs to happen, right?”

From a mathematical point of view it seems OK to me, although depending on the idea we have of `infinite time`, one might think that it is the same as “it never happens”.

• No possibility does not imply necessity. Feb 11, 2022 at 8:28
• Possibly; see en.wikipedia.org/wiki/Boltzmann_brain . Given enough time for a universe in thermal equilibrium, random interactions can eventually cause a spontaneous local decrease in entropy, which can create brains or indeed larger objects, to which essentially anything might happen. We don't know if the universe will ever reach and spend infinite time in a thermal equilibrium, though. Feb 11, 2022 at 8:58
• For a first try, every possible event X={heads, tails} (both are possible) needs to happen is just false. Feb 11, 2022 at 14:40
• I think what you probably mean is Lovejoy's principle of plenitude: "the necessarily complete translation of all the ideal possibilities into actuality". He traces it as far back as Plato. However, one has to be careful with how it is formulated to avoid incoherence. Separately possible events may not be jointly possible in a single timeline. An event X occurring earlier may rule out an event Y occurring later on even though Y was otherwise possible. It is usually applied to vaguer "forms of existence" rather than to specific events. Feb 11, 2022 at 17:12
• Feb 11, 2022 at 22:22

"Possible", "necessary" and "real" are the three modes of existence in ontologies with possible worlds. One of the main possible-worlds models has been introduced by Leibniz. But even in these ontologies, "possible" does not imply "necessary". Instead: "Possible" is defined as "real in at least one world". While "necessary" means "real in all worlds".

I would not complicate the original question with the concept of infinite time. At least, the concept of infinite time opens up new questions ...

It's not true. It is possible I kill my dog, but it's therefore not necessary to do. Even in the case of serial big bangs, where we are born again over and over, it's not necessary. A universe with infinite entropic time doe not exist. Only universes with a beginning a middle part, and an end exist. On the other hand, for something to be necessary it has to be possible.

• Reminds me of Tertullian: "That Jesus Christ is the Son of God is true because it is absurd. That dying, he was born again is certain because it is impossible." Mar 15, 2022 at 22:15

This question can depend on your definition of possible. If it means by the laws of physics alone, then no. If it was possible for an atom to decay before another atom (assuming they were the only things and not moving), it wouldn't necessarily happen. For some things, the conditions of the universe might come back to a similar state so it could happen, but atomic decay is irreversible so if it didn't happen the first time, it wouldn't happen. This goes into the multiverse theory, so I'll just say it might not be like that in this world.

If your definition of possible means there's a chance of it happening, then yes. According to special relativity, space and time are very similar. It's just another dimension. And just like matter, it's either there or not. So the future is already set (at least of our world). Therefore, the only way there would be a chance of it, is if it's true.

• Reminds me of the quote: "You have confused the true and the real." Mar 15, 2022 at 22:21

Yes, for practical purposes, "it is guaranteed to happen eventually, but not necessarily within the next 1000000000000000000000 years" is the same as "it won't happen".

The other problem for real-world reasoning is that the shape of a universe may change before infinite time has passed. Loosely speaking, our universe could collapse, freeze, become cold, disappear... all of which could make events that seemed possible in the current state become impossible before they have happened a first time.

To illustrate: Throwing a wooden dice infinite times mathematically means that each finite sequence of throws is mathematically guaranteed to happen, but likely your dice will more likely break down or rot before a given large sequence happened.

So for real-world reasoning, it would be more precise to say: "Given an infinite time Y, every event X that necessarily remains possible throughout time needs to happen, though not necessarily within any given finite waiting time."

I do not think this is true, for example this just holds true for all the scientific possibilities in our world. But this does not encompass all the logically possible worlds. The existence of a nuclear fusion supporting star smaller than a red dwarf is not possible to the existing science, however it is logically possible in another possible world different from ours which has different physical laws or no such laws at all(it can be conceived of).So accordingly, if our universe were to go on into an infinite future, no fluctuation whatsoever can ever create such a thing. Therefore if we are talking about material possibilities than yes, possibility in this case may imply necessity. But not in the case of logical possibilities. Also the question has one assumption, i.e of an infinite universe which will go on forever carrying its normal operations. Now what if someone were to ask whether the possibility of an infinite universe implies the necessity of one? Now since time has a different ontological existence than the material things spacetime encompass.## Heading ##