# Does free will contradict the theory of infinite universes

Let's imagine that we live in a world with infinite universes. One of these universes is the same as the one we live in, except for one change: this morning I choose to cut off my leg for some reason, instead of drinking coffee.

As there are infinite universes, this universe must exist. Keep in mind that I had no reason to cut my leg off, so does this mean that free will contradicts the theory of inifinite universes? So we can only have one universe?

• I don't know whether freewill could contradict the theory of infinite universes; although I personally believe the theory is false in any case (for other reasons). Yet the very fact that people can choose to act in such an irrational fashion certainly seems evidence of freewill. – Bread Oct 28 '18 at 16:21
• First, infinity of universes does not mean that every possible one is realized, second, what your argument implies is that it is determinism, not free will, that contradicts realizability of all possibilities. Because the universe where you cut your leg without a cause can not be deterministic. – Conifold Oct 28 '18 at 21:30
• In the first paragraph you say you chose to cut off your leg for "some reason". In the second, you say you had "no reason". Did you have a reason or not in this account? – alanf Oct 30 '18 at 8:01
• I dont know i am not the one who choose to cut the leg off so i have no idea why i i did only assumed it wasn't free will because i would never see myself cutting off my leg – someone Oct 30 '18 at 11:53

No, there can be infinitely many universes without there being a universe that contains each possibility or a world for every possibility. For example, an infinite number of possible worlds differ only with respect to one irrational number generated at a particular moment by an isolated random number generator.

To cover every possibility, you’d need an especially large infinity of worlds.

• Oh I see what you are saying and that change could be totally not related to any human or creature with free will right ? – someone Oct 27 '18 at 18:57
• How do real-valued random number generators work? Also: An "especially large infinity?" Do you have one in mind? How large would an infinite set be in order to guarantee that every event happens? And how do you measure largeness of infinities? Standard mathematical cardinals or perhaps ordinals? Or some other way? These two phrases of yours piqued my curiosity. – user4894 Oct 28 '18 at 0:18
• @user4894 any way you like, since possible worlds, as usually discussed, include those logically but not physically possible. – ChristopherE Oct 28 '18 at 0:21
• @ChristopherE Sorry, I added a second question as an edit and now I can't figure out which of my questions your response addressed. You conceptualized a real-valued random number generator and I'm curious as to if and how such a thing can exist consistent with contemporary physics even granting an actual infinity of multiverses. I'd strenuously argue the contrary, though not here since this site's not for that. Secondly (separate question) I am curious what the phrase "larger infinity" means to you. I know what it means to me, having studied cardinals and ordinals. – user4894 Oct 28 '18 at 0:23
• @user4894 and on the sizes of infinity, I had in mind a higher cardinality, but beyond that I’m sorry, I don’t know. I was wondering about that myself. It seems like the questioner could generate a problem by asking about something like the set of all physically possible worlds descended from this one, and there could be a way to argue that there are interesting implications of that. I was just giving the easy answer — infinite worlds per as don’t seem to me to be a problem. My previous reply was about how real number generators might work. Dodging! – ChristopherE Oct 28 '18 at 0:27

As ChristopherE pointed out in his answer, there can be infinitely many universes without every possible thing occuring in some of them.

But I think that even if every possible thing occurs in at least some universe, we might still have free will. For example, if I'm presented with a choice right now, to do A, B, or C, there will be worlds ("universes", in your terminology) where I choose A, worlds where choose B, and worlds where I choose C. But why couldn't these be worlds where I freely chose A, B, or C? In fact, that's one of the criteria of libertarian free will (that the world is not deterministic). That in order for me to have freely chosen to do A, it must have been possible that I had chosen not-A instead.

• Thats not what i said yes u can choose a or b or c but what i said was uf there is infinite universes where every possible thing would happen then there should be a universe where i choose to do something stupid and illogical which would mean that free will is imposaible if there are infinitely infinite universes where every possible thing happened – someone Oct 28 '18 at 16:25
• I'm not sure I quite understand. For.s simplicity I limited it to 3 choices, A,B,C. But in practice I suppose there might be many more, maybe infinitely many. And your choice to do something completely irrational would be among the possible options A,B,C,... Even if there's infinitely many, as long as it's among the possible choices, you still could have chosen it, right? – Adam Oct 28 '18 at 17:15
• I guess what I mean is, why does the possibility of completely illogical choices mean there's no choice? – Adam Oct 28 '18 at 17:16
• The problem is that what is even free will and how do you choose to do something its not random cause if it was then society wouldn't exist so it must be A result of all of the previous experiences and memories a person has but then if its that how come i choose to do something completely diffeeent in another world? I am sorry if i am still unclear. – someone Oct 28 '18 at 17:27