You are misunderstanding logic. Logic needs a frame of reference and can change, its not some immutable law.
Nothing is really logically impossible except from a certain frame of reference but even then it could change based on new information which would not make it impossible anymore.(this sentance is not really a good sentance, but I expect it should get the point across)
As an example, its not logical to expect me to make a large pink sphere appear next to the earth when I say "Appear!" Say I manage to do just that though. Well, you would then have new information that says it is logical because I made it happen. Based on your old frame of reference, it was illogical to expect the pink sphere to appear. However, based on your new frame of reference, created with the addition of the knowledge that, yes, I can actually make a pink sphere appear, it is logical to expect that I can.
I recomend the book "Many Worlds in One" by Alex Vilenkin if anyone has an interest in the creation of the universe.
Great book for anyone who might be new to the topic or have a basic interest, somehow he managed to actually get away without including any scientific formulas or lots of numbers in the book. While only a couple of the ideas in the book were new to me(I take an interest in this stuff), he goes over quite a bit.
Anyway, the point with mentioning that(aside from the topic at hand) is that most of the stuff behind universe creation and all that is in no way currently provable or disprovable really. Another reason to mention the book is that in the end, he hints that yes, despite being able to explain alot, there may indeed still be room for a god. But of course he doesnt cover that and only hints at it near the end, its a book on the universe, not god.
The thing that always get confused with religion and science is that they are utterly opposed and this is basically a misunderstanding. All science is would be the observation and figuring out the universe and nothing is ever completely proven, its only just been true up to that point and if something comes along that disproves something, than things get updated and changed. The problem occurs when you have people, on both sides, that end up dogmatic and decide its there job to take on the other in "combat". Its the people who use science or religion to further themselves and push information on people that are a problem. Now, I wont argue out anything about religion and science in schools as that just not the thing here and a can of worms and I have already written too much.
I have been typing out alot of stuff today.
To climb the mountain, you must believe you can.
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