A collection can be considered to have any number of objects. Recently I heard someone consider the number of events that happen in the universe at any given moment. He assumed it would be in the billions. Hard to say really. I once asked ChatGPT to calculate the number of planck units in the observable universe. It was a large number.
It’s super interesting that a conceivable collection can be indefinitely large. But to say a collection of objects has an actually infinite number of objects crosses a boundary.
Or as I once said to Dale in a moment of creative thinking, the number of objects don’t get to trail off the existential horizon and still count as part of the collection.
Defining “infinite” with the word “infinite” is circular.
Infinity is not a number.
In mathematics, things are defined much more carefully.
A set is infinite if and only if for every natural number, the set has a subset whose cardinality is that natural number. (Wikipedia on “infinite set”)
Here you see the idea of infinite being about having no limit. There is no natural number such that an infinite set does not have a subset with that cardinality. IOW if there was such a number then that number would be a limit on that set.
Since there is no such number, it technically crosses the boundary into incoherence. When we speak of the possibility of an infinite universe we do not use words such as “infinite number” which have no meaning. We talk about there being no limits like the above definition of an infinite set. We say that an infinite universe according to that possibility for the big bang would be one with spatial extent, energy amount, and objects quantities in it that have no limit.
There are legitimate scientific objections to this idea like those of a multiverse, since none of that is measurable in any way. It is scientifically indistinguishable from fantasy. On the other hand, it behooves us to acknowledge the fact when science cannot actually exclude such possibilities.
I was watching Habine Hossenfelder on this question of whether the universe is infinite and there is one part of this which I do not agree with. This is the claim that an infinite universe implies copies of ourselves. I don’t think this takes into account the fact that an infinite universe is a first order infinity and I don’t think all possibilities for finite universe is the same order of infinity. It would be interesting to see someone try a formal proof of such a thing (there is none), because I would be happy to point out the flaws.
Ah… I found a video where someone tries this. Hee hee. I can point out the flaws after all. Predictably he tries this by likening our existence to an arrangement of numbers. But that is wrong. We are not a random arrangement of numbers or atoms, and we not a product of some process producing random arrangements. We are not only the product of a process on a spacio-temporal continuum (higher order of infinity) but we are also the product of quantum fluctuations on this continuum which is also a higher order of infinity.
I was following some of the drama on the internet over her. With scientists objecting to her criticism of the scientific establishment. I think there is truth on both sides. She probably does go a bit too far in criticism of the scientific establishment, but I don’t think there is nothing to those criticisms. The scientific methodology works. But people can be goofy and dishonest.
I could be mistaken, but I think you defined an infinite collection as there being the possibility of a collection having any natural number of members in response to this comment from me:
There are a considerable number of philosophers in religion that hold on to the possibility of actually infinite collections.
Which is one reason why I think infinite numbers of things are not possible.
Infinity can be a non-numerical value, and I know there are more than one of these values… so quantity is most definitely not an illusion
Late to the conversation, but harking back to the original post, it reminds me of most of the old Ouija boards. I had one as a kid, which is sort of surprising, as I grew up in a rural Baptist area my dad was a deacon in the local church and lots of church folk considered them demonic. I think my parents got me one for Christmas. They also got me a motorcycle at age 16 when I really had little desire to have one. In retrospect, I think I was a little weird, maybe a little on the spectrum, and they were trying to normalize me.
Anyway, I remember it seemingly moving on its own and answering questions, but was pretty much aware that it was not supernatural but just wishful thinking moving it, perhaps unconsciously, much like water witches do with divining rods and such.
The human psyche does some weird things. Which are not supernatural.
I do not want to make wild claims but there are things we cannot percieve. The Holy Spirit is one, but, if you are going to accept it as real you would be wise not to discount the evil alternative (s). Admittedly not all responses on a Oiji board are malevolent but the general advice is not to play around with things you do not understand.
