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.
Thanks Phil for sharing your perspective and a little bit of your story.
My pastor was preaching on Acts 16 this weekend and made a passing comment about the slave girl with a spirit of divination. I thought to myself it interesting for this spirit to have to annoy Paul before he cast it out.
Part of that may be that we have a tendency to identify non animate things as animate ones. I think some of us on the spectrum have less of that; thus, the tendency for some of us to struggle with faith, too. I think we have a strong tendency for that in my family, too.
Exactly – you can have an infinite set of objects if you start out that way.
Only if (1) it didn’t start that way and (2) you’re trying to count them.
That’s not a statement about the limits of a collection, it’s a statement about human perception.
I was thinking that just last night when I read a comment about an infinite multiverse saying that there could be – indeed must be! – a universe where I exist but my father does not. I find that to be a contradiction, because if there was another St. Roymond who looked just like me but had a different father, it would not be me: I am defined not just by an arrangement of atoms but by the relationships between my arrangement of atoms and those of others with whom/which I have interacted.
I always wonder about that given that when I was in New York as a part of the annual United Nations Pilgrimage for Youth, my mom and sister on a whim asked a Ouija board what I was doing right then, and the answer they got was “breaking matchsticks”, which they found hilarious. So they called and asked what I was doing, and I said I was sitting in the hotel window, breaking matchsticks into an ash tray. The silence after I said that got a bit frightening!
Definitely. I have witnessed enough unexplainable behavior from a Ouija board that I cannot discount the at least occasional involvement of the supernatural – including the time when someone had been asking what it was like where “you” (the board or entity) were and asked if they/it would like some light and the pointer just locked onto “NO” and wouldn’t move, or the time someone asked, “Do you know Jesus?” and the pointer went to “YES” and kept going right out from under everyone’s hands and zoomed across to hit the wall of the room.
I remember in a Greek New Testament class when we reached that point and some of us were hoping that incident might make more sense in the original. It didn’t.
Not possible: human perception relies on starting with one thing and extending to include others. That means it is never more than a beginning on a series, never the whole series.
Ponder trying to perceive a rainbow: the best the human mind can do is reduce the refraction of light from/through million of water particles to a single “object”, a thing of color that doesn’t actually exist (indeed even then no two people ever see the same rainbow).
We even talked about this in a math education course: humans aren’t capable of grasping infinity because our brains don’t work that way. We may imagine that we can imagine infinity, but even with mathematicians that is rare at best (it’s why there are rigorous definitions plus disputes about postulates; we can manipulate symbols to represent the thing but cannot grasp the thing itself).
