Justintruth wrote:
Doesn't work because imagine that 14 causes 15 but 14 does not exist. 13 causes 14 but 13 does not exist. Every causing number can cause only if it is.
I don't see how that's an objection to my model. You are saying that if you break one link in a chain of causality, the following events won't happen. To write this post I need a computer. For me to have a computer there must be a computer factory. The computer factory requires raw materials dug out of the earth. To have the earth there must be a modern universe. To have the modern universe there must have been the Big Bang.
Break any link in that chain and the rest of it doesn't happen. No Big Bang, no forum post. Big Bang followed by modern universe followed by existence of earth followed by people digging raw materials out of the ground doesn't get me a computer, someone still needed to build a computer factory.
I don't see at all what this has to do with my example. All causal chains have the property that if one event fails to happen, all following events fail to happen as well. What does this have to do with what I said?
My example is to note that there can indeed be an endless backchain of causality. Event 0 is caused by event -1 which is caused by event -2 which is caused by event -3, and so forth. This model of an endless causal backchain has the following properties:
* Every event has a cause;
* There is no first cause.
* The interval between any two events is finite.
I suggest that this model causes problems for the cosmological argument. It's clearly not true that there must be a first cause. One can argue along the lines of, "Oh yeah? How'd all this get started?" without invalidating the simple truth of the model and the claims I have made about it.
In any event this has nothing at all to do with your objection. Sure, if there's no Big Bang then I can't mow my lawn. What of it?
Justintruth wrote:
So compare a set
I said nothing about sets. In fact one of the features of my model is that it does NOT assume a completed set of events. There is event 0, and event -1, and event -2, ... but there is NOT necessarily a completed set of all of them. My model only requires a potential infinity, not an actual infinity. I do NOT require the Axiom of Infinity for my model. Another one of my model's virtues.
Justintruth wrote:of countablely infinite items in a infinite causal series that exists to the same set that does not exist.
I confess I don't know anything about sets that don't exist. Can you give me an example? Note that you can't just say, "The set of pink flying elephants." That set DOES exist. It's the empty set. So please, explain what you mean by a set that does not exist.
Of course the "set of all sets" can be proved to not exist, since it leads to a logical contradiction. That's Russell's paradox. Is that what you mean by a set that doesn't exist? A collection formed outside of the rules of set theory? That's a pretty technical point, I can't imagine what is the relevance here.
Justintruth wrote:
Same set of integers. But one exists and the other doesn't so the integers cannot be the cause of being and if they are not then what is a cause?
Of course I never said "the integers are the cause of being" or anything remotely like that. I simply offered a model of an infinite backchain of causation in which every event has a cause and there is no first cause. If you like, you can label my events ..., E(-2), E(-1), E(0). Makes no difference.
I note in passing that our esteemed OP actually mentions this example in his blog post
http://lawrencecrocker.blogspot.com/201 ... ep-of.html. He says:
"As a set theory wonk would put it, the order type *ω, is supposed to be impossible for time."
That's actually a shorthand for my idea. The order type *ω is simply a mathematical shorthand for the natural numbers in reverse order: That is, ..., -3, -2, -1, 0. I thought this example was original with me but evidently it's been thought about before. I'll skip commenting on the irony of a professor of philosophy calling someone else a wonk.
Hope this is helpful.
ps -- I see that Professor Crocker mentioned this in his OP as well. "... time cannot be of order type *ω". But here he didn't call anyone a wonk. Well done Professor!