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TMA | KCA 16 | IAINT | No Vacancy

Welcome to Tuesday Morning Apologetics (TMA). We’re talking about the Kalam Cosmological Argument (KCA):

1. Whatever begins to exist has a cause.

2. The universe began to exist.

3. Therefore, the universe has a cause.

Our focus is now on the second premise of the KCA which is supported by an argument called, “The Impossibility of an Actually Infinite Number of Things” (IAINT):

1. An actually infinite number of things cannot exist.

2. A beginningless series of events in time entails an actually infinite number of things.

3. Therefore, a beginningless series of events in time cannot exist.

Last week I mentioned that we’ll be analyzing the first premise of the IAINT. I also mentioned that Dr Craig uses Hilbert’s Hotel to support the truth of the IAINT’s first premise. I’m not going to describe everything about Hilbert’s Hotel in this article. If you’re not familiar with it, please click here.

When we talk about Hilbert’s Hotel it’s important to understand what we’re talking about. We need to fully grasp what the situation actually is. Hilbert’s Hotel is a thought experiment that’s attempting to show that an actual infinite is plausibly metaphysically impossible. In this thought experiment we’re dealing with two actually infinite quantities.

First is the Hotel which has an actually infinite number of rooms.

Second is an actually infinite number of guests.

It’s also important to understand that the guests in this thought experiment are flesh and blood people with the ability to choose.

The ability to choose is important because even if mathematicians can, and do, make up rules that prevent certain mathematical operations, those rules would do nothing to prevent an actual person from checking out of the Hotel.

And that’s where the power of Hilbert’s Hotel lies. The absurdities that develop as a result of these two actually infinite quantities interacting. However, that just seems to be a separate issue from the second premise of the KCA. In Hilbert’s Hotel it’s never demonstrated that the Hotel’s actually infinite capacity (by itself) is a problem. While it’s easy for us to say that it’s physically impossible for a Hotel with an actually infinite number of rooms to exist (due to a variety of different physical limitations) it hasn’t been demonstrated that it’s metaphysically impossible. But that is where the absurdities come in. However, the absurdities only become apparent when people start interaction with the Hotel. And even then, the absurdities don’t seem strong enough to warrant the belief that Hilbert’s Hotel is even plausibly metaphysically impossible.

Therefore, with regard to the second premise of the KCA and the idea that of the physical world has no chronological starting point, there doesn’t seem to be an issue. If it is the case that the B-Theory of Time is an accurate model for how time is constituted in the physical world and there are an actually infinite number of “Time Coordinates”, then what is interacting with those Time Coordinates or moving from Time Coordinate to Time Coordinate? What actual absurdities are being produced?

It could be said that God is interacting with those Time Coordinates, but in what way is He interacting with them? It seems to me that God, at most, interacts with Time Coordinates by “focusing” on specific Time Coordinates and causing those ones to be the “now” that we experience (If we happen to inhabit those Time Coordinates). I just don’t see how that is any different than us focusing on a specific number, or series of numbers, in the infinity that is the Natural Numbers.

It seems eminently plausible to me that God could actualize the Physical World as a block entity with an infinite number of Time Coordinates and whichever ones He chooses to "focus" on are the “now”. I don’t think that God is managing the “Hilbert’s Hotel” that is our Physical World the same way the Manager does in the thought experiment. He isn't moving "guests" from Time Coordinate to Time Coordinate. Whatever Time Coordinates we inhabit are the ones we inhabit and that’s that. We can’t choose to check out or switch “rooms”.

We live in a Hotel specifically designed for us and there is no vacancy.

In closing, if it’s reasonable to believe that God could do something like what I've described here, then saying that it’s impossible doesn’t really help when we’re trying to argue for God’s existence. As for the second premise of the IAINT, I think that it's true and I don't really see much reason to explore it. I will if anyone has any questions about it, but, to me, it just seems obviously true. As I said previously, the first premise is the key premise and I think it's probably false.

And that means that, personally, I don’t find the IAINT to be a sound argument. I’m definitely willing to listen to those who disagree but, for now, that’s where I stand. The IAINT doesn’t lend support for the second premise of the KCA. What do you think?



  1. This video by Vsauce does a great job describing the infinites and I highly recommend watching it. How To Count Past Infinity


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