Below is a great video where Cosmic Skeptic and William Lane Craig discuss the Kalam Cosmological argument. I think it’s rather old at this point but WLC’s channel just posted it anew, motivating my current comment. Within the first ten minutes, Cosmic Skeptic makes a blunder about concepts of infinite. This article briefly outlines the issue.
Craig catches Cosmic Skeptic, but Craig’s explanation is a bit too technical, I think, for both Cosmic Skeptic and for the Average Joe. Craig rightly says that CS makes a ‘modal operator shift’. The video is posted below, and my more elementary explication of the blunder follows.
- Around 6:45, Cosmic Skeptic thinks he has provided a case of a potential infinite assuming the existence of an actual infinite, but he has done no such thing. He has simply identified a potential infinite and mislabeled it as an actual.
- Cosmic Skeptic identifies a space division scenario. In the real world, space division takes time. It is a process which occurs step-by-step and can be executed for an arbitrarily long period, but the end state can never be reached. This is precisely what a potential infinite is, as in a limit in calculus.
- Space cannot actually be infinitely subdivided for two or three reasons:
- A temporal feasibility problem: If subdivision proceeds by y steps each t time, then an infinite number of t time is required to execute an actually infinite number of y steps. However, there is no t[actual] in which we will have reached t[infinite].
- A nonexistance problem: If some width w actually is subdivided over infinite divisions, the width of each subdivided output region is (w/infinite) which is expressed variously as actually zero, zero in the limit, or undefined. In no case does the output region actually exist in physical space. It doesn’t really exist anywhere. What does exist is a limited process where you can make smaller and smaller spaces over time, but you can’t actually get to a thing with a width of 0. It would cease being a thing.
- This item isn’t a proof of failure, but it is a probabilistic argument. This is a superform of the temporal feasibility problem. The problem is that we don’t know how much time will exist in the future. We have a finite past, and we may well have a finite future. So it may be that that temporal feasibility constraint is even greater than the fact that t[infinite] can never be reached. It could be that t[k] won’t even be reached, so that even if the t[infinite] problem is somehow solved, it isn’t proven that the subdivions process is actually executable.
- As you can see from 1-3, CS just miscategorized the subdivision problem as an actual infinite. If you disagree that it’s a mischaracterization, I hope you will at least concede he is wrong on a related claim: The notion of the potential infinite, in principle and in the concrete example of the subdivisions problem, certainly doesn’t “assume the existence of actual infinites.”