Kalaam Argument, I
A. Craig's main argument:
- "Whatever begins to exist has a cause.
- "The universe began to exist.
- "Therefore, the universe has a cause."
Alternative to 2: The universe had an infinite past. Why not?
B. Hilbert's Hotel: No Vacancy--Guests Welcome.
- Infinity is weird. So what? Absurdity vs. contradiction.
C. "A collection formed by adding one member after another cannot be actually infinite."
- "If one cannot count to infinity, how can one count down from infinity?" -- Well, maybe both are feasible given infinite time?
- Why didn't the man counting from minus infinity finish earlier?
- Cf. Parmenides' argument against change, and Augustine's discussion of the beginning of the world and of time.
- A probabilistic version of the argument.
- Variant: Suppose it's Frank's task to count infinitely many numbers. Every minute, for eternity, he counted a number. But then he was always already done. What kind of a task, however, is it where you are always already done. Surely only a trivial one. But this is not a trivial task.
D. Tristram Shandy: writes autobiography, taking a year to describe a day. If an infinite past is possible, he could have finished this, since the number of days in the past is equal to the number of years.
- Note the difficulty: If the future is infinite, we just get in asrears more and more. (Can do this this with Hilbert's hotel: As compensation for losing room 1, you give the guy there two rooms. You get more and more in arrears as the process progresses, but that's OK, as in the end it's all paid back.)
- Small's objection: Not so, because each day has to be written up after it has happened. But there is a whole year of days not written up. (Craig clearly knows this--that's why he has a reductio here.) But Craig is, it seems, missing something. True, if the number of years equals the number of days, it is possible that each year is described. But it does not follow that one can fit each writeup after the day of occurrence. Indeed, we have just seen this can't be done.
- OK, so maybe we can instead allow that Shandy sometimes writes up a day before it happens--it's a plan or prophecy, not a work of history, then. (If one thinks that prophecy of free events is impossible, we may suppose Shandy to be just making things up and totally by coincidence this matching what happens.)
- Now we have the Conway objection: Craig says that at each past day, Shandy will already have finished the autobiography. But that is only true if by "infinity" we mean what is "all-encompassing".
- Hypothesis: Maybe what Craig means by "finish autobiography" is "be on a day on which the writeup contains all of the past." One need not describe the last day of one's life to finish one's autobiography--one just needs to bring it up to the point of time at which one writes. Now observe that in this sense the autobiography was finished on every past day. For there is some day that was being described over the past year. (Let's suppose we're now at midnight after that year.) That day is either the just finished day or a day yet to come (including the day right ahead) or a day further in the past. If further in the past, then the just finished day has not been described. So over the past year, one's been writing about either the last day of that year or about some future day. The year before that, one was writing about the day before that, and that was certainly in the future then. And so on. Thus, one will be always writing about a future day. But that means that one will always already have been done, the past having been all already written up, despite the fact that a day takes a year to write up.
- Why is this a problem?
- Well, this is a task that is always already finished. -- But why think of this as a task?
- Moreover, when did one have the time to do so much writing, if each day took a year to write, that one always already had been done? -- Yes, that is a feature of infinity.