Quantum Mechanics and Reformation Theology

We're studying the foundations of Reformation theology in Sunday school. I find myself having to bite my tongue and not always succeeding. However, on the following two points, I've managed to stay quiet.

Several weeks ago, the teacher stated (paraphrasing) that "we believe 2+2=4 because of the axioms of mathematics." However, in "
Quantum Computing Since Democritus", on page 10, Aaronson writes:

How can we state axioms that will put the integers on a more secure foundation, when the very symbols and so on that we're using to write down the axioms presuppose that we already know what the integers are?

Well, precisely because of this point, I
don't think that axioms and formal logic can be used to place arithmetic on a more secure foundation. If you don't already agree that 1+1=2, then a lifetime of studying mathematical logic won't make it any clearer!

Today, in passing, it was said that responsibility necessitates the free will of man. Nothing could be further from the truth. I continued my reading of Aaronson during lunch today and came across this gem on pages 290-291:

Before we start, there are two common misconceptions that we have to get out of the way. The first one is committed by the free will camp, and the second by the anti-free-will camp.

The misconception committed by the free will camp is the one I alluded to before: if there's no free will, then none of us are responsible for our actions, and hence (for example) the legal system would collapse….

Actually, I've since found a couplet by Ambrose Bierce that makes the point very eloquently:

    "There's no free will," says the philosopher;
    "To hang is most unjust."
    "There is no free will," assent the officers.
    "We hang because we must."

Looking ahead to the end of the chapter, Aaronson brings Conway's "Free-Will Theorem" into play. What he doesn't apparently discuss (I've just scanned here and there), is that this randomness is not under our control.
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