This article continues my criticism of Eliezer Yudkowsky’s meta-ethics sequence on the Less-Wrong wiki, the first being my criticism of his article on fairness. Yudkowsky’s point here is to explore the potential foundations of logic and math, specifically by ruling out the human mind.
This article of Yudkowsky’s focuses primarily on the contrast between objective math and subjective perception. Math, because it relies entirely on formal logic, is an objective framework. That means that the concepts of math can be communicated accurately and completely, without losing any detail. The mathematical statement, 2+3 = 5, which Yudkowsky uses frequently as an example, means the same thing to me as it does to him.
If, however, one were to perceive one of the numbers differently, or perhaps, one were to perceive the application of a rule differently, as a mistake, then they would have a different and wrong understanding of the equation. Specifically, Yudkowsky suggests that a neutrino flying through our brain might alter our memory and therefore our perception of the event.
Obviously, math could not rely on the Human brain for its foundation for objectivity, because people make mathematical mistakes all the time. Yudkowsky proposes some strained examples here with neutrinos, but people really do make math mistakes all the time. That is why we have students practice so much with math homework. Even with that, they will continue to make even simple mistakes throughout their life.
Instead, math’s objectivity is founded in logic, though that does not help Yudkowsky out very much. Logic, then, is founded in the universe being logically consistent. That means that effects must follow naturally from causes and that the effects are predictable from a set of causes within some reasonable expectations. While we may be able to observe that our universe seems to be logically consistent, it is not clear that that is a necessary condition for a universe or something that we should expect. R.C. Sproul often points out that the ancient Greeks believed in a pantheon of Gods who eagerly interfered in human affairs. Because their Gods were un-observable and they were expected to have such a profound effect on almost everything major, it would have been nearly impossible to separate the effects of the Gods from those of natural causes.
Similarly, quantum mechanics is inherently unpredictable, though its unpredictability does not seem to undermine the predictability of the universe as a whole. The point here is that naturalism is also potentially unpredictable, even after we have cast aside the gods of the Greeks. If the entire universe acted like quantum mechanics, it might be impossible to apply logic, at least practically.
Oddly enough, Christianity claims that God created a logically consistent universe because he is a logical being. He created it so that we could observe it and understand it. While he may act supernaturally in a way that is not visible to our senses, he does so in a logically consistent way. The miracles described in the Bible may not have been consistent with our physical laws of nature, though they were always consistent with God’s nature and were not arbitrary. Even then, they would have been exceptions and easily excluded from scientific analysis.
In the end, Yudkowsky is forced to assume the objectivity of math, logic, and a logically consistent universe, with no foundation for doing so. Alternatively, one can assume the Christian God or another god with similar properties. This necessary foundation of logic is actually considered a proof of God by Christians. Meanwhile, atheists consider the possibility that God might violate his own physical laws through a miracle a strong argument against even considering a God, at least when performing science. They are left without an alternative explanation here though and are comfortable leaving it as an assumption.