That, however, is just wrong. It is not true that all complex things emerge by gradual degrees from simpler beginnings. In fact, the most complex thing I’m aware of is the system of natural numbers (0,1,2,3, and all the rest of them) together with the laws of arithmetic. That system did not emerge, by gradual degrees, from simpler beginnings.
If you doubt the complexity of the natural numbers, take note that you can use just a small part of them to encode the entire human genome. That makes the natural numbers more complex than human life. Unless, of course, human beings contain an uncodable essence, like an immortal soul—but I’m guessing that’s not the road Dawkins wants to take. (emphasis mine)
Has there ever, ever been a case where this phrase has been more applicable? A small part of the set of natural numbers can be used to represent the genome, not to encode it in the sense that gene encoding is commonly understood. Protein molecules can not be created out of natural numbers.
Landsburg's definition of complexity of genome in terms of encoding the genome is essentially an information-theoretic one. The main idea here is that of Kolmogorov complexity. It is the right approach, of course, but it is essential to remember just what the base information is. The genome itself is not a sequence of non-random and finite set of ACTGs, only its representation is.
Of course, there is a more fundamental though more subtle issue. Kolmogorov complexity proceeds by assuming arithmetic, which assumes the set of natural numbers. To talk of the complexity of the set of natural numbers itself is completely meaningless. It is like saying that the set of alphabets of the English language is more complex than any arbitrarily complex philosophical idea (for e.g. - the map is not the territory) because the idea can be expressed by a small, finite and non-random subset of the alphabet.
Does this mean that I'm opposing Godelian platonism by comparing a mathematical set to a human construct like an alphabet? Not really. I hold an information-theoretic view of the universe. Math is the closest we get to a system that captures the fundamental notion of information.
2. On EconLog, Bryan Caplan responds to Robin Hanson in the latest Caplan-Hanson debate (on philosophy of the mind, this time). He links to an old paper by him on why he is a dualist (mind and matter/body are different - mental phenomena can not be reduced to physical ones) and not a monist/reductionist (all things are made of matter, there is no mind beyond the body, mental phenomena are completely reducible to physical ones). He refers to John Searle approvingly before critiquing him. That's for later though.
What is striking is - Caplan claims to be neither a substance dualist (that the mind is a separate substance than the body) nor a property dualist (the mind is an emergent property of the brain that is not reducible to anything simpler). Substance dualism is rather naive and uninformed by anatomy and neuroscience. Property dualism, however, is an extremely attractive position to adopt if you're going to be a dualist. Why then does Caplan reject it? He explains -
"Neither is my view property dualism; for the essence of a property is that it could not even be conceived as existing apart from something else. For example, "whiteness" could not even be imagined to exist all by itself; the reason is that it is a property, not an independent thing. But we can conceive of the mind all by itself; hence it is not a property. "
It is an old paper, so maybe Caplan has not reviewed it in quite some time, but it is rather unbelievable that he ever used/convinced himself of the trickery of 'whiteness' (as opposed to white) and the ambiguity of 'conceive' to dismiss property dualism.
I can absolutely conceive of 'white' by itself. You can argue that this is false, and that my conception of white will be a white wall, a white board, white cloth, brilliant sunlight or something physical that possesses the property of 'whiteness'. You will be right. But then, you can't genuinely believe that you can conceive of a mind independently. You can only conceive of mental phenomena - desire, choice, anger, pain. And even then, you can only conceive of how you/other sentient beings perceive these phenomena or how they are transient properties of sentient beings. And there's no reason to assume that something physical (the brain) cannot possess the properties implied by mental phenomena. That, in fact, is the very premise of substance dualism.
Which is to say, Caplan rules property dualism out either by naivette or by assumption, in very simple and direct language that makes the mistake rather obvious.