This paper questions the "arguments from design" that, from the functions of organism, their structure or their fit to the environment, inferred the fact that they have been designed by an intelligent architect. These arguments are very old, and have been pervasive in philosophy and natural history since Antiquity. Each version connects in some way functions, structure, complexity, with randomness and low probability. Darwin claimed to have solved this argument, because natural selection eliminates the need of appealing to a designer. After having distinguished several types of arguments, the paper analyzes the rational core of these arguments in terms of computational notions of complexity and randomness. The last section states the reason why natural selection solves the design argument.
Keywords: Complexity, Darwin, design argument, probability, randomness.