It is not logic, but the bravado of presentation, along with ridiculing those who disagree, that wins arguments. In arithmetic the probability of a series is the product of the probabilities forming the series. Nevertheless, e.g., it would be naïve to apply such simple arithmetic to evolutionary biology thereby misunderstanding the power of accumulation of natural selection. Logic must be crafted to fit the argument. It is the desired conclusion of an argument, which determines the logic.
“The point is that every single one of us is lucky to be alive against hyper-astronomical odds.” http://newsweek.washingtonpost.com/onfaith/panelists/richard_dawkins/2010/02/the_great_tim_tebow_fallacy.html
A human fetus cannot be identified in foresight as the person after birth. Prior to birth its identity is that of a hyper-improbability indistinguishable from every other hyper-improbability. Also, it would be illogical to view any event in the series of probabilities in isolation from the overall series of which the end product develops into the eventual person. Included in the series of events is the decision of the mother not to abort the hyper-improbability. To point to that decision as determining the existence of the end product in its eventuality as an individual historical person is illogical. To identify the end product of gestation as anything other than a hyper-improbability, i.e. the arithmetic complement of the arithmetic product of a series of probabilities, is scientifically illogical.
“What is it that makes natural selection succeed as a solution to the problem of improbability where chance and design both fail at the starting gate? The answer is that natural selection is a cumulative process, which breaks the problem of improbability up into small pieces. Each of the small pieces is slightly improbable but not prohibitively so. When large numbers of these slightly improbable events are stacked up in a series, the end product of the accumulation is very very improbable indeed, improbable enough to be far beyond the reach of chance. It is these end products that form the subjects of the creationist’s wearisomely recycled argument. The creationist completely misses the point, because he (women should for once not mind being excluded by the pronoun) insists on treating the genesis of statistical improbability as a single, one-off event. He doesn’t understand the power of accumulation.”,The God Delusion, page 121.
The problem of improbability of the mammalian eye as the end product of Darwinian evolution is solved by ignoring the hyper-improbability of the end product of the series of Darwinian events and by focusing on the probability of each Darwinian event in isolation from the probabilities of the other Darwinian events in the series. By so doing, one is dealing with individual probabilities which are not prohibitively improbable in contrast to the hyper-improbability of the end product. To identify the end product of evolution as a hyper-improbability, i.e. the arithmetic complement of the arithmetic product of a series of probabilities, is scientifically illogical.