Since I'm creating this thread, I get to go first! Yay!
In accordance with the rules of formal debate, I'll first define a few terms:
- Logic = inductive reasoning from premises to infallible conclusions
- Science = the scientific method = hypothesis testing and peer review. Includes both inductive and deductive reasoning.
- Philosophy = the study of scientifically-intractable problems (technically science is a branch of philosophy, but let's not go there)
My position is that approaches like science and logic are merely a means to an end. They are models that we apply to the universe where appropriate in order to generate accurate predictions about what will happen next. We use them because they have turned out to be very very good at this.
I personally do my best to use them all the time, but that is a philosophical position distinct from science or logic. It is based on my (unsupportable and possibly inaccurate) belief that, in the long run, a strongly predictive model of how the universe works will enable me to be happier, and on my philosophical belief that scientific and logical methods are the best way to achieve this.
If someone felt that this was not the case, or decided that happiness was not their goal in life, then IMO they would be philosophically justified in not applying scientific or logical methods. For example, if a man was suspicious that his wife's baby was not his own, he might legitimately decide that parenthood testing was not in anyone's best interest.
I don't deny that rational approaches are consistently better than all others at determining how the universe works. I do deny that the acceptance of rational approaches follows directly from this statement. Setting rationality aside isn't necessarily a daft decision, and it's something that I feel people have the right to do - as long as they don't inflict their irrationality on me.