I can certainly see that someone's attitude to reason might be an important thing, in principle. However, my general impression is that it's less important in practice than it looks: even people who speak strongly against reason being the be-all and end-all in spheres like religion don't (in my experience) seem to let that affect their willingness to be basically, well, reasonable in any tangible real-world matter. To take an extreme example, one doesn't tend to see the ignore-reason-and-follow-your-heart type of theist crossing roads without looking on the basis that God will protect them; put them in a practical situation like that and they'll look both ways just like anyone else.
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I can certainly see that someone's attitude to reason might be an important thing, in principle. However, my general impression is that it's less important in practice than it looks: even people who speak strongly against reason being the be-all and end-all in spheres like religion don't (in my experience) seem to let that affect their willingness to be basically, well, reasonable in any tangible real-world matter. To take an extreme example, one doesn't tend to see the ignore-reason-and-follow-your-heart type of theist crossing roads without looking on the basis that God will protect them; put them in a practical situation like that and they'll look both ways just like anyone else.