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You cannot do statistics without logic. Otherwise you become a data fraud, or, worse, an economist.
It is certainly true that all beliefs and all myths are worthy of a respectful hearing. It is not true that all folk beliefs are equally valid - if we’re talking not about an internal mindset, but about understanding of the external reality.
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Wherever a choice has had to be made between the man of reason and the madman, the world has unhesitatingly followed the madman. For the madman appeals to what is fundamental, to passion and the instincts; the philosophers to what is superficial and supererogatory - reason.
A philosopher uses logic without statistics, an economist uses statistics without logic, a physicist uses both.
What a brain is made of isn't the essential thing: it's how the brain functions. Its thought patterns, its reaction time, its ability to reason and generalise from experience. Why does the whole issue have to be drown down to the level of organic cells versus positrons?
I try not to think with my gut. If I'm serious about understanding the world, thinking with anything besides my brain, as tempting as that might be, is likely to get me in trouble. Really, it's okay to reserve judgment until the evidence is in.