Is it possible to think irrationally? My instincts tell me not but my philosophically-versed friends tell me that it is.
Given that it is possible to think rationally, it must be possible also to think irrationally. An analogy with the concept of biological function may usefully illustrate why this is the case. If some part of the body has a function--so, for example, if the heart has the function of pumping blood--it must be possible for it to malfunction, for otherwise the ascription to the heart of the function of pumping blood would not have any normative force. Similarly, insofar as one aims to think in accordance with the norms of thought, it must be possible for one not to think in accordance with those norms, and hence to think irrationally.
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