In Book V of the Eudemian Ethics , Aristotle discusses the excellences of thinking things through (ἀρεταί διανοετικαί, usually translated as "the intellectual virtues"), in contrast to the excellences of character or ἀρεταί ἠθικαί. Recently I wrote about the more practical of the two primary excellences of thought: φρόνησις (which I translate as "wisdom"). Here I take a first glance at the more theoretical of the two: σοφία.
It's hard to know to translate this one. Although σοφία was itself wisdom in Greek philosophy (a.k.a. "the love of wisdom"), Aristotle gives it a more speculative cast here. I'm inclined to translate it as "sagacity".
Although both wisdom and sagacity are supposed to be ἀρεταί and thus balances or means between opposing tendencies to overdo or underdo the relevant behavior, only once (in the EE but not the NE) does Aristotle lay out those tendencies and only for φρόνησις, which as previously noted he describes as a mean between cunning and foolishness. Because he does not do the same for σοφία, we need to figure it out on our own.
Using Gilbert Ryle's distinction between knowing how and knowing that, we can glean that foolishness is an absolute lack of knowing how, whereas cunning is knowing how without the benefit of insight into or guidance by what is best - i.e., τό καλόν or what is beautifully right. Similarly, the deficiency of sagacity is most likely ignorance: the absolute lack of knowing that; this might imply that the other opposite of sagacity is knowing that without the benefit of insight into or guidance by what is best - i.e., τό θείον or the divine, which for Aristotle consists of the highest objects of inquiry (θεωρία). In ancient Greece, there's one word for this corruption (μοχθηρία) of the intellect: sophism.
This analysis is consistent with Aristotle's brief description of sagacity as a combination of inquiry (θεωρία) and insight (νοῦς). Unfortunately, Aristotle does not delve into a detailed description of σοφία. However, he does demonstrate many aspects of intellectual excellence in the way he works through philosophical problems. Here we can see his perseverence, his dedication to observation, his openness to evidence, his curiosity, his conscientiousness, his pursuit of order, his independence, his seriousness, his fairness to other thinkers, his love of truth, and other admirable qualities. A full account of σοφία or sagacity would do justice to these and other intellectual virtues.
 This is also Book VI of the Nicomachean Ethics; henceforth, accepting the results of Anthony Kenny's research, I shall refer to the so-called "Common Books" by their numbering in the Eudemian Ethics.
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