In a manner that is subject to error or mistakes; in a way that demonstrates fallibility.
From the adjective 'fallible' plus the adverbial suffix '-ly'. This rare adverb appears in philosophical and academic discourse to modify actions or processes that are error-prone.
You don't often see philosophers describe their own reasoning as 'fallibly sound,' but the ones who do are surprisingly honest—they're admitting that their arguments might be right even though the human brain that created them is fundamentally error-prone.
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