In a way that demonstrates common sense; in a manner that is practical, straightforward, and based on ordinary reasoning and experience.
From 'commonsensical' + -ly (adverb suffix). The double suffix (-ical + -ly) creates the adverbial form of the philosophical adjective.
Speaking 'commonsensically' was literally an insult in academic contexts—philosophers mocked appeals to common sense as unsophisticated, until pragmatist philosophers like William James argued that common sense was actually humanity's most sophisticated reasoning.
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