Lack of orthodoxy; the quality or state of being unorthodox(noun)
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Use "unorthodoxy" in a sentence
"He should never turn back from a train of thought because it may lead to a heresy, and he should not mind very much if his unorthodoxy is smelt out, as it probably will be."
"At our first budget meeting, Richard was visibly surprised by what he would later describe, diplomatically, as the "unorthodoxy" of our arrangement with our builders."
"You can't take your eyes off him for the duration, such is the sense of mystery and unorthodoxy."