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Webster 1828 Edition

, n.

Defectiveness; as the unsoundness of timber.

Defectiveness of faith; want of orthodoxy.

Corruptness; want of solidity; as the unsoundness of principles.

Defectiveness; as the unsoundness of fruit.

Infirmity; weakness; as of body; as the unsoundness of the body or constitution.

unsoundness ‎(countable and uncountable, plural unsoundnesses)

The state of being unsound.
- 1951, John Wyndham, The Day of the Triffids
  Most likely he was accounting for that by the bias my job might be expected to give – aggravated by a phobia resulting from my recent sting – and he was wondering whether it might connote other, perhaps less harmless, unsoundnesses.

the state of being unsound