Describes someone who doesn't feel or show emotions, often seen negatively. His insensibility to her sorrow made everyone uneasy.
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Literal Numbness
Can be used to talk about actual inability to feel physical sensations, not just metaphorical. The patient's insensibility to heat due to the nerve damage was concerning.
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Appears Strong
May imply someone is tough because they 'don't feel pain', but can be misunderstood. Despite the tragedy, her insensibility was seen as strength by some.