Syllable division derived from spelling — this word is not in the pronouncing dictionary, so no phonetic transcription is shown rather than a guessed one.
insensitiveness is a noun meaning "the inability to respond to affective changes in your interpersonal environment". It carries one recorded sense.
the inability to respond to affective changes in your interpersonal environment
Forms marked · are formed by the regular rule rather than recorded in the source data. English keeps a few hundred irregulars and the rest follow the pattern, so the rule is right far more often than not — but it is a rule, and the mark says so.
Definitions, synonyms and semantic relations for insensitiveness come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.