The quality or state of being feline; possessing characteristics typical of cats such as grace, stealth, or aloofness.
From feline plus the abstract noun suffix -ness, which creates a noun describing the quality of the adjective. Standard English word-formation.
The felineness of a cat—its independence, its refusal to give unconditional approval, its sudden bursts of attention—is what makes cats psychologically different from dogs in ways we can actually measure with neuroscience.
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