It is possible for someone to be disabled but not identify as disabled. It is also possible for someone to be disabled and identify as such, but not be identified by others as disabled. 

University of Colorado at Denver

The formation of an individual's disability identity relies on both social and psycholgocial factors related to acceptance and meaning/purpose. Thus, the development of this identity is dependant on interpersonal (social) and intrapersonal (psychological) awarness. 

Defining Disability Identity Development

Grue, J. (2016). The social meaning of disability: a reflection on categorization, stigma and identity. Sociology of Health & Illness, 38(6), 957-964. 

Social Meaning of Disability

The function of understanding the formation of a disability identity is to analyze how individual variation plays a role in adapting to their adversity and to develop effective interventions.  

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