1956 (2001) Jean-Paul Sartre Being and Nothingness
"Finitude: To be carefully distinguished from "mortality." Finitude refers not to the fact that man dies but to the fact that as a free choice of his own project of being, he makes himself finite by excluding other possibilities each time he chooses the one which he prefers. Man would thus, because of his facticity, be finite even if immortal." 
1991 P. Christopher Smith Hermeneutics and Human Finitude
"It shows up in Gadamer, however, quite differently: in his insistence, namely, on human finitude and the limits of human consciousness all the while he continues to take up traditional issues of speculative philosophy." 
1992 Joan Stambaugh The Finitude of Being
Given his conception of time and space, a conception that is quite different from traditional views, finitude cannot mean only that something objectively present has limits in space and time. To begin with, being is in no possible sense of the word a being or a thing. Thus, these two points - the radically altered conception of time and space, and the fact that being cannot be represented as an objectively present being or thing - make it necessary to inquire into a meaning of finitude that goes being mere limitation in time and space.