Heidegger doesn't believe that we "have possibilities", as if possibilities were somehow things that might or might not happen.
Possibilities are not occurrences for Heidegger. Rather, human being is possibility. Existence, for Heidegger, means to be thrown into possibility all the time. The existential concept of possibility sees human being as a primal openness, as a moving process, in its very Being. Abstracting static essences from that openness may be our human tendency, but basing our metaphysical, epistemological, and logical theories on that abstracting is fundamentally misguided. We cannot grasp our being; we can never grasp "it". Trying to grasp it, to get it, heaven help us most especially trying to keep it!, is like trying to carry water in our hands.
Being is not a thing to grasp or keep. It is a movement, and it is a movement that Heidegger calls thrown projection.
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See that post with different algorithms in metabole
See the journal French Metablog with today different posts