Human existence is continuously shaped by both choices we actively make and forces beyond our control. This recognition of our inherent limitations often evokes a sense of melancholy - a longing for the roads not traveled, for the lives unlived, for the experiences that must remain as impossibilities. I want to propose the term impossibilitude to capture the sense of unease and melancholy that arises from the contemplation of unreachable realities. 

First, I’ll draw inspiration from Sartre's concept of facticity, which he used to describe the inherent limitations and constraints that define our existence. Facticity encompasses the circumstances and conditions into which we are thrown, setting the boundaries within which we must navigate our lives - it acknowledges the inescapability of our situatedness in a specific reality, imposing upon us a particular set of choices and possibilities. As Sartre put it, we are thrust into a specific context filled with historical, social, and personal contingencies. Following that logic, embedded within Sartre's notion of facticity you find the realm of impossible realities - those paths, decisions, and experiences that remain forever beyond our reach. It is in the light of facticity that the yearning for impossibilities emerges. Impossibilities refer to the potentials that could have materialized, the lives that could have been lived, and the outcomes that could have been achieved, had different paths been taken - by us or external agents that shaped our facticity. 

Additionally, Heidegger's existential analysis delves into the temporal structure of human existence - the concepts of past, present, and future intertwine to create our sense of being. Within this framework, impossibilitude occupies a unique temporal context – it lives in the gap between the past and an unachievable virtual future. It is the echo of past possibilities not embraced (again by us or the external agents that shape our facticity), reverberating through our present and future existence outside of that reality. Heidegger's emphasis on his idea of authenticity, which says that to exist authentically is to be oneself and to choose one’s own possibilities of being, that is, calling us to seize the potentiality of our being, also aligns with the concept. Again, at its core, authenticity according to Heidegger is about living one's life in a way that is true to one's own self and potentialities, which, by definition, underscores the idea that we have various potential paths before us - so the feeling of impossibilitude can be intensified when we reflect on the irreversible nature of our past decisions in light of our authentic selves.

In short,  I propose the term impossibilitude as the profound sense of yearning and melancholy stemming from the contemplation of the unreachable possibilities that remain forever unattainable, realizing that certain potentials or experiences are forever out of reach. Kierkegaard once described anxiety as the "dizziness of freedom,” meaning the overwhelming feeling of looking into the boundlessness of one's own possibilities. While Kierkegaard's dizziness of freedom is directed towards our present freedom, impossibilitude is focused on the dread we feel for past freedoms, as well as the lack thereof in our situatedness. This term emphasizes not only the impossibility of these alternate realities but also the emotional weight carried by the individual who grapples with the awareness of these infinite unrealized potentials.