Developing a theoretical foundation toward establishing a futures science requires reconstructing original roots, whereby this field is conceptualized at higher generality levels. This article aims to provide a unifying framework for expressing any of the futures (from possible to plausible, plausible to undecidable) plus the mechanisms for manipulating these futures, with a view to promoting genuine futures thinking. Despite more than sixty years of studies about “the future,” the logical status of future-based conceptualizations still remains, at best, unclear. This article proposes to fill the continuity gap through designing a generative mechanism for expanding futures concepts based on formal theory. We use the well-developed Concept-Knowledge theory from Mines ParisTech, founded on set theory without the axiom of choice. The space K represents known/knowable things (present and past facts, available knowledge, what is known-to-be-known/to-be-not-known). The space C of concepts represents what is undecidable, neither provable nor unprovable at a given time. The C-K operating mechanism logically expands C concepts relatively to K, until they result in a conjunction with K—that is, become possible—possibly requiring extra development work. The article illustrates the approach on a series of field cases, whereby the path to futures robustness starts upstream at undecidable stages, as if to open up vast conceptual reservoirs of “futurabilities”—a foundational step transcending traditional futures studies. Futuring becomes a constructive and generative process, potentially leading to accepting infinities of futures formulations, where generativity is monitored as a design-oriented logic working on knowledge. Such an approach should improve the foresight practice.