Starting point: the Fermi paradox
The post contrasts probabilistic reasoning (vast numbers of potentially habitable planets) with the persistent puzzle:
if intelligent life is abundant, why don’t we see evidence of it?
A set-theoretical move: list conditions for life
The argument proceeds by enumerating multiple necessary conditions (e.g., key chemical elements plus additional
planetary/system features). The post builds a high-dimensional configuration and highlights the resulting combinatorial explosion.
Complex causality implies a sparse set
If each condition is quite specific (covering only a small subset of planets), then their intersection can quickly shrink toward
a nearly empty set. The post illustrates this with an analogy: combine a few highly specific attributes and you may uniquely identify
a single case out of billions.
Conclusion
While not offering proof, the set-theoretical perspective is presented as a compelling reason to expect that life may be rare,
because the configuration required could be extremely unlikely to occur many times.
For the full argumentation and exact assumptions, use the PDF link above.