finite means having definite or definable limits — bounded in space, time, number, or extent, and therefore able to be counted, measured, or brought to an end.
The word entered English in the early fifteenth century from Latin finitus, past participle of finire, "to limit, set bounds, come to an end," from finis, "boundary, limit." The same root gives finish, final, and define. Its negation, 📝infinite, has travelled beside it ever since, and each word is easiest to understand against the other.
In ordinary use finite simply means limited — finite resources, a finite number of seats — and often carries a note of scarcity or mortality. Mathematics uses it strictly: a finite set has a countable number of members, and a finite quantity can be assigned a definite value. Grammar keeps a separate sense: a finite verb is marked for tense, person, or number, such as runs or ran, as opposed to the infinitive to run or the participle running. Finite differs from limited, which can describe a deliberate restriction, and from temporary, which concerns duration alone.
📝James Carse gave the word its sharpest modern use in 📝Finite and Infinite Games: a finite game is played for the purpose of winning, keeps fixed rules within agreed boundaries, and ends when someone has won. Its counterpart, the 📝Infinite Game, is played to continue the 📝play. In that usage finite names an orientation toward closure rather than a size.
I use finite in Carse's sense. In 📝Bezos Won Capitalism I called capitalism a finite game that has already been won, and in 📝No Rogan I named the internet's winner the same way. 📝Eff The Ineffable keeps 📝Charles Eisenstein's warning about reaching the infinite through finite means.