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"Finitism"は、「有限主義」です。下記”History”ご参照（＾＾
https://en.wikipedia.org/wiki/Finitism
(抜粋)
Finitism
Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects.
It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as legitimate.

History
The introduction of infinite mathematical objects was a development in mathematics that occurred a few centuries ago.
The use of infinite objects was a controversial topic among mathematicians.
The issue entered a new phase when Georg Cantor, starting in 1874, introduced what is now called naive set theory and used it as a base for his work on transfinite numbers.
When paradoxes such as Russell's paradox, Berry's paradox and the Burali-Forti paradox were discovered in Cantor's naive set theory, the issue became a heated topic among mathematicians.

There were various positions taken by mathematicians. All agreed about finite mathematical objects such as natural numbers.
However there were disagreements regarding infinite mathematical objects.
One position was the intuitionistic mathematics that was advocated by L. E. J. Brouwer, which rejected the existence of infinite objects until they are constructed.

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