Full Idea
Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects.
Gist of Idea
Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects
Source
report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.107