 Regardless of this argument (the details of which are not discussed here), many already find the assertion that there is a largest number hard to swallow. But Lavine has articulated a sophisticated form of set-theoretical ultra-finitism which is mathematically non-revisionist (Lavine 1994). He has developed a detailed account of how the principles of ZFC can be taken to be principles that describe determinately finite sets, if these are taken to include indefinitely large ones.