I came across the ultra-finitism, the idea that there is a "largest number". Even most ultra-finitists admit that the "largest number" cannot be exactly defined. Therefore my question :
Did some ultra-finist make any suggestion of at least an approximate value that should indicate the "largest number" ?
If not, why is ultrafinitism accepted as an alternative way to do mathematics ?
I can understand that some mathematicians do not like the concept of infinity. But I cannot understand that the idea to reject FINITE numbers that can be easily defined mathematically , as Graham's number , is mathematically legitimate in any sense.
I know that there were already some questions about ultrafinitism, but I did not find anywhere a suggestion which numbers are considered to be "too large".