Here is an ultrafinitist manifesto  ([link](https://arxiv.org/abs/cs/0611100)) I have co-written a few years ago:

      https://arxiv.org/pdf/cs/0611100v1

It is absolutely not a finished paper (there are a few inaccuracies, and many parts are sloppy), but it contains a brief history of ultrafinitistic ideas from the early greeks all the way to present time, a number of refs,  as well as a sketch of a programme towards a model theory and a proof theory of ultrafinitistic mathematics. 

You may also want to google the  FOM list  on "ultrafinitism", there are a few posts by Podnieks, Sazonov, myself, and a few others pro and contra ultrafinitism.