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:: Bill, thanks for the nice citations in which people mention PR functions, but I don't really think any of those speak to their notability (while they certainly do describe the PR functions!) [[User:AshtonBenson|AshtonBenson]] ([[User talk:AshtonBenson|talk]]) 00:59, 28 August 2009 (UTC)
Re Ashton, PRA: the identification of PRA with finitism is a long-running discussion in the philosophy of mathematics. Everyone I have read agrees that PRA is included in "finitism"; the point of contention is whether finitism goes beyond PRA or not, with some on each side. It is trivial to find papers where this is discussed using google. One influential paper is:
* "Remarks on finitism", Wiliam Tait, [http://home.uchicago.edu/~wwtx/finitism.pdf].
Some others are:
* "Partial realizations of Hilbert's program", Stephen Simpson, [http://www.math.psu.edu/simpson/papers/hilbert.pdf]
* "Finitistic Properties of High Complexity", Dmytro Taranovsky, [http://web.mit.edu/dmytro/www/FinitismPaper.htm]
* "Finitism and intuitive knowledge", Charles Parsons [http://books.google.com/books?id=FKIRX9mHv5IC&pg=PA249&lpg=PA249&dq=PRA+finitism&source=bl&ots=6ImBw2yHWL&sig=oiiNkSPsLNEt9P6U0kIYl9gOiUw&hl=en&ei=Oi6XSon1GJag8QbVwaGwDA&sa=X&oi=book_result&ct=result&resnum=7]
Here is a quote from Simpson on the FOM email list in 1999 [http://cs.nyu.edu/pipermail/fom/1999-February/002565.html]:
:"Tait in his 1981 paper argued that Hilbert's finitism is formalized by PRA. This conclusion is widely accepted in the f.o.m. literature. I certainly accept it..."
There are many more references than this; the relationship between PRA and finitism has been thoroughly explored in the literature. — Carl <small>([[User:CBM|CBM]] · [[User talk:CBM|talk]])</small> 01:13, 28 August 2009 (UTC)
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