[FOM] Finitist concept of consistency?

[Stephen Pollard]

Thanks to Prof. Tait for a prompt and thoughtful reply to my earlier  
post. I could still use some help; mainly because I expressed myself  
in such a roundabout way.

Suppose I prove in PRA that no natural number codes an S-proof of  
absurdity. (S is some formal theory.) A finitist can use my proof as  
a recipe for a construction that finitistically justifies the scheme

1. fX=0

where, as we would say, f is a primitive recursive characteristic  
function that tells us whether a natural number codes an S-proof of  
absurdity. ("0" means "no" here, let's say.) Suppose, now, our  
finitist colleague paraphrases scheme 1 as

2. S is consistent.

As I understand the history, Oskar Becker resisted this paraphrase  
because, as he insisted, finitists are not in a position to assert  
that S is consistent. They can declaim sentence 2 all they want, but,  
if they remain finitists, what they assert thereby will not be the  
consistency of S.

Becker's position seems correct to me. Do any FOM'ers disagree?

Stephen Pollard
Professor of Philosophy
Division of Social Science
Truman State University
spollard at truman.edu