What is a finitary proof?

logic terminology

I wonder if Schoenfield has the Hilbert-Bernays metamathematical finitism program in mind. If so, the "finitary" bit is meant at the syntactic level (formalisation of proofs), whereas the semantic content could be anything, including classical (nonconstructive) mathematics.


I 'm reading this book and i don't understand this statement but i found this in wiki Finitary

A finitary argument is one which can be translated into a finite set of symbolic propositions starting from a finite1 set of axioms. In other words, it is a proof (including all assumptions) that can be written on a large enough sheet of paper.

And i think this what kreisel meant by : a proof is finitary if we can visualize the proof

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