  The thesis that finitism coincides with primitive recursive reasoning has received a forceful defense by (Tait 1981; see also 2002 and 2005b). Tait, in contrast to Parsons, rejects the aspect of representability in intuition as the hallmark of the finitary; instead he takes finitary reasoning to be “a minimal kind of reasoning presupposed by all non-trivial mathematical reasoning about numbers.” and analyzes finitary operations and methods of proof as those that are implicit in the very notion of number as the form of a finite sequence. This analysis of finitism is supported by Hilbert’s contention that finitary reasoning is a precondition for logical and mathematical, indeed any scientific thinking  Hilbert (1931b, 267).  Since finitary reasoning is that part of mathematics which is presupposed by all non-trivial reasoning about numbers, it is, so Tait, “indubitable” in a Cartesian sense, and this indubitability as all that would be required of finitary reasoning to provide the epistemological grounding of mathematics Hilbert intended it for.