There is an argument for the finitude of the past that proceeds from the premise that it is impossible to traverse an infinite past (I refer to variants of this argument as the ITIPA). The ITIPA claims, in essence, that it follows from this premise that A-theories of time entails that the past is finite. The most prominent recent advocate of this line of thought is William Lane Craig.
My paper is a critical analysis of Craig's most recent defense of the ITIPA, which he wrote with James Sinclair. It is my contention that Craig and Sinclair's argument fails, unless one is willing to accept further premises to the effect that a strong principle of sufficient reason is correct, and attendant premises without which strong principles of sufficient reason are false. In other words, the success of Craig and Sinclair's argument depends upon the acceptance of several controversial metaphysical premises, aside from the already controversial A-theory of time. It has not been shown that A-theories of time by themselves entail that the past is finite.