I made a major rewrite of this post, in that I defined what Church and Turing were likely talking about, and importantly defined what the effective methods could do and what constraints were placed on them, or alternatively what the algorithm must do, and what constraints on the algorithms must follow.
Critically, while algorithm running times and memory/space are always finite, they are not bounded in the time or memory/space.
Also, it is universally quantified, as it includes something close to a for-all condition, rather than existentially quantified.
I made a major rewrite of this post, in that I defined what Church and Turing were likely talking about, and importantly defined what the effective methods could do and what constraints were placed on them, or alternatively what the algorithm must do, and what constraints on the algorithms must follow.
Critically, while algorithm running times and memory/space are always finite, they are not bounded in the time or memory/space.
Also, it is universally quantified, as it includes something close to a for-all condition, rather than existentially quantified.