calculability

But to hear her argument, a new level of cold calculability is seen.

Calculability is a consequence of this conformity to law.

Rules and regulations that make efficiency, calculability, and predictability possible.

Thus, a deconstructive reading of the law is a leap from calculability towards incalculability.

And to our mind such is Church's identification of effective calculability with recursivness."

Next, it was necessary to identify and prove the equivalence of two notions of effective calculability.

Post and "effective calculability" as "natural law"

In Church (1936) we see, under the chapter 7 The notion of effective calculability, a footnote 18 which states the following:

The corresponding question of the relationship between effective calculability and λ-definability had previously been proposed by the author independently."

This quest required that the notion of "algorithm" or "effective calculability" be pinned down, at least well enough for the quest to begin.

The character of calculability is imposed upon agents as they come to work in markets and are "formatted" as calculative agencies.

Another definition of effective calculability has been given by Church ... who identifies it with λ-definability.

The Heisenberg Principle clearly demonstrates the calculability of the uncertainties to which you so glibly allude.

The development ... leads to ... an identification of computability with effective calculability."

And Post had only proposed a definition of calculability and criticized Church's "definition", but had proved nothing.

The proposal to identify these notions with the intuitive notion of effective calculability is first made in the present paper (but see the first footnote to 7 below).

Calculability - objective should be quantifiable (e.g., sales) rather than subjective (e.g., taste).

Although he doesn't call it his "thesis", Turing proposes a proof that his "computability" is equivalent to Church's "effective calculability":

Calculability - goals are quantifiable (i.e., sales, money) rather than subjective (i.e., taste, labour).

(His use of the word "decision" and "predicate" extends the notion of calculability to the more general manipulation of symbols such as occurs in mathematical "proofs".)

See in particular page 100 (The Undecidable) where he defines the notion of "effective calculability" in terms of "an algorithm", and he uses the word "terminates", etc.

Rather, in correspondence with Church (ca 1934-5), Gödel proposed axiomatizing the notion of "effective calculability"; indeed, in a 1935 letter to Kleene, Church reported that:

Rather, he regarded the notion of "effective calculability" as merely a "working hypothesis" that might lead by inductive reasoning to a "natural law" rather than by "a definition or an axiom".

"The question of the relationship between effective calculability and recursiveness (which it is here proposed to answer by identifying the two notions) was raised by Gödel in conversation with the author.

His footnote 18 says that he discussed the relationship of "effective calculatibility" and "recursiveness" with Gödel but that he independently questioned "effectively calculability" and "λ-definability":