In cases where we can uniformly compute the values of a function (or decide a problem) for the class of instances we are concerned with in practice, this is typically because a polynomial time algorithm has been discovered that can be implemented on current computing hardware and hence also as a Turing machine.
A formal computational model defined to study the notion of computation, containing elementary arithmetic and capable of expressing universality, negation, and self-reference
algorithm(Philosophy of computation and information)
A fundamental concept in information and computation theory, accepted as a primitive notion alongside data set
compute(Hobbes, De Corpore, 1.2)
to collect the sum of many things added together at the same time, or to know the remainder when one thing has been taken from another
It is also possible to make a case for CET which parallels the quasi-inductive argument for CT. For in cases where we can compute the values of a function (or decide a problem) uniformly for the class of instances we are concerned with in practice, this is typically so precisely because we have discovered a polynomial time algorithm which can be implemented on current computing hardware (and hence also as a Turing machine). And in instances where we are currently unable to uniformly compute the