Yes. Absolutely. Philosophers wrestle over these sorts of phrases to tackle the metaphysics of computation endlessly.
Since 1936, the notion of Turing machines and effectively computable (and several similar phrases used by Hilbert, Goedel, Kleene, Post, and others) has been the object of much thought and discussion. Ultimately, the topic is foundational for philosophies that address logico-mathematical computation. The discussion has also been broadened philosophically beyond logical and mathematical computation to physical computation, which is viewed as a broader exploration of the relationship of computation within physicalism.
A good place to start to understand physical computation is Computation in Physical Systems (SEP). From the article referring to the Church-Turing Thesis (CTT):
Bold Physical CTT can be made more precise in a number of ways. Here is a representative sample, followed by references to where they are discussed:
- Any physical process can be simulated by some TM (e.g., Deutsch 1985, Wolfram 1985, Pitowsky 2002).
- If a physical system can be modeled by a certain kind of idealized computing machine that manipulates real-valued quantities, then that physical system can only compute Turing-computable functions on denumerable domains (Blum et al. 1989 show this to be false).
- Any system of equations describing a physical system gives rise to computable solutions (cf. Earman 1986, Pour-El 1999). A solution is said to be computable just in case, given computable real numbers as initial conditions, it returns computable real numbers as values (where, following Turing, a real number is said to be computable just in case there is a TM whose output produces any desired number of digits of that number).
- For any physical system S and observable W, there is a Turing-computable function f: N → N such that for all times t ∈ N, f(t) = W(t) (Pitowsky 1990).
Remember, the a-machine (Turing machine) is an abstract model originally based on the notion of personal (that is human) computation with the aid of a pencil and paper, and embraces human intuition to an extent, at least by an escape from it. And the Church-Turing Thesis was coined a thesis precisely because it rests on ambiguous or pre-theoretic ideas and definitions. That gives philosophers a lot of wiggle room to evaluate the Turing machine and effective computability.
Ultimately, there are thinkers such as Chalmers, Cummins, and others who seek to put forth definitions of physical computation that surround the Turing machine theoretically, and extend an understanding. One such work is Oron Shagrir's The Nature of Physical Computation in which he puts forth a view of physical computation that is termed a semantic view. On page 26, he begins a chapter entitled "Turing's Computability" that dissects the history and theory.