In a Computational Theory of Mind, how do we identify what is being computed and/or what algorithm is being executed?

In general, a process can be viewed at different levels of abstraction. So, for instance, with a modern computer, we can either focus on or abstract away the programming language and hardware, and our interpretation of what the algorithm is that is being computed changes depending on which viewpoint we adopt.

Similarly, Putnam argued that we could view a rock as implementing every finite-state automata (and Chalmers has a response, which I haven't finished reading: http://consc.net/papers/rock.html).

((Finally, I'll mention that I was inspired to ask this by this interesting discussion between Massimo Pigliucci and Eliezer Yudkowski: http://bloggingheads.tv/videos/2561, where in Eliezer seems to find it obvious that an "uploaded" copy of yourself would have the same consciousness, regardless of the details of the implementation, and Massimo challenges him on that point.))

EDIT: I ran across another interesting reference for this problem, here: http://www.biointelligence-explosion.com/parable.html (grep "chauvinism")

  • Welcome to Phil.SE! The short answer is we don't; it's the notion that it's modelled by a Turing machine that is of consequence there. Sep 12, 2015 at 20:21
  • @MoziburUllah, what is the meaning of "it's the notion that it's modelled by a Turing machine that is of consequence there"?
    – nir
    Sep 12, 2015 at 20:22
  • @user2429920, I think that in computation, what is being computed is a numerical function, not an algorithm; can you clarify your question?
    – nir
    Sep 12, 2015 at 20:24
  • @nir: it's one way of theoretically modelling computation. Sep 12, 2015 at 20:29
  • @MoziburUllah, I know of Turing machines, I just don't understand the meaning of the comment.
    – nir
    Sep 12, 2015 at 20:36

2 Answers 2


You (originally) asked how we identify the algorithm, and I would like to suggest that the focus of functionalism in general, and computational theory of mind (CTM) in particular, are functions, not algorithms; here is an excerpt from the SEP essay on Functionalism:

Functionalism in the philosophy of mind is the doctrine that what makes something a mental state of a particular type does not depend on its internal constitution, but rather on the way it functions, or the role it plays, in the system of which it is a part.

Now, I would like to go over some definitions corresponding to computation; here is how Peter Smith defines the Church-Turing thesis in his book An Introduction to Godel's Theorems, (p. 315):

The Church–Turing Thesis: The effectively computable total numerical functions are the μ-recursive/Turing-computable functions.

and the class of effectively computable functions (p. 15) (note that effectively does not mean efficiently):

A one-place total function f : Δ → Γ is effectively computable iff there is an algorithm which can be used to calculate, in a finite number of steps, the value of the function for any given input from the domain Δ.

and finally, his definition for an algorithm (p. 14):

An algorithm is a set of step-by-step instructions (instructions which are pinned down in advance of their execution), with each small step clearly specified in every detail (leaving no room for doubt as to what does and what doesn’t count as executing the step, and leaving no room for chance). The idea, then, is that executing an algorithm (i) involves an entirely determinate sequence of discrete step-by-small-step procedures (where each small step is readily executable by a very limited calculating agent or machine). (ii) There isn’t any room left for the exercise of imagination or intuition or fallible human judgement. Further, in order to execute the algorithm, (iii) we don’t have to resort to outside ‘oracles’ (i.e. independent sources of information), and (iv) we don’t have to resort to random methods (coin tosses).

So, the main point of an algorithm is that it is can be specified in terms of steps that are small enough or so called mechanical; sometimes an algorithm is specified in very abstract terms (for example pseudo code in CS books) but under the assumption that in principle each abstract step can be specified in small enough steps if we bother to fill in the gaps.

therefore, and in response to your question about hardware vs. software level of abstractions, I think it doesn't really matter what is going on at these levels, as long as we understand that in principle, there is a level in there that satisfied the criterion for an algorithm. for example, a high level language, may be too abstract to count as a specification of an algorithm in the above sense, and the hardware level may also fail to satisfy our requirement since it relies on occult quantum mechanical phenomena, but the level of machine language, somewhere in between, is probably good enough.

Now, back to functions: it seems that functionalists believe that the mind can be explained in terms of functions and that according to CTM, these functions are effectively computable.

For example, In Absent Qualia, Fading Qualia, Dancing Qualia, Chalmers advocates a principle he calls the principle of organizational invariance, which involves such concepts as the functional organization of the brain and functional isomorphs; he acknowledges your concern that a system may be analyzed at different levels of organization and writes that:

any system that has the same functional organization at a fine enough grain will have qualitatively identical conscious experiences.

and by fine enough he means:

fine enough to determine the behavioral capacities and dispositions of a cognitive system.

Shameless plug: I raise some objections to his arguments in http://philpapers.org/archive/AIDYAO.pdf - comments would be appreciated.

Note that the particular algorithms to compute these functions are practically irrelevant.

As for Yudkowski's belief in mind uploading, that belief is quite common among functionalists. A lot of people, including Chalmers, Marvin Minsky, and Google's Ray Kurzweil, believe that.

  • "Note that the particular algorithms to compute these functions are practically irrelevant." - So I didn't read the essay, just glanced at it and searched some words, but it doesn't look like he defines "behavioural dispositions" rigorously enough to me. Anyways, my response to this statement of yours would be: the algorithms are relevant, since at (what I would consider) a sufficiently fine-grained level, the behaviour is different, depending on the algorithm. What I mean is just that what functions are being computed, at a low level, differs across algorithms. Sep 13, 2015 at 22:12
  • @user2429920, naturally, different algorithms may compute different functions, but just as well, the same function may be computed by different algorithms; think of the great variety of different sorting algorithms that compute the same function.
    – nir
    Sep 14, 2015 at 11:09
  • @user2429920, if chalmers is right and neurons are fine enough for cognition, then if you can effectively compute their function (represented numerically), then according to chalmers, it would not matter how you compute it. and since a neuron is made of 10E15 atoms, its complexity implies that there could be an incredibly huge number of different ways to compute it, which make no difference what so ever for cognition.
    – nir
    Sep 14, 2015 at 11:10
  • Yes, clearly. My point is that the statement that it "computes the same function" depends on a certain interpretation of some more fine-grained physical events. My question would then be: how is this interpretation chosen? I fail to see how Chalmers' answer is not arbitrary. Sep 14, 2015 at 23:25
  • @user2429920, there is a long standing debate on the meaning of computation; e.g. whether computation is observer relative (Searle) on the one hand, or not, since when it is physically implemented it has causal relations with the environment (Dennett), and so on; that said, I have no idea what you possibly mean by: "the statement that it 'computes the same function' depends on a certain interpretation of some more fine-grained physical events".
    – nir
    Sep 15, 2015 at 11:59

I am going to interpret your question in broader terms, as an phenomenological argument about the observability of a computational machine's behavior/functioning, insofar as cognitive abilities can be identified and attributed to it.

As you can imagine (and I think you have) this discussion is extremely rich and vast, and I do not expect to be able to go much beyond the surface here, but I think that some methodological pointers can be proposed in this short format, that may be useful for future reference.

First of all, let's assume that the problem of identification, in that specific scenario, assumes that there are at least three instances at play (I'm being overly schematic here, but bear with me, it's just an exercise):

  1. The substance of the computational machine;
  2. The computational machine's hardware, its organization;
  3. The computation that it is running, its "performance", which is what is (or is not) amenable to identification.

The thing is, one doesn't need to assume that these are different levels of abstraction, that are intrinsic to the thing being observed. As it happens, my nervous system is a computational machine, but in the same right it can be identified as a biological machine, a chemical machine, or a physical machine (in the specific sense of being describable using only concepts from the physical science). These different levels of observation belong to the mind that does the observation, not to the thing.

Now, the crucial observation, one that Brian Cantwell Smith makes here, is that because there are machines that do computational things - possibly quite intelligent ones - the fact that these machines were created by humans does not entail that the final cause of those artifacts is known to those humans, or even controlled by them in any objective way.

That's why you can say, quite confidently, that identification involves at least a choice of perspective. It is thus, at least primarily, in the eye of the beholder.

  • interesting video
    – nir
    Sep 14, 2015 at 19:28
  • "That's why you can say, quite confidently, that identification involves at least a choice of perspective." - I don't see where this confidence is coming from. Sep 14, 2015 at 23:32
  • It comes from the argument that precedes this sentence. Maybe you could identify which part (or parts) of it you don't accept. Sep 14, 2015 at 23:47
  • I don't accept the implication; you'd have to spell it out for me. I suspect we might mean different things by "identification", and that you are coming at this from a more relativist point of view (or arguing for relativism WRT "identification"), whereas I'm interested in finding a "natural kind" level of analysis which would allow us to objectively identify something I'd call "the algorithm being run" by a given physical system (but that's just a name; I care about the concept, not what it's called). Sep 6, 2019 at 18:14

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