The Demise of Intelligent Design

At last?

Back in 2007, I predicted that the idea of “Intelligent Design” would soon fade into obscurity. I wrote:

My initial assessment of ID in my earliest encounter with an ID proponent* was that ID would be forgotten within five years, and that now looks to me an over-generous estimate.

*August, 2005

I was wrong. Whilst the interest in “Intelligent Design” (ID) as a fruitful line of scientific enquiry has declined from the heady days of 2005 (or perhaps was never really there) there remain diehard enthusiasts who maintain the claim that ID has merit and is simply being held back by the dark forces of scientism. William Dembski; the “high priest” of ID has largely withdrawn from the fray but his ideas have been promoted and developed by Robert Marks and Winston Ewert. In 2017 (with Dembski as a co-author) they published Introduction to Evolutionary Informatics, which was heralded as a new development in the ID blogosphere. However, the claim that this represents progress has been met with scepticism.

But the issue of whether ID was ever really scientific has remained as the major complaint of those who dismiss it. Even ID proponents have admitted this to be a problem. Paul Nelson, a prominent (among ID proponents) advocate of ID famously declared in 2004:

Easily the biggest challenge facing the ID community is to develop a full-fledged theory of biological design. We don’t have such a theory right now, and that’s a problem. Without a theory, it’s very hard to know where to direct your research focus. Right now, we’ve got a bag of powerful intuitions, and a handful of notions such as ‘irreducible complexity’ and ‘specified complexity’ – but, as yet, no general theory of biological design.

Whilst some ID proponents – Ann Gauger, Douglas Axe are perhaps most prominent among them – have tried to develop ID as science, the general scientific community and the wider world have remained unimpressed.

Then a new young vigorous player appears on the field. Step forward, Eric Holloway! Dr Holloway has produced a number of articles published at Mind Matters – a blog sponsored by the Discovery Institute (the paymasters of ID) on artificial and “natural” intelligence. He has also been quite active here and elsewhere defending ID and I have had to admire his persistence in arguing his case for ID, especially as the whole concept is, in my view, indefensible.

But! Do I see cracks appearing? I happened to glance at the blog site formerly run by William Dembski, Uncommon Descent, and noticed an exchange of comments on a thread entitled Once More from the Top on “Mechanism” The post author is Barry Arrington, current owner of UD and a lawyer by trade, usually too busy to produce a thoughtful or incisive piece (and this is no different). However, the comments get interesting when Dr Holloway joins in at comment 48. He writes:

If we can never be sure we account for all chance hypotheses, then how can we be sure we do not err when making the design inference? And even if absolute certainty is not our goal, but only probability, how can we be confident in the probability we derive?

Eric continues with a few more remarks that seem to raise concern among the remaining regulars. ( ” Geeze you are one confused little pup EricMH.” “Has a troll taken over Eric’s account?) and later comments:

But since then, ID has lost its way and become enamored of creationism vs evolution, apologetics and the culture wars, and lost the actual scientific aspect it originally had. So, ID has failed to follow through, and is riding on the cultural momentum of the original claims without making progress.

Dr Holloway continues to deliver home truths:

I would most like to be wrong, and believe that I am, but the ID movement, with one or two notable exceptions, has not generated much positive science. It seems to have turned into an anti-Darwin and culture war/apologetics movement. If that’s what the Discovery Institute wants to be, that is fine, but they should not promote themselves as providing a new scientific paradigm.

I invite those still following the fortunes of ID to read on, though I recommend scrolling past comments by ET and BA77. Has Dr Holloway had a road-to-Damascus moment? Is the jig finally up for ID? I report – you decide!

ETA link

824 thoughts on “The Demise of Intelligent Design

  1. OMagain:
    If you had a trillion dollars, what research program would you start to demonstrate the “infusion of information into DNA in the distant past by some mind via the mechanism of mind”?

    He would spend it on trying to prove that evolution is impossible. Never mind the recent expressions of good intentions to do positive science, that is all they have.

  2. OMagain: Where can you go with “mind is a mechanism”

    Not far with how colewd want to use the word “mechanism”. But if you use a more modern definition, then maybe pretty far.

    “We outline a framework of multilevel neurocognitive mechanisms that incorporates representation and computation”
    The Cognitive Sciences Revolution
    You do have to remember that we are talking about embodied minds, as KN posts (and which I also pointed out upthread). I don’t think unembodied minds exist, even though Genesis (the progressive rock group) did a great song about them “surviving on the ocean of being”.

    Watcher in the Skies

    My recent posts on mind and mechanism:

    The Demise of Intelligent Design

    The Demise of Intelligent Design

  3. Kantian Naturalist,

    But a cause that cannot be understood has effects that we do not know how to measure, which is to say that we cannot be justified in claiming that life was designed precisely because we cannot comprehend anything about what kind of being designed it.

    This is the argument that the materialists keep repeating that is inconsistence with science. If you want a simple thought experiment to show the flaw in this argument then try to empirically demonstrate that we cannot comprehend anything about what kind of being designed it.

  4. BruceS,

    Of course we know the details*.

    Let me clarify what I mean. General relativity is over 100 years old and we don’t know why atoms are creating this effect. That does not mean it has not been a theory it simply means the explanation is limited as all scientific explanations are. Today scientists are still trying to close the gap but there is no testable model yet at the atomic level.

    For science we need a mechanistic explanation to explain the cause of the effect we are observing. Details to follow perhaps 10,100, or 1000 years later.

  5. colewd:

    Let me clarify what I mean.General relativity is over 100 years old and we don’t know why atoms are creating this effect.

    For science we need a mechanistic explanation to explain the cause of the effect we are observing.Details to follow perhaps 10,100, or 1000 years later.

    It is mass/energy, not atoms. Remember the light-bending experiment in 1919 that was the first generally accepted confirmation of GR.

    No one in science s looking for the type of model of gravity and atoms you mention as I understand you, unless you mean a theory of quantum gravity, which would be better called a theory reconciling QFT and GR, not “atoms”.

    As I explained upthread, I think you are laboring under a false and outdated idea of mechanisms in science.

    As I read your posts, you are asking the same question Feynman answered about magnetism: why do magnetically opposite poles feel like they are pushing apart? Or for you: Why is mass/energy affected by gravity?

    We completely understand those issues scientifically (modulo quantum gravity). Maybe metaphysics could tell us something more “fundamental” than science, but that is debated by philosophers who specialize in these issues, some of whom deny there is any metaphysical explanation more fundamental than science.

    You are thinking, I suspect, that objects have some intrinsic properties separate from their causal* roles in scientific theories. That would be related to the philosophical position of “essences “as in Haecceeitism.

    The idea is that these hypothetical, non-scientific “essences” somehow explain what science tells us through its theories.

    But why believe that at all? It’s a metaphysical prejudice, not something that originates in science or that scientific theories address.

    ——————————
    * No, I have not forgotten about mass and charge, eg, which some may consider intrinsic essences, but which instead are best understood by their causal, {ETA] relational role in theories. But I am ignoring issues about causation in science, in particular physics.

  6. colewd: Today scientists are still trying to close the gap but there is no testable model yet at the atomic level.

    Materialistic thinking. And I had thought you were anti-materialism.

  7. BruceS,

    No one in science it looking for the type of model of gravity and atoms you mention as I understand you, unless you mean theory of quantum gravity, which would be better called a theory reconciling QFT and GR, not “atoms”.

    Here is a reference to the work going on in physics now. We start with mechanism and then peel the onion as far as we can.

    Emergent Gravity and the Dark Universe

    Erik P. Verlinde
    (Submitted on 7 Nov 2016 (v1), last revised 8 Nov 2016 (this version, v2))
    Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional `dark’ gravitational force describing the `elastic’ response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton’s constant and the Hubble acceleration scale a_0 =cH_0, and provide evidence for the fact that this additional `dark gravity~force’ explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

  8. I took a look at Eric’s “proof” that halting oracles are logically possible. It appears to be circular — that is, Eric inadvertently assumes his conclusion.

    More on this when I have access to a computer (I’m currently a victim of the power outages in California).

  9. keiths:

    More on this when I have access to a computer (I’m currently a victim of the power outages in California).

    Could you make this an OP?

  10. colewd:
    Neil Rickert,

    I am anti arbitrary shut down of ideas for ideological reasons.

    You are certainly anti-honesty when it comes to discussing anything regarding ID-Creationism or evolutionary biology.

  11. Neil Rickert,

    The whole point of ID is its attempt to shutdown evolution ideas for ideological reasons.

    Maybe the movement but not the argument. The argument is simply offering a mechanistic explanation for what we are observing in the cell. It can serve as a negative control to RMNS and neutral theory.

  12. colewd: The argument is simply offering a mechanistic explanation for what we are observing in the cell.

    That you call it “mechanistic” does not make it so.

    You would need to provide a mechanistic definition of “intelligence.”

  13. Neil Rickert,

    You would need to provide a mechanistic definition of “intelligence.”

    Is there such a thing as a mechanistic definition of mass? The comparable mechanism in this case is not intelligence but a mind.

  14. colewd: Is there such a thing as a mechanistic definition of mass?

    What’s your definition of mass?

    I already know. It’s god did it. Incorrect? How so?

  15. colewd: The argument is simply offering a mechanistic explanation for what we are observing in the cell.

    Except it does not. Where is this purported explanation?

    Unless you are seriously saying that “a mind did it” is an “explanation”?

  16. colewd: I am anti arbitrary shut down of ideas for ideological reasons.

    Everyone is free to write whatever they want. Good ideas spread. Bad ideas fester in tiny minds.

  17. colewd: Is there such a thing as a mechanistic definition of mass?

    Mass works quite well in mechanistic accounts.

    We can measure it. We can use it in logical arguments such as those involved in making predictions.

    We cannot do that with intelligence or with mind.

  18. colewd:
    Is there such a thing as a mechanistic definition of mass?

    Mass is not proposed as a mechanism. Mass has a direct effect in spacetime, at least in Einstein’s model. This happens because mass exists in space and time. We know this. It’s self-evident. Mass takes space, mass continues existing through time.

    colewd:
    The comparable mechanism in this case is not intelligence but a mind.

    It’s not comparable, and minds are not mechanisms the way you intend them to be. Again, minds are features of some life forms. You cannot propose “minds” as mechanisms, you have to propose the whole enchilada: the organisms that bear such minds, their tools, their fulfilled needs: energy, abilities, tools, culture, in order to attain what’s proposed of them, etc.

    Proposing “minds” as explanations for life’s features is like proposing “fingers” as explanations for life’s features. Like minds, fingers alone are not “mechanisms,” but one the features of certain organisms that help such organisms do something. Features that you’d be trying to “explain” with “fingers” as “The Mechanism.”

    Come on Bill. Stop it. You truly must be better than that.

  19. Corneel: After Tom’s and Neil’s remarks about dishonesty and deception, you still ask us to leave the terms ambiguous? No, that’s the wrong way around.
    If you feel methodological naturalism is a straightjacket, then we don’t need to “broaden the definition”, but you should just stop trying to work within it. And don´t ask others to call the items in your personal wishlist by any concealing terms. You should just stop insisting that we call the stuff you are doing science.

    Perhaps my terminology is sloppy, but I have no intent to be dishonest or deceptive. However, maybe they have a deeper insight into my character than I have. Dunno!

    You can call what I’m doing whatever you want. The semantic debates are irrelevant. The basic point is that we can empirically discriminate between stochastic and non-stochastic processes.

    I claim this is non-controversial, and haven’t seen anyone refute the idea in this thread, just quibbling over semantics, so perhaps we all agree in fact if not in word.

  20. Neil Rickert,

    We cannot do that with intelligence or with mind.

    We are demonstrating one of minds mechanisms as we communicate with each other.
    Your claim has no basis in fact.

  21. BruceS: What matters for resolving debates about acceptable scientific explanations for biological evolution is convincing biologists, which includes participating in the processes biologists use to challenge and justify explanations and claims.

    I’d say that what matters is what works. I’ve proposed an idea that seems like it might work. I’ve seen many people say the idea makes them unhappy. I’ve not seen anyone provide an explanation why the idea will not work. So, insofar as “what could work” = “scientific hypothesis” then it seems my work here is done. The thread has established (at least to my own satisfaction) there are no obvious reasons why the hypothesis cannot be tested. Just the usual semantic whinging that goes on when no one has a coherent refutation of the core idea and feel threatened. In other words, the usual ‘refutation’ of ID offered by the critics.

    BruceS: I’m not sure what you mean by logically possible. I take this as involving no contradiction. Since Turing defined and used them without being criticized for logical contradiction, I am not clear on what you were trying to add.

    Nothing much. The article I wrote is nothing special. The idea that halting oracles are logically possible was inconceivable for the PS crowd, and Swamidass misunderstood the original proof for the halting problem, so there is at least a contingent of fairly educated folk that don’t realize halting oracles are logically possible. This article is for them.

  22. BruceS: Scott A mentioned this possibility in the Bernay’s lectures I linked upthread. Such a device could in theory prove or disprove any math theorem (something like generate all possible text of any length and test until proof or disproof discovered). So it would be able to answer any outstanding open math question yes or no and even provide the text of a proof.

    But would human mathematicians accept it? Just saying read the text is not enough as this example shows:

    The proof no one understands

    So it will be interesting to see how you address the issues, if you have time and interest to do an OP.

    The response to this problem is the concept of a partial halting oracle. The space between Turing machines and perfect halting oracles is infinitely big, so there can be an infinite number of problems people cannot solve, and they can still be computationally more powerful than any Turing machine.

    Of course, this argument doesn’t prove that humans are partial halting oracles. It merely shows that the refutation doesn’t work. A refutation of the refutation, if you will.

    An article I wrote on the topic of partial halting oracles.
    https://www.am-nat.org/site/halting-oracles-as-intelligent-agents/

    Again, my idea is nothing special, just like proving the logical possibility of halting oracles. It is exceedingly obvious, in my opinion. However, for whatever reason, many people don’t understand, so I write the article.

  23. EricMH:
    Perhaps my terminology is sloppy, but I have no intent to be dishonest or deceptive. However, maybe they have a deeper insight into my character than I have.Dunno!

    Since your terminology and comnceptual frames are sloppy, your “approaches” lead to equivocation. For starters, you define stochastic as something that includes random, deterministic, and any combinations of them. That departs from common understanding of the word in academic and common terms. Not only that, you tend to present models and arguments that try and show that something is “not stochastic” but are actually about being not random. That’s equivocation, and that’s dishonest.

    EricMH:
    You can call what I’m doing whatever you want. The semantic debates are irrelevant.

    No, they’re not irrelevant, since your messy terminology and poor conceptual frames lead to equivocation. For another example, methodological naturalism neither claims, nor demands, that everything is stochastic. It’s called “methodological” for a reason. The word is meant to clarify limits to what science can work on, not to suggest that reality consists on only specific kinds of processes. Mistaking methodological naturalism for a full-fledged philosophical position about reality, and insisting on it after loads of clarifications, cannot be labeled as anything else but dishonesty. Sorry.

    EricMH:
    The basic point is that we can empirically discriminate between stochastic and non-stochastic processes.

    Whether this is true or not, says nothing about whether what you’re approaching/discovering is natural or supernatural. Whether that’s true or not, that says nothing about whether methodological naturalism is wrong or not as an approach to define science’s limitations, let alone about what reality consists on.

    EricMH:
    I claim this is non-controversial, and haven’t seen anyone refute the idea in this thread, just quibbling over semantics, so perhaps we all agree in fact if not in word.

    I claim that’s very controversial, and that it doesn’t need to be refuted, it has to be demonstrated. For that to occur, you need to be able to exclude the possibility that something is “random, deterministic, or any combinations of both.”

    Claiming that lack of convergence to a probability distribution proves non-stochasticity is but that, a claim. I wait until you prove your case without going into further and further assumptions about what stochastic means. Most importantly because you make a huge conceptual mess whereby stochastic ends meaning random in your processes, if not in your definitions (equivocation), and whereby you mistake our models/descriptions/concepts of phenomena for the phenomena themselves (reification).

  24. colewd:
    We are demonstrating one of minds mechanisms as we communicate with each other.
    Your claim has no basis in fact.

    So you’re really no better than that Bill.

  25. colewd: The argument is simply offering a mechanistic explanation for what we are observing in the cell.

    “A mind did it by MAGIC!” isn’t a mechanistic explanation.

  26. colewd: We are demonstrating one of minds mechanisms as we communicate with each other.

    Once again Bill dishonestly ignores the fact our communication also involves the physical interfaces of impulses physically moving finger muscles, physically pressing keyboard keys, physically encoding and transmitting electrical signals, having those signals be received and decoded and physically translated to symbols on a computer screen.

    So it wasn’t just “mind”, right Bill?

  27. EricMH:.The basic point is that we can empirically discriminate between stochastic and non-stochastic processes.

    I haven’t seen your demonstration that ‘non-stochastic processes’ in your sense of the term actually exist. You do realise that the concept of libertarian free will is hugely controversial, don’t you?

  28. EricMH: Perhaps my terminology is sloppy, but I have no intent to be dishonest or deceptive. However, maybe they have a deeper insight into my character than I have.

    Personally, I don’t believe that you are being dishonest or deceptive, but I can definitely see why others perceive your writings that way, ’cause look:

    Just the usual semantic whinging that goes on when no one has a coherent refutation of the core idea and feel threatened. In other words, the usual ‘refutation’ of ID offered by the critics.

    That’s not semantics, that’s propaganda. I think I saw Tom make a valid criticism that non-stationary random processes won’t converge either in any nontrivial sense, and haven’t seen you addressing it yet. In addition, you haven’t actually produced any calculations of tractable real-life systems. All of this would be far more convincing if you would make your hands dirty and demonstrate that “non-stochastic” processes exist before you declare your work a big success.

  29. EricMH: Again, my idea is nothing special, just like proving the logical possibility of halting oracles.

    I actually was wondering why you wrote this paper, since the logical possibility of halting oracles seems to be commonly accepted. The searching machine in your paper seems to be a version of an Accelerated Turing Machine (ATM), as discussed below.

    Just to be explicit: As best I can tell, most agree that halting oracles are logically possible. By logically possible, I mean in the sense defined at SEP: “logical possibilities are the most inclusive; they include any proposition that sheer logic leaves open, no matter how otherwise impossible it might be”.

    Accelerated Turing Machines are a standard example. They perform their first instruction in 1 time unit, the second in 1/2 unit, the third in 1/4, and so on, so instructions can be performed in 2 time units.

    As best I can tell, these machines are agreed to be able to calculate the halting function, as explained in the above linked SEP article.

    I came across this 2010 more detailed paper of which I have only read the abstract, which I understand as saying more precisely how ATMs can solve the halting problem.
    https://oronshagrir.huji.ac.il/sites/default/files/oronshagrir/files/do_accelerating_turing_machines_compute_the_uncomputable.pdf

    Logical possibility does not mean physical possibility and, as best I can tell, most agree that all proposed forms of physically implementing hypercomputation violate accepted physics.

    So I am more interested in your paper on empirically testing for halting oracles, since that would imply something violating known physics. I’m hoping for an OP on that which might also attract other commentators, especially Tom E.

  30. EricMH: It merely shows that the refutation doesn’t work.

    I am not sure which refutation you are referring to.

    Scott A’s comment was semi serious. His example was: suppose we came across some artefact which was claimed to be a halting oracle, ie it answered “yes” or “no” when asked whether any specific TM would halt and this answer was claimed to be reliable.

    Why should be believe its answer was reliable? I think we’d want, at a minimum, some explanation of how it worked, and if it required something beyond known physics, some justification for that extension.

    Although Scott did not do this, I think you can substitute human minds for that unknown artefact.

  31. Bruce, to Eric:

    The searching machine in your paper seems to be a version of an Accelerated Turing Machine (ATM), as discussed below.

    Actually, it doesn’t need to be an ATM.

    The list of Turing machines is infinite, but it will only ever take a finite amount of time to locate a particular machine in that list.

  32. Bruce:

    Accelerated Turing Machines are a standard example. They perform their first instruction in 1 time unit, the second in 1/2 unit, the third in 1/4, and so on, so [infinitely many] instructions can be performed in 2 time units.

    As best I can tell, these machines are agreed to be able to calculate the halting function, as explained in the above linked SEP article.

    There’s something fishy about the ATM solution to the halting problem. Ask yourself the following question:

    At time 2.1, is the ATM still running?

    If the ATM has halted, the answer will obviously be no. But what about the non-halting case? If the machine never halted, it must be still running. But if it’s still running, then we don’t know whether it will halt in the future, and 2 units was not long enough to find out. There seems to be a contradiction: 2 units is long enough, and 2 units isn’t long enough.

    I can see a couple of potential solutions, but neither is very satisfying.

  33. EricMH:

    The basic point is that we can empirically discriminate between stochastic and non-stochastic processes.

    If you can do that, then why aren’t you doing so?

    Why haven’t you been able to give us a single example of a non-deterministic, non-random process?

  34. BruceS: I actually was wondering why you wrote this paper, since the logical possibility of halting oracles seems to be commonly accepted.

    Entirely due to the conversation over at PS where Swamidass ‘proved’ halting oracles are not logically possible due to a butchered version of the halting argument. He apparently is unaware of Turing original diagonalization argument, of which my article is a variant.

  35. Entropy: Claiming that lack of convergence to a probability distribution proves non-stochasticity is but that, a claim.

    That’s due to the law of large numbers.

  36. faded_Glory: I haven’t seen your demonstration that ‘non-stochastic processes’ in your sense of the term actually exist.

    That’s the whole issue. I am not claiming they do exist. I am claiming that we can test whether they exist or not, at least in a probabilistic sense and appealing to Occam’s razor as I explain in the Mind Matters article.

  37. keiths: If you can do that, then why aren’t you doing so?

    Why haven’t you been able to give us a single example of a non-deterministic, non-random process?

    A slightly different topic, but one I will work on.

    The context of this discussion is the thread at ID where I pointed out the lack of a positive model for intelligence. Alan Fox asked me what I thought a positive model could be, and I said ‘non stochastic process’. Then we had this whole discussion whether such a concept even makes sense. It seems it is at least logically coherent and empirically testable, so that resolves the original point of discussion.

  38. EricMH: That’s the whole issue.I am not claiming they do exist.I am claiming that we can test whether they exist or not, at least in a probabilistic sense and appealing to Occam’s razor as I explain in the Mind Matters article.

    You seem to claim a whole bunch of things you can’t begin to support. Probably why ID-Creationism is so appealing to you with its “evidence not required” policy.

  39. EricMH: That’s the whole issue.I am not claiming they do exist.I am claiming that we can test whether they exist or not, at least in a probabilistic sense and appealing to Occam’s razor as I explain in the Mind Matters article.

    What an odd response. If we can test whether such things exist, why don’t you actually perform the test before using the concept?

  40. EricMH: That’s due to the law of large numbers.

    That’s about means for independent identically distributed variables. How would it apply to measuring some set of variables to a system that was not at thermal equilibrium?

  41. keiths: If the ATM has halted, the answer will obviously be no. But what about the non-halting case

    If I understand you correctly, that’s a subtlety that is discussed in the 2010 paper I linked upthread. They distinguish Accelerated Turing Machines from Accelerated Non-Turing Machines.

    In the more precise definition provided there, the Accelerated Turing Machine indicates whether or not the TM being tested halts with given input by writing 0 or 1 on a designated square. They are clear that they are leaving the final state of the ATM undefined.

    They call a machine where the final state is also specified an Accelerated Non-Turing Machine. They then cite other authors who do include specification of the end state for defining an accelerated machine, so I think those might also be logically possible. But the ATM as defined by the linked paper is sufficient to show how a halting oracle is logically possible.

    Thanks for doing an OP on Eric’s paper. We should probably move this discussion over to the other thread.

  42. keiths:
    Bruce, to Eric:

    Actually, it doesn’t need to be an ATM.

    The list of Turing machines is infinite, but it will only ever take a finite amount of time to locate a particular machine in that list.

    You are right. I did not read that paper closely enough. The issue is populating the table.

    An ATM can determine whether TM n halts with input m. But a full version of Eric’s table would indicate that for all pairs (n,m), which is of course still countable.

    I think one might be able to populate that countable table of whether TM n halts with input m using an ATM, but I am not sure. See the other thread where I ask this question with reference to the Wiki article on halting oracles and their limitations. Please answer question there.

  43. EricMH: Entirely due to the conversation over at PS where Swamidass ‘proved’ halting oracles are not logically possible due to a butchered version of the halting argument.

    By coincidence, an offshoot of that thread just got automatically bumped. Here is JS’s post.
    https://discourse.peacefulscience.org/t/is-god-a-halting-oracle/1836/9
    From my point of view, he is confused about the relevance of the proof that no TM can solve the halting problem, since the issue is whether it is logically possible for some halting oracle to exist. But all the proof that he gives indicates is that such a halting oracle could not be TM as a TM is usually understood.

  44. Bruce,

    They are clear that they are leaving the final state of the ATM undefined.

    That seems like a cheat to me. “Running” and “halted” are mutually exclusive and exhaustive. “Halted” is only reached if the program halts. If the program doesn’t halt, then “running” is the only remaining possibility, and that leads to the apparent contradiction I described above.

  45. keiths: If the program doesn’t halt, then “running” is the only remaining possibility,

    Seems to me you can only ever know half the story, when a program halts. But I wonder what relevance this logical problem has to evolution, biology or reality.

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