Intelligence and Halting Oracles

This was the basis of my discussion about artificial vs. natural selection… From the perspective of the organism, humans are just another part of the environment.

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Intelligence is a halting oracle, and thus cannot be reduced to chance and necessity. No physical process can solve the halting problem, so physical processes are limited by Turing machines. Consequently, intelligence transcends the physical world.

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7 posts were split to a new topic: Play on Halting Oracles

There is zero evidence that Intelligence is a halting oracle. Rather, omniscience is a halting oracle.

By definition, if intelligence can create CSI from scratch, as ID claims, then it must be a halting oracle. As long as “intelligence” is Turing reducible, it cannot create CSI. It can only pass on the same amount or reduce it, per Levin’s proof.

There is zero evidence that intelligence can create CSI from scratch by the definition of MI used by Levin. Precisely zero evidence. There is zero evidence that intelligence is a halting oracle.

Moreover, we cannot even measure MI in the definition used by Levin, so it is not even clear how we could design an experiment to test it.

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Yes, I’m just arguing by definition here. I define intelligence as that which can create CSI from scratch per Levin. Therefore, intelligence is a halting oracle.

This is your most interesting claim. What is your proof/evidence this is true? Your claim does not follow from the incalculability of Kolmogorov complexity. Something more is needed.

  1. Kolmogorov complexity is not computable.

  2. We cannot measure Levin’s MI.

What goes in the blank?

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Okay. That is a strange switch. What evidence do you have that humans have any “INTELLIGENCE” as you define it here? Other than using the same utterance, is there anything to it?

Sure, I can complete the proof. But first, if I can, what would that mean to you? Would that mean ID is done for?

Somehow we programmers write a whole lot of code that reliably halts. And we cannot write programs to do the same. That’s pretty surprising if we are not halting oracles.

I would never claim that “intelligence” is Turing reducible. Likewise, I would never claim that intelligence is a halting oracle. To me, both seem absurd.

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This is not surprising at all, because (1) human intelligence is only an unreliable guide and often fails, and (2) computer programs are designed to guard against this, even though they fail. Humans are only imperfect oracles, which is to say they are not halting oracles. Even software can be an imperfect halting oracle, which is to say it cannot be an oracle.

Halting Oracles are different. By definition, they are required to be 100% accurate ALL the time for ALL possible inputs. Thy must also terminate in a finite amount of time, so they cannot be infinite runtime. Positing the existence of non-infinite/non-omniscient Halting Oracle leads to a logical contradiction. Such contradiction arises even if humans are said oracle.

In a finite amount of time, Halting Oracles require a view of a true infinity of time, which is to say they require omniscience. Such a thing does not exist in our world but might apply to God. Whatever human intelligence is, it is not a halting oracle.

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@EricMH

Joshua is not an atheist. God brings information wherever it is needed.

But there is no evidence to show God’s operation can be detected.

So the Halting Oracle is a really good example to study further. It is proven that they do not exist in a proof by contradiction (https://en.wikipedia.org/wiki/Proof_by_contradiction).

The Problem

Does a program exist that can examine the code of any other program to determine if it halts?

The Proof

This is adapted from here: https://en.wikipedia.org/wiki/Halting_problem#Proof_concept

Suppose that there exists a total computable function halts(f) that returns true if the subroutine f halts (when run with no inputs) and returns false otherwise.

Now consider this program.

def g():
    if halts(g):
       loop_forever()

Now ask, does halts(g) return true or false? Either way we get a contradiction.

  1. If halts(g) returns True, then g() will execute loop_forever(), and will therefore not halt, resulting in a contradiction, because halts(g) should have returned False.

  2. If halts(g) returns False, then g() will halt, resulting in a contradiction, because halts(g) should have returned True.

Therefore we know that a Halting Oracle is not logically possible.

Intelligence is Not a Halting Oracle

@EricMH, I thought I’d give you an example of some code that demonstrates that humans are not halting oracles. This is describe here:

For example, the Boolean satisfiability problem can be reduced to the halting problem by transforming it to the description of a Turing machine that tries all truth value assignments and when it finds one that satisfies the formula it halts and otherwise it goes into an infinite loop.
https://en.wikipedia.org/wiki/NP-hardness

The satisfiability problem is defined here: https://en.wikipedia.org/wiki/NP-hardness
https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#Unrestricted_satisfiability_(SAT)

So it is fairly easy to construct a question that in principle no amount of human intelligence can solve. I’ll just ask a human, does this algorithm halt?

def f():
  if is_satisfiable(VERY_LARGE_SAT_PROBLEM):
    loop_forever()

It is easy to construct a hard SAT problem that cannot be solved by human intelligence. Therefore we are demonstrating that humans are not halting oracles.

The Proof Against ID

Let’s look at your claim.

You claim:

  1. CSI can only be created by intelligence.
  2. Therefore, according to your application of Levin, intelligence is a halting oracle.

That is the starting point you claim. We can add to this.

  1. Halting oracles are a logical impossibility (see above).
  2. That means the “intelligence” that creates CSI is a logical impossibility.
  3. Therefore, either claim #1 is false, or CSI is a logical impossibility.
  4. If claim #1 is false, there other sources of CSI than intelligence, then CSI is not a unique signature for intelligence.
  5. If CSI is a logical impossibly, then CSI does not exist.

Either #6 or #7 mean that ID is false.

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That just proves no Turing machine can be a halting oracle. To further conclude halting oracles are logically impossible requires the Total Turing Premise (TTP)::

Turing machines exhaust the set of all possible processes.

I don’t know the TTP has been proven. But if it has, then your argument holds and I’d concede ID is false.

Prima facie, TTP seems false because MI exists.

No that is not the case. No Turing machine was used in that proof. It is merely a logical proof based on “computability” and “complete”. If you want to say computability implies a Turing machine, fine. The key thing is that the only way around this is omniscience. This reduces down to “does God exist or not”, and demonstrates that human intelligence is not at all comparable to divine intelligence.

Now that I’ve shown this doesn’t depend on TTP, do you concede ID is false?

I tried Googling “Total Turing Premise” and found nothing. Has any work been done on this before?

In any case, even if what you said here is true, it seems to me that the burden of proof is on ID advocates to show that human intelligence can actually produce non-Turing processes, such that they can be halting oracles. Am I right?

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I haven’t heard of it before, but he defines it:

Which seems to be restating a claim that he has made before that determinism + randomness can’t increase mutual information. So it appears that he was certain of TTP until he thought it undermined ID. However, halting oracles lead to a logical contradiction. Intelligence is not a halting oracle.

There is no evidence that MI (as defined as a unique product of a mind) exists.

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Yes, that’s how it is defined.