Zombie brain in a bottle

[Robin]

Zombie brain in a bottle

Chalmers' three dimensional "Zombie" argument depends in part upon the idea that the primary intension of a physical fact is the same as it's secondary intension, or else "Russellian Monism" (see glossary below) is true.

That is to say that, for example, the reference to "mass" in an epistemically possible scenario maps identically to "mass" in the metaphysically possible world of the scenario. (A "scenario" is a specific sort of construction that involves a triplet of an epistemically possible word, an individual in that world and a time in that world.).

This seems to ignore "brain-in-a-bottle" type of scenarios. If we set the individual at the centre of the scenario as a brain in a bottle then we have a case where the epistemic properties of physical things can be quite distinct from the metaphysical properties of physical things without involving you in having to set special conditions on the definition of Materialism.

A defender of the argument might reply that we simply stipulate that the individual at the centre of the scenario is not a brain in a bottle, but that cannot be done within Chalmer's definition of a primary intension, since there is no epistemic fact that can necessitate that the individual is not a brain in a bottle.

So the primary intension of "P" is not identical to the secondary intension of "P" and therefore step 3 of his argument is invalid.

The full 2D argument I am referencing is: http://consc.net/papers/2dargument.html and the relevant definitions and discussions of two dimensional semantics here: http://consc.net/papers/twodim.html

Below is the particular version of the argument I am referencing:

(1) P&~Q is conceivable
(2) If P&~Q is conceivable, then P&~Q is 1-possible
(3) If P&~Q is 1-possible, then P&~Q is 2-possible or Russellian monism is true.
(4) If P&~Q is 2-possible, materialism is false.
(5) Materialism is false or Russellian monism is true.


I have picked out the relevant definitions here:
Glossary:

ExtensionIn possible-world semantics, linguistic expressions and/or their utterances are first associated with an extension. The extension of a sentence is its truth-value: for example, the extension of 'Plato was a philosopher' is true. The extension of a singular term is its referent: for example, the extension of 'Don Bradman' is Bradman. The extension of a general term is the class of individuals that fall under the term: for example, the extension of 'cat' is the class of cats. Other expressions work similarly.

IntensionOne can then associate expressions with an intension, which is a function from possible worlds to extensions. The intension of a sentence is a function that is true at a possible world if and only if the sentence is true there: the intension of 'Plato was a philosopher' is true at all worlds where Plato was a philosopher. The intension of a singular term maps a possible world to the referent of a term in that possible world: the intension of 'Don Bradman' picks out whoever is Bradman in a world. The intension of a general term maps a possible world to the class of individuals that fall under the term in that world: the intension of 'cat' maps a possible world to the class of cats in that world.

Primary intension: the primary intension of S is true at a scenario W iff D epistemically necessitates S, where D is a canonical description of W

Scenario: Scenarios are highly specific epistemic possibilities. On the centered-worlds version of epistemic two-dimensionalism, scenarios are identified with centered worlds.

Canonical descriptionFor a given thinker, the hypothesis that a given centered world W is actual can be seen as the hypothesis: 'D is the case, I am F, and the current time is G', where D is a complete qualitative characterization of W, and F and G are qualitative descriptions that pick out the individual and the time at the center of W. We can think of this conjunctive claim as a canonical description of the centered world in question

Russellian MonismOn this view, consciousness is closely tied to the intrinsic properties that serve as the categorical bases of microphysical dispositions (- don't ask, I don't understand it either and I am not sure that it relates to anything Bertie actually said - Robin.)

[PixyMisa]

The first premise is only true if you assume materialism is false. The argument is circular.

A big helping of epic fail from Chalmers yet again.

[PixyMisa]

Here's where he falls down a rabbit hole, never to return:

In response, I think it is clear that when we conceive of zombies we conceive of the absence of consciousness. There is no more problem with clearly and distinctly imagining a situation in which there is no consciousness than in imagining a world in which there are no angels, or in imagining a world with one particle and nothing else.
This is complete baloney.

Consciousness is, under materialism (and likewise in reality), a physical process. To conceive of a world without consciousness, you must conceive of a world where that physical process is absent. Such a world is thus significantly and measurably different to ours.

Chalmers asks us to imagine a world where materialism is true, where everything is identical to our own, except that consciousness is not present. He claims that the fact that this is conceivable demonstrates that materialism cannot be true. Instead, the question itself demonstrates that (as is universally the case with immaterialist philosophers) Chalmers cannot consistently maintain a premise that he considers counterfactual. The contradiction is not in materialism itself, but in Chalmers' introduction of dualist concepts into materialism.

This would get an F in any decent freshman philosophy class.

[Beerina]

From a computational standpoint, there's no reason whatsoever intelligence needs to be "conscious". From that alone, the question of the materialism of consciousness is irrelevant. It could be 100% simulated and, per Turing, to an external observer, there'd be no way to determine if they were conscious or not. At least until science figures out how conscious, a real artifact, arises out of physics.

The corollary to that is intelligence could very well have evolved, in this universe, but without "consciousness", even if it be theoretically possible with real-world physics. Just because physics supports phenomenon x doesn't mean any instances of x actually exist.

So:

1. A universe with physics similar to our own, but without even the possibility that consciousness could exist, could have intelligent, if non-conscious, individuals.

2. Our own universe, which has physics that supports consciousness, could very well have had such intelligent, but non-conscious individuals, too, with no conscious beings whatsoever.




The wise researcher will realize consciousness must therefore have evolved as a short cut, of sorts, to (semi-) intelligent behavior. That evolution latched onto whatever-it-is in physics that gives flickers of awareness, and found a use for it. Furthermore, parsimony suggests it evolved in much simpler animals, given they express emotions like anger, fear, pain, and even shame. To suggest the human brain "added" the associated conscious feelings busts Occam's Razor reel gudlike!

[Robin]

The first premise is only true if you assume materialism is false. The argument is circular.

Yes, in fact if you look at his strict definition it can only be conceivable if it is not ruled out a priori under ideal rational reflection.

And yet how could you have ideal rational reflection on this statement if you were missing the most important fact of all - whether consciousness was or was not physical?

So saying it is conceivable is saying that we have sufficient information to know that it cannot be ruled out a priori.

In other words it is saying that we know that consciousness is not physical.

As you say, circular.

I was going to start a separate thread on P1 after this had petered out, but no need now.

[Robin]

1. A universe with physics similar to our own, but without even the possibility that consciousness could exist, could have intelligent, if non-conscious, individuals.

But I think that what he is saying is that the physics is identical to ours, including the physics of the brains of the non-conscious individuals.

So zombie robin is physically identical to me and zombie Beerina is physically identical to you.

[Robin]

Consciousness is, under materialism (and likewise in reality), a physical process. To conceive of a world without consciousness, you must conceive of a world where that physical process is absent. Such a world is thus significantly and measurably different to ours.
Again, I agree.

The example I used to use is to imagine someone physically identical to me who has no nose. (For the record I have a nose).

So the easy part is imagining me without a nose. But can I conceive of a being that does not have a nose and is physically identical to me?

The supporters of this argument concentrate on the conceivability of ~Q but forget they have to demonstrate the conceivability of P&~Q.

[PixyMisa]

The supporters of this argument concentrate on the conceivability of ~Q but forget they have to demonstrate the conceivability of P&~Q.
Exactly.

And this - in my experience - is where immaterialist philosophers invariably fail. From Bishop Berkeley to Mary's Room and the Chinese Room and the various P-Zombie arguments, they fail to maintain consistency of the counterfactual.

[Robin]

From a computational standpoint, there's no reason whatsoever intelligence needs to be "conscious". From that alone, the question of the materialism of consciousness is irrelevant. It could be 100% simulated and, per Turing, to an external observer, there'd be no way to determine if they were conscious or not. At least until science figures out how conscious, a real artifact, arises out of physics.

The corollary to that is intelligence could very well have evolved, in this universe, but without "consciousness", even if it be theoretically possible with real-world physics. Just because physics supports phenomenon x doesn't mean any instances of x actually exist.

So:

1. A universe with physics similar to our own, but without even the possibility that consciousness could exist, could have intelligent, if non-conscious, individuals.

2. Our own universe, which has physics that supports consciousness, could very well have had such intelligent, but non-conscious individuals, too, with no conscious beings whatsoever.




The wise researcher will realize consciousness must therefore have evolved as a short cut, of sorts, to (semi-) intelligent behavior. That evolution latched onto whatever-it-is in physics that gives flickers of awareness, and found a use for it. Furthermore, parsimony suggests it evolved in much simpler animals, given they express emotions like anger, fear, pain, and even shame. To suggest the human brain "added" the associated conscious feelings busts Occam's Razor reel gudlike!
I have re-read the argument and find that you are right and I am wrong.

Nothing in Chalmer's argument necessitates that the zombies have the same brain structure as we do.

So your example 2 would perfectly fit his P&~Q and so his argument is not even remotely a problem for Materialism.

[Beerina]

But I think that what he is saying is that the physics is identical to ours, including the physics of the brains of the non-conscious individuals.

So zombie robin is physically identical to me and zombie Beerina is physically identical to you.

That immediately implies a dualist position. I see no support for the concept that a zombie me would be identical to me. By my theory, they must be different because the former would only have data processing that did not include the conscious experience, and thus must necessarily operate differently from a brain that does give rise to such, which involves the data processing addendum that consciousness supplies (among other, unconscious processes) in making decisions.

To put it bluntly, consciousness, whatever else, does processing of information and puts out outputs that aid in the brain making decisions. This is the assumed purpose of the evolution of consciousness, and not that it's a neat trick and gift from a god. But nevertheless, it can be viewed itself as a black box that takes inputs and generates outputs, and thus could be replaced by a deterministic and, specifically, non-conscious processing device. Said device might operate vastly differently from the way consciousness operates, though personally I think the conscious bit could be plug-and-placed with rather simple computational devices.

[Robin]

That immediately implies a dualist position. I see no support for the concept that a zombie me would be identical to me.
You will notice in the post above yours that I have already retracted what I said.

There is a "physically identical" version of the zombie argument but that is apparently not the version Chalmers is putting here (although it is somewhat ambiguous).

[Robin]

In fact the more closely I examine this argument the more it falls apart.

For example in one of the most important parts of the argument - where he argues from epistemic possibility to metaphysical possibility, he appears to have arbitrarily changed his own definition of "primary intension", from a function on a scenario to a function on a possible world.

[Robin]

I thought I would post this one for a laugh:

A related objection (e.g. Bailey forthcoming) holds that arguments from ideal conceivability are toothless, as non-ideal creatures such as ourselves cannot know whether or not a given statement is ideally conceivable. I think that there is no reason to accept this claim. Although we are non-ideal, we can know that it is not ideally conceivable that 0=1, and that it is ideally conceivable that someone exists. We know that certain things about the world (say, all philosophers are philosophers) are knowable a priori, and that certain things about the world (say, that there is a table in this room) are not so knowable, even by an ideal reasoner. Likewise, reasoning of the sort above gives us very good reason to think that there is no a priori entailment from physical to phenomenal truths and that zombie hypotheses are conceivable, even for an ideal reasoner.
In other words "I can know that 0 is not equal to 1 therefore I can know fundamental noumenal truths about existence"

Materialism? What was I thinking?

[Robin]

And if you think about it, that makes his entire argument boil down to "1~=0 therefore Materialism is false".

[Robin]

Another example of where Chalmers appears to be switching definitions:
For the purpose of the argument, it usually suffices to conceive of a physically identical world in which some other being, corresponding to a conscious being in this world, is a zombie or an invert.
Ok, leaving aside the circularity - this does not match his own definition of conceivability from earlier in the argument (my bolding).
One can likewise define a notion of positive primary conceivability, so that S is positively primarily conceivable when S can imagine a coherent situation that verifies S, where a situation verifies S when, under the hypothesis that the situation actually obtains, the subject should conclude that S.
So to match this definition it is not enough to conceive of the other being lacking consciousness - we would have to conceive of a situation under which - if the situation were actual - we could conclude that the other being was not conscious, or that their qualia differed from a corresponding individual in another world.

Which is not even prima facie conceivable.

[Robin]

I just realised I gave Chalmers two dimensional semantics an extra dimension in the OP.

I will have to invent three-dimensional semantics to cover for that one. You would probably need to wear special glasses.

[Beerina]

A related objection (e.g. Bailey forthcoming) holds that arguments from ideal conceivability are toothless, as non-ideal creatures such as ourselves cannot know whether or not a given statement is ideally conceivable.

The whole conceivability thing trips on a complexity issue, if you ask me. Just because you think you have properly formulated a concept doesn't mean you have. There could be buried in it some logical inconsistencies that are not obvious whatsoever, thus effectively making your concept a "round circle" that cannot actually exit, even though you don't realize it.


And not to get too much into computational complexity here, but there are many problems that are so complex there is no possible way to solve them short of essentially running a full-blown simulation. And then there's the Goedel argument, wherein the "ideal creature" suggested in the quote above doesn't, and cannot, actually exist. Even theoretical creatures such as infinite gods choke on the halting problem, or an infinite version of it anyway.

[Robin]

The whole conceivability thing trips on a complexity issue, if you ask me. Just because you think you have properly formulated a concept doesn't mean you have. There could be buried in it some logical inconsistencies that are not obvious whatsoever, thus effectively making your concept a "round circle" that cannot actually exit, even though you don't realize it.


And not to get too much into computational complexity here, but there are many problems that are so complex there is no possible way to solve them short of essentially running a full-blown simulation. And then there's the Goedel argument, wherein the "ideal creature" suggested in the quote above doesn't, and cannot, actually exist. Even theoretical creatures such as infinite gods choke on the halting problem, or an infinite version of it anyway.
He seems to go both ways on the unknowable truth thing.

In one document he says that unknowable mathematical truths might be considered an exception.

In the other he basically claims that there are no unknowable mathematical truths and any that we can identify now are only a function of our cognitive limitations.

He appears to be at odds with the mathematical community on that one.

But I suppose he is going to say, for example, that there might be non-algorithmic methods to determine if any algorithm halts.

It does seem to be going out on a limb for him to be basing he entire method of semantic analysis on the hypothesis that there are no unknowable truths.

[Robin]

But it all goes back to the circularity thing.

If the possibility of P&~Q is inconsistent with Materialism and Materialism were knowably true then P&~Q could be ruled out a priori (unless of course Materialism might be contingently true, in which case the argument would fail anyway).

So the claim that P&~Q cannot be ruled out a priori is identical to the claim that Materialism cannot be knowably true.

And if he is ruling out the possibility of unknowable truths then it equates to the claim that Materialism is false.

So in order to justify the first premiss he has to first prove that Materialism is false.

[Paul C. Anagnostopoulos]

Isn't Chalmers one of those fellows who argues that conceivability implies logical possibility?

http://cognet.mit.edu/posters/TUCSON3/Van_Gulick.html

~~ Paul

[Paul C. Anagnostopoulos]

Nothing in Chalmer's argument necessitates that the zombies have the same brain structure as we do.
Are you sure? Isn't this his argument:

1. If physicalism is true, then it is not possible for there to be a world in which all the physical facts are the same as those of the actual world but in which there are additional facts. (This is because, according to physicalism, all the facts are fully determined by the physical facts; so any world that is physically indistinguishable from our world is entirely indistinguishable from our world.)

2. But there is a possible world in which all the physical facts are the same as those of our world but in which there are additional facts. (For example, it is possible that there is a world exactly like ours in every physical respect, but in it everyone lacks certain mental states, namely any phenomenal experiences or qualia. The people there look and act just like people in the actual world, but they don't feel anything; when one gets shot, for example, he yells out as if he is in pain, but he doesn't feel any pain.)

3. Therefore, physicalism is false. (The conclusion follows by modus tollens.)

Notice that physicalism is declared false even though there is only the possibility of such a world. It appears that the "final ontology" must pertain to all possible worlds, not just our world. I've never understood this.

It all comes down to the conceivability of a clone world without consciousness. Chalmers thinks he can conceive of it. Dennett thinks he is wrong.

~~ Paul

[Robin]

Are you sure? Isn't this his argument:

1. If physicalism is true, then it is not possible for there to be a world in which all the physical facts are the same as those of the actual world but in which there are additional facts. (This is because, according to physicalism, all the facts are fully determined by the physical facts; so any world that is physically indistinguishable from our world is entirely indistinguishable from our world.)

2. But there is a possible world in which all the physical facts are the same as those of our world but in which there are additional facts. (For example, it is possible that there is a world exactly like ours in every physical respect, but in it everyone lacks certain mental states, namely any phenomenal experiences or qualia. The people there look and act just like people in the actual world, but they don't feel anything; when one gets shot, for example, he yells out as if he is in pain, but he doesn't feel any pain.)

3. Therefore, physicalism is false. (The conclusion follows by modus tollens.)

Notice that physicalism is declared false even though there is only the possibility of such a world. It appears that the "final ontology" must pertain to all possible worlds, not just our world. I've never understood this.

It all comes down to the conceivability of a clone world without consciousness. Chalmers thinks he can conceive of it. Dennett thinks he is wrong.

~~ Paul
I linked the argument I was using at the top. Initially I agreed with you but reading the argument itself this is not obviousl

[Robin]

Notice that physicalism is declared false even though there is only the possibility of such a world. It appears that the "final ontology" must pertain to all possible worlds, not just our world. I've never understood this.
Chalmers makes a distinction made between epistemically possible worlds and metaphysically possible worlds. If P&~Q is true in an epistemically possible world (what he calls the primary intension) then this does not rule out Materialism.

But he claims that if P&~Q is true in a metaphysically possible world (secondary intension) then this rules out Materialism.

Presumably the idea is that if Materialism is true it is necessarily true and therefore there ought to be no metaphysically possible world containing non-physical stuff.
It all comes down to the conceivability of a clone world without consciousness. Chalmers thinks he can conceive of it. Dennett thinks he is wrong.

But as I pointed out earlier, if you take Chalmers strictly at his word about the definition of conceivability then none of it could be conceivable.

Because it does not entail conceiving the physically identical being to be non-conscious (or differently conscious) - it involves imagining a situation where - if the situation were actual - you could conclude that the physically identical being was non-conscious (or differently conscious).

That is an entirely different kettle of fish. I might conceive that my green is different from your green but I can't imagine the situation where I could conclude that.

[Paul C. Anagnostopoulos]

Presumably the idea is that if Materialism is true it is necessarily true and therefore there ought to be no metaphysically possible world containing non-physical stuff.
I wonder where philosophers get this idea?

But as I pointed out earlier, if you take Chalmers strictly at his word about the definition of conceivability then none of it could be conceivable.
You said:

Nothing in Chalmer's argument necessitates that the zombies have the same brain structure as we do.
How did you decide this? I believe Chalmers proposes a zombie world that is "physically indiscernible from our world." After all, if the zombie world is physically different, who is going to argue against the possibility that consciousness might not exist there?

http://plato.stanford.edu/entries/zombies/

~~ Paul

[Robin]

I wonder where philosophers get this idea?
I have no idea - it is just groupthink as far as I can see.

I can show you an essay in which Thomas Nagel argues that Physicalism actually implies the conceivability of Zombies and suggests this is a big problem for Physicalism
You said:
Wait a minute - it is the "physical mirror of our world" version that could not be conceivable using Chalmer's definition.

I say it is not conceivable because it would ask us to imagine a situation where we could actually conclude that a person who behaves as though he is conscious is not in fact conscious, or worse, that a non-conscious individual could conclude that he is not conscious.

My other objections do not presuppose one thing or the other, we can regard Chalmers' hypothesis that "P&~Q" as something, the very possibility of which rules out Materialism as a sort of black box or oracle and the objections still stand.
How did you decide this? I believe Chalmers proposes a zombie world that is "physically indiscernible from our world." After all, if the zombie world is physically different, who is going to argue against the possibility that consciousness might not exist there?

http://plato.stanford.edu/entries/zombies/

~~ Paul
Here is the part from the Chalmer's article which he calls "the most explicit and careful form", so I take it to be the most representative one.
Here P is the conjunction of all microphysical truths about the universe, specifying the fundamental features of every fundamental microphysical entity in the language of microphysics. Q is an arbitrary phenomenal truth: perhaps the truth that someone is phenomenally conscious, or perhaps the truth that a certain individual (that is, an individual satisfying a certain description) instantiates a certain phenomenal property. P&~Q conjoins the former with the denial of the latter.

If Q is the truth that someone is phenomenally conscious, then P&~Q is the statement that everything is microphysically as in our world, but no-one is phenomenally conscious. In this version, P&~Q says that the world is a zombie world. If Q is the truth that a certain individual instantiates a certain phenomenal property, then P&~Q is the statement that everything is microphysically as in our world, but that it is not the case that the individual in question instantiates the relevant phenomenal property. In this case, it will suffice for the truth of P&~Q that the world is a zombie world, or simply that the individual in question is a zombie in a physically identical world. It will also suffice that the individual in question is an invert, who has an experience that differs slightly from the corresponding experience of the corresponding individual in our (physically identical) world.
Now I initially took this as you did that this is the "physical mirror" version and disagreed with Beerina on that basis.

But saying that the "fundamental microphysical identities" are the same is not exactly saying it is an exact physical mirror. It could just mean that the fundamental particles behave in the same way but not necessarily that all the same things happened in this universe.

So in his most careful and explicit presentation of the argument he does not use "physically indiscernable", but "physically identical" which might be taken two ways.

Here he discusses whether the conceivability of Zombies presupposes epiphenomenalism:
On such a view, physically identical beings without consciousness will presumably have large causal gaps in their functioning (or else will have some new element to fill those gaps), but there is nothing obviously inconceivable about such causal gaps.
Now what does this mean? Does it mean that the causal gaps result in different functioning? Or does he mean that they function identically and that some things happen for no reason at all?

That is not entirely clear to me and I have actually read Chalmers blog where he wonders whether or not a zombie would behave like a conscious being or not.

So it seems to me that Chalmers believes zombies are conceivable, but has not managed to completely conceive of one yet.

[PingOfPong]

I think you're all zombies who are trying to fool me into thinking that you're conscious. I'm the only real person in the world because none of you can prove that you have the subjective experience of awareness.

[Ron_Tomkins]

Hmmm.... braaains... (http://laughingsquid.com/wp-content/uploads/zombie-natalie-20081020-132930.jpg)

[Robin]

I think you're all zombies who are trying to fool me into thinking that you're conscious. I'm the only real person in the world because none of you can prove that you have the subjective experience of awareness.
Actually we are both figments of someone elses imagination.

[Paul C. Anagnostopoulos]

But saying that the "fundamental microphysical identities" are the same is not exactly saying it is an exact physical mirror. It could just mean that the fundamental particles behave in the same way but not necessarily that all the same things happened in this universe.
I would take that as meaning the world is an exact copy. But then again, I'm not the sort of person who would make up phrases like "fundamental microphysical identities." Again, if the world is not physically identical, there may very well be a lack of qualia.


So it seems to me that Chalmers believes zombies are conceivable, but has not managed to completely conceive of one yet.
Well then he should shut the heck up about it. :D

~~ Paul

[Robin]

I would take that as meaning the world is an exact copy. But then again, I'm not the sort of person who would make up phrases like "fundamental microphysical identities." Again, if the world is not physically identical, there may very well be a lack of qualia.
Personally I think he is being deliberately vague about this.

If conceivability of S requires that the subject concludes that S is the case and the subject is the zombie behavioural twin of a non-zombie then a conscious person should conclude that they are not conscious.

Or I should somehow conclude that a person I meet who has all the outward signs of consciousness is not conscious. In order to satisfy his definition I have to imagine the situation where I am able to draw that conclusion.

[PingOfPong]

Actually we are both figments of someone elses imagination.

That's exactly what an unconscious zombie would say.

[Robin]

That's exactly what an unconscious zombie would say.

I know, we are sooo predictable.

[Jeff Corey]

I think you're all zombies who are trying to fool me into thinking that you're conscious. I'm the only real person in the world because none of you can prove that you have the subjective experience of awareness.

That's what I've always though about the silly p-zombie argument. I'm supposed to think about a universe identical to ours where I can't think.

[Robin]

That's what I've always though about the silly p-zombie argument. I'm supposed to think about a universe identical to ours where I can't think.
Ah, but if you read down about three quarters of the way you will find that he allows there might be at least one conscious individual among the zombies who is able to think about the others not being able to think.

That fixes the problem right up :)

[Paul C. Anagnostopoulos]

Ah, but if you read down about three quarters of the way you will find that he allows there might be at least one conscious individual among the zombies who is able to think about the others not being able to think.
Aha! That's the person who was lucky enough to be an exact physical duplicate. Everyone else has defective neurons.

~~ Paul

[Robin]

Aha! That's the person who was lucky enough to be an exact physical duplicate. Everyone else has defective neurons.

~~ Paul
Or perhaps he is the Solipsist. Everyone else is just part of his dream and that is why they are not conscious.

[Beerina]

He seems to go both ways on the unknowable truth thing.

In one document he says that unknowable mathematical truths might be considered an exception.

In the other he basically claims that there are no unknowable mathematical truths and any that we can identify now are only a function of our cognitive limitations.

He appears to be at odds with the mathematical community on that one.

But I suppose he is going to say, for example, that there might be non-algorithmic methods to determine if any algorithm halts.

Yes. Ever since Turing, Goedel, & Co., we have known that "There are things Man was not meant to (or, more accurately, is not capable to) know has been relegated to a practical phenomenon at best. In theory, though not yet proven, the human mind is capable of understanding anything that is possible for a finite entity to understand. Only practical issues like time, "RAM", and "processing speed" limit us. And that is grossly lessened thanks to computers themselves, an augmentation of our mind, and also by our thinking about "thinking" and "data processing" itself.



But I suppose he is going to say, for example, that there might be non-algorithmic methods to determine if any algorithm halts.

Mathematicians have the "oracle" concept that magically gives the correct answer, leaving you with the duty of merely checking if the answer works, which is usually magnitudes easier than figuring out how to figure out the answer in the first place.

This is actually at the core of the "Does P = NP?" problem.


But computational theory deals not just with computing answers, but with computing how to compute answers. What is possible, in toto, to figure out. In that view, problems of how to solve problems (and problems of how to solve problems of how to solve problems, and so on, ad infinitum), nothing has a special status. It's all problems, with data as input.

So his "non-algorithmic methods", if they work, suggest one of two things:

1. A finite computational model more powerful than Turing/computers/human mind (in theory), which would be immensely of interest to people who study such things, not to mention physics and the universe at large.

2. An infinite model, ala a true, godlike Oracle who can give magical answers. Needless to say, this would also be of interest.

Note that "purely random" is a possible, but incredibly slow method of determining solutions. I.e. generate random computations and feed them your data, and see if they produce a (correct) output within some length of time however long you care to wait.

That is a sloppy, slow version of just trying every single finite algorithm, which Goedel and Turing and others showed how to enumerate. (I.e. every single algorithm can be expressed as a computer program, so to speak, and can be constructed and given a number according to some simple rules. You can, in theory, search this "space" for the proper solution to any problem you desire. Of course, it makes playing Chess by computer look magnitudes simpler than playing tic-tac-toe.)

[Robin]

That is a sloppy, slow version of just trying every single finite algorithm, which Goedel and Turing and others showed how to enumerate. (I.e. every single algorithm can be expressed as a computer program, so to speak, and can be constructed and given a number according to some simple rules. You can, in theory, search this "space" for the proper solution to any problem you desire. Of course, it makes playing Chess by computer look magnitudes simpler than playing tic-tac-toe.)
Nevertheless this is probably what Chalmers had in mind.

But wouldn't it be the case that things like the algorithm to find the nth digit of omega simply would not exist in the space?