A Coherent Madman and His Little Self-referential Problem

 

The madman or religious maniac can be entirely coherent and systematic yet also be completely divorced from the world. His system of beliefs may also be entirely self-contained and even self-generated.

Alternatively, his set of beliefs may be based on certain foundational premises, from which his entire system is derived. However, the foundational premises may be utter nonsense even though their implications and entailments are valid (i.e., valid, though not sound).

For example, one such foundational premise may be:

“Every statement in this Holy Book is true.”

Thus not only would he have numerous statements which he could believe (i.e., the ones in his Holy Book); he could also believe all the propositions that are entailed or implied by these statements.

For example, one such statement in the Holy Book could be:

“Accept everything that your heart says is true.”

From this statement he could infer numerous other statements of belief that aren't even directly connected to the original statements he's accepted in the Holy Book itself. However, this could also lead him to reject certain statements in the Holy Book.

For example, his heart may tell him that certain statements in the Holy Book are untrue. He would therefore have a tailor-made system of beliefs which both makes him accept many statements in the Holy Book and yet also allows him to reject the ones he thinks are untrue (or which he simply dislikes).

Then he'd have a problem with self-reference. That is, the Holy Book says of itself:

“Everything in this book is true.”

Though another statement in the Holy Book also says:

“Accept what your heart says is true.”

Which he does. His heart tells him that certain statements in the Holy Book are false. So according to the Holy Book and the man himself, the Holy Book says that everything within it is true and that everything one’s heart says is true. Though the heart says that certain statements in the Holy Book are false. Thus the Holy Book says that everything it says is true; though it also accepts a statement that makes some of its other statements false.

If this man hadn't accepted the foundational statement that “Everything this book says is true”, he wouldn’t have accepted the statement that one should accept what the heart says (i.e., even if it says that certain statements in the Holy Book are false).

We can say that there are two systems now: the man’s and the Holy Book’s. The man’s system grew out of the Holy Book; though the Holy Book allowed him to disregard certain statements within it.

Of course if the Holy Book says that “Everything in this book is true” then that statement itself must also be true. Though, again, the Holy Book contains a statement which allows the possibility that a person needn't accept everything within it.

There is also the self-referential problem of the Holy Book referring to itself. Say that the statement “Everything in this book is true” was said or written at time t¹; though the work itself wasn't finished until time t². Then that statement about the book (which is within the book) was written or said before the book was actually completed. If that's the case, how was it known at time t¹ that everything said or written after would be true if there was no knowledge of such future statements?

There are two answers to this.

One is that although the statement “Everything in this book is true” at the beginning of the book, it mightn't have been written or said until the end of the book. It may be entirely coincidental that the book was compiled with the self-referential statement at the beginning rather than at the end.

Another answer would be that God created the entire book in one go. Therefore it's just a fortuitous that the self-referential statement is at the beginning. In that case, that statement is neither at the end nor the beginning of the book. All statements came together at the same moment in the mind of God. Of course we aren't omniscient like God; therefore our version of the book must contain that statement somewhere in the work: either at the beginning, the end or even in the middle. Again, if God is outside of time, then it makes no sense to say that the statement of self-reference occurs at a particular time within the book. The Holy Book is an abstract object in the mind of God and so it doesn't partake of temporal sequence.

However, isn’t

i) “Everything within this book is true.”

similar to

ii) “Everything within this statement is true.”?

(This is a version of the well-known statement, “This statements is false.”)

However, they're not identical in form. The first sentence (i) seemingly refers to something else – viz., “this book”; whereas the second statement (ii) refers only to itself qua statement. However:

The book the first statement refers to is the book that contains the statement that refers to the book.

So statement (i) is still self-referential; though not entirely so because there are many statements in the book other than “Everything within this book is true”. That statement refers both to itself and every other statement in the book. If the self-referential statement weren't true, then neither would all the other statements in the book be true.

The second statement (ii) above is more clearly self-referential than the first statement. Perhaps it only achieves this because it is without content. It says of itself that everything within itself is true. However, in a certain sense there's nothing within itself. What is this “everything” that's “within” the statement? It quantifies using the term “everything” . Though the only thing that's in the statement (other than the subject-term) is the predicate “is true”. How can the clause “everything within this statement” be true? It's not making a claim about anything other than itself.

Thus

“Everything within this statement is true” is true if and only if everything within statement S is true (its quasi truth conditions).

Thus the statement is true if and only if it is true. It doesn't parallel the form of the T sentence

The sentence ‘Snow is white’ is true iff snow it white.

because here the predicate “is true” refers to the sentence that claims that snow is white. Thus there's a reference to both snow being white and to the sentence which says “Snow is white”. This is unlike the truth predicate in the self-referential statement because this truth predicate applies to both a statement with truth conditions (i.e., snow's being white) and to the metalinguistic sentence that says “The sentence....' is true iff '....”.

Is Consciousness the Brain Carrying Out Computations?

 

Hilary Putnam once held the position (i.e., in the 1960s) that consciousness is literally the brain computing. That also had the implication (for some people) that it's not necessarily the brain that causes consciousness: it's computation itself. This is the case even if it's computation of a particular kind (in conjunction with its physical or biological implementation) that's required for consciousness. Thus it followed from this, according to Putnam, that if computation is everything, then consciousness can occur in a computer or even in Putnam's own “brain in a vat”. Again, what matters are the computations, not the physical basis of those computations. (To be accurate, in his 1967 paper, Putnam hardly refers to consciousness as such. He talks about “mental states”.)

Daniel Dennett also argued that the computations of the brain are consciousness. This doesn't mean that such brain computations result in consciousness in some kind of causal and temporal sequence. It means that when the brain's computations occur, so too do conscious events. They're one and the same thing. Or, as Dennett himself puts it, it's not a case of brain computations occurring (in what he calls the “Cartesian Theatre”) and then we become conscious of those computations. Instead, when brain-computations occur they actually constitute consciousness. When the brain computes: that's what consciousness is. That's what we're aware of when we're conscious; though we aren't necessarily aware of them as computations (or as anything).

This is similar to John Searle's view in which he says that there's no causal and temporal sequence from a brain state to a mental state in that the mental state is the brain state. The brain state and mental state occur at one and the same time. It isn't a case of brain state at time t¹ causing mental state at time t². Both the brain state and the mental state occur at t¹.

The mental state is the state as experienced from the inside (as it were); whereas the brain state could (in theory at least) be observed by neuroscientists. However, it need hardly be said that Searle doesn't believe that this has anything to do with computations (as such). In his case, it's a point about the (causal) relations between the brain and consciousness; not between computations and consciousness.

Finally, it needn't be the case that consciousness is always (or at all) computation. We can substitute all the references to 'computation' in the above with the words 'brain event' or 'brain state'; as Putnam himself did in his paper of 1967.

References

Dennett, Daniel. (1991) 'The Cartesian Theater and “Filling In” the Stream of Consciousness'.

Putnam, Hilary. (1967) 'The nature of mental states', in Mind Language and Reality: Philosophical Papers, Volume 2.
Searle, John. (1997) The Mystery of Consciousness.

Holisms (3) – Definitional Holism

One

A definition isn't just an appendage to the word under scrutiny. The word would have no meaning if it weren't for the definitions we supply in order to facilitate understanding.

A word isn't atomic in nature. We can't say, for instance, that the word ‘freedom’ means, well, freedom and leave it there. Neither can we accept (on a naturalistic reading) some kind of abstract and non-individuated meaning or proposition which would allow us to escape from our linguistic system. Even if we were to allow for abstract and non-spatiotemporal meanings or propositions, they would still become material or concrete (as it were) as soon as they were expressed and communicated – which would need to be done, evidently, in some natural language or other.

Two

It seems counterintuitive, at least initially, to think that the primary relation is not between words and things, but between words and other words. This isn't so surprising when, for example, we think of the classic example of defining ‘bachelor’ as ‘unmarried man’. However, these words are taken to be synonyms. But try explaining or defining a word like ‘freedom’ again. This certainly doesn't have a reference in a strict sense of the term. Thus we are moved on, immediately, to words like ‘liberty’, ‘choice’, ‘will’ and so on. And try getting further without bringing in terms which are themselves as much in need of defining or explaining as the original word ‘freedom’. Of course it may be the case that we arrive back at the word ‘freedom’ or use this term as part of some of the other definitions.

This word isn't as problematic as words like ‘thing’ and ‘experience’. Try defining those words without reference to things or experience.

It may follow, then, that if a word has a definition which includes terms themselves not defined (or even if we provide simple synonyms for the definiendum) then the speakers may not fully understand the word’s meaning. They may not even understand their own usages of the word in question because any full meaning (or full understanding) can only belong to the linguistic system itself. Any definition or explication of a word's meaning must reach an arbitrary finishing point if the game of understanding is to begin in the first place. And that stopping place will be contingent, if not exactly arbitrary.

Three

Words are defined by other words, which are themselves defined by other words. No word, concept or thing is ever captured in a “finite web” of meaning. This is Karl Popper on this problem:

“The derivation [of a term] shifts the problem of truth back to the premises, the definition shifts the problem of meaning back to the defining terms (i.e., the terms that make up the defining formula). But these, for many reasons, are likely to be just as vague and confusing as the terms we started with, and in any case, we should have to go on to define them in turn; which leads to new terms which too must be defined. And so on, to infinity.”

That must surely be the problem with definitions: they too will contain terms which themselves will need defining.

A similar problem is apparent when it comes to a logical argument and the premises on which it is based. That is, the premises of any argument may themselves depend on further premises and conclusions that may act as justifications for the validity or truth of the initial premise. Thus we have on our hands a regress of justification. However, the game can't go on forever.

This is why we must, at some point, simply accept premises, arguments or definitions if we're to get going on our philosophical or logical enterprise. The premises that we accept, however, needn't be seen as being “self-evident”, “indubitable” or anything like that. They simply need to be the starting points of reasoning if we are to avoid an infinite regress.

In a sense, it's precisely because definitions depend on their own un-defined terms that all words (or nearly all words) are inherently somewhat vague. That's because the meaning of a single word can be said to depend upon all the meanings of all the words in the symbol-system to which it belongs. We can't have a precise definition if the definiendum itself contains terms that aren't themselves defined. Though even if we do in fact define the terms in the definition, these definitions will themselves require elaboration and definition. And so on indefinitely.

The holist position on this problem will be that we must take into account the symbol-system to which the words under definition belong. But this too is problematic. How can we really take on board an entire symbol-system each time we want to define a term? Does this mean going on an infinite regress? Or if not an infinite regress, does it mean taking on board all the other words in a symbol-system? (Or perhaps a large sub-system of the larger system?) So, in that respect, the regress won't be infinite: it will be circular. This essentially means that we will arrive back at some of the terms which we actually started with.

This means that there are jut as many problems with holism (or coherentism) as there are with atomism.

Similar points to those above were raised by, amongst others, Bradley in the 19th century. Because of the problem of holism, Bradley concluded that no statement could be entirely/absolutely true. Similarly, we may now say that no definition is ever free from vagueness precisely because of its containment within a larger symbol-system.

Susan Greenfield & John Searle on Artificial Consciousness

 

Let's start off with a longish quote from the neuroscientist, writer and broadcaster Susan Greenfield:

“The idea [of a conscious robot] is ridiculous. Consciousness entails an interaction between the brain and the body, trafficking a myriad of chemicals between the two. To reproduce that, you would have to build a body with a whole range of chemicals, and the three-dimensionality of the brain would have to be preserved to the very last connection.” 

Susan Greenfield puts what can be called the case for biologism when it comes to consciousness. The way Greenfield expresses this position seems to make her an even stronger proponent of biologism than John Searle (who'll be discussed in a moment).

Her argument appears to be excruciatingly simple. It's this:

In order to create artificial consciousness we would need to build a biological brain and a biological body.

Or less extremely:

In order to create artificial consciousness one would need to replicate a biological brain and a biological body.

Or even more simply:

In order to replicate x, one would need to replicate everything of x (which has y) – down to its material constitution.

You could ask what would be the point of replicating biological brains and biological bodies when we already have them. (Though the replication of brains and bodies - regardless of consciousness - would be an incredible thing.) This would be equivalent to a scientific model that literally replicated every aspect of that which it is modelling.

Another way of putting this is to say that Susan Greenfield's position is the exact opposite of functionalism. That is, it's not functions (or computations, algorithms, etc.) which matter to consciousness: it's the material constitution (or "substrate") which underpins it.

Isn't that why Greenfield talks in terms of “trafficking a myriad of chemicals between” the brain and body and then goes on to say that “to build a body with a whole range of chemicals, and the three-dimensionality of the brain would have to be preserved to the very last connection”?

Here Greenfield goes beyond material constitution (which would include biochemicals) to stressing the “three-dimensionality of the brain”. Thus we've moved beyond material constitution to the shape/dimensionality of the brain. (In any case, three-dimensionality - at least in the abstract - would be easy to replicate.)

Again it would seem that the replication of consciousness would require the replication of both the brain and body in their entirety. That would be a pointless act of replication in terms of replicating consciousness. Though in terms of creating artificial-life-with-consciousness it would be earth-shattering.

Despite all that, the Chalmers, Penroses and dualists among us may still ask Susan Greenfield and others the following question:

What if we carried out this act of perfect replication (of both brains and bodies) and it still turned out that the replica didn't have consciousness?

Even though that's a subject for another day, I suspect that some philosophers would discount this possibility in an a priori manner.

John Searle

Many philosophers and scientists have called John Searle a dualist. He, in return, says that those who stress function and ignore biology are effectively creating a non-material Cartesian reality populated with functions or computations (rather than with Cartesian “ideas” or “thoughts”). Searle himself writes:

“I believe we are now at a point where we can address this problem as a biological problem [of consciousness] like any other. For decades research has been impeded by two mistaken views: first, that consciousness is just a special sort of computer program, a special software in the hardware of the brain; and second that consciousness was just a matter of information processing. The right sort of information processing -- or on some views any sort of information processing --- would be sufficient to guarantee consciousness..... it is important to remind ourselves how profoundly anti-biological these views are. On these views brains do not really matter. We just happen to be implemented in brains, but any hardware that could carry the program or process the information would do just as well. I believe, on the contrary, that understanding the nature of consciousness crucially requires understanding how brain processes cause and realize consciousness.. ”

Searle continues:

“Perhaps when we understand how brains do that, we can build conscious artifacts using some nonbiological materials that duplicate, and not merely simulate, the causal powers that brains have. But first we need to understand how brains do it.”

It can be said that there can be an artificial mind without having an artificial (human) brain. However, isn't that precisely the claim that's being disputed?

To John Searle, it's all about what he calls “causal powers".

This refers to the ostensible fact that a certain level of complexity is what's required to bring about those causal powers which are necessary for intentionality, mind and consciousness.

Despite that, Searle never never says (as far as I know) that biological brains are the only things capable - in principle - of bringing about consciousness and intentionality (therefore semantics, in Searle-speak). He only says that biological brains are the only things known which are complex enough to do so.

So it really is all about the biological and physical complexity of brains and therefore their causal powers.

His basic position (like Greenfield's) on this is that if computationalists or functionalists, for example, ignore the physical biology of brains and exclusively focus on syntax, computations or functions (the form/role rather than the physical embodiment), then that will surely lead to a kind of dualism. What he means by this is that there's a radical disjunction created between the actual physical reality of the brain and how these philosophers explain - or account for - intentionality, mind and consciousness.

Again, Searle doesn't believe that only brains can give rise to minds. Searle's position is that only brains do give rise to minds. He's emphasising an empirical fact; though he's not denying the logical and metaphysical possibility that other things can bring forth minds.

Gerald Edelman also holds the position that the mind

“can only be understood from a biological standpoint, not through physics or computer science or other approaches that ignore the structure of the brain”. 

Then Edelman - in order to demonstrate his point - puts the seemingly extreme position of “functionalists” (such as Marvin Minsky) who “say they can build an intelligent being without paying attention to anatomy”.

So if one says that biology matters, one's also saying that functions aren't everything (though not that functions are nothing).

Finally, according to Francis Crick, psychologists (as well as philosophers) 

“have treated the brain as a black box, which can be understood in terms merely of inputs and outputs rather than of internal mechanisms”.

Thus, to Greenfield, Searle, Edelman and Crick, consciousness really is all about biological brains.

References

Crick, Francis. (1996) quoted in The End of Science, by John Horgan

Edelman, Gerald. (1996) quoted in The End of Science, by John Horgan
Greenfield, Susan. (1999) quoted in Predictions: 30 Great Minds on the Future (edited by Sian Griffiths).
Searle, John. (1999) 'Consciousness'

Artificial Intelligence (AI): All About Algorithms?

...Thoughts-Computations-Rules-Algorithms...

Many "cognitivists" believe that the brain is a computer. (Sometimes they say “a kind of computer”.) Thus, as a result of this belief, they attempt to discover the computational processes which enable such things as perception and learning. However, expressed in that manner (as it often is), things are a little unclear.

Such cognitivists believe that the brain is also a machine – a computing machine.

Computationalists (computationalism is a branch of cognitivism) claim that all thought is computation. But what does that mean? Are the words 'thought' and 'computation' are virtual (or literal) synonyms?

This is more clearly the case because it seems that almost all conscious processes in the brain are deemed to be thoughts; and thus also deemed to be computations.

That not only includes the thought that 1 plus 1 equals 4 or that Snow is white; but also the rotation of a mental image in the mind, imagining the smell of a rose and so on. Then again, if rotating a mental image is classed as a thought, then why can't it also be classed as a computation? Especially since, in computationalism, they appear to by synonyms.

It all now depends on what we mean by the word 'computation'.

For a start, we can make the following claims:

i) All of a computer's processes are computations.

ii) Not all conscious human mental processes are computations.

Similarly, we can say:

iii) Many human mental processes are thoughts.

iv) No computer computations are thoughts (i.e. because thoughts have semantic content, intentionality, reference, etc.).

Rules Rule, Okay?

Is everything that happens consciously in the mind a computation? Or, perhaps more tellingly, is it all rule-governed? Jerry Fodor doesn't think so. He says that

“some of the most striking things that people do – ‘creative’ things like writing poems, discovering laws, or, generally, having good ideas – don’t feel like species of rule-governed processes”.

The way Fodor puts his position doesn't really help matters Sure, such things may not “feel like species of rule-governed processes”. However, that doesn't mean that they aren't rule-governed processes. Far from it. This is the same phenomenological approach that's applied to free will. Here again most people “feel like” they have free will. Though, on close inspection, that claim (about what things feel like) amounts to almost nothing.

On Fodor's behalf it can now be asked what something's being rule-governed could possibly mean in the varied contexts of “writing poems, discovering laws, or, generally, having good ideas”. Are these disparate things really united by the following of rules (if at the non-conscious level)? Well that would depend on what's meant by the words “rules-governed”. 

We can take this somewhat further.

If writing poems, discovering laws and having good ideas are rule-governed, then these creative processes must be following some kinds of algorithm. And following on from that, they must be computable. What's more, this could mean that these processes are rote in some (or sometimes all) respects. Not in the sense of conscious acts of rote learning (or memory); but in the respect that the brain (or physiological system) has 'acquired' certain modules/faculties/etc. - or that such things are innate.

Haven't we simply moved from one technical term (i.e., 'rule-governed') to two more – 'algorithms' and 'computable'? After all, the words 'algorithms' and 'computations' can both be be cashed out in terms of following rules or being rule-governed.

So let's quote a definition of the word 'algorithm' as it's specifically used in reference to computers:

“An algorithm is basically an instance of logic written in software by software developers to be effective for the intended 'target' computer(s) to produce output from given input (perhaps null).”

The mention of 'logic' (along with the very mechanical way of describing both what an algorithm does and how it comes to be) seems to make Fodor's earlier claim a little more convincing. Can we say that “an instance of logic” (or instances of logic) is required to “write poems, discover laws, or, generally, having good ideas”? Yes, we can! It's certainly the case that - in a limited sense - instances of logic/algorithms will be involved in these processes. The thing is, it surely can't be said that it's all about logic or algorithms. 

We can now say that logic or algorithms can be applied to some things (or to all things!) which aren't themselves logical or algorithmic.

Bad Computers

Kurt Gödel is often brought into the picture in order to show us what humans have and what computers (ostensibly) don't have.

For example, there's much talk about human brains having a "rule-free flexibility" and “unlimited mathematical abilities”. Thus there's also talk about “intuition” and “direct insight”. Of course these abilities can be seen to run free (conceptually speaking) of other things that computers don't have: such as qualia, emotions and suchlike. Then again, some would say that they all form a Gödelian package.

In concrete terms, there's the argument that humans can solve computational problems which computers can't solve. (Note that this hasn't got anything directly to do with computers not being able to write poems or have an orgasm.) This Gödelian claim that “no such limits apply to the human intellect” is, as Alan Turing argued in 1950, often “merely stated, without any sort of proof”.

In any case, various consequences are put forward as being a result of computers not having our (as it were) Gödel faculty. They include the fact that most computers crash for trivial reasons (e.g., because of faulty software or bad input). This is said to be due to the rule-fixated nature of computers; unlike human beings who have (as stated) a Gödel faculty.

All this is seen to be a direct result of computers needing a rule or algorithm for literally everything they do. More concretely, computers show no intuition or insight; and, in most cases, they don't learn from their mistakes or learn not to make mistakes. (Though this isn't true of all computers or even all aspects of each computer.)

Here again philosophers stress human uniqueness. Hubert Dreyfus, for example, argues that there are many examples of mental activity and behaviour that aren't a question of following rules. As Dreyfus himself puts it, computers lack the “immediate intuitive situational response that is characteristic of [human] expertise”. Consequently, persons 

“must depend almost entirely on intuition and hardly at all on analysis and comparison of alternatives”. 

Basically, some people argue that these Gödelian things can't be programmed into a computer.

The science writer John Horgan also tells us what computers are bad at. He writes:

“ Computers may excel at precisely defined tasks such as mathematics and chess.... but they still perform abysmally when confronted with the kind of problems – recognising a face or voice or walking down a crowded pavement – that human solve effortlessly.” (1996).

To state the obvious, the above are all programming problems. And they're programming problems because the number of variables the computer (as well as a person) needs to take into account when it comes to “recognising a face or voice or walking down a crowded pavement” are huge (or indefinite) in number. However, persons, it can be argued, don't (really?) need to be programmed in these cases: they react situationally. That is, persons can act upon - and react to - novel situations; even though (it can be said) these situations aren't entirely novel.

The philosopher George Rey also states the case that computers don't have a full logical package. He writes:

“Intelligence requires doing well under non-ideal conditions as well... But performing well under varied conditions is precisely what we know existing computers tend not to do. Decreasingly ideal cases require increasingly clever inferences to the best explanation in order for judgements to come out true; and characterising such inferences is one of the central problems confronting artificial intelligence...” (1986)

Here again we see that in all the cases in which a computer doesn't have a rule or algorithm to follow, then it doesn't know what to do. Of course you can create rules which tell a computer what to do when there are no existing rules; though that would depend on the nature of these meta-rules as well as upon the new conditions the computer is facing.

To sum up in the language of logic: computers aren't very good at “inferences to the best explanation” when they find themselves in “non-ideal conditions”.

Good Computers

Nonetheless, all sorts of new factors have been added to computers to simulate intuition or Gödelian intelligence. Such things as quantum computers based on “entangled qubits”, the introduction of random factors (e.g., annealing approaches) and hardware neural nets have been added into the computer-pot.

In any case, we already know about computer randomness. Even von Neumann machines can modify their own programmes (i.e., they can learn). That means that some of their responses (or output) are unpredictable. All this is achieved, in general, by equipping a computer with certain random elements which the computer can work on to produce outputs which are unexpected (i.e., which have moved beyond the programmed data). Indeed all this was theorised about by Turing as long ago as 1938.

Even with early Turing machines there was a requirement that such machines be able to follow their own rules or show what some people (at the time) called “initiative”. It was said that a programmer could engineer an element of randomness into the computer (or into the programme). That was what Alan Turing himself tried to do with his “Manchester computer” (1948-50). That meant that such randomness (as it were) would bring about “intuition” (or initiative) in the Turing machine – or even free will!

So when (not if):

i) A random element is introduced into a Turing machine (or a computer),

ii) and that computer manages to follow rules not laid down by the programmer,

iii) and as a result of that it solves its own problems,

iv) then that computer has learned something of its own accord or it even has “intuition”.

Thus there's no “appearance” about it! In this limited respect, the computer is free from its programmer. Or it has a “will” which is independent of its programmers. This isn't to say that it has either a mind or a (free) will in the human sense; though the independence (or freedom) is certainly real.

I think it would also be correct to say that a Turing machine “could have done something else” with the same input. That is, the same random change (mentioned by Turing) to the Turning machine can have different results in terms of what it produces. (E.g., a different calculation or even a different action – though a calculation is an action of sorts.)

More specifically in terms of today's computer programmes, there's what is called “machine learning” in which computer programmes have the ability to “self-modify”. These include programmes which themselves include ensemble learning, current-best-hypothesis learning, explanation-based learning, decision-tree learning, reinforcement learning, Bayesian statistical learning, instance-based learning and so on.

Despite all that, it's still said (by some) that none of these things (not even collectively) produce a Gödelian mind. That's because all these additions can still be reduced to Turing machines (along with their limitations). Sure, they make computers much better; though it's still said that they don't make them Gödelian.

References

Dreyfus, Herbert. (1992) What Computers Still Can't Do

Fodor, Jerry. (1975) The Language of Thought
Horgan, John. (1996) The End of Science
Rey, George. (1986) 'A Question about Consciousness'
Turing, Alan. (1939) 'Systems of logic defined by ordinals'
-- (1950) 'Computing Machinery and Intelligence', Mind LIX:433-460.