Daniel Dennett’s Crude Ad Hominems — As Found in His Book, ‘Intuition Pumps’

Some academics (or professional) philosophers have a problem with the American philosopher Daniel Dennett (1942-) because he’s a successful writer of what’s called “popular philosophy”. (Note: The English philosopher Timothy Williamson makes a distinction between “popular philosophy” and “populist philosophy” — see here.) I don’t. After all, although Dennett has written many popular books on philosophical subjects, many of his arguments can also be found in his academic (i.e., technical) papers. Still, it’s true that as time has gone by, Dennett has written less and less academic stuff.

Is that automatically a bad thing?

Having said all that, in Dennett’s book, Intuition Pumps and Other Tools for Thinking, some of his ad hominems against his detractors are terrible: i.e., really gross and crude. So, yes, I was a little surprised by the many snide comments Dennett uses against his philosophical opponents.

Ad-Hominem Passages From Daniel Dennett

Here are five examples:

(1) Dennett: “‘I just can’t conceive of a conscious robot!’ Nonsense, I replied. What you mean is that you won’t conceive of a conscious robot.”

Response: Even if there is an element of truth in what Dennett says above, he must still know that not all people are entirely — or even at all — driven by their emotional reaction to this issue. That said, some — perhaps many — people are indeed offended — or depressed - by the very notion of a “conscious robot”.

Of course it may well also be the case that Dennett himself has an emotional reaction to this issue. That is, perhaps Dennett “won’t conceive” of the possibility that a “conscious robot” is impossible… or at least highly unlikely.

And when did Dennett become a mind-reader?

For a verificationist and/or neo-behaviourist, he seems to be very good at reading those contents of other people’s minds — those contents which most certainly haven’t been expressed in verbal behaviour.

(2) Dennett: “We found his [John Searle’s] though experiment fascinating because it was, on the one hand, so clearly fallacious and misleading argument, yet, on the other hand, just as clearly a tremendous crowd-pleaser and persuader.”

Response: Dennett surely shouldn’t claim that the Chinese room argument is “clearly fallacious and misleading”. It may be false or badly argued. But why the hyperbolic words “clearly fallacious” and “misleading”? Fallacious and misleading to whom? To Dennett and to the other people who have exactly the same position on this as he does? It’s odd, then, that the tens of thousands of words which have been written on this subject were all written in response to an argument that is, apparently, clearly fallacious and misleading.

What’s worse, Dennett even hints (or perhaps explicitly states) that the Chinese Room argument is an argument specifically designed to please crowds! Of course Dennett may be arguing that crowd-pleasing has been an unintentional result of the argument. That said, judging from the rhetoric, hyperbole and amateur psychiatry Dennett indulges in (both here and elsewhere) -— I simply doubt that.

(3) Dennett: “You don’t want me to disable this device [this person’s “intuition pump”]; you like the conclusion so much — Strong AI is impossible, whew! — that your eyes glaze over at the prospect of being dragged through a meticulous critique of a vivid, entertaining argument that supports your fervent hope…. The details don’t really interest you, only the conclusion. What an anti-intellectual copout!”

Response: This is Dennett reading other people’s minds again!

What’s more, Dennett even appears to indulge in amateur psychiatry (or simply psychology) with his talk of “eyes glazing over, “fervent hope”, etc. He even accuses the people who hold different views on this of being (if not in these precise words) dunderheads, philistines and even plain dishonest.

Factually, I doubt that more than one in ten of the people who’re sceptical (or simply critical) of some of the claims of Strong A.I. would ever say that “Strong AI is impossible”. There’s no need for this modal hyperbole from Dennett. And, from what I’ve read, John Searle (1932-) himself has never made such an absolute claim about Strong AI.

(4) Dennett: “To many people consciousness is ‘real magic’. If you’re not talking about something that is supercalifragilisticexpialidocious, then you’re not talking about consciousness, the Mystery Beyond All Understanding.”

Response: As with all the other quotes from Dennett, admittedly there’s an element of truth in the words above. But only an element! In other words, it depends on which philosopher of consciousness he’s talking about and what exactly that philosopher argues. In addition, depending on the quotes in this selection, that degree of truth depends on precisely what Dennett claims about other people and their specific arguments regarding Strong AI.

So sure - there are some philosophers and many laypeople who see consciousness as once they saw God, the soul, the paranormal, ley lines, astral travelling, the flat earth, etc. Yet there are also many philosophers and laypeople who don’t have this kind of mindset on the supposedly supercalifragilisticexpialidocious nature of consciousness. Alternatively, even if they do, they may still not be woo merchants. In addition, there are those who believe that consciousness is a “Mystery”. However, they don’t also believe that it’s “Beyond All Understanding”. That is, they may simply believe that consciousness is a mystery at this present moment in time. So such people don’t believe that this must remain so for evermore.

(5) Dennett: “I am suggesting, then, that David Chalmers has — unintentionally — perpetrated the same feat of conceptual sleight of hand in declaring that he has discovered ‘The Hard Problem’.”

Response: This last quote from Dennett may be a little unfair because he does, after all, use the word “unintentionally” about David Chalmers’ position. However, I’m struggling to see how Chalmers could carry out a “conceptual sleight of hand” and do so “unintentionally”.

The ironic thing is that Chalmers is very sympathetic to artificial intelligence — even if only to Weak AI. (See Chalmers’ discussion with Dennett here.) It’s just that alongside his embrace of (weak) A.I. Chalmers does still believe that there’s a Hard Problem of consciousness.

And then there’s the gross sarcasm (or do I mean irony?) from Dennett again.

It seems that Dennett simply can’t accept that Chalmers has “discovered” the Hard Problem as a result of thinking deeply about the subject over many years. Instead, Dennett believes that Chalmers has “perpetrated” a “slight of hand”.

Conclusion

Having quoted all the above, the very mentioning of someone else’s ad hominems (rather than his arguments) could itself be deemed to be an example of an ad hominem! Then again, one shouldn’t take a pure (or absolute) position on ad homs. Sometimes they may be perfectly acceptable in philosophical writing — though only if they’re backed up by argument, data, etc. In any case, I said that I was surprised by Dennett’s ad homs. I also said they were crude. I didn’t say that ad homs — in and of themselves — are automatically a bad thing.

I’ll put more meat on that claim with my very own ad hominem.

For a long time I’ve believed that Dennett thinks that many — or even all — the philosophers who don’t agree with his philosophical views on this subject are… well, religious. Or, at the very least, Dennett believes that they have (not Dennett’s own words!) “secret religious leanings” which motivate their positions. Now that’s simply false. It may be true about some of Dennett’s critics. However, it’s certainly not true of all of them. And even if some of Dennett’s critics are indeed religious, he (as a philosopher) shouldn’t simply assume that they are. What’s more, he must still concentrate on their arguments.

Talking about religion — here’s my second ad hominem.

I certainly suspect that Dennett is a little dogmatic and even theological when it — specifically — comes to his behaviourist and verificationist positions on philosophical matters. So it can certainly be said that materialists (or physicalists/reductionists/verificationists/scientists/etc.) can be dogmatic — as can those who uphold literally any position on any subject. (Anti-materialists, for example, can be very dogmatic too.) This is why it’s wise to make a distinction between materialism (or reductionism/verificationism/etc.) and those people who uphold this philosophical position.

This means that materialism (or reductionism/etc.) itself can’t really be dogmatic partly because there are so many varieties of such a theory (or position). And surely an abstract philosophical position (theory) can’t be dogmatic in itself — only its human adherents can be.

[I can be found on Twitter here.]

A Short Note on Science and Empiricism

Not only is there empiricism within philosophy, there’s also an empiricist position towards science. Indeed some philosophers have argued that science itself is empiricist (at least in the past).

The Scottish philosopher Dave Hume (1711–1776) put this case very simply when, according to the Irish philosopher Ernan McMullin (in his 1984 paper ‘A Case for Scientific Realism’), he “restricted science to the patterning of sense impressions”. Of course this also — at least partly — stemmed from Hume’s well-known position on causality. And causality was nearly always seen (i.e., up until the late 19th and early 20th centuries) as the “cement of the universe” (J. L. Mackie). Indeed the rejection of causation (or, more correctly, necessary causal relations) was at the heart of empiricist philosophy. In Hume’s case (at least according to McMullin), he

“simply rejects the notion of cause according to which one could try to infer from these impressions to the unobserved entities causing them”.

There are obviously many problems with empiricism. More specifically, there are problems with “empiricist science”.

Take elementary particles.

The fact is that no one has ever observed an elementary particle (such as an electron or certainly a quark). However, people do observe things which lead them to believe that electrons exist.

Take the cloud chambers which are (or were) used by scientists to discover elementary particles and their nature. Charged entities (such as electrons) leave ionized tracks which betray their presence (or at least their former presence). Nonetheless, you still can’t say that you’ve observed an electron. All you can say is that you’ve observed an ionized track in a cloud chamber.

Alternatively, Ernan McMullin writes:

“An electron may be defined as the entity that is causally responsible for, amongst other things, certain kinds of cloud tracks.”

McMullin goes into more detail when he argues that an electron “will be said to exist [] if a number of convergent sorts of causal lines lead to it”.

There are many other simple reasons as to why an empiricist approach to science fails. Or the least you can argue is that empiricism is inadequate.

Take the Devonian geological period.

McMullin calls this period (or its postulation): “a theoretical entity”. It’s a theoretical entity primarily because it can’t be observed. However, clearly that doesn’t mean that we should reject it as a theory or even as a genuine period in the Earth’s history. In other words, even though the Devonian period can’t be observed, we can still say that this period existed roughly 400 to 350 million years ago. McMullin also says that during the Devonian period

“the dominant life form on earth was fish and a number of important developments in the vertebrate line occurred”.

The American theoretical physicist, string theorist and mathematician physicist Brian Greene (1963-) also offers some choice examples from the history of science.

Firstly, James Clerk Maxwell’s electromagnetic fields. Greene writes:

“James Clerk Maxwell’s architecture introduced a significant step in abstraction. Vibrating electric and magnetic fields are not the kinds of things for which our senses have evolved a direct affinity. Although we can see ‘light’ — electromagnetic undulations whose wavelengths lie in the range our eyes can detect — our visual experiences don’t directly trace the undulating fields the theory posits.”

Then elsewhere Greene mentions general relativity and quantum mechanics:

“Now, I’ve seen watches tick and I’ve used rulers to measure, yet I’ve never grasped spacetime in the same way I grasp the arms of my chair. I feel the effects of gravity, but if you pressed me on whether I can directly affirm that I’m immersed in curved spacetime, I find myself back in the Maxwellian situation… Probability waves give rise to predictions for where there this or that particle is likely to be found, but the waves themselves slither outside the arena of everyday reality.”

Shockingly (or perhaps not), then, it can be argued that this line of reasoning may lead us to happily embrace such things as the multiverse, strings, branes and whatnot, as it does in the particular case of Brian Greene. Whether these theories (or things) clash violently with empiricist science is, of course, an issue all on its own.

[I can be found on Twitter here.]

The Quantum World = The Mathematics

 First things first.

This essay may appear to advance two mutually-contradictory positions. On the one hand, it argues that without the mathematics (or, more correctly, without the mathematical formalism/s), there would be no quantum world — or at least no quantum mechanics. Yet, on the other hand, this essay also argues against Pythagoreanism — at least as it applies to this specific issue.

The main anti-Pythagorean argument in the following is that the world (or Nature) isn’t literally mathematics (whatever that may mean) or “made up” of numbers. It’s simply that, in quantum mechanics at the very least, without the mathematics, we’d have (almost) nothing.

Pythagoreanism: Things are Numbers

Pythagoreans believe that the world literally is mathematical. Or, perhaps more accurately, they believe that the world literally is (without the suffix “cal”) mathematics. I make this either/or distinction because if a physicist argues that “the world is mathematical”, then that may only mean that the world can be accurately — even very accurately — described by mathematics. The Pythagorean, however, states that “things are numbers”. Such a person therefore establishes a literal identity between the maths and the world (or parts thereof).

Yet we don’t need to accept the latter.

Having said all the above, it may well be the case that this essay does indeed advance a Pythagorean position — at least when it comes to quantum mechanics. That’s because it’s sometimes hard to tell what the Pythagorean position actually is. For one, it’s hard to make sense of the locution that the world is mathematical or that it’s made of numbers.

So the question which must now be asked is this:

What is it for “things” to be “numbers”?

To repeat: the Pythagorean position isn’t to only to argue that mathematics can describe (or model) things — it’s to argue that things literally are numbers. But what does that actually mean? And, as a consequence of that, it can now be asked if the statement “All things are numbers” is to be taken poetically or literally. Taken literally, it hardly makes sense. Taken poetically, it still requires much interpretation.

One interpretation of the Pythagorean position is that if things are numbers, then it’s no surprise that — for example — string theory is on top of things when it comes to describing reality. What I mean by that is this:

i) If things are numbers,
ii) and numbers are also used to describe (or model) things (which are numbers),
iii) then numbers are describing (or modelling) numbers.

That would mean that we never escape from numbers. Who knows, perhaps that’s precisely the result which Pythagoreans want!

To change tack a little.

The physicist John Archibald Wheeler (1911 — 2008) provided the best riposte to Pythagoreanism in physics. (I’m not entirely sure if this was his intention.)

It’s often been said that Wheeler used to write many arcane equations on the blackboard and stand back and say to his students:

“Now I’ll clap my hands and a universe will spring into existence.”

According to Pythagoreans, however, the equations are the universe.

And, after that comment, Steven Hawking (1942–2018) trumped Wheeler with an even better-known quote. He wrote:

“Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?”

The American science writer Kitty Ferguson (1941-) offered a (possible) Pythagorean answer to Hawking’s question. She suggested the possibility that “it might be that the equations are the fire”. Alternatively, could Hawking himself have been “suggesting that the laws have a life or creative force of their own?”. Again, is it that the equations are the fire?

So what, exactly, does “breathe[] fire into the equation [to] make a world”?

John D. Barrow

Mathematics is an extremely useful tool. The English cosmologist, theoretical physicist and mathematician John D. Barrow (1952–2020), however, went one step beyond that truism. Barrow actually put his — arguably — Pythagorean position in the following way:

“By translating the actual into the numerical we have found the secret to the structure and workings of the Universe.”

Of course almost everyone can happily accept the Universe and its parts are assigned numbers… Or are described by numbers… Or are captured by numbers… Or are explained by numbers… Or are (to use Barrow’s own words) translated into numbers. The thing is, that’s not actually a Pythagorean position.

So, as a consequence of all the words above, it’s no wonder that so many people have believed that through maths (as Barrow puts it) “we have found the secret to the structure and workings of the Universe”. Yet even here there must be a non-Pythagorean (as it were) remainder. What I mean by this is that maths finds the secret of things which already and separately exist — in this case, the “structure and workings” of the world. Surely it doesn’t also need to be argued that these structures and workings are literally mathematics (or literally numbers).

… Or perhaps it does.

To repeat: to the Pythagorean, the world and its parts are actually mathematical. This means that it isn’t that maths is simply helpful for describing the world — the world itself is mathematical. Indeed one must take this literally. Here’s Barrow again on the Pythagorean position:

“[The Pythagoreans] maintained ‘that things themselves are numbers’ and these numbers were the most basic constituents of reality.”

Barrow then became ever clearer when he continued in the following manner:

“What is peculiar about this view is that it regards numbers as being an immanent property of things; that is, number are ‘in’ things and cannot be separated or distinguished from them in any way.”

Moreover:

“It is not that objects merely posses certain properties which can be described by mathematical formulae. Everything, from the Universe as a whole, to each and every one of its parts, was number through and through.”

As stated earlier, it’s hard to grasp what the sentence “things themselves are numbers” even means. Can we really argue that reality and its parts are mathematics (as in the “is of identity”)? Can we really argue that reality and its parts are literally made up of numbers or equations? And can we even argue that reality and its parts somehow instantiate maths, numbers or equations?

Max Tegmark

The physicist and cosmologist Max Tegmark (1967-) also puts the contemporary case for Pythagoreanism in the following very concrete example:

“[If] [t]his electricity-field strength here in physical space corresponds to this number in the mathematical structure for example, then our external physical reality meets the definition of being a mathematical structure — indeed, that same mathematical structure.”

To spell out the passage above.

Max Tegmark isn’t simply arguing that mathematics is perfect for describing the “electricity-field strength” in a particular “physical space”. He’s arguing that the electricity-field strength is a “mathematical structure”. That is, the mathematics we use to describe the electricity field is one and the same thing as the electricity field. Thus, if that’s really the case, then the so-called “miracle of mathematics” is hardly a surprise! And that’s because — as already stated above — we essentially have a situation in which maths is describing maths. And if maths is describing maths, then the word “describing” is surely not the right word to use in the first place.

Tegmark gives us more detail on his position when he tells us that

“there’s a bunch of numbers at each point in spacetime is quite deep, and I think it’s telling us something not merely about our description of reality, but about reality itself”.

It can be argued that Tegmark contradicts himself in the above.

At one point Tegmark argues that a field “is just [ ] something represented by numbers at each point in spacetime”. Note here that we have the two words “something [my italics] represented”. Yet elsewhere Tegmark also argues that the field “is just” (or just is) a mathematical structure — the latter two words implying that all we have is number. To repeat: Tegmark argues that the field is “represented” by “three numbers at each point in spacetime”. Yet he doesn’t (in this passage at least) also say that the field is a set of numbers (or even a “structure” which includes numbers).

So perhaps there’s a difference between arguing that (as the original Pythagoreans did) “things themselves are numbers” and arguing that the world is mathematical. (I may be drowning in a sea of grammar here.) The latter may simply state that the world exhibits features which are best expressed (or described) by mathematics. The former, on the other hand, states that the world literally is mathematics.

Now take the case of string theory.

Michio Kaku and String Theory

Not only is string theory seemingly more dependent on mathematics than all the other areas of physics (though, of course, that can be debated), it seems that some physicists even see string theory as being a “branch of pure mathematics”.

The string theorist Michio Kaku (1947-), for example, doesn’t hide from this when he quotes a “Harvard physicist” saying as much. In Kaku’s own words:

“One Harvard physicist has sneered that string theory is not really a branch of physics at all, but actually a branch of pure mathematics, or philosophy, if not religion.”

After Kaku puts the Pythagorean position, he then quotes Albert Einstein (i.e., as backup) stating the following:

“‘I am convinced that we can discover by means of purely mathematical construction the concepts and the laws… which furnish the key to the understanding of natural phenomena.’”

Einstein went deeper when he added these words:

“‘Experience may suggest the appropriate mathematical concepts, but they most certainly cannot be deduced from it.’”

Now all the words above do indeed sound Pythagorean (or, more broadly, Rationalist) — at least on the surface. And Einstein seems to more or less come clean about this in his final sentence. Thus:

“‘In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.’”

The strange thing is that Kaku also seems to offer us a mutually-contradictory account (in his book Beyond Einstein) of Einstein’s position on mathematical physics. Kaku writes the following words:

“Einstein revealed a clue to the way he arrived at his great discoveries: he thought in physical pictures. The mathematics, no matter how abstract or complex, always came later, mainly as a tool by which to translate these physical pictures into a precise language.”

Indeed elsewhere in the same book Kaku also writes:

“[] Feynman, and other great scientists []thinks in terms of pictures that express the essential physical concept. The math comes later.”

If we return to Kaku’s own position.

As for the charge (if it is an charge) of Pythagoreanism against Kaku, don’t take my word for it: take the words of the man himself. Firstly Kaku lays out the essential Pythagorean position in this way:

“Not surprisingly, the Pythagoreans’ motto was ‘All things are numbers.’ Originally, they were so pleased with this result that they dared to apply these laws of harmony to the entire universe.”

Then Kaku continues by arguing that “with string theory” what we have is “physicists [] going back to the Pythagorean dream”.

Quantum Mechanics

Philip Ball

The science writer Philip Ball (1962-) argues (in his book Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different) that the mathematics of quantum mechanics “doesn’t say anything about the ‘real world’”. Many physicists — and some philosophers — have also echoed that sentiment. Yet that may appear to be an odd position. It’s odd because if the mathematics of quantum mechanics is extraordinarily successful when it comes to predictions, applications, engineering, technology and whatnot, then (perhaps almost by definition) surely it simply must be about the real world…

Yet what work is the word “real” actually doing here? Does it imply that we (or the maths) must mirror the world? But how does — or would — that work? And even if the maths perfectly describes physical phenomena in terms of their magnitudes, values, strengths/charges, velocities, spatial dimensions/positions, etc., then is all that actually a case of mirroring the world itself? Surely if the maths of quantum mechanics mirrored the world, then it would look — and even be — the same as that world. In that case, what purpose would such mirroring actually serve? (Think here of the often-made claim: The best model of x is x itself.)

So it can be argued that maths can’t — literally — mirror the world.

Despite saying that, one thing is still certainly the case.

As stated in the introduction, without the maths, we’d have almost (or even literally) nothing to say about the quantum world — real or otherwise. When it comes to the quantum world, the usual (as it were) means of ownership aren’t available to us. That is, we can’t observe, feel, smell or (often) even imagine the quantum world. Thus the maths is all we’ve got.

All this is excellently expressed in the following passage from the science writer John Horgan (1953-):

“[M]athematics helps physicists definite what is otherwise undefinable. A quark is a purely mathematical construct. It has no meaning apart from its mathematical definition. The properties of quarks — charm, colour, strangeness — are mathematical properties that have no analogue in the macroscopic world we inhabit.”

Thus if maths is all we’ve got, then it’s not really a surprise that many physicists (i.e., the more philosophical ones) argue that quantum mechanics doesn’t really say anything about the real world. (This has been said since Niels Bohr in the 1920s.) Or, at the very least, everything important — or even relevant — that’s said about the quantum world is said by the maths.

So when Philip Ball also writes that Richard Feynman could only do “quantum theory” (i.e., the maths), then that’s not a surprise. That’s because it can be argued that the maths is all we’ve got and all Feynman had. Indeed when we stray beyond the maths into interpretation, then we (perhaps by definition) can’t help but get things wrong.

Or at least that’s one (sceptical) scenario we must consider.

Again, it’s not a surprise that — even — Feynman didn’t “know what the maths means”. That may be because the words what the maths means are — almost — meaningless. At the very least, there’s a hint here that we can’t go beyond the maths. Yet it’s still the case that so many philosophers, and a somewhat lesser number of physicists, believe that the maths is only second best to something far… deeper.

John Gribbin

The British science writer and astrophysicist John Gribbin (1946-) appears to agree with these conclusions. That is, as a consequence of much of what’s been said above, it can be concluded that all the imagery, picture painting, metaphors, analogies, etc. we find in the popular accounts — and even the technical interpretations — of the quantum world are simply (to use Gribbin’s own words)

“crutches to help us imagine what is going on at the quantum level and to make testable predictions”.

Indeed Gribbin also believes that

“none of [the quantum mechanical interpretations] is anything other than a conceptual model designed to help our understanding of quantum phenomena”.

Indeed Gribbin also talks about the interpretations of quantum mechanics:

“I stress, again, that all such interpretations are myths, They are not, any of them, uniquely ‘the truth’; rather, they are all ‘real’, even where they disagree with one another.”

Many will read Gribbin’s words as being very radical — and even deflationary — when it comes to quantum mechanics. Yet, despite all the above, Gribbin also happily acknowledges that all these quantum interpreters genuinely believe that their very own interpretations are true. He writes:

“[T]he interpreters and their followers will each tell you that their own favoured interpretation is the one true faith, and all those who follow other faiths are heretics.”

And that passage comes straight after Gribbin had told us that

“[a]t the level of equations, none of these interpretations is better than any other”.

Thus, logically, “none of the interpretations is worse than any of the others, mathematically speaking”. That said, all this hinges on precisely how we’re supposed to take the phrases “at the level of equations” and “mathematically speaking”.

Gribbin also becomes very psychological (or aesthetic) when he concludes (as the very end of one of his books) that we are

“free to choose whichever one gives you most comfort, and ignore the rest”.

Again, there may well be an argument that all the interpretations of quantum mechanics are superfluous when it comes to predictions, tests, experiments, technology, etc. However, that certainly doesn’t mean that all these interpretations are “equally good”. They may all be equally bad in the sense that they don’t make the slightest bit of difference when it comes to to mathematical theory, predictions, (quantum) technology, etc. However, are they all equally good in literally every other respect?

Despite all Gribbin’s words above, he still stresses the importance of what he calls a “physical model” of “mathematical concepts”. He writes (in his Schrodinger’s Kittens and the Search for Reality) that “a strong operational axiom” tells us that

“literally every version of mathematical concepts has a physical model somewhere, and the clever physicist should be advised to deliberately and routinely seek out, as part of his activity, physical models of already discovered mathematical structures”.

Yet even in Gribbin’s case and on a final quasi-Pythagorean reading, it’s still clear that a “mathematical concept” comes first and only then is a physical model found to square with it.

[I can be found on Twitter here.]

Colin McGinn’s Important Paper, ‘Can We Solve the Mind-Body Problem?’

Our brains are made of matter: neurons, biochemicals and other physical stuff. All these things are (as it were) “flesh and blood”. So, the British philosopher Colin McGinn (1950-) asks, how can “technicolour phenomenology arise from [this] soggy grey matter?”. In other words, why does the brain produce, cause or give rise to something so different from matter itself? What makes the brain so different to all the other human organs? More specifically, what is it, exactly, about billions of neurons that gives rise to consciousness or experience?

These questions were asked (if not in these precise ways) in Colin McGinn’s well-known and important paper, ‘Can We Solve the Mind-Body Problem’. That paper was published in 1989 in the journal Mind.

Mind and Brain

Despite all the above, the main issue of McGinn’s paper is not one of how or why consciousness arises from the the brain. It raises the possibility that the link between the brain and the mind (or, more accurately, consciousness/experience) may be — permanently? — closed off to us.

McGinn calls this “cognitive closure”. And the “property” responsible for that cognitive closure he names P.

McGinn focuses on our (possible) cognitive limitations.

But firstly let’s take different species of animals. McGinn tells us that they are

“capable of perceiving different properties of the world and no species can perceive every property things may instantiate”.

Think here of bats and echolocation. Dogs too can hear sounds which we can’t even register and they have a far better sense of smell than human beings. So what’s true for other animal species will also be true for human beings.

Yet all these examples only display sensory — i.e., not cognitive — limitations and extensions.

So let’s get back to cognitive closure.

McGinn’s (or our) P is a real (or actual) property. It may even be concrete (e.g., part of the brain). Thus McGinn doesn’t believe that he’s (to use his own term) “irrealist” about P. That said, McGinn does cite the possibility that P is noumenal. As with Kant, noumena are permanently unknowable — by (Kantian) definition. (Kant also believed — living before Darwin - that the structures of the mind-brain would remain static for… well, the rest of time.)

It’s the very nature of the mind-brain link which renders P permanently closed off to us. Yet despite that possibility, P could still be — at least according to McGinn — part of a respectable naturalistic theory. Again, we shouldn’t be irrealist or mysterious about P. (Many philosophers do see Colin McGinn as a mysterian.) That said, one can’t help but see x as being mysterious if that x is also believed to be permanently closed off to us.

So does McGinn actually think in terms of permanent cognitive closure?

Hume, Locke and Kant

McGinn discusses another case of closure which occurred in the philosophy of David Hume (1711–1776).

To Hume, our perceptual limitations determine our cognitive limitations. (Hume was a thoroughgoing empiricist.) More clearly, Hume believed that because our “ideas” are always copies of sensory “impressions”, then that also meant that our concept-forming system itself must always rely on— in whichever ways — those impressions. Thus nothing can transcend the information provided by impressions. (It can be asked here what was Hume’s philosophical position — as an empiricist — on such things as the existence of distant stars, the past, other minds, mathematics, etc.)

Now for Locke.

According to McGinn, the English philosopher John Locke (1632–1704) also believed that “our ideas of matter are quite sharply constrained by our perceptions”. To Locke, this also meant that (to use McGinn’s words) “the true science of matter is eternally beyond us”. Mind-free matter is a (to use Locke’s own well-known phrase) “something-I-know-not-what”. In concrete and specific terms, this means (or in the 17th century it meant) that we can never know what, say, solidity “ultimately is”. (Why does McGinn feel the need to use the word “ultimately”?) Again, this doesn’t mean that Locke believed that nature “is itself inherently mysterious”. (It can be asked how McGinn knows that Locke didn’t think this.) According to McGinn’s Locke, the mystery simply

“comes from our own cognitive limitations, not from any objective eeriness in the world”.

Kant, on the other hand, believed that knowledge begins with impressions (or, more accurately, with “phenomena”). However, he also believed that impressions aren’t the sole source of our knowledge. That’s primarily because Kant postulated innate a priori concepts and categories which (as it were) get to work on phenomena.

Back to McGinn

Colin McGinn explicitly states his position with regards to P. To repeat: he claims to resolutely shuns what he calls “the supernatural”. P must be “natural”. (How does he know this?) He goes on to say that

“it must be in virtue of some natural property of the brain that organisms are conscious”.

McGinn then concludes:

“There just has to be some explanation for how brains subserves minds.”

Again, why must P be natural? Is this a case of McGinn having (as it were) faith in naturalism? Alternatively, is McGinn’s theory of P naturalist in the first place?

Alan Turing on Intuition and Human-Machine Computation

What is a computation?

According to Alan Turing (writing in 1936/7), when it comes to human beings, a computation is the following:

A computation occurs when the human mind carries out a mental action according to a rule.

The words above (which aren’t Turing’s own — exact — words) don’t mean that people know that they’re following a rule. (Therefore people don’t know what that rule is.) Human grammar, after all, is also rule-governed; though not all children — and even many adults — can formulate the grammatical rules they employ. Nonetheless, almost everyone still follows these rules. (This is similar to both the philosopher’s notion of tacit knowledge and Noam Chomsky’s theory of innate universal grammar.)

It was said that computability is the mind’s following a rule. Well, Turing believed that this is usually the case. So does that mean that there can be computability (or computations) without the following of rules?

More specifically, when machines (or computers) modify their own behaviour, is that an example of not following a rule?

It’s certainly the case that computers can do things which weren’t predicted by their programmers (or designers). So does that mean that such computers aren’t following any rules? After all, they could be following new rules which they have (as it were) created themselves. So not following the programmers’ rules doesn’t automatically mean that computers aren’t following any rules at all.

We can even say that such computers have genuinely learned (forget the semantics for now) something which wasn’t fed into them by their programmers (or designers). However, they may still be following rules. In fact the new rules may be the logical/mathematical consequences of the programmers’ old rules.

That said, how does all this stuff about rule-following computers directly connect with the brains and minds of human beings?

Alan Turing did think that the human brain is a machine… Or at least he thought that many — perhaps all — of the functions of the brain are that of a machine. Nonetheless, he also believed that the brain is so complex that it can give us the impression of not following a rule.

Now it seems clear that it’s the complexity of the brain that generates only an “appearance” of the brain not following a rule (see here). So that basically means that even though the brain appears not to be following a rule, it may still be doing so. It’s just that the brain is so complex that the investigator — or even the (as it were) owner of the brain — couldn’t know all the rules which the brain is following. Similarly, the complexity of the brain may also generate the belief that it is an “indeterministic machine”. Yet if the brain were truly indeterministic, one could also question its status as a “genuine machine”. (Douglas Hofstadter, for example, seems to have believed — at least at one point in his career — that if a “machine” does go beyond the rules, then, by definition, it can’t actually be a machine — see here.)

Following on from all this, does that mean that if the computer has learned something — or has created its own rules — that it’s displaying (or showing) what’s often called “genuine intelligence”? After all, the computer has gone beyond what the programmer programmed. It can be supposed that all this depends on the semantics of the word “intelligence” (as with the word “learned” earlier). If not following the rules of the programmer is a case of genuine intelligence, then the computer is displaying genuine intelligence. Nonetheless, is not following the rules of the programmer really genuine intelligence or is it something else? In that case, what exactly is it?

Intuition

So what is intuition?

It depends on how the word is used and in which context it’s being used. In Alan Turing’s case, we (or mathematicians) use our intuition when seeing the truth of a formally unprovable Gödel sentence. That’s because Gödel sentences can’t be proved. Nonetheless, they’re true and they’re taken to be true.

How do we know they’re true without mathematical proof?

According Kurt Gödel himself, it’s through the use of human intuition (see here).

And if a Gödel sentence can’t be formally proved, then it can’t be shown to be true through “mechanical” methods. Again, it can’t be proved because proof is deemed to be a mechanical process (at least in this respect).

Another way of looking at intuition is with another of Turing’s ideas: the “oracle”.

In the case of a Gödel sentence, the mathematician (or the oracle) simply “has an idea” that the Gödel sentence is true. That is, he doesn’t use a mechanical method to establish its truth. He has an idea (or an intuition) that it is true. This hints at the brain (not the mind) working in ways which are way beyond conscious thought. That is, intuition is a result of the brain (not the mind) indulging in unconscious processes.

You may now ask how something can be established as true — especially in mathematics — without proof. You may also ask how truths can be established — especially in maths — only on the flimsy basis of a mathematician’s (or even of hundreds of mathematicians’) intuition or his simply “having an idea”.

Computer scientists — and the philosophers of mind who focus on computer/brain comparisons (or who even see the brain-mind as a literal computer) — will like Turing’s conclusion (of 1945/6) that algorithms are enough to account for all mental activity. Bearing in mind the previous comments about intuition, Turing believed that algorithms also encompassed non-mechanical intuition.

Just as intuition follows algorithms (therefore rules), Turing believed that what he called “initiative” didn’t require uncomputable steps either. In other words, both human and computer initiative is also a mechanical process. (That would make the idea of computer’s showing initiative less problematic for the simple reason that what it’s doing is still a computable — or mechanical - process.) However, as stated earlier when it was mentioned that computers may go beyond the rules (or programmes) created by the programmer, even if a computer departs from the computations which were programmed by the programmer, it would still be following a (new) rule, indulging in computations, or following mechanical processes.

Indeed — what else could a computer (or machine) be doing?

Another way of looking at a computer’s — or a Turing machine’s — ability to follow its own rules (or to show initiative) is for the programmer to engineer an element of randomness into the computer (or into the programme). That was what Turing did with his Manchester computer of 1948/50. That means that such randomness is deemed to (as it were) bring about intuition (or initiative). However, it would still be intuition (or initiative) that’s grounded in computation or in mechanical processes. The randomness, therefore, would simply be a result of the computer not abiding by the programmer’s rules (or programmes). It wouldn’t — or doesn’t — mean that the computer has gone beyond rules or computations.

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