Deflating Quantum Mechanics: Pictures, Images & Analogies

The use of the words “deflating quantum mechanics” isn't meant in the sense of offering any challenge to quantum mechanics (QM) itself. Of course not. For a start, I'm not a physicist. (One would need to be a great physicist to challenge the fundamentals of quantum theory.) This piece, instead, is primarily aimed at the interpretations of QM by the layperson and indeed even by some physicists. In other words, quantum theory is fine by me. What I do have a problem with is commentators deliberately attempting to make QM even more (as it's often put) “weird” than it actually is. In addition, there's also of the problem of people focusing entirely on quantum weirdness.

More relevantly, it's argued that this quantum weirdness is largely brought about when people use images, pictures or analogies which are only applicable to the everyday world, and then applying them to the quantum realm. This - almost by definition - must surely be like pushing square shapes into round holes. In other words, it's bound to make QM weird/er.

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It would seem that one of the main positions advanced in this piece is partly contradicted by a well-known quote from Albert Einstein. Namely:

“If I can't picture it, I can't understand it.”

So despite Einstein's words, it can also be said: 

If you can picture the phenomena of quantum mechanics, then you don't understand them. 

Werner Heisenberg, for example, argued that all the imagistic or analogical descriptions of QM are problematic. More precisely, he stated the following:

“Progress in science has been bought at the expense of the possibility of making phenomena of nature immediately and directly comprehensible to our way of thought.”

In other words, in order to make the scientific 

“phenomena of nature immediately and directly comprehensible to our way of thought”, 

scientists have relied on images, pictures and analogies which simply don't do the (complete) job. On the other hand, when scientists don't use such analogies, pictures or images, then QM is incomprehensible to “our way of thought”.

There's a deep problem here - at least for laypersons!

So what if it's partly the overuse of imagery and analogies which makes QM seem so weird? Sure, QM is indeed weird. Nonetheless, using images, picture and analogies which are applicable to the macro-scale (then applying them to the micro-scale) can't help but make things weirder. On the other hand, without imagery and the requisite mathematics, how does any layperson or even physicist know that QM is weird at all?

It's not only laypersons who have problems with “picturing” the phenomena of QM - physicists do too. And since the failures (or limits) of the imagination have just been been stressed, here's the philosopher Ernan McMullin stating the following:

“If we cannot quite imagine what they are, this is due to the distance of the microworld from the world in which our imaginations were formed, not to the existential shortcomings of electrons...”

Of course all this depends on what exactly is meant by the word “picturing” or “imagining”. It also depends on what's meant by the words “understanding quantum mechanics”. Sometimes the problem is also to do with the concepts we use to describe QM phenomena. In other words, it's not only about imagery.

Take a classic example: “wave-particle duality”.

Perhaps part of this problem is that the wave description isn't very apt in the first place. That is, waves at the subatomic level aren't like waves in the sea, in your bath or even like waves at all. (The graphic representations of the “peaks and troughs” of the interference pattern, for example, may not help.) This is why Erwin Schrodinger, for one, decided to call them “wave functions” instead of "waves". In other words, the wave description (even if only analogical) was never satisfactory to Schrodinger and indeed to many other physicists.

So what about particles?

The American philosopher Ernest Nagel once discussed the “puzzling characteristics” of particles. These puzzling characteristics were seen to have been “incompatible”. (The word “incompatible” isn't a synonym of “contradictory”.) More precisely, Nagel argued that electrons are

“construed to have features which make it appropriate to think of them as a system of waves”.

Yet, on the other hand, electrons “also have traits which lead us to think of them as particles”.

Since waves and particles have just been discussed, it's worth noting here what the astrophysicist and writer John Gribbin has to say on this. Gribbin ostensibly takes an extreme position on this part-rejection of analogies, images and pictures. He writes:

“In the world of the very small, where particle and wave aspects of reality are equally significant, things do not behave in any way that we can understand from our experience of the everyday world...all pictures are false, and there is no physical analogy we can make to understand what goes on inside atoms. Atoms behave like atoms, nothing else.” 

It can of course be said that even if it's correct that

“all pictures are false, and there is no physical analogy we can make to understand what goes on inside atoms”,

then it may still be the case that (at least for laypersons) that's all we've got. Indeed without the mathematics, all we have are pictures, images and analogies. So we'd better make do with all that. And surely John Gribbin isn't arguing that pictures, images and analogies serve no purpose. Indeed he can't be arguing that because his books make extensive use of them. Having said that, all Gribbin's pictures, images and analogies do come with words of warning (as can be seen in the quote above).

In fact we can even say that the very use of the words “particle” and “wave” may mean that Gribbin himself is using pictures or images and/or being analogical. That is, if “in the world of the very small” it's the case that

“things do not behave in any way that we can understand from our experience of the everyday world”,

then why is Gribbin using the words “particle” and “wave” in the first place?

Concepts

It's not only QM that's the problem here.

According to Freeman Dyson (who was talking about a “new theory [of] black holes”), the problem was that Stephen Hawking (at least at that point) was “still groping in the dark for concepts which will make his theory [of black holes] fully intelligible”.

All this depends on what Dyson meant by “concepts”. After all, he might have only been referring to mathematical concepts. In fact Dyson continued by saying that

“[a]s usual when a profoundly original theory is born, the equations come first and a clear understanding of their physical meaning comes later”.

So not only is it the case that the mathematics isn't equal to the later images, pictures and analogies which people use for physical phenomena: at first the mathematics isn't even equal to anything “physical” at all. Or, more precisely, the maths isn't equal to the “physical meaning” which may - or will - “come later”.

This shouldn't be a surprise because mathematics itself is an abstract realm and numbers and equations (not their written symbols, etc.) are said (at least by some philosophers and physicists) to be “abstract objects”. Thus the equations Dyson referred to only became (as it were) concrete when given a “physical meaning” or when applied (in this case) to black holes.

So here we have a disjunction between mathematics and reality/nature that's only brought together when the mathematics is given a physical meaning or when applied to reality. However, even then it can be said that the disjunction still exists in a strong way. This means that whereas many scientists stress the unity of maths and physical reality, the opposite (as with string theory!) can also be stressed.

So we can still ask this question:

Freeman Dyson talked about the concepts which will make the theories of physics fully intelligible... but fully intelligible to whom?

Was it to himself and Stephen Hawking? To other physicists generally? Or to laypersons?

Scales and Levels

Richard Feynman once wrote (when talking about an electron taking “many paths” at the same time) the following:

“[Quantum mechanics] describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is – absurd.”

Perhaps when Feynman used the words “common sense”, that common sense position may primarily be a result of attempting to think of (or visualise) what happens at the quantum-mechanical scale in the same way in which one thinks of (or visualises) what happens at the everyday scale.

Feynman himself singled one such scale: the scale of the atom. He said that

“if an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple”.

We also have this from the nuclear physicist Kenneth W. Ford:

“For example, to picture the nucleus, whose size is about 10^-4 to 10^-5 of the size of the atom, one may imagine the atom expanded to, say, 10,000 feet or nearly two miles... A golf ball in the middle of New York International Airport is about as lonely as the proton at the center of the hydrogen atom.”

Think also the extra dimensions of string theory. Only four of string theory's extra dimensions are observable. (That's if you can literally observe macro-object-free spacial or time dimensions.)

Even if extra dimensions do exist, they may still be (or are) incredibly small; as well as “compacted”. Thus the very idea of extra dimensions bears little relation to those portrayed in horror and science-fiction films. Indeed, way back in 1926, the extra dimension suggested by Oskar Klein was thought be curled up and too small to be detectable. Thus only something equally small could (as it were) live in this extra dimension.

And strings themselves are fantastically smaller than protons, neutrons and electrons. Let Freeman Dyson explain by going even further with superstrings:

“First, the entire universe. Second. The planet Earth. Third, the nucleus of an atom. Fourth, a superstring. The step in size from each of these things to the next is roughly the same.The Earth is than the visible universe by about twenty powers of ten. An atomic nucleus is smaller than the Earth by twenty powers of ten. And a superstring is smaller than a nucleus by twenty powers of ten. That gives you a rough measure of how far we have to go in the domain of the small before we reach superstrings.”

In any case, things at different scales (or things of different types) display remarkably different kinds of behaviour.

Take fleas, which can jump 100 times their own height. Take the bacteria that survive below freezing point. And on the moon, astronauts can float. However, these examples are still in a different logical space to the things which occur at the quantum scale. At the QM scale, some things are deemed to be "paradoxical" and even "logically contradictory". Nothing a flea or astronaut does can be described that way.

So when we're talking about the subatomic scale, things are almost bound to be fundamentally different. And when we get down to the scales tackled by string theory, then you'd hardly expect the kind of things you experience in your local pub.

Scales and Superposition

There's a big problem with this emphasis on the importance of scales when it comes to QM. This means that it will need to be said why it is that these scales (i.e., the micro and macro scales) should make such a profound difference to things.

Take superposition.

It's often argued that superposition is only applicable at the micro-scale. It's also argued that it “cancels out” at the macro-scale. More technically, it's said that when there are many superpositions at the quantum level, then when such superpositions are taken together, they produce a macro-state that is “definite”. That is, such a “probabilistic collapse” would result in a definite statistical process at the macro-level.

Nonetheless, this very-neat division also needs to be explained: it has been rejected.

Put simply, there are good reasons to expect superpositions at the macro-level too. Indeed there are “interpretations” (for example, Hugh Everett's) which state that superpositions do occur at the macro-level: it's just that we only experience one such state of each superposition.

We can also take Professor Brian Greene's general point about this far-too-neat micro/macro division:

“It's not as though the universe comes equipped with a line in the sand separating things that are properly described by quantum mechanics from things properly described by general relativity. Dividing the universe into two separate realms seems both artificial and clumsy.”

This position seems to back up a point Roger Penrose has made about how different levels of description (which, he argues, are brought about by the effect of “measurement” or observation) determine Greene's “line in the sand” between the quantum realm and the “classical” realm. In Penrose's own words:

“Since randomness comes in, quantum theory is called probabilistic. But randomness only comes in when you go from the quantum to the classical level. If you stay down at the quantum level, there's no randomness. It's only when you magnify something up, and you do what people call 'make a measurement'. This consists of taking a small-scale quantum effect and magnifying it out to a level where you can see it. It's only in that process of magnification that probabilities come in.”

Thus Penrose particularly notes how randomness is a consequence of observing quantum phenomena at the “classical level”. Nonetheless, this can still be deemed to be an epistemic problem, rather than an ontological one. That is, the probabilities (or randomness) arise not from the ontology of the quantum world, but from our epistemic access to it.

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Philosophical Questions About Philosophy

Philosophy can be defined or described in accordance with how it has been practiced in the Western tradition. Alternatively, the word 'philosophy' can be defined simply in terms of dictionary definitions or even according to its etymology.

The latter approach isn't very helpful. At least not from a metaphilosophical perspective. Similarly, saying that philosophy, for example, was simply the “study of all examples of knowledge” (at least for some ancient Greeks) isn't going to get us very far either. For a start, it simply begs the question: What is knowledge?

And neither does etymology help us. Namely, philo = love; phia = wisdom. One problem with taking the etymology of the word 'philosophy' seriously (as Martin Heidegger did) is that it seems to be the case that philosophy should be all about the self – or about the “lover of wisdom”. In other words, “how to live well”, “how to live the good life”, “how to be fulfilled and happy", etc. Clearly all this has only been a small aspect of Western philosophy; and, perhaps, a big aspect of various religions. It can even be classed as self-centered. (In certain strands of existentialism, it's mainly about living a sincere life – sincere to one's genuine self.)

Here questions abound. Why should philosophy be all about how to live one's life? Why should I live the good life rather than the bad life?

Some have explicitly said that “philosophy is committed to self-knowledge”. There's some truth in this in that Socrates famously said “know thyself”. Though was that really about the self or was it more about the self's relation to knowledge about the world/reality generally? In other words, if one knows oneself (therefore one also knows where one's going wrong – intellectually), then one will have a better philosophical grip on the world or reality.

We can also answer the question “What is philosophy?” by asking a similar questions about the sub-branches of philosophy. For example, we can ask: What is metaphysics? Here too we can become all etymological and say that the Greek word meta-physika literally means "what comes after physics". That's not very helpful either. (What's meant by “after” or “meta”?) So let's forget dictionary or etymological definitions and go with the following.

According to Wikipedia, metaphysics is “the study of existence, causation, God, logic, forms and other abstract objects”. So why isn't metaphysics the study of cups or cats? Can one study "existence" in the abstract? The point here is that we can't help but be metaphilosophical (or simply philosophical) in pursuit of an answer to the question “What is metaphysics?”.

What is Philosophy?

Every statement on what philosophy is - or what it should be - will elicit the question: Why do you believe that philosophy is x? The philosophical opponent can easily tell the original philosopher his own view on what he thinks philosophy is - or what he thinks it should be. If that occurs (which it often does), then what happens next? How is the what-is-philosophy question settled when rival views are on the market place? Surely the opposing positions on philosophy will be debated; though I doubt that the debate will be settled. And I also doubt that they can be settled by taking various metaphilosophical positions on the what-is-philosophy question.

Let's take a couple of examples.

One philosopher can say that philosophy is about “finding the fundamental nature of everything”. Why should a philosopher do that? And doesn't this stance on philosophy simply assume that there is a fundamental nature of things taken individually or a fundamental nature of “everything”? What if there are no such fundamentals? And, even if there are, why should a philosopher see them as important? (Though classing something as “fundamental” sort of gives the game away.)

Alternatively, a philosopher may say that philosophy is about (or should be about) intellectual unification. Specifically, unifying the insights from other disciplines; particularly science and philosophy itself. Another philosopher may say that such a position is impossible. He may also dd that science itself is a discipline which simply doesn't require philosophy. (Many scientists - particularly biologists - have said this.) Indeed such a philosopher may say that philosophy itself should incorporate science and its findings. Thus - from such a place - it would be very difficult to take a useful (or genuine) metaphilosophical position on science.

The Question: “What is Philosophy?”

Some of statements and arguments from philosophers on the nature of philosophy seem well-trodden. That is, they're simply of the traditional “What is philosophy?” variety.

For example, a philosopher can say that “philosophy doesn't rely on faith or revelation”. Instead it relies on “reason” or on (in 21st century pretentious terms) “cognitive criticality”. Nonetheless, such a position of faithlessness or lack of revelation doesn't automatically make philosophy a science either. Some philosophers might have said that there's no need to rely on observations or experiments in philosophy. A contemporary philosopher, on the other hand, may say that sometimes philosophers indulge in thought experiments (as the the Wykeham Professor of Logic at the University of Oxford, Timothy Williamson, does in his The Philosophy of Philosophy) which are very like the thought experiments engaged in by scientists (Williamson cites Galileo). Nonetheless, they're still not physical experiments as they're commonly understood in science. In addition, observations may be said to be prerequisites for just about any kind of philosophy. And technically it can also be said that observations (or at least “a posteriori reasoning”) can defeat seemingly a priori claims or statements.

Bertrand Russell on Philosophy

Bertrand Russell seems to have believed that when it comes to the definition of the word 'philosophy' (or to a description of the practice of philosophy), one can't help but be metaphilosophical. (Of course Russell never used the word 'metaphilosophy'; or even the words 'the philosophy of philosophy'.) In his The Wisdom of the West, Russell wrote:

“Definitions may be given in this way of any field where a body of definite knowledge exists. But philosophy cannot be so defined. Any definition is controversial and already embodies a philosophic attitude. The only way to find out what philosophy is, is to do philosophy."

Surely it can said that a definition of the word 'science' won't be equally as problematic as the word 'philosophy'. In addition, one will need to take a philosophical stance on what science is (if not on the word 'science' itself). Similarly, would all scientists agree on such a definition? Thus it can't be the case that simply because the word 'philosophy' is about philosophy that all definitions will be more problematic (or controversial) than definitions (or descriptions) of science.

So let's rewrite a bit of Russell's quote. Thus:

The only way to find out what science is, is to do science. (Or at least see how science is done.)

So it can be said that this controversy (or problem) is also the case with the definitions of many other words. That's unless one simply stipulates: This is how this dictionary defines the word x.

Despite saying all that, the analytic approach to philosophy, for example, certainly “embodies a philosophic attitude” and that attitude is “controversial”. The same can be said of deconstruction, phenomenology, structuralism, etc. - i.e., virtually any way of doing philosophy. Of course one would now need to distinguish positions within philosophy from positions on philosophy itself.

It's hard to grasp Russell's final sentence in the quote above. (Namely: “The only way to find out what philosophy is, is to do philosophy.") Surely there can't be such a case of (as it were) a priori philosophising. Firstly, a student of philosophy must read the books of certain philosophers and only then can he write about the things they too have written about. He may even adopt the prose style of those philosophers. Later he'll probably make a self-conscious attempt to write a certain kind of philosophy in a certain kind of way. In no way will he simply discover his own voice the first few times he writes philosophy. If he didn't do all that, then isn't it likely that he'd be doing stream-of-consciousness expressionism rather than philosophy? Unless, again, he's literally writing genuine philosophy from an a priori position; which, surely, is almost impossible. Sure, in order to “find out” if one can do philosophy one will need to “do philosophy”. And then one will discover which approach one likes. However, an original position can't come about simply as a result of doing philosophy from nowhere.

Finally, we must conclude that the question “What is philosophy?” is itself philosophical in nature. Or at least we need to indulge in philosophy in order to discover an answer to that question.

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Kitty Ferguson's *The Fire in the Equations: Science, Religion and the Search for God*

Many scientists will have a snooty attitude towards a book called The Fire in the Equations: Science, Religion and the Search for God. Indeed a subset of them will also have a snooty attitude towards all popular science books.

Such scientists may assume two things:

i) That the author, Kitty Ferguson, doesn't really know her science.

ii) That the science bits are really just sneaky preludes to the God and religion bits.

I should know about this, i) and ii) are what I thought... before I actually read Ferguson's book!

These scientists (if I'm not misrepresenting them) would be wrong on both counts. Kitty Ferguson really does know her science. And, secondly, the science she know isn't cheaply  shoehorned into some kind of rationalised theism or into a defence of religion generally

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Kitty Ferguson expresses a degree of scepticism towards both the God of the Scientists (to rewrite the well-known phrase “the God of the philosophers”) and the God of the Theologians. And it's here where Ferguson clarifies the title of her book: The Fire in the Equations.

Ferguson firstly notes Steven Hawking's position:

“If the Mind of God is only a euphemism for the sum of all the laws of physics, then God is not beyond the reach of science.”

Ferguson then allows Steven Hawking to express the limits to this God of the Scientists. Hawking writes:

“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 author offers a possible answer to Hawking's question by saying that the it “might be that the equations are the fire”.

However, Ferguson deftly sees the problem with both these positions. Firstly, she has a problem with Hawking when he said that that he “use[s] the term God as the embodiment of the laws of physics”. Surely this can't be the case. Could this really be the same God as the one worshiped and known by billions of people throughout the ages? So let's take Ferguson's response to that possibility:

“If one interprets God as 'the embodiment of the laws of physics', does that mean one believes 'God' is accessible only to physicists?”

Alternatively, could Hawking “be suggesting that the laws have a life or creative force of their own?”. In other words, is it that the “equations are the fire”?

And Ferguson spots another problem with God the Mathematician when she writes:

“If mathematical consistency is more powerful than God (if God has no choice but to conform to mathematical consistency), then God isn't really God. Mathematical consistency is God.”

Thus it may be the case that, ultimately, Ferguson strikes some kind of middle ground between the God of the Physicists and the God of the Theologians. In other words, she suggests a kind of pluralism: a happy acceptance of Wittgensteinian “language games”. Thus:

“Science and religion are, for them [the pluralists], two different descriptions which together give us a fuller understanding than either description alone could provide.”

However, there is indeed a stark possible alternative to this. Namely:

“If the descriptions are mutually exclusive, then that is disturbing.”

But it's not only scientists who can be (as it were) exclusivists, so too can religious people. Ferguson writes:

“Others who believe in God deem this [Wittgensteinian?] approach unsatisfactory, saying that God, in their experience, insists on occupying a front-line position in all descriptions, all conceptual schemes, all experimental situations. This God is a presence, not merely a way of thinking about or describing the universe.”

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As stated in the introduction, Kitty Ferguson does know her stuff. On almost every page there are magnificent explanations of various scientific subjects – from quantum mechanics to black holes to worm holes. There are also insights into various scientific issues. In other words, this isn't only a popular science book: it's also jam-packed with Ferguson's own very illuminating takes on physics and cosmology.

In any case, four chapters of this eight-chapter book hardly mention God or religion. And when they do, it's often only tangentially. Thus the book is indeed very roughly split into two halves; though this split is neither absolute nor is it made explicit in the introduction. Indeed even in a chapter called 'The Elusive Mind of God', both God and religion are only tackled tangentially. Here, as with three other chapters, science is primary and many pages don't mention God at all. One can even say that there's a certain sense in which the second part of the book isn't a conclusion to the first part. In many respects it flows seamlessly from the first part even though religion and God are discussed much more in the second section. It may even be the case that those who're only interested in science could skip the second part. However, I strongly suspect that Ferguson herself would see this as defeating the object of her book (or at least one of the objects of her book).

As obliquely stated in the introduction, Kitty Ferguson is just as sceptical (or simply critical) of the science which leads people towards God (as it were) as she is towards the science which leads people in the opposite direction.

Having said that, it can be mischievously be said that Kitty Ferguson puts her own position into the mouth of a Standard journalist who was writing in 1882 after the death of Charles Darwin. On page 1, Ferguson quotes the aforesaid journalist stating the following:

“True Christians can accept the main scientific facts of Evolution just as they do of Astronomy and Geology, without any prejudice to more ancient and cherished beliefs.”

Ferguson then quotes a sermon which was given at St Paul's Cathedral by a Canon H.P. Liddon. The canon congratulated Charles Darwin on “the patience and care with which he observed and registered minute single facts”. Yet Ferguson doesn't let the canon have it all his own way either. Later on in the book, Ferguson quotes the science historian, John Hedley Brooke, stating the following:

“The trouble with such accounts [of Darwin's methods] is that they can trivialize the logic of discovery. They assume that the 'facts' were somehow there, waiting at the Galapagos for Darwin to process. Darwin himself knew better than that.”

And it's not only canons who are given a hard time. Great scientists are too. For example, Ferguson has this to say on Steven Hawking:

“In April of 1980 Hawking had the audacity to suggest we had come so far that before the end of the twentieth century we might find the theory that would explain everything that is happening, has happened or ever will happen in the universe. Eight years later he wrote that after we have that theory in hand we might just go on (not scientists alone, but all humanity) to know the mind of God. Which calls to memory an ironic piece of history trivia. In the late 1890s Prussia closed its patent office on the grounds that all possible inventions had been invented. It wasn't long afterwards that Albert Einstein, in a Swiss patent office, began toying with ideas which would revolutionize science.”

And, later, Ferguson deflates science itself in the following manner:

“... science doesn't make any claim to have discovered the ultimate truth about anything.... [Scientists] don't speak of 'the verdict of science', but of 'the standard model'... They speak of 'approximate theories'.... They speak of 'effective theories', which means that something we can work with for the present while knowing it isn't absolutely and unequivocally correct.”

This statement on science is fine because (on the whole) scientists would happily accept it. In that sense, my use of the word “deflates science” isn't quite right simply because the transitional nature of science is something in its favour. Interestingly enough, Tolstoy (among many others) saw this as a very bad thing. He wrote (in his What is Religion?) these ridiculously rhetorical words (not quoted by Ferguson) in 1902:

“What we call science today is merely a haphazard collection of disconnected scraps of knowledge, most of them useless, and many of which, instead of giving absolute truth provide the most bizarre delusions, presented as truth one day and refuted the next.”

Ferguson even offers us a Kuhnian sociological and psychological account of science when she tells us that in science

“individual preference, cultural conditions, religious and anti-religious belief, political and economic interests, our value system, the spirit-of-the-time, the current fads of science”

also need to be acknowledged or taken into account. Ferguson pursues this theme later when she discusses the academic milieu of science. She comments on the phrase the “tyranny of old men” and warns of those on

“university committees, government committees, grant committees, editorial boards, and corporate boards, who determine whose theories and proposals are taken seriously, whose paper gets published, whose theory is tested”.

In his book (not quoted by Ferguson), The Trouble With Physics, the physicist Lee Smolin roughly concurs with Ferguson when he says that

“[p]eople with impressive technical skills and no ideas are chosen over people with ideas of their own partly because there is simply no way to rank young people who think for themselves. The system is set up not just to do normal science but to ensure that normal science is what is done... I've heard many colleague say they are on what is a trendy in order to get tenure, after which they will do what they really want.”

However, as with Ferguson's words on science's transitional nature, scientists should also be happy with this acknowledgement of psychological and sociological factors within science. The problem is that many scientists most certainly aren't happy with it! They speak of “Kuhnian relativism” or “mob psychology”. Yet they should also realise that such negative quirks and political biases are – at least in principle – usually ironed out. That's primarily because, as Bertrand Russell put it, science is essentially a communal activity which has a “community spirit”. Thus, even though these negative things occur, on the whole they won't reign supreme in the world of science. This is Russell (not quoted by Ferguson) in full:

“A body of individually probable opinions, if they are mutually coherent, become more probable than any one of them would be individually. It is in this way that many scientific hypotheses acquire their probability. They first fit into a coherent system of probable opinions, and thus become more probable than they would be in isolation.”

But Ferguson is sceptical here too. She asks us two questions:

i) “Will science, as an instrument for learning about reality, prove strong enough to overcome all the glitches and stumbling blocks, the fads and false leads, the good but mistaken intentions, the arrogance and the assumptions, the din of many voices urging us down one path or another?"

ii) "Is it correct to believe that eventually the truth will out?”

So of course what Russell says happens in science isn't always foolproof. Then again, it's far better than nothing. Nonetheless, Ferguson's philosophical questions about both science and the practice of science are, as ever, very powerful.

Simple Problems with the Law of Excluded Middle?

To state the Law of Excluded Middle in formal terms:

For any proposition, either that proposition is true or its negation is true.

Indeed the Latin has it that the law states tertium non datur: "no third [possibility] is given"...

One point to note is that the LEM can be seen as either a semantic or an ontological principle – or, indeed, as both. However, philosophers and logicians have tended to stress either one or the other, not both. (This may seem odd because LEM is often expressed in propositional terms and uses the symbol p.)

The Law of Excluded Middle is semantic in the sense that any statement of it is true by virtue of meanings of the words which express it. That is, according to their semantics. However, as various philosophers have put it, the LEM is also “true of the world itself”. (Others have said is that it's “true of thought itself”.) That can mean that even if the statement

Boris Johnson is either mortal or not mortal.

were never uttered or expressed, then it would still be the case that Boris Johnson is either mortal or not mortal. That is:

i) If no one had ever expressed P (which they might not have done until now), or even if we didn't have a notion of mortality,

ii) then it would still be the case that P is either true or false.

Aristotle himself made this point in his Metaphysics. Thus:

“It is impossible, then, that 'being a man' should mean precisely 'not being a man', if 'man' not only signifies something about one subject but also has one significance... And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one whom we call 'man', and others were to call 'not-man'; but the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be in fact.”

Aristotle summed up this inelegant passage much more simply when he stated that "it will not be possible to be and not to be the same thing".

In propositional logic, this can be expressed as ¬(p ∧ ¬p). (Note that the Law of Excluded Middle isn't the same as the Principle of Bivalence, which states that a proposition p is either true or false.) That logical statement just made (i.e., ¬(p ∧ ¬p)) includes the symbol p, which means it's about a proposition. Thus ¬(p ∧ ¬p) is a propositional version of the ontological LEM. This means that the LEM can also be written in this way: ¬(A ∧ ¬A); in which A symbolises something non-semantic or non-propositional.

It can be said that the statement “Boris Johnson is either mortal or not mortal” also includes hidden premises (such as “Boris Johnson is a human being”, “All human beings are mortal”, “Mortal beings die”, etc.). Alternatively, as W.V.O Quine might have said, we need to know the specific definitions of the words contained in the statement in order for it to work as an example of the Law of Excluded Middle. Having said that, the symbol p can also be seen as an autonym (i.e., self-referential). That is, as a symbol with no specific content (as also with the variables x and y).

Examples

Take the statement:

He's either in the room or he's not in the room.

Isn't that an instance of the Law of Excluded Middle? However, suppose this man is half in and half out of the room.

If this man is only half in the room, then he’s still in the room. The Law of Excluded Middle (or its statement) doesn't stipulate how much of his body needs to be in the room. It simply states that he's either in the room or he isn’t. This doesn’t stop him from being half out of the room either. The LEM would only be non-applicable if no part of this man were in the room. Thus saying

He's in the room and he's not in the room.

isn't the same as saying

He's half in and he's half out of the room.

In the first statement there's a conjunctive part of the whole statement which states that the man isn't in the room at all. And in the second part, there's a conjunctive claim that he’s half in the room. So they aren't actually the same. The LEM would only be contradicted if the man were half in the room and, at the very same time, he weren't half in the room. (Alternatively, if half of the man were in the room and yet the whole of him were outside the room.) It's these formulations which are self-contradictory.

The same goes for this statement:

The ball is either black or it's not black.

Someone may now say:

What if the ball is half black?

The same argument holds. In the second statement above, we wouldn't be referring to the entire ball: only to the black part of the ball (or to the non-black part). In that case, the LEM isn't about the whole ball. So if we take the black part of the ball, then it's either black or it's not black. If someone now says, “This part isn't black - it's white”, then it's not black. So in both cases it's either black or it's not black, as the LEM states.

Again, if you want to talk about a black-and-white stick (rather than an all-black stick), then the LEM can easily accommodate it. The statement would then be:

The stick is black and white or the stick isn't black and white.

So we're talking about a particular stick which happens to be both black and white. Now someone may reply:

Well, in fact the stick also has little flecks of grey on it.

So be it. Now we can reply with this:

The stick is either black and white with little grey flecks on it or it's not black and white with little grey flecks on it.

Thus we need to specify which object or part of an object the statement refers to. The original claim about something being black was exclusively about the colour black, not about a black-and-white stick. To contradict it, one is essentially saying that black is not black, which is a denial of the Law of Identity (i.e., A = A). The LEM is derived from - and dependent upon - the Law of Identity.

Graham Priest's Integral Atom

Here's another case which is highlighted by the logician and philosopher Graham Priest.

Priest cites (in his 'Logicians Setting Together Contradictories') the example of radioactive decay. He asks us the following question:

“[S]uppose that a radioactive atom instantaneously and spontaneously decays. At the instant of decay, is the atom integral or is it not?”

Now for the traditional logic of this situation. Priest continues:

“In both of these cases, and others like them, the law of excluded middle tells us that it is one or the other.”

Yet couldn't the atom be neither integral nor non-integral when it instantaneously and spontaneously decays? (Priest talks of either/or or “one or the other”; not neither/nor.) Or, alternatively, at that point in time it may not be an atom at all.

This appears to be a temporal problem which must surely incorporate definitions - or philosophical accounts - of the concepts [instantaneously] and [spontaneously]. Nonetheless, if they define time instants which don't exist (i.e., the period from t to t¹ doesn't exist), then Priest may have a point. However, can an atom - or anything else - “decay” (or do anything) in a timespan which doesn't actually exist? How can decay - or anything else - occur if there's no time in which it can occur?

So what of Priest's own logical conclusion when it comes to atomic decay? He claims that the aforementioned atom

“at the point of decay is both integral and non-integral”.

This isn't allowed – Priest says - if the Law of Excluded Middle has its way. The Law of Excluded Middle tells us that the said atom must be either integral or non-integral; not “both integral and non-integral”.