The Copenhagen Interpretation of Quantum Mechanics Is Not Idealist in Nature

 

The Copenhagen interpretation of quantum mechanics — and even quantum mechanics generally — has been both loosely and strongly associated with the philosophical position of idealism (see here).

Of course there are almost as many varieties of idealism (from subjective idealism to absolute idealism to pluralist idealism) as there are idealists. So this isn’t the place to run through all of them. In any case, the kind of idealism I have in mind will become clear in this essay itself.

So take as an example the following passage (written in 2005) from Harry Nielsen:

“ Almost unbelievably perhaps, [the academics who developed quantum mechanics] chose to interpret the strangeness of quantum behaviour by denying the existence of physical reality. And as a standard textbook interpretation of quantum mechanics, physicists have been taught for the last 80 years that physical reality therefore only exists as a result of the act of observation. This is the ‘Copenhagen interpretation’ of quantum mechanics, developed in the late 1920’s by Niels Bohr and Werner Heisenberg. To quote Heisenberg: ‘I believe that the existence of the classical ‘path’ can be pregnantly formulated as follows: The ‘path’ comes into existence only when we observe it’.”

Of course the above doesn’t actually mention “idealism” — yet the general gist seems to be that the Copenhagen interpretation is idealist (or at least subjectivist). And it isn’t at all odd that this writer thought this way about this interpretation of quantum mechanics.

So it’s important to stress that the Copenhagen interpretation of quantum mechanics is not idealist. Or at least the Copenhagen interpretation itself can be interpreted as not being idealist. That said, it is difficult to explain why that’s so. Indeed not many physicists — or even philosophers — have fully clarified why that is so.

Finally, there are stronger arguments which assert that quantum mechanics — if not the Copenhagen interpretation itself — is entirely subjectivist in nature. Yet there are clear differences between subjectivism and idealism. Indeed Harry Nielsen’s words above can be interpreted as only claiming that the Copenhagen interpretation is subjectivist, not idealist.

Various philosophers (such as Karl Popper) have also argued against those who claim that quantum mechanics is subjectivist , let alone idealist (see Popper here).

Arthur Mach’s Position

It is therefore convenient that there’s a short and simple passage (as quoted in Karl Popper’s The Logic of Scientific Discovery) from the Austrian physicist Arthur March (1891–1957) which perfectly clarifies this issue.

Firstly, Arthur March makes an explicit anti-idealist statement. (It’s not clear if that was his main intention — indeed it probably wasn’t.) He wrote:

“Naturally nobody is so mad as to assert that a body ceases to exist the moment we turn our backs to it [].”

(March was referring to quantum bodies such as particles; not cups, trees or human beings.)

An idealist, on the other hand, would argue that

a body ceases to exist the moment we turn our backs to it.

And that’s because, to an idealist, “a body” — and everything else — only exists in the individual mind or in some kind of collective mind. Thus it does indeed cease to exist when “we turn our backs to it”. (Unless, that is, it still exists in the mind of God — as with Bishop Berkeley immaterialism, in some other being’s mind or in a collective mind.)

Arthur March, on the other had, stated that it is “mad [] to assert” that idealist position. Yet March did preface that phrase with the following words:

“One may say perhaps without fear of being misunderstood [] that for the physicist a body has reality only in the instant in which he observes it.”

It’s worth noting the phrase “for the physicist”.

This isn’t an expression of a philosophical view or even of a layperson’s position. As a physicist, March was speaking entirely qua physicist.

So even though it may be problematic to stress observation alone, this is still the stress of a physicist qua physicist. And, almost by definition, a physicist is only concerned with the observations of — and experiments on — a (in March’s word) body.

Thus March, qua physicist, stated that the

“[body] does cease, in the moment, to be an object of inquiry for the physicist”.

Why is that? It’s

“because there exists no possibility of saying anything about it which is based on experiment”.

March’s statement above is true by definition. That is, what comes before the experiment can’t actually be part of the experiment. Or if someone does “say[] anything about it”, then what he says can’t be based on the experiment and is therefore not itself physics. Indeed even the mathematical formalism and/or the wave function required for the experiment has nothing to “say” about any bodies before the experiment.

The wave function has just been mentioned.

Thus the standard interpretation of the wave function is that — in itself — it has no physical interpretation. It is purely a mathematical function. A tool. Something physicists use to do things with. Of course it can then be given a physical interpretation.

Take the Schrödinger equation.

This doesn’t tell us what the wave function is — other than in purely mathematical terms. The physical meaning of the equation — i.e., what entities, etc. are posited — is a product of the interpretation of quantum mechanics the physicist adopts.

And even when physicists do “guess” at the (as it were) before-observation, that too is only a use of the wave function; which, again, is a large abstract mathematical object made of smaller mathematical objects.

So, basically, Arthur March, qua physicist, wasn’t interested in what might have been the case before the experiment. And, presumably, he wasn’t that interested in what was the case — i.e., in the experimental area — after he took off his white coat and packed up his bags to go home. Alternatively, if he was interested in both the before and after of the experiment, then it was as a philosopher or a layperson, not as a physicist.

Conclusion

As hinted at in the introduction, it is at least partly understandable that some people see the Copenhagen interpretation as idealist. In the passage in the introduction, for example, Harry Nielsen quoted Werner Heisenberg. So I’ll help Nielson’s cause along by also quoting Heisenberg stating the following:

“[A]n ‘objective’ physics in this sense, i.e. a sharp division of the world into object and subject has indeed ceased to be possible.”

Such passages from Heisenberg and others have provided grist to the mill for various idealists, mystics, New Agers and whatnot. Yet even here (on my reading of idealism at least) an idealist simply can’t make any distinction at all between “object and subject”. (Of course it is possible that the word “object” can be defined in such as way that it squares with idealism.) That’s because (to an idealist) literally everything is in the individual’s (or experimenter’s) mind. (Either that, or everything is in a collective mind or in the mind of God.) In other words, there is simply no object in idealism — we only have a subject or subjects.

[I can be found on Twitter here.]

Peter Hacker on Philosophers and Scientists Violating Everyday Words

 

“[Expressions] can and are violated by unconsciously crossing ordinary uses of expressions with half-understood technical ones.” — P.M.S Hacker

It can be asked why philosophers, academics and scientists use everyday words in new ways. Why don’t they simply create completely new technical terms (i.e., neologisms) to do the jobs they need to do? Is it because these new uses (or meanings) of the everyday words are strongly related to the old uses (or meanings)? Is it because academics, scientists and philosophers want to elicit easier understanding by using everyday words in new ways? Alternatively, are such philosophers, academics and scientists simply playing fast and loose with everyday words?

The British philosopher P.M.S. Hacker (1939-) has a very-strong position on these issues.

The fairly obvious point is that Hacker’s position on how academics, philosophers and scientists use everyday words in new ways is philosophical. More accurately, it’s a very-clear expression of a very particular philosophy. That philosophy is Wittgensteinianism — as expressed, in this case, by a late-20th and early-21st century British philosopher.

Peter Hacker believes in what’s been called the “linguistic-therapeutic approach” to philosophy, as originally advanced by Ludwig Wittgenstein. That is, he believes that the words and concepts used by everyday people should be taken as given by philosophers. Consequently, he sees the role of philosophy (as did Wittgenstein) as one of dissolving (or resolving) philosophical problems by examining (among other things) how words are actually used in everyday life. More precisely, Hacker deems such philosophical problems to be primarily conceptual in nature. To him, this also means that these problems can be dissolved (or resolved) purely by “linguistic analysis”.

Take a specific example of this. Hacker believes that the “problems” and “mysteries” of consciousness dissolve once we realise that everyday words are either being (to use his own word) “misused” or that new technical terms simply don’t have any real content. 

For example, Hacker believes that the term “qualia” is a (as Daniel Dennett has also put it ) “philosopher’s artefact”. (See Hacker here.)

Clearly this philosophical stance is related to what was once called ordinary language philosophy.

This was a philosophical stance (rather than a specific school) which saw traditional philosophical problems as being rooted in the misunderstandings philosophers make when they distort (or simply change) everyday words. The upshot is that using everyday words in new ways can often create philosophical problems, rather than help solve them.

Despite all the above, philosophers, academics and scientists aren’t the only (as it were) culprits here. Laypeople are too. That is, everyday words often take on new meanings among laypeople. Indeed, it’s a commonplace to state that language always changes and adapts. And even in everyday terms, the same word can be used in different ways within different contexts. (This is something that Wittgenstein himself emphasised.)

Consequently, is what some philosophers, academics and scientists do really that different to what the “folk” do?

Hacker on Philosophical & Scientific Violations of Everyday Words

There’s something a little off-putting about Peter Hacker’s stern 1950s-Oxford-University (or public school) way of putting things.

Take the following passage from Hacker’s ‘Languages, Minds and Brains’ contribution to the book Mindwaves:

“[I’m only concerned with] what makes sense and what does not. The bounds of sense can be violated by the misuse of technical, not ordinary expressions no less than the misuse of ordinary ones.”

Hacker sounds like a Wittgensteinian professor who’s giving one of his own philosophy students a good telling off. More specifically, his phrase “the bounds of sense” seems a little pompous. (That phrase is actually borrowed from Peter Strawson’s book The Bounds of Sense.) It’s not entirely clear what the words “bound of sense” mean within Hacker’s philosophical context.

Hacker also refers to technical terms being “misuse[d]”. This is odd because technical terms are coined by specific academics, scientists, philosophers, artists, novelists, etc. at specific times for specific purposes. So such terms are virtual neologisms anyway — even when it’s a case of using everyday words in new ways.

So can we be so strict about technical neologisms? After all, the terms “wave”, “spin” and “information”, for example, are very technical and very specific, yet the words themselves also have an everyday use and origin.

Yet, on the surface at least, surely it’s taking a tremendous liberty if a philosopher, scientist or academic uses an everyday word in a completely different way. This is Hacker’s take on that issue:

“And, in particular, [expressions] can and — in the cases I have examined — are violated by unconsciously crossing ordinary uses of expressions with half-understood technical ones.”

Of course, a scientist, academic or philosopher may well argue that he’s not using that everyday word in a completely different way. But he will usually admit that he is using it in some kind of different way. (For example, the physicist’s use of the word “information” is — arguably — not completely divorced from its everyday use.)

Hacker also talks of “unconsciously crossing ordinary uses of expressions with half-understood technical ones”. Yet usually it is conscious — often very conscious — crossings of ordinary terms with new technical uses that can be seen. In addition, new technical uses of everyday words may be very well understood (i.e., not “half-understood”) and still bear no relation to how they’re used by laypersons.

Hacker’s Examples From Psychologists and Neurophysiologists

Hacker then comments on neurophysiologists and psychologists using everyday words in new ways. (This is his own personal bugbear.) He writes:

“Secondly, it is not open to the neurophysiologist or psychologist to shrug off these criticisms on the grounds that he is using ‘language’, ‘represent’, ‘communicate’, ‘recognize’, etc. in a special technical sense, and that it is not he but his gullible reader (such as myself) who is guilty of crossing the ordinary use with his special technical one."

Firstly, it’s entirely understandable that when a layperson reads a word that he’s read many times before that he expects it to be used in the same way as before. Moreover, he’ll understand it in the same way as before. That said, the philosopher, academic or scientist may simply say that this reader should already know that the word is being used in a technical and/or new way because the context in which these words are embedded will make that very clear. In other words and to take Hacker’s own examples: if the layperson reads the words ‘language’, ‘represent’, ‘communicate’ and ‘recognize’ in the context of a piece of psychology or neurophysiology, then perhaps the reader should already know — or at least suspect — a technical meaning (or use) for these words.

That said, these technical uses of everyday words also crop up all over the place. They most certainly don’t only appear in academic papers. They can be found in popular journalism, in “popular science” books, on television/radio, etc. That is, the occur when and where no specialised knowledge is assumed or required. And, in these cases, technical terms — under the guises of everyday words — most certainly wont be understood in their new senses. What’s more, it can be argued that at least some academics, scientists and philosophers actually play on this conflation. And they do so because these crossovers (between everyday words and their new technical uses) make their words and theories more sexy, radical and saleable. In other words, such academics, philosophers and scientists know full well that they’re using old words in a technical way, even though they also know that these words will only be understood in their everyday senses.

So at least some academics, philosophers and scientists know that many (to use Hacker’s words) “gullible reader[s] [will be] guilty of crossing the ordinary use with [their] special technical one[s]” — and that’s precisely what they want! That crossing is a means to make their theories more sexy and saleable.

[Think here of Markus Gabriel’s book title Why The World Does Not Exist. In that book Gabriel uses the words “world” and “exist” in very technical ways. Yet when these words are actually understood in their philosophical and technical senses, then that immediately softens the impact of the title’s sexy punch.]

As it is, Hacker argues that the guilty academic, scientist or philosopher is having his cake and eating it. He writes:

“For were he so to argue, the initial analogy with which his story began, and which so impresses us all, is no analogy whatever [].”

In other words, such an academic, scientist or philosopher wants laypeople to fuse the everyday word with the same word used in his/her own technical manner. Or, in Hacker’s own example, such a academic, scientist or philosopher starts off by using that word in a way that’s akin to an “analogy”, and then he/she castigates the layperson for not taking it in its purely technical sense.

What’s more, it’s quite possible that some technical terms can’t be understood at all analogically. (Think here of the many disputes in quantum mechanics about the word “spin” or even “wave”!) Yet such everyday words are often used analogically simply to (as it were) entice the layperson in. More specifically and with Hacker’s own examples, the words ‘language’, ‘represent’, ‘communicate’, ‘recognize’ as used by (some) psychologists and neurophysiologists simply don’t have the same meanings as those very same words as they’re used in their everyday contexts.

A Less Stern Position on Semantics

A more (to use a word from Hacker) everyday position is to argue that it’s not really that “sense” is being “violated” or that “ordinary expressions” are being “misused”. It’s mainly a simple problem of understanding what some people say or write.

That said and as Humpty Dumpty once stated:

“When I use a word, it means just what I choose it to mean — neither more nor less.”

So Humpty Dumpty was right to argue that people — and that includes scientists, academics and philosophers — are free to use everyday words in their own new ways. However, surely that’s only as long as they back up their new uses. And there’s still a problem with Hacker’s word “misuse”. In fact it’s hard to even fathom who — or what — would decide if a term had been misused and what arguments would be deployed to characterise such misuse. On the other hand, it’s easy to understand basic problems of communication.

Perhaps this is to be too liberal. After all, if a scientist, philosopher or academic uses the word “cat” to refer to beans, then surely he’s misusing the word “cat”. Sure, that’s an extreme and silly example — but it gets the point across.

My own personal take on this is to say that when I’ve asked people to explain to me what they mean (or to “define [their] terms”), others have said that my request is “rhetorical”, “political” or “arrogant”. This is very odd. I simply want to know what people mean by their words. Now should I have pretended that I understood their use of words? Should I have patronised the writer of the words? Should I have simply guessed and based my guess on some kind of purely emotional, intuitive and immediate reaction to the words?

It’s easy to accept that some responders may ask for definitions for rhetorical, political or arrogant reasons. However, surely that isn’t always the case. And even if they do, then that still means that there must have been a problem with communication.

Now of course there are many complex and difficult issues relating to understanding, conversational implicature, “the play of the sign”, semantic indeterminacy, the inscrutability of reference, etc. However, I don’t think that these philosophical or semantic issues are that relevant to what’s just been discussed in this essay. In simple terms, if I don’t understand what people are saying, then I don’t understand what people are saying.

****************************

Note: More Passages from Peter Hacker

Here is a handful of other passages from Hacker’s ‘Languages, Minds and Brains’ contribution to the book Mindwaves:

“But, of course, there is no picture in the visual cortex representing what we see.”

“There are no symbols in the brain that by their array express a single proposition, let alone a proposition that is known to be true.”

“[] I flounder in the mixed metaphors [] cells are not in the business of building perceptual concepts [] or any other kind of information in either sense of the term.”

“[W]hen biologists talk of the ‘genetic code’ they are not using the word ‘code’ in the sense in which a code is essentially related to a language…”

“[H]e comes perilously close to saying that when a person sees an object there is a map, a representation of the object. [] But now he must explain who or what sees or reads the map. If it is neither the mind nor a gnostic cell, what can it be?”

[I can be found on Twitter here.]

Stephen Hawking’s Philosophical(!) Position on the Uncertainty Principle

 

In a debate called ‘Scientists vs Philosophers’ (on YouTube), the host opens up with this question:

“Why is it that so many physicists are bashing philosophers nowadays?”

Take Stephen Hawking.

As many people (especially philosophers!) know, Stephen Hawking (1942–2018) wasn’t very keen on philosophy and made that clear a couple of times in his later life.

The following is what Hawking himself said on the subject of philosophy:

“Traditionally these are questions for philosophy, but philosophy is dead. Philosophy has not kept up with modern developments in science, particularly physics. Scientists have become the bearers of the torch of discovery in our quest for knowledge.”

What’s more, Hawking made the following incredible claim about his own (philosophical!) position:

“Model-dependent realism short-circuits all this argument and discussion between the realist and anti-realist schools of thought.”

So perhaps it wasn’t philosophy simpliciter that Hawking was against; but only philosophy “which has not kept up with modern developments in science”. (Many philosophers themselves have said the same about their fellow philosophers.) As it is, I don’t believe that Hawking was actually being selective about philosophy; though it’s worth raising that possibility.

It’s strange, then, that in his book The Grand Design (cowritten by Leonard Mlodinow) Hawking himself indulges in a fair bit of philosophy.

So here’s a taster of Hawking’s philosophy:

“There is no picture- or theory-independent concept of reality. Instead we will adopt a view that we will call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science.”

Sure, it might have been the case that Stephen Hawking didn’t see his own model-dependent realism as a philosophical position. He might have seen it as a simple description of the methodologies and facts of physics. Yet that too would have been both a philosophical position and also very naïve.

In addition, it’s also worth noting here that Hawking classed himself as “a positivist”. This is what he wrote in his book The Universe in a Nutshell:

“Any sound scientific theory [] should in my opinion be based on the most workable philosophy of science: the positivist approach put forward by Karl Popper and others… If one takes the positivist position, as I do, one cannot say what time actually is. All one can do is describe what has been found to be a very good mathematical model for time and say what predictions it makes.”

The words above make Hawking’s rejection of philosophy even stranger.

As it is, this essay is going to concentrate on Hawking’s philosophical words on on the realism-vs.-anti-realism debate — as it specifically relates to the uncertainty principle.

Firstly, a few words on realism in science.

Realism vs. Anti-Realism

In the following Stephen Hawking mentions “realism”. He wrote:

“Though realism may be a tempting viewpoint, as we’ll see later, what we know about modern physics makes it difficult one to defend.”

Obviously it’s the case that realism is most certainly a philosophical — i.e., not a scientific — term.

On the surface at least, Hawking seems to be taking some kind of anti-realist position. This, by definition, must be as philosophical a position as realism. Yet the fact is that (as it were) practising scientists — and perhaps even theoretical physics — needn’t take any position on the realism-anti-realism debate. They could simply “shut up and calculate”. In addition, most physicists probably never even think about this issue at all. Indeed other physicists would argue that taking a realist or anti-realist position wouldn’t — and doesn’t — make the slightest bit of difference to what they do.

I said earlier that Hawking adopted some kind of anti-realist position. More accurately, however, he adopted what he called “model-dependent realism” (as discussed in the introduction).

So not only did Hawking indulge in philosophy: he even went so far as to concoct his own philosophical theory! (Of course model-dependent realism isn’t entirely Hawking’s work.)

Now for the uncertainty principle.

Hawking on the Uncertainty Principle

Stephen Hawking dug himself even deeper into his own philosophical hole when he discussed the uncertainty principle. He wrote:

“For example, according to the principles of quantum physics, which is an accurate description of nature, a particle has neither a definite position not a definite velocity unless and until those quantities are measured by an observer.”

Some physicists may argue that there’s not much — or even any — philosophy in the words above. Yet that simply isn’t the case.

Firstly, stating that

“a particle has neither a definite position not a definite velocity unless and until those quantities are measured by an observer”

is an explicitly philosophical position. Indeed Hawking didn’t even say that

we cannot know if a particle has a definite position/velocity before measurement.

He stated that

a particle has neither a definite position nor a definite velocity unless we measure such a thing.

That is Hawking’s statement about the ontological situation of x before measurement. In addition, Hawking was saying something about x.

Again, many physicists have argued that (other) physicists needn’t say anything about whether a particle has a “definite position” or a “definite velocity” before being “measured”. Raising that very question (or subject) is itself philosophical. Instead, all scientists really need is the mathematical formalism (including the wave function), the predictions, the experiment itself, the observations, etc.

After all, from a purely scientific point of view, if a scientist can’t know whether the particle has a definition position, etc. before the measurement or experiment, then what scientific purpose does a postulation of “its” previous status actually serve? (This is a point that Werner Heisenberg, Wolfgang Pauli, etc. made in the 1920s and 1930s.)

All this means that when Hawking was being philosophical when he so much as raised these issues. Indeed he offered his own philosophical position on them!

Hawking continued:

“It is therefor not correct to say that a measurement gives a certain result because the quantity being measured had that value at the time of the measurement.”

In the words above, Hawking became even more philosophical. That is, qua scientist, he didn’t need to say anything about what status the “quantity” had before measurement. But he did. Hawking took an explicitly philosophical position on this. That is, he said — or implied — that it is (philosophically) wrong to believe that

“a measurement gives a certain result because the quantity being measured had that value at the time of the measurement”.

On the other hand, Hawking believed that it is (philosophically) right to believe that

“in some cases individual objects don’t even have an independent existence” [i.e., before measurement].

But how could Hawking have known that?

In addition, he would have needed to defend his position philosophically — and many philosophers and indeed physicists have done so.

So the philosophical position may be one (or both) of the following:

(1) We can simply never know what state a particle (or “quantity”) had before measurement.

Alternatively:

(2) It makes no sense at all to believe x had a particular state before measurement.

Hawking seems to have opted for that latter philosophical interpretation when he said that these “individual objects [] exist only as part of an ensemble of many”. This is an indirect reference to the wave function. That is, there is an ensemble of individual objects until there’s an observation — and then we (as it were) bring about a single definite object. (Put differently: until the wave function is collapsed, we have an ensemble of individual objects.)

But note that not only was Hawking doing philosophy, a (quasi?)realist position is also hidden in his words. That is, Hawking did say something about the world (or individual objects) before any measurement. In detail, he wrote:

“In fact, in some cases individual objects don’t even have an independent existence but rather exist only as part of an ensemble of many.”

Thus Hawking believed that there was an “ensemble of many” individual objects (or quantities) before any measurement.

So isn’t the belief that there is an ensemble of many individual objects before measurement just as realist a position as the belief that there’s a definite object in a definite state before measurement?

In addition, isn’t it the case that in order to be consistent, Hawking should have said nothing about this previous state. He should have only talked about (in whichever order) the wave function (or the mathematical formalism) for the experiment, the experiment itself, the predictions, the observations and so on.

[I can be found on Twitter here.]

Albert Einstein’s Philosophy of Science — Circa 1916

 

i) Introduction

ii) Science is Observation, Induction and Cataloguing?

iii) Intuition and Deductive Thought

iv) Truth

There’s no reason to assume that Albert Einstein’s philosophy of science will be on a par with his physics — at least as it was expressed in his Relativity: The Special & the General Theory (1916). And indeed it isn’t. This means that, in terms of this essay alone, his words have been focussed upon not because of their insight or profundity, but primarily for their historical and philosophical interest.

When referring to Relativity: The Special & the General Theory, Einstein himself mentioned philosophy. Or, more accurately, he wrote that in his book he intended

“to give an exact insight into the theory of Relativity [] from a general scientific and philosophical point of view”.

So, in the case of this essay, Einstein’s “philosophical point of view” as it concerns science (rather than, specifically, Relativity) will be concentrated upon.

The following will attempt to show what Einstein thought (at least in 1916) of science (actually, physics) itself. It can therefore be asked if Einstein’s account of science/physics corresponds to what other physicists/scientists thought at the time. In addition, we’ll see what Einstein thought of the layperson’s view of science.

In terms of detail , Einstein’s philosophy of science only takes up three paragraphs in a book of 132 pages (plus a few words on the philosophy of geometry, which will be covered later). And all that’s in one appendix — Appendix III.

In terms of Relativity: The Special and the General Theory itself.

This book began life as a short paper and it was eventually published as a book in 1916. (My English edition dates from 1920; which is the same edition as in the image above.) This book’s aim (to quote Einstein’s own already-quoted preface) was to give

“an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics”.

(Oddly enough, there is a fair amount of mathematics in this book! Far more than you’d see in most — or even all — contemporary “popular science” books.)

Science is Observation, Induction and Cataloguing?

Albert Einstein offered his overall account of what laypersons — and possibly even some scientists — took science to be (at least in 1916).

Firstly, he stressed induction and observation. He wrote:

“From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction.”

The layperson’s basic take on science is that science is essentially inductive. Or at least this is what’s usually believed to be the layperson’s view. The problem here is that most laypersons don’t actually philosophise about science at all. And they rarely — if ever — use the word “induction” or “inductive”. That said, some philosophers tell us that a person may have the concept of a word without actually ever using the word itself. So laypersons may have the concept [induction] without ever using the word “induction”.

What’s more likely is that laypersons stress observations — as do scientists themselves. So Einstein continued:

“Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison.”

Thus “individual observations” are often believed to drive the entire scientific show. At least that’s the layperson’s view. But, once again, only empirical research can establish what laypersons actually believe. Yet, anecdotally, this does seem to be the usual position.

Anyway, on this picture of science, scientists go outside and … observe. Alternatively, scientists carry out experiments and then simply observe what happens. According to Einstein’s take on the layperson’s take, scientists collect all their observations together into a large pot (or at the least they collect their “statements” about the observations together), and then they attempt to make sense of them. Or, in Einstein’s own words, scientists extract “empirical laws” from their observations.

In this bald form, it’s hard to know what all that even means.

Clearly, innumerable other factors would be required in order to extract empirical laws from observations alone. And then the situation becomes even more complicated when “general laws” are “ascertained” from those observations and empirical laws.

Einstein was absolutely correct to detect the profound naivety of this view of science. And that’s why he went on to write the following words:

“Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise.”

Thus scientists are (or were) often seen as merely cataloguing nature — or cataloguing their observations of nature. (This is almost like scientific “stamp collecting”; as with - to be a little crude - Francis Bacon (1561 -1626) and his own philosophy of science — see here.) In this way, it was believed that everything can be kept scientifically kosher — or empirical. (The reader might have detected unwritten scare quotes around Einstein's use of the word empirical.)

Of course one can immediately ask why scientists were cataloguing the things they were cataloguing in the first place. Why were they observing those parts of nature and not other parts? Why did they want to “compile[]” the things they compiled and not other things? In other words, there must have been prior factors — above and beyond what it is they observed — that brought about those very same observations.

Einstein himself then explained why this view is both simplistic and naive. He continued:

“But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science.”

So it’s clear that Einstein wasn’t actually ruling out entirely the layperson’s view of science. This means that observations — and even cataloguing — are indeed part of the story of science. That said, these things, according to Einstein, “by no means embrace[] the whole of the actual process”. And it’s here that Einstein adds “intuition and deductive thought [to] the development of an exact science”.

Einstein also wrote the following:

“The theory finds the justification for its existence in the fact that it correlates a large number of single observations [].”

That reference to a “correlat[ion] of a large number of single observations” is a perfect account of some kind of inductive process. For example, from the observation — and then correlation — of a large number of white swans, a subject may (or will ) conclude that “all swans are white”. Alternatively and in Einstein’s case, a scientist may develop a (to use Einstein’s word) “theory” about swans and why they are all white (which may even include natural laws of some kind).

Einstein had also already mentioned “induction” (though in a critical way) when he wrote:

“we may imagine the process of evolution of an empirical science to be a continuous process of induction”.

One may also ask how a scientist “correlates a large number of single observations”. (Alternatively, how someone connects the dots about all swans being white.) After all, if the theory “finds its justification [in the] fact that it correlates a large number of single observations”, one may suggest that theories were already required in order to enable those correlations. In simple terms, already-existing and accepted theories would have been required (or needed) in order to find a new theory. In the white swans case, in order to conclude that all swans are white, the person who concluded that must have already accepted various other things about swans, the colour white, the whiteness of swans, the nature of observations, etc.

Intuition and Deductive Thought

For me personally, Einstein’s stress on what he calls “intuition” and “deductive thought” (in the quote above) is a little odd. Then again, that may simply be because I live in different times and use different jargon about these same issues.

In any case, many philosophers of science today would stress theory here — not intuition and deductive thought. Of course theory is also intimately tied to both intuition and deductive thought.

But firstly, the word “intuition”.

In philosophy and mathematics, that word often has very specific and indeed technical meanings (see here). So one wonders if Einstein used it in that way himself. Perhaps Einstein simply meant “speculation”, “theorising” or “free thought” by “intuition”. That is, all thought that goes above and beyond the observational data. Indeed all the thought that’s also required to make sense of the observations - and even bring about the observations.

So what about Einstein’s “deductive thought”?

Well, in a general and perhaps vague sense, if we have observations (or statements about them), then we can deduce things from those observations. That is, the observations don’t stand on their own. Scientist need to make sense of them. And they can also deduce (not always logically) other things from them.

However, Einstein used the word “deductive thought” because later he says that

“the investigator develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms”.

This is Einstein (provisionally) treating physics as a kind of (pure) deductive logic. That is, instead of premises from which a conclusion can be derived (or axioms in mathematics which lead to theorems), we have observations and/or “fundamental assumptions” which lead to theories. And, in fact, Einstein himself says that “[w]e call such a system of thought a theory”. Of course all this is very neat and tidy and science (or scientific thinking) isn’t really — or always — like that.

Einstein also used the words “the so-called axioms”. And that is a roundabout admission that physics is physics and (pure) logic is logic.

Truth

Einstein’s concludes by saying that if the theory “correlates a large number of single observations”, then “it is just here that the ‘truth’ of the theory lies”. Readers will have noted the scare quotes around the word truth. And this is an extremely important aspect of Einstein’s philosophy of science and indeed of science itself.

The layperson often sees truth as a central goal of all science. Yet many scientists have never seen it in quite the same way. And that’s because truth is a tricky character for scientists.

In any case, elsewhere in Relativity: The Special and the General Theory, Einstein explicitly states that in geometry (if not science), truth doesn’t really have any role. Or, if it does, then the truths of geometry are very different to the truths spoken of by laypersons and even scientists.

For example, take Einstein's words on Euclidean geometry. He wrote:

“We cannot ask whether it is true that only one straight line goes through two points. We can only say that Euclidean geometry deals with things called ‘straight line,’ to each of which is ascribed the property of being uniquely determined by two points situated on it. The concept ‘true’ does not tally with the assertions of pure geometry, because by the word ‘true’ we are eventually in the habit of designating always the correspondence with a ‘real’ object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.”

Put basically, Einstein believed that truth in “pure geometry” (like logic) is essentially a matter of convention. (In terms of this stress on conventions — and, indeed, other things — Einstein might have been influenced by Henri Poincaré. They actually met in 1911— see here and here.) Alternatively and as Einstein later says, geometry is a matter of “logical connection[s]” or what can be derived from axioms. What is important here is that geometrical “truth” has nothing to do with what Einstein himself calls “correspondence” or “objects of experience”.

Nonetheless, Einstein later did tell us why laypersons tie both geometry and truth to physics — or at least to the physical world. He continued:

“It is not difficult to understand why, in spite of this, we feel constrained to call the propositions of geometry ‘true.’ Geometrical ideas correspond to more or less exact objects in nature, and these last are undoubtedly the exclusive cause of the genesis of those ideas.”

Einstein’s words above highlight a long-running debate in the philosophy of mathematics. In that debate philosophers have attempted to ascertain which way the temporal and metaphysical arrow points. Thus:

1) From “exact objects in nature” to mathematical “ideas”.

Or:

2) From mathematical ideas to objects in nature (which needn’t be seen as being exact anyway).

However, Einstein concluded by saying that “[g]eometry ought to refrain from such a course” of seeing truth in the same way as laypersons do (i.e., as a matter of correspondence with objects in the physical world).

To repeat: most laypersons (as Einstein has just hinted) do see truth as some kind of correspondence between what people say (or write) and the world (or aspects of the world). For example, the statement “All swans are white” is believed to be true because it is seen to correspond with the fact that all swans are white. (Each italicised word in that sentence presents its own problems.) Of course there are many difficulties with what’s called the correspondence theory of truth which can’t be tackled here. But, in terms of Einstein’s own position, after putting scare quotes around the word truth when it comes to “pure geometry”, he then writes that truth — at least partly — consists in “corresponding” with the “empirical data”.

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