Against Platonism in Physics (With Lee Smolin)

[Most of the quotes in this piece are taken from Lee Smolin's Time Reborn: From the Crisis in Physics to the Future of the Universe, which was published in 2013.]

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This piece focuses on Lee Smolin's position on what he takes to be Platonism in (mathematical) physics. Smolin's words are also used as a springboard for discussing other issues and positions (including my own) within this general debate.

Firstly, Platonism in physics is tackled as it was explicitly stated by the physicists John Wheeler and Stephen Hawking. Max Tegmark (as a Platonist) is also featured. The position advanced by Tegmark is that mathematics can perfectly describe the world/reality because the world/reality is itself mathematical. Wheeler and Hawking argued against such a position (or at least they appeared to).

Then there's a section on a position best described as “the-map-is-not-the-territory”. This too inevitably focuses on Platonism in physics. It also asks the question as to how, exactly, (mathematical) models relate to the world/reality.

There's also discussion of the relation between mathematical objects and mathematical concepts as this is brought out within the specific context of Platonism in physics.

An old problem is then discussed: the precise relation between our world and the Platonic world. The issue of (as it were) “causal closure” was the traditional focus of this particular debate; though other aspects are tackled in the following.

Finally, mathematical structuralism - and how it relates to Platonism in physics - is discussed. This leads naturally on to the final section which discusses what Smolin calls “intrinsic essences” (or what philosophers call “intrinsic properties”).

Psychologisms

Lee Smolin puts a psychological and sociological slant on the issue of Platonism in physics when he discusses the personal motivations of Platonic philosophers and mathematicians. He writes:

“Does the seeking of mathematical knowledge make one a kind of priest, with special access to an extraordinary form of knowledge?”

It can safely be said that this was true of Pythagoras, Plato and their followers. Whether or not it's also true of an everyday mathematician or philosopher ensconced in a university department in Nottingham or Oxford, I don't know. Having said that, Smolin does speak about a friend of his in this respect. Smolin tells us that he “sometimes wonder[s] if his belief in truths beyond the ken of humans contributes to his happiness at being human”.

In any case, it's probably best to leave the personal psychologies of Platonists there. After all, if Smolin argues that Platonists are Platonists for reasons of personal psychology, then Platonists can also argue that Smolin is an anti-Platonist for reasons of personal psychology. And where does that get us?

Fire In the Equations

The physicist John Archibald Wheeler provided the most powerful riposte to Platonism in physics. In an oft-quoted story, we're told 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 Max Tegmark and others, however, the equations are the universe - at least in a manner of speaking - and perhaps not even in a manner of speaking! (More of which later.)

Then Steven Hawking (in his A Brief History of Time) nearly 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 science writer Kitty Ferguson (in her The Fire in the Equations) offers a possible Platonist answer to Hawking's question by saying 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”?

The theoretical physicist Lee Smolin, on the other hand, explains why the idea that “mathematics is prior to nature” is unsupportable. He writes:

“Math in reality comes after nature. It has no generative power.”

More philosophically, Smolin continues when he says that “in mathematics conclusions are forced by logical implication, whereas in nature events are generated by causal processes in time”.

The Platonist will simply now say that mathematics fully captures those “causal processes”. Or, in Max Tegmark's case, the argument is that the maths and the causal processes are one and the same thing.

More relevantly to the position of people like Tegmark, Smolin says that

“logical relations can model aspects of causal processes, but they're not identical to causal processes”.

What's more, “[l]ogic is not the mirror of causality”.

Yet according to Tegmark:

i) Because the models of causal processes are identical to those processes,

ii) then they must be one and the same thing.

More precisely, Tegmark's argument is as follows:

i) If a mathematical structure is identical (or “equivalent”) to the physical structure it “models”,

ii) then the mathematical structure and the physical structure must be one and the same thing.

Thus if that's the case (i.e., that structure x and structure y are identical), then it makes little sense to say that x “models” (or is “isomorphic with”) y. That is, x can't model y if x and y are one and the same thing.

So Tegmark also applies what he deems to be true about the identity of two mathematical structures to the identity of a mathematical structure and a physical structure. He offers us an explicit example of this:

electric-field strength = a mathematical structure

Or in Tegmark's own words:

“' [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.”

In any case:

i) If x (a mathematical structure) and y (a physical structure) are one and the same thing,

ii) then one needs to know how they can have any kind of relation at all to one another. [Gottlob Frege's “Evening Star” and “Morning Star” story may work here.]

In terms of Leibniz's law (Smolin is a big fan of Leibniz and frequently mentions him), that must also mean that everything true of x must also be true of y. But can we observe, taste, kick, etc. mathematical structures? (Yes, if they're identical to physical structures!) In addition, can't two structures be identical and yet separate (i.e., not numerically identical)? Well, not according to Smolin's Leibniz.

All this is perhaps easier to accept when it comes to mathematical structures being compared to other mathematical structures (rather than to something physical). Yet if the physical structure is a mathematical structure, then that qualification doesn't seem to work either.

All this is also problematic in the following sense:

i) If we use mathematics to describe the world,

ii) and maths and the world are the same thing,

iii) then we're essentially either using maths to describe maths or using the world to describe the world.

What's more, maths can't be the “mirror” of anything in nature if the two are identical in the first place. In other words, any mathematical models which are said to “perfectly capture nature” (or causality) can only do so because nature (or causality) is already mathematical. If that weren't the case, then no perfect modelling (or perfectly precise equations) could exist. Thus, again, that perfect symmetry (or isomorphism) can only be explained (according to Tegmark) if nature and maths are one and the same thing.

Just Maths?

A sharp and to-the-point anti-Platonist position is also put by the science writer, Philip Ball. He writes:

“... equations purportedly about physical reality are, without interpretation, just marks on paper”.

In other words, what exactly (as Hawking put it above) “breathes fire into the equation [to] make a world”?

The Philip Ball quote above also highlights two problems.

i) The fact that we can make mistakes about physical reality.

ii) That even if the equations are about physical reality, they're not one and the same as physical reality.

Indeed, even Ball's “interpretation” won't make the equations equal physical reality.

So let's go all the way back to Galileo (as Smolin himself does).

Surely we must say that “Nature's book” isn't written in the language of mathematics. We can say that Nature's book can be written in the language mathematics. Indeed it often is written in the language of mathematics. Though Nature's book is not itself mathematical because that book - in a strong sense - didn't even exist until human beings began to write (some of) it.

Perhaps I'm doing Galileo a disservice because he did say that

“we cannot understand [Nature] if we do not first learn the language and grasp the symbols in which it is written”.

Yet Galileo was talking about our understanding of Nature here - not just Nature as it is “in itself”.

Nonetheless, Galileo also said that the the “book is written in mathematical language”. So was he also talking about Nature as it is in itself being mathematical? Perhaps Galileo wasn't only saying that mathematics is required to understand Nature. There is, therefore, an ambivalence here between the idea that Nature itself is mathematical and the idea that mathematics is required to understand Nature.

Sure, ontic structural realists and other structural realists (in the philosophy of physics) would say that this distinction (i.e., between maths and the world) hardly makes sense when it comes to physics generally - and it doesn't make any sense at all when it comes to quantum physics. Nonetheless, surely there's still a distinction to be made here.

The Map is Not the Territory

Philip Ball (who's just been quoted) puts the main problem of Platonism perfectly when he says that

“[i]t's not surprising, the, that some scientists want to make maths itself the ultimate reality, a kind of numinous fabric from which all else emerges”.

Thus, in more concrete terms, such mathematical Platonists fail to see that the “[r]elationships between numbers are no substitute” for the world/reality. Indeed, adds Ball, “[s]cience deserves more than that”.

This is the mistaking-the-map-for-the-territory problem. As the semanticist Alfred Korzybski once put it:

“A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness.”

Indeed we can take this further and say that “all models are wrong”.

This the-map-is-not-the-territory idea is put by Smolin himself when he tells us that “[m]athematics is one language of science”. In other words, the maths (in mathematical physics) isn't self-subsistent: it needs to be tied to reality: it isn't reality itself. Thus,

“[maths] application to science is based on an identification between results of mathematical calculations and experimental results, and since the experiments take place outside mathematics, in the real world, the link between the two must be stated in ordinary language”.

More directly, Smolin tells us that

“the pragmatist will insist that the mathematical representation of a motion as a curve [for example] does not imply that the motion is in any way identical to the representation”.

What's more:

“By succumbing to the temptation to conflate the representation with the reality and identify the graph of the records of the motion with the motion itself...”

Then Smolin tells us about one Platonist (or Tegmarkian) conclusion to all this. He writes:

“Once you commit this fallacy [i.e., of mistaking the map for the territory], you're free to fantasise about the universe being nothing but mathematics.”

Finally, Smolin puts his particular slant on the importance of time in all of this. He writes:

“The very fact that the motion takes place in time whereas the mathematical representation is timeless means they aren't the same thing.”

How Can Maths Model Nature?

To put it at its most simple and - perhaps - extreme. The Platonic mistake is to move from the fact that mathematics can be (almost) perfect for describing or modelling the world to the conclusion that the world must therefore be intrinsically mathematical itself. Smolin captures this position when he discusses the work of Isaac Newton. According to Smolin, Newton's world was

“infused with divinity, because timeless mathematics was at the heart of everything that moved, on Earth and in the sky”.

Slightly earlier, Smolin had also written that

“[w]hen Galileo discovered that falling bodies are described by a simple mathematical curve, he captured an aspect of the divine”.

We can of course ask if Galileo thought in these terms himself: even if only at the subconscious level. However, would that even matter to Smolin's take on this?

In any case, is mathematics “at the heart of everything that move[s]” or is it simply a tool for description or modelling? Max Tegmark (again) may argue the following:

i) If mathematics is “at the heart of everything that moves”,

ii) and it's also a perfect tool for description and modelling,

iii) then in what sense is the world not itself mathematical?

Indeed Smolin himself goes way beyond Galileo and Newton and says that “the whole history of the world” [in general relativity] is “represented by a mathematical object”. 

Now if we turn to quantum mechanics and the words of Philip Ball, he says that superposition is “considered only as an abstract mathematical thing”. It's also the case the the/a wavefunction is also a “mathematical object”.

If we get back to mathematical models.

It was said earlier that mathematics can describe (or even perfectly model) nature and that the physicists who aren't Platonists have no problem with this. How could they? Indeed Smolin himself tells us that “[i]t's impossible to state these laws [i.e., Newton's laws] without mathematics”. This is often said about quantum mechanics. Yet Smolin is going beyond that and saying that it's also true “the first two of Newton's laws”. More specifically, Smolin says that “[a] straight line is an ideal mathematical concept”. That is, “it lives not in our world but in the Platonic world of ideal curves”.

In terms of “acceleration” and the “rate of change of velocity” (to take just two examples), it was the case that “Newton needed to invent a whole new branch of mathematics: the calculus” in order to “describe it adequately”. But here again we mustn't conflate the maths with what the maths describes (or models).

Philip Ball (again) puts this position as it applies specifically to Hilbert space. He tells us that “a Hilbert space is a construct – a piece of maths, not a place”. He then quotes the physicist Asher Peres stating the following:

“The simple and obvious truth is that quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.”

Ball also mentions Max Tegmark's position. He writes:

“If the Many Worlds are in some sense 'in' Hilbert space, then we are saying that the equations are more 'real' than what we perceive: as Tegmark puts it, 'equations are ultimately more fundamental than words' (an idea curiously resistant to being expressed without words). Belief in the MWI seems to demand that we regards the maths of quantum theory as somehow a fabric of reality.”

Mathematical Objects and Mathematical Concepts

Smolin has a problem with such mathematical objects. He (implicitly) argues against this Platonic position when he says (in a note) that

“[m]athematicians like to speak of curves, numbers, and so forth as mathematical 'objects', which implies a kind of existence”.

However, it's fairly clear that Smolin has a problem with this position. He says that you may want to call these “mathematical objects” by the name of “concepts”. That, on one interpretation, surely takes mathematical objects out of the Platonic world and places them in the realm of human minds. (Except for the fact the concepts too can be seen as “abstract objects”.)

Stephen Hawking (for one) certainly didn't believe that maths and nature are one - and he too talked about “concepts”. He once wrote that “mental concepts are the only reality we can know”. Furthermore he stated: “There is no model-independent test of reality.”

This seems to mean that Hawking went further than simply saying that mathematics describes (or perfectly models) nature. After all, he stresses the importance of “mental concepts”. However, it can still be said that the models of physics are of course mathematical and accurate. Thus even if we require mental concepts to get at these mathematical models, the models can still perfectly capture “reality”. So whichever way we interpret Hawking's words, he certainly doesn't seem to put a Platonic position (or replicate Tegmark's stance) on mathematical physics.

Smolin himself distinguishes mental concepts from mathematical objects when (in a note) he writes:

“If you aren't comfortable adopting a radical philosophical position [i.e., of believing in mathematical objects] by a habit of language, you might want to call them [mathematical objects] concepts instead.”

In that passage Smolin doesn't seem to explicitly commit himself to mathematical concepts (rather than mathematical objects); though elsewhere he is more explicit when he also talks about “inventing” (i.e., not “discovering”) mathematical objects. It's also interesting to note that Smolin puts a Wittgensteinian position. Wittgenstein, for example, once wrote that “a cloud of philosophy condenses into a drop of grammar”. Smolin, on the other hand, talks about “adopting a radical philosophical position [because of] a habit of language”.

In any case, Smolin defines a “mathematical object” thus:

“Mathematical objects are constituted out of pure thought. We don't discover the parabolas in the world, we invent them. A parabola or a circle or a straight line is an idea. It must be formulated and then captured in a definition... Once we have the concept, we can reason directly from the definition of a curve to its properties.”

Of course there are a couple of words in the passage above which a Platonist may have a problem with. Firstly, the word “invent” (as in “we invent [mathematical objects]”. And then there's the use of the word “concept” (i.e., rather than “object”). In Fregean style, we can have a “concept of an object”. Thus an abstract mathematical object can generate (as it were) various mental concepts. In terms of “[o]nce we have the concept”, then certain things logically and objectively follow from that concept. So it's the philosophical nature of the concept which raises questions.

How Do We Get to the Platonic Realm?

Even if the Platonic mathematical realm does indeed exist, then it' still the case that we still need to gain (causal) access to it. This is a problem that's often been commented upon. Smolin himself puts it this way:

“One question that Jim [a friend of Smolin] and other Platonists admit is hard for them to answer is how we human beings, who live bounded in time, in contact only with other things similarly bounded, can have definite knowledge of the timeless realm of mathematics.”

Plato himself answered Smolin's question when he argued that we have “intuitive” (or even genetic) access to this abstract realm from birth. (He elaborated on this in his slave boy story.)This doesn't seem to solve the problem of causal access to a Platonic realm. Thus, as a addendum to this argument about causal access (or the “causal closure” of both the human world and the Platonic world), Smolin says that “[b]ecause we have no physical access to the imagined timeless world, sooner or later we'll find ourselves just making stuff up”. In other words, even if the Platonic realm does exist and we can also gain access to it, that doesn't mean that we can't get things wrong or make mistakes about it.

Smolin himself says that “[w]e get the truths of mathematics by reasoning, but can we really be sure our reasoning is correct?”. What's more:

“Occasionally errors are discovered in the proofs published in textbooks, so it's likely that errors remain.”

I suppose Plato himself might have argued that we can't get things wrong because our intuition somehow guarantees access to the truths found in this realm. Or, more correctly, if we use our reason (or intuition) correctly (as Descartes also argued), then we simply can't go wrong.

So now here's Smolin quoting Roger Penrose (who's a personal friend of Smolin) putting the Platonic/Cartesian position just mentioned:

“You're certainly sure that one plus one equals two. That's a fact about the mathematical world that you can grasp in your intuition and be sure of. So one-plus-one-equals-two is, by itself, evidence enough that reason can transcend time. How about two plus two equals four? You're sure about that, too! Now, how about five plus five equals ten? You have no doubts, do you? So there are a very large number of facts about the timeless realm of mathematics that you're confident you know?”

It's of course the case that many philosophers and mathematicians will say that one doesn't need a “timeless realm” to explain all that's argued in Penrose's words above. It can, for example, be given a Wittgensteinian explanation in terms of rules and our knowledge of the rules. Our “intuitive grasp” (as it's sometimes put) of basic arithmetic can also be partly explained by cognitive scientists, evolutionary psychologists or philosophers.

It's also interesting that Penrose gives basic arithmetical examples as demonstrations of our Platonic intuition. So what about higher or more complex maths? Do mathematicians have immediate intuitions about such equations or do they need to work at them? And if they do need to work at them, then surely intuition must have a minimal role to play.

In one of his notes, Smolin gives another argument as to why the Platonic realm and the human realm can never be split asunder. He writes:

“It's also not quite true to say that the truths of mathematics are outside time, since, as human beings, our perception and thoughts take place at specific moments in time – and among the things we think about are mathematical objects.”

The Platonist would say that Smolin is conflating the Platonic realm with the fact that we can gain access to that realm. That is, one realm can still be abstract and timeless even if we concrete and time-bound human beings can gain access to it.

But here we have a analogue of the mind-body problem. That is, what is the precise relation between the time-bound and concrete world and the timeless and abstract world? Smolin himself explains the Platonic position in terms of human psychology. He continues:

“It's just that those mathematical objects don't seem to have any existence in time themselves. They are not born, they do not change, they simply are.”

Smolin uses the word “seem” in the above (as in “seem to have any existence in time”). That implies that what seems to be the case may not actually be the case. Yet Smolin does then say that mathematical objects “are not born, they do not change, they simply are”. Here he may simply be putting the position of the Platonist. Again, even if mathematical objects aren't born, we still need to explain our access to them and acknowledge the possibility of getting things wrong about them - even systematically getting things wrong!

Interestingly, Smolin offers us a kind of “conventionalist” middle way when he states that

“[w]e invent the curves and numbers of mathematics, but once we have invented them we cannot alter them”.

A Platonist would have a profound problem with the word “invent”. However, even though we may indeed invent numbers (or functions), once they're invented or created, then they become (as it were) de facto Platonic objects. That is, they're then set in stone and other things must necessarily follow from them. This is something that a philosopher like the late Wittgenstein might have happily accepted. That is, that rules and symbol-use themselves create the “objectivity” (or at least the “intersubjectivity”) of maths - and also, perhaps, even the timelessness of mathematics.

Structuralism

Interestingly enough, Smolin puts his anti-Platonist position by adopting the position of mathematical structuralism. (There are also types of mathematical structuralism which are Platonist - see here.) Firstly (in a note) he expresses the essence (as it were) of mathematical structuralism when he says that “relationships are exactly what mathematics expresses”. He then makes the ontological point that

“[n]umbers have no intrinsic essence, nor do points in space; they are defined entirely by their place in a system of numbers or points – all of whose properties have to do with their relationships to other numbers or points”.

Moreover, “[t]hese relationships are entailed by the axioms that define a mathematical system”. It can be said that Platonists believe that numbers do have an "intrinsic essence". In other words, a system doesn't gain its nature because of the relations between numbers: the relations between numbers are parasitical on the nature of numbers themselves. After all, the following can be argued:

i) If numbers didn't have an intrinsic essence,

ii) then they couldn't engender the precise relations to other numbers which they have in each system.

Indeed:

i) If numbers have intrinsic essences,

ii) then those essences can't be dependent on the systems to which they belong (or, indeed, to any system).

iii) Therefore those intrinsic essences must come before all systems of relations.

Of course the obvious point to put against that position was put by Paul Benacerraf in 1965. The French philosopher wrote:

“For arithmetical purposes the properties of numbers which do not stem from the relations they bear to one another in virtue of being arranged in a progression are of no consequence whatsoever. But it would be only these properties that would single out a number as this object or that.”

In simple terms, we can say that the number 1 is (partly) defined by being the successor of 0 in the structure determined by a theory of natural numbers. In turn, all other numbers are defined by their respective places in the number line. So, again, it can of course be said that the “essence” of, say, the number 2 is that it comes after 1 and before 3. But surely then its intrinsic essence is determined by its relations to 1, 3 and to other numbers. Perhaps, then, relations and numbers are two sides of the same coin. Having said that, it's still hard to understand what the intrinsic essence of a number could be when that essence is taken separately to that number's relations to other numbers, functions, etc.

Of course this foray into the philosophy of mathematics completely ignores the precise relation between mathematical structuralism and the world. Despite saying that, Smolin does make an explicit philosophical commitment to mathematical structuralism. He writes:

“If there's more to matter than relationships and interactions, it is beyond mathematics.”

Thus Smolin firstly began by articulating the/a position of mathematical structuralism and ends up stating a position that's very close to ontic structural realism. However, the ontic structural realist argues that there's no “beyond mathematics” – or at least that there's nothing beyond the “relationships and interactions” of physics which are described by mathematics. Yet Smolin himself appears to leave it open that there may well actually be a beyond mathematics. And elsewhere in his writings Smolin seems to state that there are “intrinsic properties” (qualia, etc.) beyond mathematics and even beyond physics itself.

Intrinsic Essences, Qualia, Etc.

Smolin makes it explicit that he (at the very least) acknowledges the possibility of “intrinsic properties” as they occur in both minds (i.e., qualia) and in inanimate objects. For example, he writes:

“We don't know what a rock really is, or an atom, or an electron. We can only observe how they interact with other things and thereby describe their relational properties. The external properties are those that science can capture and describe – through interactions, in terms of relationships.”

The passage above might well have been written by someone like David Chalmers or Philip Goff – both of whom are advocates of panpsychism. In the case of panpsychists, the “what is” (or “what it is like to be”) of a rock can be explained by referring to its experiences (or to its “proto-experiences”). These experiences are therefore the “intrinsic essences” (to use Smolin's own term) of rocks for panpsychists (if not for Smolin himself). Clearly, according to the passage above, philosophical relationalism (or relationalism in physics itself – which Smolin thoroughly endorses) doesn't capture these intrinsic properties.

So it's no surprise that Smolin continues on the theme of intrinsic essence. He writes:

“The internal aspect is the intrinsic essence; it is the reality that is not expressible in the language of interactions and relations.”

We can of course ask why Smolin accepts the very existence (or reality) of an “internal aspect” of anything when many philosophers and other physicists reject this idea.

What's more, Smolin ties all this to both consciousness and qualia. Firstly he writes the following:

“What's missing when we describe a color as a wavelength of light or as certain neurons lighting up in the brain is the essence of the experience of perceiving red. Philosophers give these essences a name: qualia.”

Again (like Smolin's “intrinsic aspect” earlier), why does Smolin need to use the somewhat archaic word “essence” (archaic at least according to certain philosophers) at all? Why believe in essences?

Finally, Smolin writes:

“Consciousness, whatever it is, is an aspect of the intrinsic essence of brains.”

So clearly Smolin has been reading some contemporary (analytic) philosophers. It's just a little odd that he begins with the words “consciousness, whatever it is”; and then goes on to tell us exactly what it is: “the intrinsic essence of brains”.

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How To Write Like an Analytic Philosopher

There certainly is a specific prose style when it comes to much analytic philosophy. Of course there's a general academic prose style (or prose styles) too. The analytic philosophy prose style can therefore be taken to be a variation on that.

Academics will of course say - and justifiably so - that this style is required for reasons of objectivity (or “intersubjectivity”), clarity, the formal requirements of academic research, stylistic uniformity and whatever. However, there's clearly more to it than that.

One qualification I'll make about that is that the better known (or even famous) analytic philosophers become, the more likely they'll take liberties with that prose style. In parallel, postgraduates and young professional analytic philosophers will take the least liberties with it. (Possibly that's a good thing too.) This basically means that if you've gone through the academic mill and proved your credentials, then you can relax a little in terms of one's prose style. (For example, one can use the word “I” rather than royal “we” - or the “one” I've just used.)

One point I'd like to stress is how the academic style is used to hide the philosophical, subjective and even political biases of the academics concerned. That means if you employ the right self-consciously dry academic style, then very few on the outside will detect any (obvious) biases. Indeed such academics are often seen (by many laypersons) as algorithmic machines devoted to discovering the Truth.

As for the philosophy under the prose.

The Cambridge philosopher Hugh Mellor (D.H. Mellor) once classed Jacques Derrida's work as “trivial” and “willfully obscure”. Mellor did so in his attempt to stop Derrrida receiving an Honorary Degree from the University of Cambridge.  Of course a lot of analytic philosophy is also “trivial”. It's also the case that some analytic philosophers hide that triviality under prose which is “willfully obscure”. Having said that, such analytic philosophy won't of course be trivial or willfully obscure in the same way in which Derrida's work is (that's if it is). That is, it won't be poetic, vague and oracular. Instead, analytic triviality is often hidden within a forest of jargon, schema, symbolic letters, footnotes, references, “backward Es” (to quote Hilary Putnam), words like ceteris paribus and the like. In other words, basic analytic academic prose will be used to hide the trivialities and increase the obscurities. So, again, in Derrida's case it's a different kind of obscurity. (Though, in the continental tradition, it can be equally academic.)

How To Write an Analytic Philosophy Paper

What postgraduates of analytic philosophy tend to do when they write a paper is focus on an extremely narrow “problem”; as well as an extremely-narrow take on that extremely-narrow  problem. Then they'll read everything that's been written on that subject in the last five or ten years (at least by the big or fashionable players). They'll then make notes on - and collect quotes from - what they've read. Thus the resultant paper will also be chockablock with references, footnotes, etc. (though not necessarily chockablock with quotes). It will be written in as academic (or dry) style as possible: indeed, self-consciously so. That will mean that there's often a gratuitous use of symbols, lots of numbered points, schema, and other stylistic gimmicks which sometimes have the end result of making it look like a physics paper.

In crude and simple terms, what often happens is that analytic postgraduates attempt to write like older academics and the contemporary philosophers they've only-just read. Thus, in that sense, they're ingratiating themselves into a professional academic tribe.

In terms specifically of references.

Take William G. Lycan’s medium-length paper ‘The Continuity of Levels of Nature’. This paper includes fifty-two references to other philosophers’ texts. We can also cite Jaegwon Kim’s ‘Supervenience as a Philosophical Concept’, which has fifty-one such references.

Then there's the the sad case of footnotes.

Footnotes often make analytic-philosophy papers very difficult to read because they sometimes take up more space (on a given page) than the main text. (Click this link for an example of what I'm talking about.) In addition, if the reader were to read all the footnotes as and when they occur, then he'd loose the “narrative thread” of the central text. (For that reason, aren't notes best placed at the end?) Finally, doesn't this excessive use of long and many footnotes verge on academic exhibitionism?

Postgrad students will also focus on the fashionable/up-to-date issues or problems and read the fashionable/up-to-date papers on those issues or problems - even if such things are simply new stylistic versions of what old philosophers have already said. (Though with endless examples of Derrida's “sign substitutions”: that is, when an old word/concept is given new name.) Indeed it has been said (e.g., by A.J. Ayer way back in the 1950s) that many postgrad students rarely read anything that's older than twenty years old. And many postgrads are so convinced that what is new is always better than what is old that they don't feel at all guilty about their fixation with the very-recent academic past.

In terms of the philosophising itself.

It can be said that when a postgraduate student (of analytic philosophy) thinks about the nature of an aspect of the philosophy of mind (to take an arbitrary example), all he primarily does is read and think about what Philosopher X and Philosopher X (usually, very recent philosophers) have said about the nature of that aspect of the philosophy of mind. This often means that he may well be caught in a intertextual trap. (Though, of course, it’s unlikely that any student would rely on only two philosophers of mind.) Indeed all the student's responses, reactions and commentaries on that aspect of the philosophy of mind will also be largely intertextual in nature.

So in order to get a grip of why I've used the word “intertextual” (a word first coined by the Bulgarian-French semiotician and psychoanalyst, Julia Kristeva), here's a passage from the French literary theorist and semiotician, Roland Barthes:

“Any text is a new tissue of past citations. Bits of code, formulae, rhythmic models, fragments of social languages, etc. pass into the text and are redistributed within it, for there is always language before and around the text. Intertextuality, the condition of any text whatsoever, cannot, of course, be reduced to a problem of sources or influences; the intertext is a general field of anonymous formulae whose origin can scarcely ever be located; of unconscious or automatic quotations, given without quotation marks.”

Thus when students study philosophy at university, it seems that reading "texts" often seems far more important than independent thinking or reasoning. Indeed, isn't that called “research”?

On the other hand, many philosophers (or wannabe philosophers) would like to flatter themselves with the view that their own philosophical ideas have somehow occurred ex nihilo. Yet genuine ex nihilo philosophical thought is as unlikely as ex nihilo mental volition or action (i.e., what philosophers call “origination”).

In Praise of Style and Clarity

The analytic philosopher Simon Blackburn has little time for those philosophers who glory in the complexity of their own philosophical writings. Blackburn believes that philosophy's “difficulties were compounded by a certain pride in its difficulty”. It's ironic, then, that some of the great philosophers were also good writers. Blackburn himself cites Bertrand Russell, Gilbert Ryle and J.L. Austin. (I strongly disagree with Blackburn's final choice... but there you go.) I would also cite Plato, Descartes, Bishop Berkeley, David Hume, Schopenhauer, etc. As for the 20th century: Hilary Putnam, Richard Rorty, Thomas Nagel, Jaegwon Kim, John Searle and particularly various other American analytic philosophers - i.e., as opposed to English ones. (It's often the case that as English analytic philosophers are to American analytic philosophers, so Continental philosophers are to English analytic philosophers.)

Bad writing, technicality and sheer pretentiousness, however, shouldn't imply that all work on the difficult minutia of philosophy should be shunned or limited in any way. Of course not. Some papers are bound to be complex and difficult. Not necessarily because of the subject’s difficulty; but simply because the issues and problems will be technical in nature and therefore have a high number of unfamiliar terms. However, often technical terms can be gratuitous – though it depends on the philosopher concerned.

Blackburn makes some other interesting points about philosophical prose – at least in its bad guise. He quotes John Searle stating:

“If you can’t say it clearly you don’t understand it yourself.”

This position is backed up by the science writer, Philip Ball (who writes about scientists, not philosophers):

“When someone explains something in a complicated way, it's often a sign that they don't really understand it. A popular maxim in science used to be that you can't claim to understand your subject until you can explain it to your grandmother.” 

(Perhaps this is where Searle got his view from.)

So all the times we think critically of ourselves for not understanding a particular analytic philosopher’s prose, perhaps all along he didn’t understand his own prose. Or, more relevantly, perhaps he didn't understand the philosophical ideas he was trying – badly – to express. Thus we might have assumed our own cognitive limitations or simply the damned complexity of the subject. Nonetheless, perhaps all along it was just a case of the philosopher concerned being a bloody poor writer – regardless of the complexity of his ideas. Either that or he might well have been just plain pretentious!

Certainly such guilty philosophers don’t follow the Quintilian dictum (as quoted by Blackburn):

“Do not write so that you can be understood, but so that you cannot be misunderstood.”

Of course, literally speaking, if one writes “so that you cannot be misunderstood”, then one must also be writing “so that you can be understood” - the two things go together. Despite that, the philosopher Bernard Williams (also quoted by Blackburn) offered an obvious riposte to this “impossible ideal”:

“Williams snapped at that and said it was 'an impossible ideal. You can always be misunderstood', and of course he’s right. But I think the point of Quintilian’s remark isn’t 'write so as to avoid any possible misunderstanding’ but to remember that it’s difficult and that it’s your job to make it as easy as you can.”

It's interesting to note here that Williams’ impossible-ideal argument can also be used in favour of the idea that there will always be someone in one’s own culture (or even profession) - no matter how rational - who'll misinterpret at least something you write or say. Indeed perhaps everyone who reads or listens to you will misinterpret you in some small or large way. The idea of a perfect communication of a complete and perfect meaning to a perfect interpreter seems to be a ridiculous ideal. It seems to be almost – or even literally – impossible... and for so many reasons.

So philosophers will always be “misunderstood” by someone in some way. Indeed each person will misunderstand a philosopher in some way - whether that way is large or small. All we have left (as writers or philosophers) is to realise that “it’s [our] job to make it as easy as [we] can”. We can't be expected to do more than this. We can't guarantee the perfect communication of our ideas or the perfect understanding of our ideas by other people (as anyone who uses social media already knows). And even if we allow this slack, perhaps, in the end, it simply doesn't matter that much because communication doesn't require either completely determinate meanings or completely determinate interpretations. We seem to manage quite well in most situations without perfect languages and other philosophical ideals. So perhaps we can't (to use a term from Derrida again) “mathematicise” meaning, interpretation and understanding.

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A Short Study of a Ketamine-for-Depression Study

In March, 2019, a new antidepressant became available in the United States. This has been classed as "the first fundamentally new medicine for depression in decades". The controversial thing is that it's based on the anesthetic, ketamine. (The drug itself is called Spravato.) Some psychiatrists have said that this drug was approved with little evidence to back it up (see later comments); and also under standards that were less rigorous than those required for “conventional” antidepressants.

Experiments on Mice

Mice were the guinea pigs (as it were) in one bit of research on ketamine. The researchers induced depression/stress in mice by restraining them in mesh tubes or by injecting them with corticosterone (a stress hormone). It was then seen that the mice began to loose their taste for sweet water and didn't struggle when dangled by their tails. (All this raises animal welfare issues; which are too complex and tangential to go into here.)

It can be asked how the scientists came to know that the depression/stress of these mice had lifted. Did the mice express that view? Of course not. So it must have been behavioural evidence that convinced those involved in this research.

Well, three hours after a dose of ketamine, the mice’s behaviour did indeed improve (at least in these cases).

Of course no one can really make a big deal about ketamine making mice (or people) feel better “within hours”. (Typical antidepressants can take weeks to start working.) In terms of fast action, alcohol and cannabis can make people feel better within minutes. LSD and “magic mushrooms” can do the same thing within around 30 minutes to an hour. Indeed I suppose that a heavy smash on the head could (in theory) do the same within seconds.

It was thought (at first) that ketamine “spurred” new synapses (i.e., the connections between neurons). In turned out that newly created synapses aren't actually involved in ketamine's behavioural and mood effects. Nonetheless, synapses are still part of the story of ketamine and its effects.

This shows us that we should never take a single study as gospel, or even a whole group of studies. We - laypersons and scientists alike - often need to sit back and take stock.

For example, who remembers when depression was seen to be all about serotonin? A few weeks later (to be rhetorical), it was seen to be all about dopamine or cat piss. Thus any research into depression (or indeed into anything science-based) should be taken with extreme care. That's not a “anti-science” statement. It's simply a statement about particular “research projects” (or “studies”) at particular points in time. Indeed being slightly sceptical about the glut of often contradictory scientific findings is often a highly scientific and rational position to take. If one were to accept all of them all of the time, then one would be rendered highly confused and, indeed, irrational.

This also means that one shouldn't be committed to particular scientists, particular studies, or even particular disciplines within science. Instead one should be committed to the communal reality of science as a whole; which usually has a self-correcting bias.

The physicist Lee Smolin (in his The Trouble With Physics) sums part of this up neatly in the following passage:

“Scientists often do exaggerate and distort the evidence. Age, status, fashion, peer pressure all do play a role in the workings of the scientific community... But I would suggest that enough scientists adhere to enough of the ethic [i.e., the scientific ethic] that in the long run progress continues to be made...”

The anti-depression industry is huge. So we must also factor in financial clout and political pressure/power into these studies, as well as the importance of the U.S. Food and Drug Administration. I mention the the FDA because it approved a nasal spray (as stated in the intro) which contains a form of ketamine (i.e., esketamine) for depression only in March, 2019.

Technical Terms Galore

Of course there are lots of technical terms to cope with in these studies. For example, we're told that ketamine slowly coaxes nerve cells in order to sprout new neural connections. More technically, some 12 hours after ketamine treatment, new dendritic spines began to appear in the neurons found in a part of the prefrontal cortex of mice. These dendritic spines have been seen to to be replacing those lost during the period of stress or depression.

Prima facie, there's an assumption here that new neural connections are automatically a good thing. So what if a paranoid schizophrenic is making new neuronal connections which all re-enforce his paranoia? And isn't it the case that new neural connections are being made all the time in animal brains?

In any case, the neuroscientist Alex Kwan (of Yale University) happily tells us that there “is still a lot of mystery in terms of how ketamine works in the brain”. But isn't that the case with so many drugs which effect the brain and therefore the mind – even those which have been on the market for decades? 

Having put certain negatives, there will be a temptation to criticise the positives simply because it's ketamine that we're talking about here. Yes, ketamine is not only a drug – it can also be an illegal drug (i.e., it's a “controlled substance”). Though, as everyone knows, the various social, moral and legal lines between illegal and legal drugs are often vague, highly contingent and very rarely backed up with good arguments.