James Ladyman on Structural Realism

In his Understanding Philosophy of Science), James Ladyman says that “structural realism” was “introduced” by the philosopher John Worrall. 

This position - within the philosophy of science (though mainly within the philosophy of physics) - has it that structures are fundamental. What's more, structures are real (hence the word “realism”).

At the heart of structural realism is the idea that physics essentially deals with structures, not with “things” or entities. More importantly, it is these structures which are retained in physics; not the things which physics posits. That is, such structures can be passed on from an old theory to a new theory (i.e., when both theories are - ostensibly - about the same phenomenon or problem).

Thus structural realism is a realism about structure, not about things, conditions or “empirical content”. As Ladyman puts Worrall's position:

“... we should not accept full blown scientific realism, which asserts that the nature of things is correctly described by the metaphysical and physical content of our best theories. Rather, we should adopt the structural realist emphasis on the mathematical or structural content of our theories.”

More relevantly

“Since there is (says Worrall) retention of structure across theory change, structuralism realism both (a) avoids the force of the pessimistic meta-induction (by not committing us to beliefs in the theory's description of the furniture of the world), and (b) does not make the success of science... seem miraculous...”

Thus structural realism has an argument against the well-known position of “pessimistic meta-induction”: i.e., such pessimism only applies to “empirical content” and “theory”, not to structure. That is, structure is retained “across theory change” and thus total inductive pessimism is unjustified.

So three questions arise here:

i) What is structure?

ii) Is structure really retained “across theory change”?

iii) And (this is related to i) above) how is structure distinguished from “empirical content” and “theory”?

Henri Poincaré's Structuralism

James Ladyman traces structural realism back to Max Plank and Henri Poincaré. For example, Ladyman quotes Plank stating the following:

“... 'Thus the physical world has become progressively more and more abstract; purely formal mathematical operations play a growing part.'...”

Indeed Plank's position is one which most physicists would uphold; even if they wouldn't use Plank's precise wording. Of course this is simply an indirect acknowledgment that that there would be no physics without “mathematical operations”; or, more broadly, without mathematics itself.

Thus, in a broad sense, the structural realism position is that it's all about the maths. Or, at the least, it's all about the mathematical structures noted by physicists.

Ladyman also tells us that Poincaré

“talks of the redundant theories of the past capture the 'true relations' between the 'real objects which Nature will hide for ever from our eyes'...”

So here Poincaré's response to the pessimistic meta-induction is to argue that “true relations” are retained from theory to theory; even if the things or phenomena mentioned in the theories aren't. As can also be seen, Poincaré uses different jargon to contemporary structural realists in that he talked of “true relations” rather than “structures”. Then again, structural realists also make extensive us of the word “relations”. After all, it's the structures of the physical world which account for these relations; and, in a sense, they're also constituted by such relations.

Nonetheless, Poincaré does seem to depart from contemporary structural realism when he talked about “real objects”. As can be shown, structural realists (especially ontic structural realists) dispense entirely with objects or things - “real” or otherwise. Or at least they believe that “every thingmust go”. Despite that, since Poincaré qualifies his reference to “real objects” with the clause that “Nature will hide [these real objects] for ever from our eyes”, then it can be said that Poincaré – effectively - did indeed dispense with objects/things too. That is, when Poincaré used the phrase “for ever from our eyes”, presumably he wasn't only talking about literal visual (or observational) contact with real objects. He must have also meant any kind of contact with them – including (as it were) theoretical contact. Thus Poincaré's real objects were little more than Kantian noumena and therefore of little use in physics. Then again, since Poincaré was also a Kantian, noumena might well have had a role to play in his metaphysics and physics.

So was Poincare a Kantian and a structural realist at one and the same time?

Just as Poincaré used the words “true relations” instead of the word “structure”, so the philosopher of science Howard Stein uses the word “Forms”. That is, Stein says (as quoted by Ladyman) that

“our science comes closest to comprehending 'the real', not in its account of 'substances' and their kinds, but in its account of the 'Forms' which phenomena 'imitate' (for 'Forms' read 'theoretical structures', for 'imitate', 'are represented by'”.

Clearly Stein is attempting to tie contemporary structural realism to a long philosophical - and indeed Platonic - tradition. He does so with his use of the words “Forms” (with a platonic 'H') and “imitate”. Then again, he also rejects the equally venerable (i.e., in the history of philosophy) “substances” and “kinds”.

Having said that, this very same passage can be read as expressing the position that Forms (or “theoretical structures”) are actually imitating (or “representing”) “substances and their kinds”. So, as with Kantian noumena, it's not that substances don't exist: it's that our only access to them is through theoretical structures: i.e., through the mathematical structures and models of physics. If this reading of Stein is correct, then that makes his position almost eliminativist. As with Kant's noumena, Poincaré's “real objects” and ontic structural realism's “things”, aren't Stein's “substances” also (to use Wittgenstein's words) “idle wheels in the mechanism”? What purpose do they serve? Do they serve as a abstract Kantian “grounding” or as a Lockean “I know not what”? Or, to quote Wittgenstein again, perhaps it's best to conclude: “Whereof one cannot speak thereof one must be silent.”

Examples from Physics

Maxwell and Fresnel

James Ladyman cites John Worrall's example of the structural elements of Augustin-Jean Fresnel's theory (of light waves) passing over to James Clerk Maxwell's later theory. Ladyman quotes Worrall thus:

“... 'There was an important element of continuity in the shift from Fresnel to Maxwell.'... ”

More relevantly, this

“'was much more than a simple question of carrying over the successful empirical content into the new theory'...”

However, neither was it just a case of “carrying over or the full theoretical content or full theoretical mechanisms”.

Thus, if it's not just a case of “empirical content” and “theoretical content” being “carried over”, then what else was also carried over? The answer to this is: structure. That is, Fresnel's theory shares a certain structure with Maxwell's later theory. Or as Worrall himself puts it:

“... 'There was continuity or accumulation in the shift, but the continuity is one of form or structure, not of content.'...”

Clearly Worrall doesn't see Fresnel's and Maxwell's theories as only being (what's often called) “empirically equivalent”. He states that it's not (only) “empirical contents” which are passed on. That must mean that the two theories are also theoretically “under-determined” by the empirical content.

This means that Fresnel's and Maxwell's theories are neither empirically nor theoretically identical. So does that mean that these two theories are structurally (or formerly) identical instead? Worrall may not also believe in complete structural identity between these two (or any) separate theories. However, he clearly does believe that structural identity is more important (or more substantive) than any empirical or theoretical identity.

Thus it follows from all this that we'll now need to know how it is, precisely, that structure is distinguished form both empirical and theoretical content when it comes to the theories of Fresnel and Maxwell – and indeed when it comes to any comparative theories in physics.

Newton & Quantum Mechanics

Worrall also attributes a structuralist position (if not an explicit acceptance of structuralism) to Issac Newton. Worrall describes Newton's structuralist reality (if not his position) in the following manner:

“... 'On the structural realist view, what Newton really discovered are the relationships between phenomena expressed in the mathematical equations of his theory.'... ”

In certain respects, this is certainly true. For example, it's often and justifiably stated that quantum mechanics wouldn't so much as exist without its mathematical descriptions and predictions. John Horgan, for one, states that

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

Isn't all the above just as true of much of Newton's work? However, it's certainly the case that Newton wasn't an eliminativist when it came to things/objects (or when it came to Poincaré's “real objects”). Despite that, it was still “mathematical equations” which captured the things or phenomena Newton was accounting for in his theories.

The question (as with quantum mechanics) is:

Is there any remainder after the mathematics (or mathematical structure) is taken away?

What's left? Kantian noumena or, well, literally nothing? Of course it's hard to defend an eliminativist position when it comes to Newton and the concrete things he was talking about (e.g., stars, the moon, etc.). However, eliminativism seems much more appealing and justified when it comes to the micro world of quantum mechanics. In this realm, everything really does seem to be mathematical. Quite simply, there are no genuine equivalents to the moon, stars and even gravity (at least Newtonian gravity) in the quantum realm. In other words, our only access to the micro world is through mathematics. Clearly, that can't also be said of the world as described by Newton.