‘who’s afraid of underdetermination?’ (‘not i’, said the structural realist)

‘Who’s afraid of underdetermination?’ (‘Not I’, said the Structural Realist)

John WorrallPhilosophy, Logic & Scientific MethodLondon School of Economics

Part 1: Laudan and Leplin leave things much as they were

2 main theses 1. What they claim: There is no “general

guarantee of the possibility of empirically equivalent theories” (449)

1’ What the argument – if successful - would establish: ‘any finding of empirical equivalence is both contextual and defeasible’


2. The empirical equivalence of T and T’ does not entail that the choice between T and T’ is evidentially underdetermined:

“ One of a number of empirically equivalent theories may be uniquely preferable on evidentially probative grounds” (450)

AND as a consequence “The thesis of underdetermination, at least in

so far as it is founded on presumptions about the possibility of empirical equivalence for theories .. stands refuted.” (466)


Argument for thesis 1 (1’) uses 3 premises (i) VRO: the ‘variability of the range of the

observable’ (ii) NAP: the ‘need for auxiliaries in prediction’ (iii) IAA: the ‘instability of auxiliary

assumptions’


First note an important ambiguity in the term ‘empirically equivalent’ (and in their definition: “theories are empirically equivalent just in case they have the same class of empirical, viz observational, consequences.” (451)


What (i)-(iii) entail is allegedly that: T and T’ may be empirically equivalent at one

‘stage of science’ but not at some later stage. VRO is a ‘mistake’ – but …


Use of auxiliaries just seems sloppy IF T and T’ are ‘single’ ‘isolated’ theories then IF Duhem is right (AND he is!) THEN T and T’ are automatically empirically

equivalent since both have set of empirical consequences = Ø


IF we include all the necessary specific, auxiliary, instrumental assumptions to create two theoretical frameworks F and F’ (built around the ‘core’ T and T’)

THEN problem simply re-arises with F and F’ Of course this tie may be broken later – by

addition of a further auxiliary to one or other, but the other can then catch up.

Exactly the Duhem way into underdetermination

Part 1: Laudan and Leplin leave things much as they were So there is a general proof of empirical

equivalence Given any finite set of data D and any rival core

theories T and T’ we can always engineer the auxiliaries so that both F and F’ entail D.


So in fact everything rests on thesis 2- viz 2. The empirical equivalence of T and T’ does

not entail that the choice between T and T’ is evidentially underdetermined:

“ One of a number of empirically equivalent theories may be uniquely preferable on evidentially probative grounds” (450)


This has to be correct of course (as those of us who think that there is a

solution to the ‘Duhem problem’ have long banged on about)

Prediction/Accommodation


L & L’s own arguments somewhat obfuscatory A. ‘significant evidential support may be

provided for a theory by results that are not empirical consequences of the theory.’ (460)

B. ‘true empirical consequences need lend no evidential support to a theory.’ (ibid)


B just rests on a confusion between ‘no support’ and ‘not much support’

A: argument 1 – ‘next instance’ argument 2 – ‘spread of support’ to rest of a

theory BUT only when theory is unified My prediction/ accommodation distinction

similarly dependent on this sort of judgment So back to where we always were

Part 2: Underdetermination and Structural Realism

Underdetermination and Structural Realism

“But these are merely names of the images which we substituted for the real objects which Nature will hide for ever from our eyes. The true relations between these real objects are the only reality we can attain ….”

“If the relations are known to us, what does it matter if we think it convenient to replace one image by another’

In fact anything you said about those ‘images’ would be ‘illusory’/’meaningless’

(Or at best of some heuristic value)


Hence (E)SR: although our current theories may not be true, their basic theoretical terms may have no real referent – and we cannot, in principle, know whether or not they have -, nonetheless it is reasonable to believe that they are – at least approximately – structurally correct.


That is, the structure of our successful theories reflects to some extent the real structure of the universe.

And it’s reasonable to believe this, despite scientific “revolutions”, precisely because structure is preserved (or quasi-preserved) through “revolutionary” change.

And of course because each successive theory has enjoyed striking and independent predictive success (NMA)


SR is clearly committed to the view that the full cognitive content of any theory T is captured by the Ramsey sentence of T

And a good job too!

Why the only sensible view is the ‘Ramsey view’ First, what is the RT of any given T? Ramsey’s whole approach – just like the whole

underdetermination issue - is based on making a distinction between theoretical and observational terms.

Why the only sensible view is the ‘Ramsey view’ Any scientific theory S will therefore involve a

number of theoretical predicates T1,…, Tn and a number of observational predicates O1,…,Om

So we can write S as S (T1,…,Tn; O1,…,Om)

Why the only sensible view is the ‘Ramsey view’ Then the Ramsey sentence RT of T is formed by (i) replacing all occurrences of any theoretical

predicate Ti by a variable Θi to form S (Θ1,…,Θn; O1,…,Om); and (ii) existentially quantifying on all those

variables to form: VΘ1, …,VΘn S (Θ1,…,Θn; O1,…,Om)

Why the only sensible view is the ‘Ramsey view’

So why is it obvious that the full cognitive content of any theory T is captured by its RT?

First and foremost: everybody agrees (though then forgets it) that standard referential semantics is entirely misleading

At any rate when it comes to theoretical ‘terms’ in science

You – obviously – can’t stand outside of all theory and compare what the theory says with an independently given reality


‘Global descriptivism’ (at least so far as theoretical terms are concerned)

Causal referential talk would be ‘just more theory’

Unless you appeal to something mystical (clearly unobservable but nonetheless somehow apprehendable ‘semantic glue’)


If asked ‘what does ‘gluon’ mean’? I can only rehearse the latest theories involving gluons

N.B. All of those theories (Lots of mistakes made by leaving some theory

‘outside’ (i.e. unRamseyfied)) That is, a gluon, so far as we can tell, is the

whatever it is that does this that and the other (as stated by those theories)

But then if you have accepted this, you have accepted the ‘Ramsey view’

Ramseyfication and Underdetermination

Lots of ways of convincing yourself there is a problem with underdetermination that are immediately obviated once you accept Ramsey.

For example: 1. The ‘natural’ argument 2. Tacking paradox 3. Schmelectron theory 4. As if


1. The ‘natural’ argument: Take any theory T and take the set O of the

theory’s consequences that are expressible entirely in the observation language

Take any conservative extension of O back into the full language

There are indefinitely many of those BUT R(T) is itself expressible in the observation

language


If we restrict initially to the data set, then things are different –

But that takes us back to Duhem and unity


2. The Tacking paradox T’: GTR & God exists has the same set of

observational consequences as T: GTR Moreover so does T’’: GTR & ¬ God exists T’ and T’’ are mutually inconsistent You want to say that T’ and T’’ are only

nominally different – they have no ‘cognitive content’ not already held by T


R(T’) = R(T) & a tautology* = R(T) R(T’’) = R(T) & a tautology** = R(T) * VΦVx (Φ x) (take Φ = x=x) ** V Φ Λx(¬ Φ x) (take Φ = ¬(x=x))


Take T:current theory of electrons T’ says the same except that you consistently

substitute ‘schmelectron’ for ‘electron’ R(T) = R(T’)


4. T: theory of electrons T’: Everything is as if electrons (as described by

T) exist Always mystified by this – T’ just a

reformulation of T Just a reexpression of the Ramsey sentence If you add ‘ but actually they don’t exist’? Only sense that can be made is surely forward-

looking But this theory of the future will be a different

theory with a different Ramsey sentence


Summary: 1. The ‘Duhem problem’ can be solved

satisfactorily – hence the main way into alleged undetermination is pre-blocked

(Laudan & Leplin only appear to add something to this.)

2. Several of the other ways in which you might think there is a problem of underdetermination evaporate once you take the Ramsey view.

The ‘Ramsey view’ and the Newman ‘objection’

Since so many people seem to believe that the result shows that SR collapses into anti-realism, let me start to try to erode that belief:

1. Neither Ketland nor Putnam nor Newman has proved that SR entails that any two ‘empirically equivalent’ theories, in the normal sense, are equally true (or approximately true or, rather, approximately reflect an external reality)


2. Not just a question of getting the data right. First the two theories share all the consequences expressible in the observational language

3. And clearly some of these may be theoretical in anyone’s book – e.g. ‘there are unobservables’ (i.e objects with no (directly) observable properties) is (a) purely in the observation language and (b) clearly theoretical.

The ‘Ramsey view’ and the Newman ‘objection’ 4. Moreover, the theories that SR takes to

reflect external reality are not only (predictively) empirically successful but also unified.

(So SR would claim that Copernican theory reflects reality better than Ptolemaic, despite their ‘data’ equivalence (not empirical equivalence), because of the greater unity of Copernican theory.)


5. Surely the RT says that the theoretical terms exist – it characterises them in observational terms, or – better - in how they interrelate with one another and how they structure the phenomena – but this is patently not to eliminate them.

(6. Cp Quine’s famous account of ontological commitment)


(7. David Lewis ‘My proposal could be called an elimination of theoretical terms, if you must; for to define them is show how to do without them. But it is better called a vindication of theoretical terms; for to define them is to show that there is no good reason to want to do without them.’)

Is Structural Realism really realism?

Many will be unconvinced: if this is really the SR that you defend, then for all you say,it isn’t really realism.

Danger of quibbling about words – call it anti-realism if you like

(there certainly are ‘realisms’ that it is anti!) Doesn’t count on either of Putnam’s definitions A. A realist needs to assert that a theory T may

be false even though its RT is true


B. A realist asserts that the theoretical terms in our current successful theories in mature science refer (though she can then allow that what those theories say about the entities to which they refer is only ‘approximately’ rather than outright true)

(In fact SR asserts that the mode of reference of its terms is just as problematic, uncharacterisable as the approximate truth of a theory T.)


So why do I hold that the right judgement is that SR is a version of realism?

What is realism? 1. “Metaphysical” realism: the assertion of the

existence of a reality independent of the human mind???

NO: 1’. There exists a structured reality of which the mind is a part; and, far from imposing their own order on things, our mental operations are simply governed by the fixed laws which describe the workings of Nature.


2. “Methodological realism” = 1’ + the structure of reality is at least in part intelligible to the human mind

3. Scientific realism = 1’ + 2 + successful theories – the unified theories that explain the phenomena without ad hoc assumptions – are ‘approximately true’.


IF you are wedded to a correspondence or semantic view of truth as your account of corresponding with reality, then SR does not count.

But there is no reason why the way in which a theory mirrors reality should be the usual term-by-term mapping described by traditional semantics

Is Structural Realism really realism? SR takes it that the mathematical structure of a

theory may globally reflect reality without each of its components referring (or being known to refer) to a separate item of that reality.

If you insist on reference for truth (or “near reference” for approximate truth) then SR is not realism

BUT there’s no sustainable version of realism attainable if you thus insist

Is Structural Realism really realism? SR takes it that the mathematical structure of a

theory may globally reflect reality without each of its components referring to a separate item of that reality.

If you insist on reference for truth (or “near reference” for approximate truth) then SR is not realism

BUT there’s no sustainable version of realism attainable if you thus insist

Structural realism is the only viable position (my confusion, following Poincaré)

Is Structural Realism really realism? Duhem([1906], 28): The highest test, therefore, of our holding a

classification as a natural one is to ask it to indicate in advance things which the future alone will reveal. And when the experiment is made and confirms the predictions obtained from our theory, we feel strengthened in our conviction that the relations established by our reason among abstract notions truly correspond to relations among things.

That’s all it is! Accept it!

‘who’s afraid of underdetermination?’ (‘not i’, said the structural realist)

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