The Newman Objection to Ramsey Sentence Structuralism

There appears to be considerable confusion about what the Newman Objection to Ramsey Sentence Structuralism actually is. Three examples of this that I have in mind are:

• insisting that Newman shows that the Ramsey sentence $\Re(\Theta)$ of a theory $\Theta$ states only a cardinality condition, 
• insisting that the structural content of a theory $\Theta$ (i.e., the content of $\Re(\Theta)$ beyond $\Theta$ having an empirically correct model) is more than cardinality content, 
• redefining "empiricism" to be much stricter than, e.g., van Fraassen allows (i.e., empirical regularities). 

An example of this is Worrall 2007, in "Miracles and Models: Why the Reports of the Death of Structural Realism May Be Exaggerated" (in O’Hare (ed.), Philosophy of science (Royal Institute of Philosophy 61):

The argument in its crispest form goes as follows:
1. SSR is committed to the view that the Ramsey sentence of any scientific theory T captures the full ‘cognitive content’ of that theory.
2. However, as Newman showed, the Ramsey sentence of any theory imposes only a very weak constraint on the universe—it amounts in essence to a mere cardinality constraint, and so if there are sufficiently many objects in the universe then the Ramsey-version of T, for any T, will be true.
3. However it is clear that standard scientific theories impose much more stringent constraints on the universe if they are to be true than merely a constraint on the minimum number of entities the world must include.
4. Hence SSR is committed to an account of the cognitive content of scientific theories that is plainly untenable and is, therefore, itself untenable. (Worrall 2007, pp. 140-141.)

("SSR" stands for "Structural Scientific Realism", which is another name for what I'm calling Ramsey sentence structuralism.)

But this is not the argument and this is not the Newman objection to Ramsey sentence structuralism. In fact, Premise 2 is mistaken and contradicts the basic technical result that is involved (see below). The objection is this:

Ramsey sentence structuralism $\approx$ Constructive empiricism

where "$\approx$" here means "is more or less equivalent to".

Here, Constructive empiricism is the anti-realist/instrumentalist view, associated with van Fraassen (The Scientific Image, 1980), that accepting a scientific theory $\Theta$ is believing that $\Theta$ has an empiricaly correct model $\mathcal{A}$. Ramsey sentence structuralism is the view that the synthetic content of a scientific theory $\Theta$ is given by its Ramsey sentence $\Re(\Theta)$. Strictly speaking, Constructive empiricism is, primarily, an epistemic view, concerning theoretical justification, whereas Ramsey sentence structuralism seems like a semantic view: a view about the content of theories. The connection between the epistemology and semantics is that Ramsey sentence structuralism involves a strictly empiricist and descriptivist view of the semantics of "theoretical terms".

The objection is that there is little difference between advocating Ramsey sentence structuralism and advocating constructive empiricism. That is, Ramsey sentence structuralism is a form of anti-realism about scientific theories. Equivalently, so-called Structural "Realism" is a form of anti-realism.

There is a small difference between Ramsey sentence structuralism and Constructive empiricism, and this difference can be clarified by various results of the following sort, which use reasoning first given by Max Newman in 1928 against Russell's version of structuralism set out in Russell 1927, The Analysis of Matter. Let $\Theta$ be a finitely axiomatized theory in 2-sorted interpreted language $(L, \mathcal{I})$, where $\mathcal{I}$ is an interpretation of $L$. Let the cardinality of the theoretical domain of $\mathcal{I}$ be $\kappa$. Let $\Re(\Theta)$ be the ramsification of $\Theta$. Then:

$\Re(\Theta)$ is true if and only if $\Theta$ has an empirically correct model $\mathcal{A}$ whose theoretical domain has cardinality $\kappa$.

On this 2-sorted setup, one separates quantification over observables from quantification over non-observables, which allows one to define the cardinality of the theoretical domain and fix empirical content as being entirely about observable objects. But there are variations on this setup, and the corresponding results are rather sensitive to how one formulates the alleged O/T distinction and defines "empirical adequacy". However, all give more or less the same outcome.

I've written two articles on this topic, "Empirical Adequacy and Ramsification" (BJPS 2004) and "Empirical Adequacy and Ramsification II" (in Leitgeb & Hieke (eds.) 2009, Reduction, Abstraction, Analysis).

So, as I see it (and this is formulated also in Demopoulos & Friedman 1985 and many other places), the underlying Newman Objection runs as follows:

1. The truth of $\Re(\Theta)$ is equivalent to $\Theta$ having an empirical adequate model of the right cardinality.
2. Therefore, the sole content of $\Re(\Theta)$ beyond empirical adequacy is cardinality content.
3. Therefore, the sole difference between Constructive empiricism and Ramsey sentence structuralism is this cardinality content.
4. Therefore, Ramsey sentence structuralism is more or less equivalent to Constructive empiricism.

The central assumption in the argument, i.e., Premise 1, is a theorem of mathematical logic. The three further conclusions are drawn from this, modulo certain definitions. There is a certain unavoidable vagueness in the argument (e.g., concerning the exact framework for formalization of scientific theories, the definition of "empirical adequacy", and what counts as "more or less equivalent").

Many other authors have written on this topic. In particular, I'd draw attention to:

• William Demopoulos and Michael Friedman. 1985: "Critical Notice: Bertrand Russell's The Analysis of Matter: Its Historical Context and Contemporary Interest", Philosophy of Science.
• William Demopoulos. 2003: "On the Rational Reconstruction of our Theoretical Knowledge", BJPS.
• William Demopoulos. 2011: "Three Views of Theoretical Knowledge", BJPS.
• Peter Ainsworth. 2009. "Newman's Objection", BJPS.

[UPDATE: 18th April. I've updated this post in a number of ways, including a quote from John Worrall and some further clarifications.]