Forthcoming in: SYNTHESE
Ramsification and Inductive Inference
Panu Raatikainen
Abstract. An argument, different from the Newman objection, against the view that the
cognitive content of a theory is exhausted by its Ramsey sentence is reviewed. The crux
of the argument is that Ramsification may ruin inductive systematization between
theory and observation. The argument also has some implications concerning the issue
of underdetermination.
1. Introduction
Scientific realism proposes that we are justified in believing that successful theories of mature
science are at least approximately true, and that the unobservable theoretical entities they
postulate really exist. The standard argument in favour of this view is the so-called “nomiracles argument”: the practical and observational success of science would be miraculous
if scientific theories were not at least approximately true descriptions of the world, and the
theoretical objects they postulate did not exist. Then again, arguments exist which seem to
undermine scientific realism, and the no-miracles argument. Most importantly, perhaps, there
are arguments which lean on the actual history of science and radical theory changes therein –
for example, the notorious “pessimistic meta-induction”, and also various less general
arguments to the same effect. Roughly, the thesis is that many past theories in science have
turned out to be to a large extent false, and their theoretical terms non-referring; therefore – it
is concluded – it is not justified to expect that the theoretical entities postulated by present
theories exist either (see Laudan 1981).
The view known as Structural Realism has emerged over the past two decades and seems to
enjoy some popularity among philosophers of science. It aims to be a middle-of-the-road view
between full-blown scientific realism and empiricist antirealism which is thoroughly sceptical
about unobservable theoretical entities (and theories dealing with them), and to take both
these oppositional arguments seriously. Very roughly put, the epistemological form of
structural realism holds that our knowledge of the world is limited to its structure; the
metaphysical form of structural realism holds that in fact it is only structure that exists
independently.
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However, the arguments from the history of science are not the only type of arguments which
threaten scientific realism. In particular, any sort of realism, whether structural or of a more
standard kind, must be able the reply to the challenge of arguments from the alleged radical
underdetermination of theory by observation. The standard response is to grant that deductive
underdetermination (i.e. that the theory cannot be logically derived from the evidence; or, that
two incompatible theories may have exactly the same deductive observational consequences)
is unavoidable, but insist that we also need to take into account the inductive relationships
between observations and theory – and that this allows one to discard any radical
underdetermination (see e.g. Laudan 1990, 1998; Ladyman 2002; Psillos 2005). Anyone
willing to defend even a modest rationality of science must therefore allow considerations
concerning inductive and not only deductive relations between theories and observations. And
this has some relevance in what follows.
In contemporary philosophy, structural realism was introduced by John Worrall (1989),
though it arguably has some prominent predecessors. He considered in particular the
development of the theory of light in physics and the transition from ether theory to the theory
of the electromagnetic field – one of the most difficult historical cases for scientific realism to
accommodate. Worrall suggests that there was, after all, an important element of continuity in
this shift; that more than just empirical content was preserved in it – namely, the form or
structure of the former theory. However, Worrall adds, the content of the theories is radically
different. More generally, he submitted that we should not believe that our scientific theories
can manage to discover the nature of the postulated theoretical entities, as standard scientific
realism suggests; rather, we should only commit ourselves to the structural content of our
theories. Yet, this is more than only their empirical content, which is all that empiricist
antirealism allows. It is proposed that such structural realism can both avoid the difficulties
pessimistic meta-induction etc. raises and does not make the success of science miraculous –
it is “the best of both worlds”. Structural realism has found many advocates in the philosophy
of science. (See Ladyman 2008 for an excellent overview.)
The concept of ‘structural content’ of a scientific theory, essential for structural realism,
obviously needs clarification. One standard way of doing this, advocated by Worrall himself
as well as by Elie Zahar, for example, is in terms of Ramsey sentences. Worrall and Zahar
(2001), in particular, argue that the cognitive content of a theory is exhausted by its Ramsey
sentence. There are now also other ways of working out the idea of structural content (see
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Ladyman 2008), but the variant that utilizes Ramsification is certainly popular. I shall call the
brand of structural realism which explicates structural content in this way “Ramsifying
Structural Realism”. In what follows, I focus solely on this sort of structural realism.
More generally, the view that the factual content of a theory is faithfully captured by its
Ramsey sentence seems to be quite popular in philosophy. For example, David Lewis, Frank
Jackson, and a number of philosophers following them in the so-called Canberra Plan (see e.g.
Braddon-Mitchell & Nola 2009) make a heavy use of Ramsey sentences, and apparently hold
related views. The arguments below are directed against all such views which hold the
cognitive content of a theory is exhausted by its Ramsey sentence.
2.1. Theories and Their Ramsey Sentences
If the theory S is presented in a standard form with theoretical predicates and relations T1, T2
…, Tn, and observational predicates and relations O1, O2…, Om, the Ramsey sentence SR
of S is obtained by first replacing all the theoretical predicates with second-order variables,
and then, to the result of this replacement, prefixing the existential quantifiers with respect to
those second order variables. Thus, if the original theory S is written as
S(T1, T2 …, Tn, O1, O2…, Om),
then SR is:
(∃X1) (∃X2) … (∃Xn) S(X1, X2 …, Xn, O1, O2…, Om).
Here are some important logical properties of Ramsey sentences (cf. Psillos 2006) (the
background logic assumed is a suitable system of second-order logic):
SR is a logical consequence of S.
SR has exactly the same first-order observational consequences as S.
S1 and S2 have incompatible observational consequences iff S1R and S2R are incompatible.
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S1 and S2 may make incompatible theoretical assertions and yet S1R and S2R can be
compatible.
If S1R and S2R are compatible with the same observational truths, then they are compatible
with each other.
Thus, at first sight, Ramsey sentences seem to suit well the purposes of structural realism, and
to capture the cognitive contents of theories.
2.2. The Newman Objection
There is, however, a popular objection to Ramsifying Structural Realism and related views,
the idea of which goes back to Newman’s (1928) critique of Russell’s version of structuralism
– hence its name, the “Newman objection”. 1 The objection was revitalized in contemporary
debate by Demopoulos and Friedman (1985). Generally, the objection is that if a theory is just
consistent, and observationally adequate,2 then the corresponding Ramsey sentence is almost
trivially true, provided that the domain only has a sufficient cardinality. Therefore, the
objection continues, Ramsifying Structural Realism collapses into a radical empiricist denial
of theoretical entities, and cannot provide a middle ground between that view and full-blown
realism with respect to these entities. (For some complications, and for a careful and rigorous
development of the objection, see Ketland 2004). Cruse (2005) and Melia and Saatsi (2006),
on the other hand, subtly defend the Ramsey sentence approach against the Newman
objection. It may well be that the Newman objection can be further defended against these
critiques (cf. Ketland 2009, Ainsworth 2009). But at the moment, there does not seem to be a
wide consensus concerning the issue, and the fate of the Newman objection remains
somewhat open.
3. Argument from Inductive Systematization
Be that is it may, there is another line of reasoning, independent of the Newman objection,
which poses a serious problem for any view which contends that the cognitive content of a
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theory is exhausted by its Ramsey sentence – an argument of which all parties of the present
debate seem to be ignorant. It concerns the inductive rather than deductive relations between
observations, theories and their Ramsey sentences. And we have seen above that because of
the threat of radical underdetermination, it is in any case obligatory to take into account such
inductive relations as well.
The idea was briefly suggested by Hempel (1958), developed in much more detail by
Scheffler (1963, 1968), and culminated in Niiniluoto’s conclusive though unfortunately little
known defence of this argumentation strategy (Niiniluoto 1972, 1973; see also Tuomela 1973,
1974). As philosophers today seem to be almost universally ignorant of these arguments, it is
perhaps proper to remind the philosophical community about them and review the main
points.
3.1. Inductive Systematization
The principal conclusion of the argument is that Ramsification ruins inductive systematization
between theories and observation. The notion of inductive systematization was introduced by
Hempel (1958). It was discussed in the philosophy of science in the 1960s and early 70s (see
Niiniluoto 1972), but seems to have disappeared from the philosophy of science literature. Yet
it is a quite natural and relevant general concept.
By the term “systematization”, Hempel simply meant any deductive or inductive argument
which has as its premises both some singular statements and one or more laws, and as its
conclusion a singular statement (or empirical law), and which serves as an explanation,
prediction or postdiction (inferring the past), or something similar.
It is illuminating to consider first the notion of deductive systematization: Let S be a theory
formulated in a language L, and let LO be the observational sublanguage of L. Let e and h be
some contingent statements of LO.
A theory S achieves deductive systematization (with respect to LO) iff
h is deducible from S ∧ e,
h is not deducible from e,
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for some factual observational e and h.
Let I then be an inducibility relation characterized by some set of inductive rules. The
following arguments are relatively independent of the particular choice of rules.
We may note in passing, though, that two standard explications for inducibility are as follows
(where p is some probability measure defined for the language):
(i) Positive relevance criterion
e induces h iff p(h/e) > p(h).
(ii) High probability criterion
e induces h iff p(h/e) > k, for some constant k > 0.5.
Be that as it may, the notion of inductive systematization is then completely analogous to that
of deductive systematization, except that one adds the condition that the theory and
established empirical evidence do not even deductively entail the induced statement at stake.
S is said to achieve inductive systematization (with respect to LO) if and only if
(i) I(S ∧ e, h)
h is inducible from (S ∧ e)
(ii) ¬ I(e, h)
h is not inducible from e alone
(iii) h is not deductively derivable from S ∧ e.
3.2. Scheffler’s Argument
Following Hempel’s (1958) suggestion, Scheffler (1963, 1968) argued that Ramsification
may fail to preserve inductive systematization. Here is Scheffler’s argument:
Consider the following simple theory S1, where O1 and O2 are assumed to be (possibly
complex) observational predicates, and T a theoretical predicate:
S1
(∀x)[(T(x) → O1(x)) ∧ (T(x) → O2(x))]3
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By Ramsifying this, we get
S1R
(∃X)(∀x)[(X(x) → O1(x)) ∧ (X(x) → O2(x))]
Now S1 is non-analytic, but S1R, its Ramsey sentence, is in fact a truth of second-order logic
and apparently analytic. That is, in this simple case, Ramsification converts a substantive
first-order theory into a second-order logical truth and thus entails a loss of substantive
content. Exactly the same difference occurs with the theory
S2
(∀x)[(T(x) → O1(x)) ∧ (T(x) → ¬ O2(x))],
and its Ramsification:
S2R
(∃X)(∀x)[(X(x) → O1(x)) ∧ (X(x) → ¬O2(x))].
Note now that as S1R and S2R are both logical truths of second-order logic, they are logically
equivalent. Scheffler next submits that S1 achieves inductive systematization between O1(a)
and O2(a).4 However, if S1R also achieved inductive systematization between O1(a) and O2(a),
it would follow that, analogously, S2R would achieve inductive systematization between O1(a)
and ¬O2(a). However, S2R is logically equivalent to S1R. Consequently, they cannot possibly
achieve inductive systematization between both O1(a) and O2(a), and O1(a) and ¬O2(a).
Therefore, Scheffler concludes, S1R cannot achieve inductive systematization between O1(a)
and O2(a), and thus Ramsification of a theory can ruin inductive systematization.
So how does the original theory S1 achieve inductive systematization between O1(a) and
O2(a)? One might reason as follows (but see below). Assume that there is an individual a
which shows (according to S1) the symptoms of T, i.e., O1(a). This evidence is supposed to
give inductive support for T(a), by the first conjunct of S1. One can then, by the second
conjunct of S1, conclude O2(a). Thus, so the reasoning goes, S1 achieves inductive
systematization between O1(a) and O2(a).
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3.3. Critical Responses to Scheffler’s argument
Scheffler’s argument, however, has not remained unchallenged. Convincing as it may at first
appear, two objections have been raised against it.
First, under closer scrutiny, it turns out that the reasoning (see above) to the effect that S1
achieves inductive systematization between O1(a) and O2(a) uses two principles which cannot
both hold for inducibility:
“The rule of converse entailment”: If h is deducible from e, then e is inducible from h – used
when inducing T(a) from O1(a);
“The rule of special consequence”: If h is inducible from e and b is deducible from h, then b is
inducible from e – used when going from T(a) to O2(a).
However, it is well known that these rules of induction are not acceptable together: jointly
they entail that every statement confirms every other 5 (Hempel 1945; Skyrms 1966; Hesse
1970a, 1970b; Niiniluoto 1972). Hence, Scheffler’s argument – as it stands – fails. 6
Second, it has been argued that even the original theory S1 “has no empirical content”
(Hooker 1968), is “immune to observational confirmation” (Bohnert 1968) or is “empirically
trivial” (Stegmüller 1970), and therefore cannot possibly achieve inductive systematization in
the first place.
3.4. The Objections Answered
As Niiniluoto (1972) points out, the basic difficulty in the accounts of Scheffler, Hempel and
others is that they attempt to show that inductive systematization is established indirectly, that
is, by means of at least two-step arguments going ‘through’ theories, as it were, via theoretical
terms; for example, that O2(a) may be induced from O1(a) assuming S1 in two steps, first
from O1(a) to T(a), and then from T(a) to O2(a). This idea presupposes transitivity conditions
that no reasonable explicate of the inducibility relation seems to possess.
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Niiniluoto (1972), however, shows that this problem can been solved by interpreting the
condition (i) of the definition of inductive systematization as a one-step inductive argument.
No transitivity problems then arise. That is, one may interpret the condition “h is inducible
from e and T”, as a one-step inductive argument from the conjunction ‘T ∧ e’ to ‘h’ – that is,
in Scheffler’s case, from the conjunction
O1(a) ∧ (∀x)[(T(x) → O1(x)) ∧ (T(x) → O2(x))]
to O2(a).
According to this suggestion, theories play a direct, rather than indirect or mediating, role in
the establishment of inductive systematization. Interpreting the case in this way, Scheffler’s
argument can be saved from the first objection.
Put differently, Niiniluoto (1972) makes evident that Scheffler’s argument is valid given the
following principle:
(P)
If S achieves inductive systematization between e and h, and S ′ is logically
equivalent to S, then S ′ does not achieve inductive systematization between
e and ¬ h.
And this principle is satisfied by all the most natural explicates of inducibility, for example
the positive relevance criterion and the high probability criterion (see above).
But what about the influential objection to Scheffler’s argument (by Hooker, Bohnert, and
Stegmüller), according to which even the original, non-ramsified theory S1 does not achieve
inductive systematization, because it has no deductive observational content? Consider the
following three statements:
(1*) Theory S has no contingent deductive observational consequences.
(2*) Theory S is not observationally testable.
(3*) Theory S does not establish inductive systematization (w.r.t. LO).
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The objection of Bohnert, Hooker and Stegmüller to Scheffler’s argument supposes the
following:
(a)
(1*) ⇒ (2*)
(b)
(2*) ⇒ (3*)
Niiniluoto (1973), however, demonstrates in detail that (a) and (b) cannot be jointly accepted,
and hence that (1*) ⇒ (3*) does not hold, no matter how “testable” in (2*) is explicated. Note
in particular that (1*) ⇒ (3*) amounts to the claim that if a theory achieves inductive
systematization, then it also achieves deductive systematization. But that is certainly a long
way from being unproblematic.
In sum, the Hempel-Scheffler argument can, after all, be defended against the critiques,
improved, and shown to be basically correct. As such, it arguably presents an unsurmountable
problem for the claim that the cognitive content of a theory can be captured by its Ramsey
sentence.
4. Underdetermination Revisited
The above argument provides a bonus: at the outset of this paper, the underdetermination
challenge was mentioned, as well as the standard response that by also taking into account
inductive and not only deductive relations between theories and observation, at least the
massive and radical type of underdetermination can be ruled out. Although the suggestion
appears plausible, it has apparently never been rigorously demonstrated that it would make a
difference. However, our above considerations illuminate this idea, too: our two theories S1
and S2 are empirically equivalent when it comes to deductive relations (namely, neither of
them deductively entails any observational sentences) – the choice between them is therefore
deductively underdetermined. Observation can nevertheless speak in favour of one of them at
the expense of the other. For example, observing O1(a) and O2(a), O1(b) and O2(b), etc. would
provide an inductive confirmation of S1 and disconfirmation of S2. Our argument thus also
provides a clear example of a pair of theories such that the choice between them is
deductively but not inductively underdetermined.
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Acknowledgements
Earlier versions of this paper have been presented in the philosophy of science seminars in
Helsinki and Athens. I would like to thank both audiences for the useful feedback. I am
especially indebted to Stathis Psillos for his valuable comments. Finally, I am grateful to the
two anonymous reviewers for their helpful comments.
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Notes
1
Obviously, Newman himself did not address Ramsey sentences, as his paper predates Ramsey’s
seminal paper (Ramsey 1931). Nevertheless, the contemporary objection to Ramsification in question
owes so much to Newman’s argument that it is appropriate to call it “the Newman objection”; cf.
(Demopoulos & Friedman 1985).
2
How exactly “empirical adequacy” should be explicated here turns out to be more complicated than
initially assumed; see (Ketland 2004, 2009).
3
This theory can be viewed as a simplified version of Hempel’s theory of ‘white phosphorus’
(Hempel 1958, 214-15).
4
Strictly speaking, of course, inductive systematization between statements, say, O1(a) and O2(a),
has not been defined. Inductive systematization is rather defined with respect to the language LO
which includes them. We take O1(a) as e, put either O1(a) or ¬O2(a) for h, and finally, take either S1
or S2 or the Ramsey sentence of one or the other as S, in the definition of inductive systemazation,
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and ask whether h is inducible from (S ∧ e) or not. If it is, then we have achieved inductive
systemazation with respect to LO.
5
Put h ↔ (e ∧ b). Then h is inducible from from e by Converse Entailment, and b is deducible from
h. Hence e confirms b, by Special Consequence. But e and b could be just any given statements;
therefore a relation of confirmation satisfying both these conditions is trivial.
6
This problem was identified, not by the opponents of Scheffler, but by Niiniluoto (1972) – just in
order to reply to it.
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