A Dynamic Interaction Between Machine Learning and the Philosophy of Science


A Dynamic Interaction Between Machine

Learning and the Philosophy of Science

JON WILLIAMSON
Department of Philosophy, King’s College London, Strand, London WC2R 2LS, UK; E-mail:

jon.williamson@kcl.ac.uk

Abstract. The relationship between machine learning and the philosophy of science can be
classed as a dynamic interaction: a mutually beneficial connection between two autonomous
fields that changes direction over time. I discuss the nature of this interaction and give a case

study highlighting interactions between research on Bayesian networks in machine learning
and research on causality and probability in the philosophy of science.

1. Introduction

How is machine learning related to the philosophy of science?
One view is that machine learning and the philosophy of science are

essentially the same subject. Both are concerned with explicating the relation
between theory and evidence. Both are concerned with how theories are
posited. Both are concerned with how theories are tested. Both are concerned
with finding out what makes a theory a good theory.

This is the view taken by Kevin Korb, who stresses ‘the fundamental
identity between the two disciplines’:1

the two disciplines are, in large measure, one, at least in principle. They
are distinct in their histories, research traditions, investigative meth-
odologies; however, the knowledge which they both ultimately aim at is
in large part indistinguishable.2

As evidence for this Korb takes the similarity between meta-learning in
machine learning and the search for scientific method in the philosophy of
science, and the common concern with accounting for inductive simplicity
and theoretical terms. Korb predicts then that ‘machine learning and the
philosophy of scientific method will coalesce.’3

There are, however, fundamental differences between the two disciplines
which cast doubt upon this view. First there is a difference in subject matter:
while the two disciplines may share common concerns, this is a case of
overlap rather than identity. The philosophy of science is a broad-ranging
subject, which covers the debate between realism and instrumentalism, the

Minds and Machines 14: 539–549, 2004.

� 2004 Kluwer Academic Publishers. Printed in the Netherlands.



foundations of quantum mechanics, the units of selection, as well as the
nature of causal claims in econometrics. Such topics may have points of
relevance to machine learning but are not its subject matter. On the other
hand, machine learning has wide scope too – inducing plans for guiding a
robot around a room, the analysis of database biases, parsing natural lan-
guage, optimisation algorithms for search, for example – these are not the
topics addressed by philosophers of science.

The second difference is a divergence of aims. Philosophers of science want
to understand science – why science is practised the way it is, how it ought to
be practised, and what scientific theories tell us about reality, for instance –
and this leads to a desire to work within the languages of science, which are
predominantly extensions of natural language rather than formal languages,
and to favour optimality over practicality, i.e. to develop normative accounts
of scientific reasoning that lead to reliable conclusions rather than lead
quickly to conclusions. On the other hand machine learning researchers want
to develop techniques that allow machines to learn, and this leads to a desire
to work with machine languages or formalisms that can easily be imple-
mented, and to favour practicality over optimality, i.e. to develop compu-
tationally practical algorithms that may sacrifice optimality.

These differences between the two disciplines motivate the view that the
two disciplines are distinct but connected. This is the view taken by Paul
Thagard, for example, who envisages a very close relationship between the
two subjects:

Philosophy is continuous with science, differing only in that it deals with
issues that are more general, speculative, and normative than those found
in individual sciences. The branches of philosophy concerned with
reasoning are continuous with psychology and artificial intelligence.4

Hilan Bensusan puts the relationship thus:

Machine learning and philosophy of science are different endeavours:
their goals are different in nature. They nevertheless intersect. As they
intersect, they can collaborate. With care. It is not a case for a merger. It
is rather a case for an affair.5

This is also the view that I shall espouse here. I shall argue that there is a
two-way relationship between the two distinct disciplines: the philosophy of
science can guide machine learning just as machine learning can help the
philosophy of science. More particularly I shall argue that there is a dynamic
interaction between the philosophy of science and machine learning. The
concept of dynamic interaction will be explained in Section 2. I will give an
overview of evidence for this relationship in Section 3, and examine a case
study in closer detail in Section 4.

JON WILLIAMSON540



While a debate about the identity/lack of identity of machine learning
and the philosophy of science may call to mind certain obscure heresies that
beset the early Christian church,6 resolving this issue is important for the
following reason. If the disciplines are identical it makes sense to merge
research institutes that are currently separated. If, however, the disciplines
are distinct but dynamically interact then such a merger would be detri-
mental – it would be more fruitful to proceed independently but with an
exchange of ideas.

2. Dynamic Interactions

Donald Gillies and Yuxin Zheng put forward the concept of a dynamic
interaction between two disciplines in Gillies and Zheng (2001) and charac-
terised it as follows:

(1) A connection is established between two different fields or subjects (A
and B say).

(2) Both sides may then benefit from this connection, or, more specifically,
from the resulting interaction.

(3) The relationship between the two sides is not static but dynamic.
Suppose, for example, the flow of ideas is at first principally from A to
B. It will then characteristically happen that, after a while, the direction
of the flow of ideas is reversed and ideas from B start to influence A.
Typically the interaction between A and B has two phases separated by
a turning point, although, as is to be expected, the turning point is not
precisely defined.

(4) Although the two sides interact, it is important that each one should at
the same time preserve some degree of autonomy. As our above anal-
ysis of the dynamic nature of their relationship in (3) shows, this is a
necessary condition for further development.7

In the same paper Gillies and Zheng provide two examples. They posit a
dynamic interaction between the philosophy of mathematics and the phi-
losophy of science: the Vienna Circle, who were crucially influenced by
philosophy of mathematics, particularly the foundationalism and logical
approach of Frege and Russell, invigorated the philosophy of science; later
an ailing philosophy of mathematics was lent new life by Lakatos extending
Popper’s fallibilist philosophy of science to mathematics in his ‘Proofs and
Refutations’, and recent applications of Kuhn’s theory of scientific revolu-
tions8 and Lakatos’ methodology of scientific research programmes9 to
mathematics. Their second example is a dynamic interaction between
the philosophy of mathematics and computer science: the Turing machine,

MACHINE LEARNING AND THE PHILOSOPHY OF SCIENCE 541



the k-calculus, type theory and first-order logic arose from problems in the
foundations of mathematics and were in turn a strong influence on many
aspects of computer science; automated theorem proving has led to a re-
newed interest in the notion of mathematical proof.10

A dynamic interaction is, by definition, a good thing for both sides. Such a
symbiotic relationship revitalises the two disciplines and ensures their con-
tinued survival. An understanding and analysis of the concept of dynamic
interaction is also important, for two reasons. The first is retrospective: the
existence of dynamic interactions helps explain the success and longevity of a
field. The second is prospective: the prospect of dynamic interactions can be
used to justify inter-disciplinary research, inter-community discussion and
cross-fertilisation of ideas.

3. Overview of the Interaction

In this section I shall give an overview of some of the interactions between the
two subjects, many of which are attributable to the clear analogy between
hypothesis choice in science and model selection in machines.11 In Section 4
we shall see in more detail how interactions can help both subjects by looking
at a case study.

At the methodological level, the philosophy of science has had a pervasive
influence on machine learning. The 1920s saw the establishment of the
Vienna Circle study group and the beginning of the rise of logical positivism
as a key movement in the philosophy of science. Integral to their approach
was the use of logic as a framework for scientific reasoning. The movement
was extremely important half way through the twentieth century when Alan
Turing put forward his vision of learning machines,12 and the early machine
learning systems of the 1960s were quick to put the learning problem into a
logical framework. By the end of the 1960s the positivists were in decline and
an aversion to the normative logical approach to science had set in, in favour
of the more descriptive positions championed by Kuhn and Lakatos. Some
scepticism towards the symbolic approach to AI followed,13 and progress on
the foundations of neural networks allowed an alternative line of develop-
ment in machine learning. However it was not long before a resurgence of
formal methods gripped the philosophy of science, in the shape of Baye-
sianism. Bayesian philosophy became important in AI in the 1980s and 1990s
with the development of probabilistic expert systems and probabilistic
frameworks for learning. Now Bayesian techniques for the machine learning
of formal models are widespread, as are Bayesian models themselves.14

Machine learning has influenced the controversy in the philosophy of
science between inductivism and falsificationism: Gillies argues that the
success of the GOLEM machine learning program at learning a scientific

JON WILLIAMSON542



hypothesis provides evidence for inductivism.15 Proponents of falsification-
ism remain sceptical about machine learning,16 but further successes in the
automation of scientific hypothesis generation may dampen their ardour.
Machine learning has also proven invaluable to the philosophy of science as a
means of testing formal models of scientific reasoning, including inductive
reasoning,17 abductive reasoning,18 coherence-based reasoning,19 analogical
reasoning,20 causal reasoning (Section 4), and theory revision.21

4. Case Study: Bayesian Networks

Bayesian networks have been the hotbed of a particularly productive inter-
action between machine learning and the philosophy of science, largely due
to the fact that the two disciplines share a common interest in causality and
probability, two notions which are connected in a Bayesian network.

Philosophers of science have been concerned with the relationship between
causality and probabilistic independence and dependence since the 1950s.
Hans Reichenbach, for example, advocated a version of the principle of the
common cause, which says that any two probabilistically dependent events,
neither of which causes the other, must be effects of one or more common
causes, and the two events must be probabilistically independent conditional
on these common causes.22 Patrick Suppes characterised the relationship in
terms of probabilistic dependence rather than independence: cause and effect
are probabilistically dependent conditional on the effect’s other causes.23

Wesley Salmon subsequently penned an influential critique of both these
views.24 By the 1980s there had been much exploration of the issues, but little
consensus as to the exact relationship, and there was little indication that
further philosophical consideration of the issue was leading to a resolution.

Then in the 1980s Judea Pearl took Bayesian philosophy of probability
and a principle closely related to the principle of the common cause as a
starting point for his theory of Bayesian networks.25 The causal Markov
condition says that a cause is probabilistically independent of any of its non-
effects conditional on its direct causes. A Bayesian network contains two
components: a directed acyclic graph that represents the causal relations on a
domain of variables, and probability tables in which the probability distri-
bution of each variable conditional on its direct causes is specified. The causal
Markov condition is assumed as a link between the causal graph and
probability, and under this assumption a Bayesian network determines a
joint probability distribution over the variables.26 Bayesian networks were
originally intended as a formalism for causal reasoning in expert systems, but
are now also used as a general framework for representing and learn-
ing probability functions. In fact, Bayesian networks were very rapidly
adopted by the expert system and machine learning communities,27 and the

MACHINE LEARNING AND THE PHILOSOPHY OF SCIENCE 543



question naturally arose as to whether this acceptance was attributable to the
causal Markov condition: the success of Bayesian networks might be taken as
evidence in favour of the causal Markov condition as a link between causality
and probability.

If the causal Markov condition is a valid assumption, the question also
arises as to whether the condition can be used to characterise the causal
relation itself: a causal structure may in some sense be the smallest structure
to satisfy the condition. Indeed machine learning techniques for learning
Bayesian networks have been proposed as a way of automating the task of
causal discovery,28 and the success of such techniques can be used to support
a probabilistic analysis of causality based on the causal Markov condition.
Such considerations have sparked intense philosophical debate on the nature
of causality,29 and it is clear that machine learning has invigorated issues in
the philosophy of science.

In sum, issues in the philosophy of causality and probability influenced the
development of Bayesian networks, and the machine learning of Bayesian
networks in turn has spurned new philosophical debates about the nature of
causality and learning causal relationships. Can the philosophy of science
offer machine learning any further insights concerning Bayesian networks? I
shall now outline some thoughts in this respect – these are more thoroughly
documented in Williamson (2004).

The causal Markov condition implies Reichenbach’s principle of the
common cause, which has been central to the philosophical discussions of the
relationship between causality and probability. Indeed the philosophical lit-
erature contains many well-known counter-examples to the principle! If these
counter-examples are to be taken seriously then the causal Markov condition
cannot hold in general – and in fact it turns out that the failures of the causal
Markov condition are quite widespread, and that where causal and proba-
bilistic knowledge is incomplete (as it often is in the application of Bayesian
networks) the causal Markov condition is unlikely to hold.30 Thus a Bayesian
network is unlikely to accurately represent the physical probability distri-
bution over its domain.

So what explains the success of Bayesian networks? In my view their
success may be attributed to the fact that, even though Bayesian networks are
an imperfect representation of physical reality, they are the best models
available given the limited knowledge at hand. This can be made precise as
follows. Bayesian networks contain two types of knowledge: a causal graph
and the probability tables. Now according to the objective Bayesian inter-
pretation of probability,31 an agent should set her belief distribution over the
variables in question to the probability function that maximises entropy gi-
ven the constraints imposed by her background knowledge. (This is the belief
distribution which represents background knowledge but which is otherwise
maximally non-committal.) But the probability function that maximises en-

JON WILLIAMSON544



tropy given the knowledge in the causal graph and probability tables of a
Bayesian network is precisely the probability function determined by the
Bayesian network itself.32 Hence, even though the causal Markov condition
may fail and a Bayesian network may not correctly represent the physical
probability distribution on its variables, the network is the model one ought
to adopt if one’s background knowledge is represented by the components of
the network. A Bayesian network is the best model given limited knowledge.

If this is the case, then one should adopt a two-stage methodology when
employing Bayesian networks: first form a Bayesian network involving causal
and probabilistic knowledge to hand (this is the best model from an objective
Bayesian point of view); secondly when there is enough domain data refine
this Bayesian network using machine learning techniques to better represent
a target probability distribution.33 This allows one to integrate causal
background knowledge with machine learning techniques in a unified for-
malism, and shows how philosophical considerations to do with the objective
Bayesian interpretation of probability can have a bearing on machine
learning methodology.

By following the story of Bayesian networks we see how the philosophy of
science can interact dynamically with machine learning. The Bayesian
interpretation of probability inspired the formulation of Bayesian networks.
Machine learning techniques were soon developed to learn Bayesian net-
works and these techniques allow the possibility of testing philosophical
analyses of causality. Meanwhile considerations arising from the philosophy
of probability motivate a new approach to learning Bayesian networks and
integrating background knowledge.34

5. Conclusion

The conditions of Gillies and Zheng for a dynamic interaction appear to have
been met in the case of the philosophy of science and machine learning: several
connections exist between the two disciplines to the benefit of each side, the
relationship varies through time, and both sides remain autonomous.

By adding this interaction to those of Section 2 we obtain a chain of
interactions from computer science to machine learning – as in Figure 1. Of
course several further connections directly link computer science and ma-
chine learning, but they are not altogether autonomous disciplines so there is
no direct dynamic interaction between them.

Figure 1. Dynamic interactions: computer science, the philosophy of mathematics, the
philosophy of science and machine learning.

MACHINE LEARNING AND THE PHILOSOPHY OF SCIENCE 545



This new dynamic interaction may contribute to the success of both the
philosophy of science and machine learning, and prospects for future inter-
actions can be invoked to encourage proponents of both sides to look for
further points of cross-over and pursue inter-disciplinary research.

Acknowledgements

Thanks to the UK Arts and Humanities Research Board for partially
funding this research, and to Donald Gillies for useful comments.

Notes

1 Korb (2001, p. 1).
2 Korb (2001, p. 1).
3 Korb (2001, p. 5).
4 Thagard (1988, p. 189).
5 Bensusan (2000, p. 4).
6 Nestorianism, for example, held that Jesus was two distinct persons, one human and one
divine. The Council of Ephesus, convened in 431, concluded that Jesus was one person with

two distinct natures, one human and one divine.
7 Gillies and Zheng (2001, p. 438).
8 See Gillies (1992).
9 See Corfield (1997).
10 See Gillies (2001a) and Barendregt (1997) for further insights into this interaction.
11 See Bensusan (2000) and Korb (2001) for further discussion of connections between the two
disciplines.
12 Turing (1950, Section 7).
13 Dreyfus (1972).
14 The influence of Bayesian philosophy on machine learning has often been indirect, via

Bayesian statistics. I am grateful to an anonymous referee for emphasizing this point.
15 Gillies (1996).
16 Allen (2001).
17 Muggleton and de Raedt (1994), Flach (1995).
18 Dimopoulos and Kakas (1996), Poole (1998), Flach and Kakas (2000), Magnani (2001,
Section 4.4).
19 Thagard (1988, 1992, 2000).
20 Hofstadter and Group (1995).
21 Darden (1998).
22 Reichenbach (1956). Spohn (1980) also advocated an explication of the link between

probability and causality in terms of probabilistic independence.
23 Suppes (1970).
24 Salmon (1980).
25 See Pearl (1988, 1993) and also Gillies (2001b) for an account of this development.
26 See Pearl (1988) or Neapolitan (1990) for the details.
27 See for example the proceedings of the conferences on Uncertainty in Artificial Intelligence
at www.auai.org.

JON WILLIAMSON546



28 Spirtes et al. (1993), Korb and Nicholson (2003).
29 See Pearl (1988), Spirtes et al. (1993), McKim and Turner (1997), Glymour and Copper
(1999), Hausman (1999), Hausman and Woodward (1999), Korb (1999) and Pearl (2000).
30 Williamson (2004, Chapter 4).
31 See Jaynes (2003), Rosenkrantz (1977), William and Corfield (2001).
32 Williamson (2004, Sections 5.8, 6.1).
33 See Williamson (2004, Chapter 6) for a more detailed proposal here.
34 For further applications of Bayesian networks to the philosophy of science see Hartmann
and Bovens (2000), Bovens and Hartmann (2000) and Bovens and Olsson (2000).

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