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Philosophy of Science:
Models in Science
Kristina Rolin 2012
Questions
What is a scientific theory and how does it relate to
the world?
What is a model? How do models differ from
theories and how do they relate to the world?
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Theories in logical empiricism
Synthetic
Analytic
Synthetic
Theoretical
statements
Translations
Observation
statements
Observation
statements
Translations
Observation
statements
Theories of theories: part I
The “syntactic” conception of theory (the so called
“received view”):
A theory is a collection of statements that can have a
formal representation as an axiomatic system. We
can separate the logical structure of the theory from
its empirical content. (The “syntax” is the study of the
rules that determine how sentences are formed.)
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Theories of theories: part I
Statements are given an interpretation (and empirical
content) by means of “correspondence rules.”
Example:
Formal representation: For every x it is the case that
if H(x), then M(x).
Correspondence rules: H(x)= x is a human being;
M(x)= x is mortal.
Empirical content: All human beings are mortal.
Theories of theories: part II
The “semantic” conception (the model-theoretic conception):
A theory is a collection of models and theoretical hypotheses.
Models are non-linguistic entities. A theoretical hypothesis is a
statement asserting some sort of relationship between a model
and a class of real systems in the world.
Giere, Ronald. 1988. Explaining science: A cognitive approach.
The University of Chicago Press.
Suppe, Frederick. 1989. The semantic conception of theories
and scientific realism. University of Illinois Press.
Van Fraassen, Bas. 1980. The scientific image. Oxford
University Press.
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Model: an example
The “simple gravity
pendulum” satisfies the
equation
T=2
where T is the period of time
for one complete oscillation,
and l is the length of the
pendulum. The model is
“constructed” so that the
equation describes it
truthfully (Giere 1988, 79).
Idealization
In any real system:
•
There is friction and air
resistance,
•
the rod is not weightless,
•
the rod is not rigid, and
•
the mass of the bob is
not located in one point.
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Theoretical hypothesis: an example
The positions and velocities of
the earth and the moon in the
earth-moon system are similar
to those of a two-particle
Newtonian gravitational model
(in some respects and to some
degree) (Giere 1988, 81).
“To believe a theory is to believe
that one of its models correctly
represents the world” (Van
Fraassen 1980, 47).
”Fictions” in science?
Theories consist of fundamental laws that do not represent
any real system in the world.
Fundamental laws (such as F=ma) are abstract, and they
can relate to a real system only via models that are
representations of concrete phenomena in the world.
Models are constructed so that fundamental laws can
feature in them. Such laws do not apply directly to a real
system in the world. Hence, the fundamental laws “lie.”
A “simulacrum” account of explanation: Models do explain
well even though they are not literally true of any real
system in the world.
Cartwright, Nancy. 1983. How the Laws of Physics Lie. Oxford:
Clarendon Press.
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Theoretical hypothesis
A theoretical hypothesis is true or false depending
on whether the asserted relationship between a
model and a real system holds.
The relationship between a model and a real
system cannot be one of truth or falsity since
neither is a linguistic entity (Giere 1988, 80).
”Truths” in science?
“A ‘theory of truth’ is not a prerequisite for an
adequate theory of science.” (Giere 1988, 81).
The relation between a model and a real system
is isomorphism (sameness of structure) (Van
Fraassen 1980, 46).
The relation between a model and a real system
is similarity (with respect to some aspects and
to some degree) (Giere 1988, 81).
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Scientific representations
as “maps”
“A theoretical hypothesis asserts
the existence of similarity
between a specified theoretical
model and a designated real
system. But since anything is
similar to anything else in some
way or other, the claim of
similarity must be limited … to a
specified set of respects and
degrees” (Giere 1988, 93).
Models as partial representations
”A model is an interpretative description of a
phenomenon that facilitates access to that
phenomenon” (Bailer-Jones 2009, 1).
“Facilitating access” involves focusing on specific
aspects of the phenomenon, disregarding others. As a
result, models are partial representations.
Bailer-Jones, Daniela. 2009. Scientific models in
philosophy of science. The University of Pittsburgh
Press.
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model
statements
real
system
A set of statements defines a model and a theoretical
hypothesis claims that there is a relationship of similarity
between the model and a real system in the world.
Theor.
statements
Observ.
statements
real
system
The “received view” of theories: Observational statements are
true statements of a real system in the world, and they give
support to theoretical statements.
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The Hypothetico-Deductive Model
Problem
Discovery
Hypothesis is
falsified.
Hypothesis
Deduction
Observable
Consequences
No
Consequences
correspond to Yes
observations?
Hypothesis
receives
support.
Models in logical empiricism
Models were seen as preliminary steps to theories
(“it is only a model”). Mature theories were
thought to render models redundant (Bailer-Jones
2009, 82).
In the rational reconstruction of scientific
knowledge, theories play a central role, not models
(92).
Models can play a central role in the context of
discovery but not in the context of justification
(93).
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Models in logical empiricism
Logical empiricism was at pains to explain why
theories postulate non-observable entities that are
difficult to construct out of observations (e.g.,
electromagnetic waves).
A model-based conception of theories provides an
explanation: such entities are part of models.
Models in Kuhn’s paradigms
Paradigms include many different things besides theories
(understood as statements), such as “exemplars” and
“concrete puzzle solutions.” These are claimed to play a
central role in the learning of scientific practice.
Yet, if models are understood as “exemplars” or
“concrete puzzle solutions,” it is not clear how they
relate to theories (understood as statements).
Kuhn acknowledges that visual representations play a
significant role in scientific knowledge: a change of
paradigm is described as a ”gestalt shift.”
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Analogies in science
Models are not literal descriptions of nature but they stand
in a relation of analogy to nature.
Positive analogy refers to those aspects that two things
(e.g., billiard balls and molecules) are known to have in
common. Negative analogy refers to those aspects that are
known to be different.
Neutral analogy refers to those aspects for which
commonality or difference is yet to be established. These
aspects are interesting because they allow scientists to
make predictions (e.g., knowledge of the mechanics of
billiard balls can be used to make predictions about the
expected behavior of gases).
Hesse, Mary. 1966. Models and analogies in science. University
of Notre Dame Press.
Analogies are not models
Analogies are relationships between a model and a
real system (Bailer-Jones 2009, 56 and 74).
Analogies are often instrumental in scientific
discovery, in the formulation of new hypotheses,
and in the process of constructing new models
(61).
Analogies are often used for the purpose of
illustration in science instruction (62).
Analogies are used to transport mathematical
methods from one domain to another (73).
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Metaphors in science
Models help us understand why the use of
metaphorical language is common in scientific
theories (even though many metaphors in science are
“dead”): e.g., electric field, light wave, excited state,
chemical bonds, black hole, brain as a computer,
critical mass in the social sciences.
Keller, Evelyn Fox. 1985. Reflections on Gender and
Science. Yale University Press.
Schiebinger, Londa. 1993. Nature’s Body: Gender in
the Making of Modern Science. Beacon Press.
Models as mediators between
theories and the world
Models come in a variety of forms – that is, they
employ different external representational tools.
Whereas theories aim to be general, models aim to
match specific empirical situations well.
Morgan, Mary, and Morrison, Margaret (eds.). 1999.
Models as Mediators. Cambridge University Press.
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Today’s message
A model-based conception of theories has the following
virtues:
It can account for the role of unobservable entities in
scientific theories: Such entities are part of models.
It can account for idealization and approximation in
scientific theories: Models are partial representations of
some phenomena in the world.
It can account for the persistence of analogies and
metaphors in scientific theories: Analogies and
metaphors are not models but the use of analogies and
metaphors in science is a spin-off of models (BailerJones 2009, 117).
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