Philosophy of Science: Models in Science

Transcription

1 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? 1

2 Theories in logical empiricism Synthetic Theoretical Analytic Translations Translations Synthetic Observation Observation Observation Theories of theories: part I The syntactic conception of theory (the so called received view ): A theory is a collection of 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.) 2

3 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 Explaining science: A cognitive approach. The University of Chicago Press. Suppe, Frederick The semantic conception of theories and scientific realism. University of Illinois Press. Van Fraassen, Bas The scientific image. Oxford University Press. 3

4 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. 4

5 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 How the Laws of Physics Lie. Oxford: Clarendon Press. 5

6 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). 6

7 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 Scientific models in philosophy of science. The University of Pittsburgh Press. 7

8 model real system A set of 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. Observ. real system The received view of theories: Observational are true of a real system in the world, and they give support to theoretical. 8

9 The Hypothetico-Deductive Model Problem Discovery Hypothesis is falsified. Hypothesis Deduction No Observable Consequences Consequences correspond to observations? Yes 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). 9

10 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 ), 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 ). Kuhn acknowledges that visual representations play a significant role in scientific knowledge: a change of paradigm is described as a gestalt shift. 10

11 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 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). 11

12 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 Reflections on Gender and Science. Yale University Press. Schiebinger, Londa 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.) Models as Mediators. Cambridge University Press. 12

13 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 (Bailer- Jones 2009, 117). 13