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PH201/400 – Week 17 Scientific Representation. Recall from Last Week. 1 st Type of Models: Models of Phenomena They are a model of a selected part or aspect of the world, a phenomenon: The Schelling model of social segregation The Fibonacci model of population growth
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PH201/400 – Week 17 Scientific Representation
Recall from Last Week 1st Type of Models: Models of Phenomena They are a model of a selected part or aspect of the world, a phenomenon: • The Schelling model of social segregation • The Fibonacci model of population growth • The billiard ball model of a gas • The Bohr model of the atom • The Lorenz model of the atmosphere • The Lotka-Volterra model of predator and prey • The MIT model of quark confinement • ...
Recall from Last Week 1st Type of Models: Models of Phenomena They are a model of a selected part or aspect of the world, a phenomenon: • The Schelling model of social segregation • The Fibonacci model of population growth • The billiard ball model of a gas • The Bohr model of the atom • The Lorenz model of the atmosphere • The Lotka-Volterra model of predator and prey • The MIT model of quark confinement • ...
The Problem Question: In virtue of what is a model a representation of something else? More formally, the problem is: what fills the blank in: ‘M is a scientific representation of T iff ___’, where ‘M’ stand for ‘model’ and ‘T’ for ‘target system’. (For a more detailed discussion of the problems of representation see the additional reading on Moodle.)
What Representation Is Not Definition: X represents Y iff X is a mirror image of Y.
Problem: This account of representation is wrong, and seriously misleading! Representation ≠ Mirroring • counterexamples: • from art • from science.
Notice: Mirror images is alike … … but representations are not!
Moral: All these picture are very different, yet they represent the same object, namely Mont Saint Victoire. So they are not mirror images, but they are representations! And what is more: They warrant different inferences, and failure to take this into account can lead to serious mistakes!
Example 1: Mirror theory of rep: The mountain is pink and blue. But it isn’t!
Example 2: Mirror theory of rep: The mountain is square and has vertical stripes. No, this is wrong!
The same is true for scientific representation! An abundance of representational kinds and strategies is not a prerogative of the fine arts! There are different kinds of representations in the sciences too.
Example: Models of the nucleus Liquid Drop Model Shell Model
Virgina Woolf: “Art is not a copy of the world; one of the damn things is enough.” We add: “Science is not a copy of the world either.”
The “Menu” • Available Positions in the Debate: • Conventionalism • Similarity • Structuralism (Isomorphism) • Inferentialism • Direct Fictionalism • Representation-As
The “Menu” • Available Positions in the Debate: • Conventionalism • Similarity • Structuralism (Isomorphism) • Inferentialism • Direct Fictionalism • Representation-As • (For a more detailed discussion of the these positions see the additional reading on Moodle.)
2. The Similarity Account Similarity and representation initially appear to be two closely related concepts, and invoking the former to ground the latter has a philosophical lineage stretching back at least as far as Plato’s The Republic. Similarity 1: A scientific model M represents a target T iff M and T are similar.
Problems: • Similarity has the wrong logical properties: similarity is reflexive and symmetric but representation isn’t. • Confusion of misrepresentation and non-representation. • Similarity is not sufficient for representation: Putnam’s ant. Accidental similarities. • “Everything is similar to everything else” • Frigg (2006), Suárez (2003)
Giere’s nuanced similarity account: Compulsory reading. Similarity 2: A scientific model M represents a target T iff a model user provides a theoretical hypothesis H specifying that M and T are similar to one another in relevant respects and to relevant degrees. This account solves the problems of Similarity 1. Exercise: show how.
Problems: • Similarity has become an idle wheel in explaining why M represents T. • What is similarity in respects and degrees? Various theories of similarity. • Does all representation involve similarity? Tube map, litmus paper, models like the Phillips-Newlyn machine, … • What does similarity mean in the case of non-material models?
3. The Structuralist Account The structuralist account is a cousin of the similarity account. Simple version: Similarity 1: A scientific model M represents a target TiffM and T are isomorphic. This needs unpacking
Set theoretic structure: A non-empty set U of individuals called the domain (or universe) of the structure S, and a non-empty set R of relations on U. Often it is convenient to write these as an ordered triple: S=<U, R>. Example: U={a, b, c} r={<a, b>, <b, c>, <a, c>} R={r} S=<U, R>
Important: Nothing about what the objects are matters for the definition of a structure; we can ‘strip away’ the ‘material’ nature from the individuals in the domain of the structure and replace them by ‘dummy entities’. Operations are specified purely extensionally. That is, n-place relations are defined as classes of n-tuples and it is not important what the relation ‘in itself’ is. The only thing that matters is between which object it holds.
Crucial Move: Models in mathematics and in science are the same! ‘[T]he meaning of the concept of model is the same in mathematics and the empirical sciences.’ (Suppes 1960a, 12) ‘According to the semantic approach, to present a scientific theory is [...] to present a family of models – that is, mathematical structures offered for the representation of the theory’s subject matter’ (van Fraassen 1997, 522)
Structure 1: S1=<A, R1> • Structure 2: S2=<B, R2> • Then S1 and S2are isomorphic iff there is a mapping f: S1S2 such that • f is one-to-one • f preserves the system of relations in the following sense: if the elements a1, ..., an of S1 satisfy the relation r then the corresponding elements b1=f(a1), ..., bn=f(an) in S2 satisfy r’, where r’is the relation in S2 corresponding to r. • Core idea of structuralism: Representation is isomorphism between model and target.
Problem 1: Descriptive adequacy. Scientists often talk about model-systems as if they were physical things. Newton, when introducing his model of the planetary system, did not present a mathematical structure. Rather he described a hypothetical situation in which one sphere orbits around another sphere in the absence of confounding factors.
Problem 2: Heuristic Fictional scenario plays a crucial role in understanding how a model relates to reality. Example: Fibonacci model Quite soon the real number of rabbit pairs will start diverging dramatically from the value the model predicts. The above equation is not about rabbits per se; it is about rabbits that never die, etc. It is crucial to appreciate this fact if we want to know under what circumstances and to what extent conclusions derived in the model can be expected to bear out in the real system. This is important to know when using the model, but—and this is the crucial point—there is nothing in the mathematics that tells you any of this!
Problem 3: Representation Recall: Models are structures and they represent targets by being isomorphic to them. But: an isomorphism holds between two structures and not between a structure and a part of the world per se. In order to make sense of the notion that there is an isomorphism between a model-system and its target-system, we have to assume that the target exemplifies a particular structure. For a discussion see Frigg (2006)
4. Representation-As Nelson Goodman and Catherine Elgin Elgin Reading on Moodle
Representation-As – The Intuition Thatcher represented as a boxer
Representation-As – The Intuition Churchill represented as a bulldog
Scientific models represent very roughly in the same way: • The Philips-Newlyn model represents the economy as system of pipes and reservoirs. • The Kendrew model represents myoglobin as a plasticene sausage on sticks. • The metal-can model of a ship represents the ship as metal can. • … Representation-As – The Intuition
Notation: X-- the object that does the representing In example: the drawing Y -- the real-world target of the representation In example: Thatcher (the real person) Z – kind of a representation In example: Boxer
Definition: ‘when [X] represents [Y] as [Z] … [it] is because [X] is a [Z]-representation that denotes [Y] as it does. [X] does not merely denote [Y] and happen to be a [Z]-representation. Rather in being a [Z]-representation, [X] exemplifies certain properties and imputes those properties or related ones to [Y].’ (Elgin: Telling Instances, 10)
Definition: ‘when [X] represents [Y] as [Z] … [it] is because [X] is a [Z]-representation that denotes [Y] as it does. [X] does not merely denote [Y] and happen to be a [Z]-representation. Rather in being a [Z]-representation, [X] exemplifies certain properties and imputes those properties or related ones to [Y].’ (Elgin: Telling Instances, 10) This sets the agenda
(a) Denotation Denotation is the two-place relation between a symbol and the object to which it applies. ‘Pictures, equations, graphs, charts, and maps represent their subjects by denoting them. They are representations of the things that they denote.’ (TI, 2)
