Information Can Preserve Structure Across Scientific Revolutions

1. Information Can Preserve Structure Across Scientific Revolutions John Collier Philosophy and Ethics University of KwaZulu-Natal http://www.ukzn.ac.za/undphil/collier

2. The Incommensurability Problem is a real problem • I won’t argue it here, but I have argued elsewhere that incommensurability results from no having explicit resources for comparing theories that depend on different interpretation methods at a deep level. • These methods depend on tacit assumptions that in principle can never be made fully explicit. • This leads to what I have called pragmatic incommensurability, where problems of semantic comparability are caused by differing tacit assumptions that depend on the context of interpretation (paradigm).

3. Empiricism is the source • Recognized by Hanson, and especially Feyerabend. • Incommensurability arises from two widely held assumptions: • Pragmatic maxim: any difference in meaning must make a difference to possible experience. • Verificationism: the meaning of any statement is given by the conditions under which it can be verified. • Taken together, these two assumptions imply the infamous Quine-Duhem Thesis. • Specifically, any two theories have extensions that are equally compatible with the evidence O through addition of suitable auxiliary hypotheses, since verification conditions will include the additional hypotheses.

4. Resolving incommensurability • I have argued that the problem is to make the differing tacit assumptions explicit, to allow semantic comparability. • We can use areas of tension between paradigms to track down these tacit assumptions. • This has happened in some cases in the past, e.g., Newtonian gravitation and General Relativistic gravitation spacetimes resolved through a common representation in affine geometry. There are other examples, but the wave and particle accounts in Quantum Mechanics, for example, are not yet resolved.

5. Incommensurability comes from differing classifications • Kuhn argued (Second Thoughts on Paradigms) that incommensurability arose because of differing classifications whose presuppositions are not explicit. • Therefore the problem of comparing theories under different paradigms cannot be resolved (Forster) by Bayesian inductive methods alone, since these presuppose classifications.

6. Structuralism? • Structural realism holds that what is real are structures. • Our theories are correct inasmuch as the logical structure of the theory corresponds to the causal structure of its intended interpretations (Hertz, Rosen). • But, Wolfgang Balzer showed that there are too many possible interpretations of a structure to allow unique (or even usefully restricted) comparison of theory structures across paradigms.

7. Information to the rescue? • Several authors have argued that theories can be compared on information content alone. • Logical-linguistic (Carnap and Bar-Hillel): across structures, but assumes given classifications from language. • Statistical (Forster): same problem as probability accounts – assumes classifications. • Algorithmic (Dorling, various others): assumes theoretical terms, and hence classifications.

8. Measurements are constant across paradigms • Although the interpretation of observations is theory dependent, the observations methods themselves can remain constant. • Change of theory can introduce new methods of observation and measurement, but these do not change immediately. • So initially two competing theories have a common base of observation instances. • So that there is at least something that remains constant over paradigm shifts.

9. Information flow between theories • Barwise and Seligman account for information flow in distributed systems through infomorphisms. • An infomorphism is a relation between two classifications (consisting of types) and what they classify (tokens). • A complete classification is a theory of what it classifies. • If the tokens are specific observations, then they are the same in each classification independently of the classification. • This simplifies the problem of finding an infomorphism. • If we can find an infomorphism across paradigms, we can give an account of the relative information of the theories.

10. Information in a structure

11. Infomorphism

12. Definition of infomorphism An infomorphism is a pair f of functions ‹f, f› between two classifications A and C, one from the set of objects used to classify A to the set of objects used to classify C, and the other from C to A, such that the biconditional relating the second function to the inverse of the first function holds for all tokens c of C and all types of A, f(c) ╞A α if and only if c╞C f( α). The biconditional is called the fundamental property of infomorphisms.

13. So what do we have? • The bottom arrow between the tokens is guaranteed because they are identical. • If there is a problem, it is with the mapping at the top between classes (types). • What is required is that the types of the later theory classify the tokens of the other theory under the transformation. • The identity of the tokens under both classifications guarantees this if they group the same tokens. This allows the information to be carried between theories by the tokens, as is normal in information flow.

14. So what next? • The above shows that it is possible to permit an information flow between different paradigms. • However the way in which the classification required to get the flow must be structured may not represent the intuitive basic classification of the new theory, or indeed of either theory. • This gives a clue as to how we must rearrange our classifications of observations in order to compare theories, though it does not give us rules to do so. • If this is done, then we can compare theories according to Dorling’s method, or, indeed, use Forster’s.

15. Thank you! John Collier http://web.ncf.ca/collier/