The Miracle Argument and Transient Unterdetermination

1. The Miracle Argument andTransient Unterdetermination Paul Hoyningen-Huene Leibniz Universität Hannover Center forPhilosophyandEthicsof Science (ZEWW)

2. The subject of the talk TU  ¬ MA TU = transient underdetermination MA = miracle argument

3. Outline 1. Transient underdetermination 2. The miracle argument 3. The miracle argument in the light of transient underdetermination 4. Presuppositions of the miracle argument 5. Conclusion

4. Transient Underdetermination (TU) Idea: A given (finite) set of data does not unambiguously determine a single theory Notation: Let D1 be a finite set of data Let T1 be the set of theories such that T1 := {T, T is relevant for and consistent with D1}

5. Definition of TU: 1st attempt TU holds iff  T (T  T1)  T (T T1(T T))] “(T T)” means that T and T are not compatible Note that there are many possible sources for the incompatibility of theories, including incommensurability! This is too weak as a definition of TU: the existence of two minimally differing theories consistent with the data fulfills the condition It is only a necessary condition for TU We need the possibility of radically false theories that are compatible with the available data

6. TU: Notation Partition of T1 into the two subsets: (approximately) true theories and radically false theories (not even approximately true) T1AT := {T  T1, T is true or approximately true} T1RF := {T  T1 is radically false} Of course, T1AT T1RF = T1 Assume the idealization T1AT T1RF = Ø Intuitively, radically false theories operate with radically false basic assumptions in spite of their agreement with the available data (e.g., at some historical time, phlogiston theory or classical mechanics)

7. Definition of TU: 2nd attempt TU holds iff T1RF ≠ Ø For the purposes of my argument, this is still too weak: there must be “quite a few” radically false theories in T0 This is supported by the intuitive idea of TU: In T1, there are many more approximately true theories than true theories, and many more radically false theories than approximately true theories (Stanford, e.g.: unconceived alternatives)

8. Definition of TU: 3rd attempt In order to formalize this idea, I need the concept of a measure on the space of theories A measure is a generalization of the concept of volume for more general “spaces” Simplistic example for a theory space and a measure on it: Space of theories: {Tk Tk: F(x) = k with 0 ≤ k < ∞} Possible measure: μ({Tk Tk: F(x) = k with a ≤ k ≤ b,}) := b - a

9. Simplistic example F(x) b F(x)=k b-a a x

10. Definition of TU: 3rd (and last) attempt Let μ be a measure on the set of theories T1 Definition of TU: TU holds iff μ(T1AT) << μ(T1RF) In what follows, I will presuppose transient underdetermination in this form

11. The miracle argument (MA) Idea: If a theory correctly predicts something it has not been devised for, then this fact cannot be purely accidental: the theory must be at least approximately true Define: “use-novel predictive success of a theory”: the successful prediction of data by a theory which were not used in its construction Example: quantitative prediction of light bending in GRT “Scientific realism”: well-established physical theories are approx. true Miracle argument for scientific realism: • Scientific realism is the best explanation for use-novel predictive success of theories; other philosophical positions make it a miracle • Use-novel predictive success exists • Therefore, it is reasonable to accept scientific realism Let us articulate this argument more explicitly

12. The miracle argument (2) Recall our notation: Let D1 be a finite set of data Let T1 be the set of theories such that T1 := {T, T is relevant for and consistent with D1} T1AT := {T  T1, T is true or approximately true} T1RF := {T  T1 , T is radically false}

13. The miracle argument (3) The miracle argument is especially impressive if one assumes transient underdetermination: μ(T1AT) << μ(T1RF) This means: for any T  T1, it is very probable that T  T1RF This means: due to TU, any theory fitting some data is probably radically false In other words: TU supports anti-realism

14. The miracle argument (4) Here comes the miracle argument: Let N be some use-novel data (relative to D1) Let there be a theory T*  T1 capable of predicting the novel data N Does T* belong to T1AT or to T1RF?

15. The miracle argument (5) If T*  T1AT, its novel predictive success is not surprising because it gets something fundamental about nature (approximately) right If T*  T1RF, its novel predictive success would be surprising because T* lacks all resources for successful novel predictions; it would be a miracle Therefore, it is very probable that T*  T1AT In other words: use-novel predictive success supports scientific realism (for the respective theories)

16. TU & MA But TU strikes back: Apply TU again to the situation with the new data set D2 := D1 N We have D2 := D1 N is a finite set of data T2 := {T, T is relevant for and consistent with D2} Clearly, T*  T2 Define in the same way as earlier T2AT := {T  T2, T is true or approximately true} T2RF := {T  T2 , T is radically false}

17. TU & MA (2) TU states: μ(T2AT) << μ(T2RF) As T*  T2, we get T* is very probably radically false, contrary to what the miracle argument claims STOP, shouts the scientific realist, you cheated! T* is not just an ordinary member of T2 to which μ(T2AT) << μ(T2RF) applies T* is special in that it was able to predict N on the basis of D1 whereas the ordinary member of T2was fitted to D2 := D1 N

18. TU & MA (3) However, this difference of T* from the other members of T2 is purely pragmatic and not intrinsic Every member of T2, once you happen to hit upon it by looking for a theory that fits data D1, can be used to predict N! Thus, T* is an ordinary member of T2 Because of TU: μ(T2AT) << μ(T2RF), we really get: T* is very probably radically false, contrary to what the miracle argument claims

19. TU & MA (4) Thus, the core assumption of the miracle argument: For any radically false theory fitting some data, it is very improbable (or even impossible) to make a use-novel prediction is false, given TU Reason: Given TU, there are far more radically false T*’s  T1 making a use-novel prediction N than approximately true T*’s  T1 making the use-novel prediction N In other words: TU kills MA Question: How come that the Miracle Argument appears to be so plausible?

20. Presuppositions of MA Remember the crucial assumption of MA: For any radically false theory fitting some data, it is very improbable (or even impossible) to make a use-novel prediction In Putnam’s words: “The positive argument for realism is that it is the only philosophy that doesn’t make the success of science a miracle” There are two (hidden) presuppositions in these statements: • There is a uniform answer, i.e., an answer that is not specific of T, to the question why T is successful regarding use-novel predictions • There are only two alternative answers of the required kind, namely realism and antirealism

21. Presuppositions of MA (2) Both presuppositions are extremely problematic • Why a theory is successful regarding use-novel predictions may have very different reasons: sheer luck, mutual cancellation of erroneous assumptions, the novel predictions only appear to be novel, similarity to more successful theories (not yet known), approximate truth, etc. • Even among the uniform answers, there are other alternatives, i.e., empirically adequate theories Thus, even without TU, MA is highly problematic

22. Conclusion • In general, the miracle argument is a highly problematic argument • Given transient underdetermination in the form discussed, the miracle argument is definitively invalid • The realist and the antirealist have different “intuitions” about this question: For a use-novel successful theory, what is more likely: that it is (approximately) true or that its errors cancel each other out in a most advantageous way?