Underdetermination: Duhem, Laudan

Philosophy of Science
Curtis Brown

Two criticisms of conventional views about the relation between theory and evidence from the Duhem selection:

1. Holism.  (Laudan calls this "the ambiguity of falsification" on p. 326.)  This is the idea that evidence does not bear directly on a hypothesis alone, but rather on a hypothesis in conjunction with many additional theoretical claims (as well as assumptions about particular facts, e.g. about the experimental setup).
   
   Let H be the hypothesis we wish to test; let A₁, A₂, and A₃ be the additional theoretical and particular assumptions needed to deductively imply an observation statement, and let O be the observation statement.
   
   Then we may think of Duhem as making the following point.  If H, together with A₁, A₂, and A₃, implies O, then the following conditional will be true:
   
               (H & A₁ & A₂ & A₃) → O
   
   From this, together with ~O, we can deduce, not ~H, but only
   
               ~(H & A₁ & A₂ & A₃)
   
   Which (by DeMorgan's laws) is equivalent to
   
               ~H ∨ ~A₁ ∨ ~A₂ ∨ ~A₃
   
   --that is, we can conclude only that at least one of the hypothesis or our starting assumptions is false.  Observation and logic will not tell us which one is false.
    

2. Crucial Experiments Impossible.  Duhem argues that crucial experiments are impossible in science.  A crucial experiment is supposed to be an experiment which will definitively decide between two alternative theories.  The idea seems to be that a crucial experiment enables us to make a disjunctive syllogism.   Suppose that we have two rival hypotheses, H₁ and H₂.  Lumping all our auxiliary assumptions into the single symbol A, we have, let us suppose:
   
               1. H₁ ∨ H₂
               2. (H₁ & A) → O₁
               3. (H₂ & A) → O₂
   
   and let us suppose that the observations predicted by the two hypotheses are mutually incompatible, so that
   
               4. O₁ ↔ ~O₂
   
   Now we perform the crucial experiment. Suppose we find that O₁. By 4, we know that ~O₂. So from this together with 3, we can conclude that ~(H₂ & A). Of course, at this point we hit the problem of holism; all we know now is that ~H₂ or ~A, but we don't know which.  However, suppose for the sake of argument that we can in fact conclude that ~H₂. Then from 1, we can conclude that H₁. The crucial experiment has validated H₁ by ruling out H₂.
   
   At this point we reach Duhem's second criticism, namely that this form of argument only works if we in fact know that 1, i.e. that one or the other of our two hypotheses is correct. But we can never rule out the possibility that other hypotheses we haven't thought of yet, incompatible with H₁ and H₂, are true. A disjunctive syllogism works only if we know that we have exhausted the possibilities and then ruled out all but one of them. But we can't ever be certain that we have found all the possible hypotheses that might explain the evidence.
   
   (Nonscientific example: In "Some Assembly Required," Buffy (the vampire slayer) and friends are trying to figure out why a corpse is missing from the cemetery, and dig up another grave to gather observational evidence. H1: flesh-eating demon. H2: army of zombies. O1: grave with corpse. O2: grave without corpse. Clearly condition 4 is satisfied. When they don't find a corpse, they conclude that a voodoo practitioner is raising an army of zombies. However, it turns out that 1 is false: the truth is a completely different hypothesis, H3, namely that a science student has been gathering parts to make a Frankenstein-style companion for his dead but reanimated brother.)
    
3. Humean Underdetermination (HUD): Laudan uses the term "Humean Underdetermination" to refer to the view that for any observable evidence O, there is an indefinite number of hypotheses which, together with auxiliary assumptions, logically imply O. One instance of this is the familiar problem of fitting a curve to a set of points. There will always be an infinite number of different curves that pass through any finite set of points.

Laudan thinks all of these points (well, really he only addresses 1 and 3) are correct and to some extent important, but that they do not have significant relativistic consequences. All of these points involve deductive underdetermination. Relativists have concluded that, since logic doesn't compel one theory choice over another, there must be a significant nonrational component in theory choice.

But L points out that to show this would require not merely deductive underdetermination, but ampliative underdetermination. (An "ampliative inference" is one which goes beyond what you could infer by means of deduction alone: for instance, an inference from the evidence to claims about the future, or the distant past, or things too small or far away to observe directly. If we use the term "induction" broadly enough, an ampliative inference is just an inductive inference.) That is, what needs to be shown is not that observation plus deduction will not determine theory choice, but rather that "ampliative inference" will not determine a unique choice of theory. Laudan argues that no one has in fact shown this.

Last update: October 1, 2008
Curtis Brown | Philosophy of Science | Philosophy Department | Trinity University