Hayley Clatterbuck, The Logic Problem and the Theoretician's Dilemma

While surfing around I ran across Hayley Clatterbuck's, essay,  The Logical Problem and the Theoretician’s Dilemma, Philosophy and Phenomenological Research doi: 10.1111/phpr.12331 in a journal I usually don't read. It is almost good, just tiptoes up to goodness and gets no farther, leaving some oddities and bad arguments along the way and huge opportunities untouched. It reminded me of two occasions. On one, Judea Pearl asked a dinner party of UCLA philosophers "Why don't you guys do anything?" On another, after hearing two hours of lectures by Alvin Goldman on the difference between "hard wired" and "soft-wired" capacities, Allen Newell asked: "So what has your laboratory discovered about hard wired capacities?"

Clatterbuck's problem is the warrant for attribution of understanding to creatures that are not human. She rightly sees that claims of behavioral evidence for such attributions come face to face with the behaviorist version of Hempel's Theoretician's Dilemma.  She first proposes that understanding can be established by having independent observable stimuli with correlated responses, inviting explanation by a mediating variable. She represents this by a graphical causal model, roughly

E1 :  S1                         R1 
                      U
E2: S2                           R2

with arrows S1 -> U; S2 -> U; U -> R1; U -> R2. Citing the Causal Markov Condition, which she modestly says she does not fully understand, she claims the graphical model above implies that R1 and R2 are correlated.  (That is correct but since S1 and S2 are mutually exclusive, they are associated, so perhaps they should be collapsed into a single variable with 2 values; but Clatterbuck does not want the experimental treatment to be a variable common cause of the results.) She rightly goes on to object that nothing says the mediating variable U has to be some state of understanding; it could be a lot of different things.  So she goes on to suggest that designs are needed in which U -> R1 is a positive association and U -> R2 is negative, or vice-versa.  I guess the idea is that understanding would produce positive associations in some circumstances and negative ones in others that were perceptually similar.  So here is a good reason for positing a mediating variable, essentially using Reichenbach's common cause principle, and an argument I don't fully understand for it's interpretation.

However that works out, her discussion is lexically odd.  She says that the graphical model shown, which produces (with Faithfulness) an association between R1 and R2 is "syntactical" but the revised model that produces a negative association is "semantic."  Associations are syntactic but negative associations are semantic?Since "syntactic" is a term of abuse in contemporary philosophy of science, I wonder at the rationale for her terminology.  But on to something more serious.

She argues, I think, that the schema illustrates a way round the Theoretician's Dilemma. Following John Earman, Clatterbuck argues that prior evidence, call it E,  provides “inductive support” for some theory t, and t entails (and hence predicts) some new phenomenon N which thus would not have been predicted without recourse to t.  Earman puts the argument in Bayesian terms, as does Clatterbuck.  But if t entails N then Pr(N, E) ≥ Pr(N, t, E) hence Pr(N | E) ≥ Pr(N | t, E) Pr(t | E) = Pr(t | E): the novel phenomenon is at least as probable on the prior evidence as is the theory on the same evidence.  The Bayesian could skip the theory and go directly to the predicted phenomenon.  So that doesn't work.

Towards the end of her essay, she reformulates the idea in a way that I think she takes to be just an elaboration of Earman's (bad) argument, but is not: “In a case of within‐domain extrapolation, an empirical regularity within a domain is redescribed in terms of a theoretical relation which is then extrapolated to unobserved cases of that same domain. In a case of cross‐domain extrapolation, empirical regularities in domain A and B are redescribed in terms of the same theoretical relation, and it is induced that what is true of A is also true of B.”

I read this suggestion this way: given data from cases in one domain, find "theoretical" features of those cases that hold in another domain, and use those invariant features to predict about data in this second domain.  That would be a reason for theories. 

Ok, how can that be done...what is the script, the recipe? How can such invariant theoretical features be found? Nada. Full stop in Clatterbuck's essay. My graduate student, Biwei Huang, has an illustration for neuroscience. Taking fMRI images from subjects in one laboratory, she identifies strengths of some neural causal relations ("effective connections" in contemporary neuropsychology jargon) that separate autistic subjects from normals. She then uses the presence (or absence) of these connections and their strengths inferred from  fMRI scans from another laboratory (another "domain")  to predict autistic versus normal in the second laboratory (actually, in each of several other laboratories). 

This is a pretty neat illustration of the invariance strategy whose suggestion I attribute to Clatterbuck. And it does defeat the Theoreticians Dilemma: you couldn't make comparably accurate predictions by, say, comparing the correlations among fmri signals in different brain regions in subjects in one lab with those in another lab. People have tried.  

Huang's example is just that, not a general procedure for learning theoretical invariants for cross-domain classification.  My colleague, Kun Zhang, has developed one, explicitly in those terms.  Of course, that leaves a lot of room for work on the description of general procedures for other kinds of cross-domain invariants, of which physics provides many examples, e.g., classical thermodyanmics.

Afterword: Goldman replied to Newell that there is a division of labor: philosophers help science by posing the problems and distinctions; psychologists investigate them in the laboratory. Newell said thanks, but psychologists have no trouble doing both jobs. 

References

B. Huang, Diagnosis of Autism Spectrum Disorder by Causal Influence Strength Learning from Resting-Stae fMRI Data, M.S. Thesis, Department of Philosophy, Carnegie Mellon University, 2018.

Gong, M., Zhang, K., Huang, B., Glymour, C., Tao, D., & Batmanghelich, K. (2018). Causal Generative Domain Adaptation Networks. arXiv preprint arXiv:1804.04333.