Structural Realism and the Problem of Interpretation
Worrall’s particular flavor of structural realism (SR henceforth) seems to point to two possibilities for structural continuity: continuity concerning strict mathematical formalism or continuity concerning structural elements (of reality) that goes significantly beyond mere formalistic conservatism. My problem is this: if the claim of SR is simply that the formalism of physical mathematics is conserved between previous theories and subsequent theories, then: (1) it seems very difficult to counter the critique that this continuity is based on merely pragmatic values, and; (2) there is nothing particularly ‘realist’ about the assertion that equations, formulas, etc, are historically conserved between theories apart from interpretation. So, at least it seem to me, that Worrall was after the more significant interpretation of SR; namely, that the mathematical formalism has ‘latched’ on to quantifiable relations between elements existing in reality and that it is these relations, instantiated by the formalism, that is conserved between theories as opposed to simply the formalist structure of mathematical physics.
But at this point another problem arises for me: mathematics uninterpreted is nothing more than syntactic manipulations of symbols expressing abstract concepts that cannot legitimately be said to be about anything. So it seems that mathematical physics, insofar as the field presupposes that these syntactic manipulations can even successfully capture/represent the relations physics quantifies, is burdening mathematics with an ontology that goes beyond that which is contained within mathematics as an independent enterprise. So, again, it would seem that any attempt to apply mathematics to any given field is going to require superfluous (from the perspective of math) ontological commitments that then stand in need of interpretation (interpretation that cannot be said to be strictly mathematical). And this is where I see Worrall’s problems begin to mount, especially in light of Psillos’ critiques concerning the interpretation of the application of a strictly formal system.
Essentially, so I read Psillos, either the formalism is conserved and SR says nothing interesting about realism, or, the formalism is burdened with extraneous ontological commitments that necessarily stand in need of interpretation, in which case it is not strictly the formalism that is being conserved but implicit theoretical assumptions, background theories, etc., that are snuck in under the radar, as it were, coasting in on the claim that it is just the formalism that is conserved.
I am positive that I am missing some possible interpretations/counterarguments here and I hope to begin discussing these as soon as they are presented…