Ioannis Votsis

Consider the aims of the following three influential philosophical views. The semantic view of theories aims to supply the proper form and content of scientific theories. Structural realism aspires to delimit the epistemology and ontology of science. Mathematical structuralism seeks to reveal the epistemological and ontological nature of – you guessed it – mathematical objects. Given their divergent aims they may seem like unlikely bedfellows, but the semantic view of theories, structural realism and mathematical structuralism share enough ground to be able to benefit or suffer from some of the same reasons. What unites the three views is the purely structural analysis of their respective subject matter. The semantic view sees theories as nothing more than families of models, i.e. sets of structures. Representation, according to this view, is a matter of establishing mappings between some models of the theory and target domains. Structural realism judges scientific knowledge and perhaps even ontology to be wholly structural. Mathematical structuralism proclaims that the objects of mathematics are specifiable only up to isomorphism.

This paper counters an objection raised against one of Bertrand Russell’s lesser-known epistemological views, viz. ‘‘structural realism’’ (SR). In short, SR holds that at most we have knowledge of the structure of the external (i.e., physical) world. M. H. A. Newman’s allegedly fatal objection is that SR is either trivial or false. I argue that the accusation of triviality is itself empty since it fails to establish that SR knowledge claims are uninformative. Moreover, appealing to Quine’s notion of ontological relativity, I suggest that far from being false, SR knowledge claims seem to be the most that we can hope for.

Kyle Stanford (2006) argues that the most serious and powerful challenge to scientific realism has been neglected. The problem of unconceived alternatives (PUA), as he calls it, holds that throughout history scientists have failed to conceive alternative theories roughly equally wellconfirmed (by the available evidence) to the theories of the day and, crucially, that such alternatives eventually were conceived and adopted by some section of the scientific community. PUA is a version of the argument from the underdetermination of theories by evidence (UTE) but departs from it in two significant ways: (i) there is a shift from artificially produced rival theories - of the kind typically talked about in the underdetermination debate - to actual rivals and (ii) there is a shift from empirically equivalent rivals to rivals that are equally well-confirmed by the available evidence at a given point in time. In this talk I will argue that by these shifts Stanford successfully manages to find more historical evidence for PUA (than do proponents of UTE), but only at the expense of making his thesis ineffectual.

Structural realism has various diverse manifestations. One of the things that structural realists of all stripes have in common is their endorsement of what I call 'the structural continuity claim'. Roughly, this is the idea that the structure of successful scientific theories survives theory change because it has latched on to the structure of the world. In this talk I elaborate, elucidate and modify the structural continuity claim and its associated argument. I do so without presupposing a particular conception of structure that favours this or that kind of structural realism but instead by concentrating on neutrally formulated historical facts. The result, I hope, throws light on what a structural realist must do to evidentially benefit from the historical record of science. The implicit argument underwriting the structural continuity claim can be reconstructed as follows: Premise (1) Only structural elements of predictively and explanatorily successful scientific theories have been (and will be) preserved through theory change. Premise (2): Preservation of an element implies or at least is good evidence for its (approximate) truth. Premise (3): Non-preservation of an element implies or at least is good evidence for its falsity. Conclusion: It is probably the case that only structural elements are (approximately) true. In this summary I restrict my comments to the first premise. Several points can be raised with respect to it. First, not all structures are created equal. Some play no active role in the predictive and explanatory success of a theory because they do not correspond to any structure in the world. Their non-preservation would therefore not encumber the structural realist. Traditional scientific realists have long employed a distinction between essential and idle posits to weed out those elements of theories that played no substantial role in their predictive and explanatory success..