What the discussion around knowledge-how mainly shows, I think, is that the relation between propositional attitudes, cognitive structures or representations, and the behavioral evidence for their respective presence are still not well understood. It seems that we find it surprisingly difficult to disentangle our different ways of talking about ourselves and others in terms of what we believe, on the one hand, and in terms of the information that our brains (or some other division of the body-environment) process on the other. The main difficulty seems to be that we take ascriptions of propositional attitudes to mirror psychologically real relations between subjects and propositions. As such, we feel the need to tell a story about how propositional attitudes are realized in the brain. The measurement view enables us to employ a less committal way of representing someone’s psychological states that largely leaves open how the cognitive system manages to coordinate its behavior with the environment. The constraints that are put on cognitive architecture by successful ascriptions of propositional attitudes are really quite weak. To be sure, if the measurement view is to be proven correct, there must be a homomorphic mapping from an empirical structure into the propositional structure. But homomorphisms abound. Any number of homomorphisms can be found between any two structures. And as far as we can tell, the structure of propositions is homomorphic to the course of the sun and the stars. This is why we can employ intentional explanations for just about any system we want. The measurement view becomes informative when we have formalizations of the two structures and a measurement theory that describes the particular homomorphism of interest that holds between them. Then we can tell what we learn about the empirical structure by means of reasoning about propositions. An attempt to infer the empirical structure from the representational structure alone must fail.
In the case of propositional attitudes, I ultimately doubt that the mapping is best conceived as holding between internal cognitive architectural structure and propositional attitude ascriptions. Propositional attitudes might rather be measurements of structures of observable behavior. Propositional attitudes are ascribed on the basis of observable behavior together with some standards of folk psychology—such as that one believes what one sees or what one is told by trustworthy peers. Propositions might provide standardized ways of identifying behaviorally relevant circumstances, including what someone saw, was told, and aims for, that would otherwise have to be identified less systematically by way of particular situations and individual histories. I can tell that you know that the earth is an approximate sphere—you've certainly learned it somewhere. I do not need to go back in your learning history until I find the moment in which someone uttered a sentence with the respective meaning—which would allow for similar predictions and explanations.
Taking propositional attitude ascriptions to be measurements of structures of observable behavior would also be very much in line with Ryle’s original, rather behaviorist discussion of knowledge-how. With reference to our use of mental vocabulary to describe the behavior of others, Ryle writes that “we go beyond what we see them do and hear them say, but this going beyond is not a going behind, in the sense of making inferences to occult causes; it is going beyond in the sense of considering, in the first instance, the powers and propensities of which their actions are exercises” (1949, p.51). The powers and propensities are in turn understood as complex dispositions, describable in terms of their acquisition and manifestation conditions. The move from a structure of observable behavior to a propositional structure would take the place of acknowledging the role of so-called internal states; for now we can exploit inferential relations among propositions for explanation and prediction. But these propositional attitudes need not be understood as internal states. Instead they could be taken as measurement representations of Ryle’s powers and propensities. Ryle notwithstanding, however, we need not give up cognitive psychology. Ascriptions of propositional attitudes and cognitive representations would relate via the behavior that each is to explain—they provide complementary explanations of the same behavior. For Bartels and May’s explanation of practical knowledge this would mean that it is not part of a theory of an empirical structure for measurements of propositional attitudes. It would be a cognitive-psychological explanation of a behaviorally characterized psychological phenomenon called practical knowledge. The main point of this commentary, though—namely, that Stanley and Bartels and May are up to different things and that little can be inferred about cognitive architecture from Stanley’s analysis of knowledge-how—remains untouched.
In closing, I want to mention one reservation that can be held against the particular cognitive-architectural account presented by Bartels and May. Given that concepts remain a vexed issue in contemporary discussion, that they are traditionally closely related to propositions, and that it is notoriously difficult to find good grounds for attributing representations of a certain kind and with a specific content to cognitive systems that are not able to verbally express their beliefs, a semantic reading of conceptuality might be worth considering. Concepts might be broadly conceived of as the constituents of thoughts, i.e., (trains) of propositional attitudes. In our case: whatever is a constituent of knowledge-how would count as a concept. One effect of this would be that the reliance on non-conceptual capacities in order to explain certain forms of knowledge-how, like that of patient DF, would not be open to Stanley. But as an alternative, Stanley could accept demonstrative concepts and claim that some forms of knowledge-how are distinguished by their involvement. Admittedly, Bartels & May would have to change their terminology; their abilities approach to concepts is not compatible with concepts being the constituents of propositions alongside a semantic reading of propositionality. But nothing much seems to be lost by this. Quite possibly, mentalistic vocabulary is just not the best way to come to grips with the structure of cognitive systems.