The second lecture of Dynamics of Reason was much more substantive than the first. There were two main parts, a positive one and a negative one.

The positive part was putting forward what I take to be the most important part of Friedman’s lectures, his conception of relativized a priori. I’m not completely clear on it, but it seems like it is supposed to be a combination of Kantian and Carnapian perspectives. Kantian because it wants to answer questions about the very possibility of something, in particular how science is possible. Carnapian because it does this through Carnap’s general setup of linguistic frameworks. The frameworks come with two different sorts of rules, L-rules and P-rules. L-rules are the mathematical and logical rules for forming and transforming sentences. P-rules are the empirical laws and scientific generalizations.

Following the first lecture, Friedman takes the L-rules to be constitutive of paradigms, in Kuhn’s sense. They are the rules of the game, so to speak. This diverges with Kuhn in at least one respect. The L-rules are supposed to be listable whereas Kuhn doesn’t think all aspects of a paradigm can be made explicit. Some can, but things like familiarity with equipment and some other sorts of know-how cannot be.

The P-rules are the substance of normal science. The P-rules are treated as internal questions. The L-rules are treated as external questions.

The relativization of the a priori comes in when Friedman notes that some P-rules, some scientific hypotheses, cannot even be formulated, much less be used to describe the world, until some bit of math is available. The math, in the corresponding L-rules, is presupposed by the P-rules. They are required for the possibility of formulating and applying the P-rules themselves, to put it in a Kantian way. One example of this is the calculus and Newton’s laws of mechanics. Friedman notes that Newton’s laws are, in their mathematical presentation, formulated in terms of the calculus. Additionally they only make sense against the background of a fixed inertial frame, which concept is given in an L-rule.

The claim seems to be that the L-rules of a framework provide the possibility of knowledge, a priori, within the area of that framework. The relativization is supposed to get around Kant’s big problem, which was that he tethered his source of a priori knowledge to something that would provide Newton’s laws and use Euclidean geometry. Since it is possible to switch between frameworks, and thus switch between L-rules, one can have sources of a priori knowledge, but relativized to a given framework. That said, I’m not sure I’m comfortable this idea of relativized a priori knowledge. Friedman says that it provides a foundation for knowledge, but it seems awfully mutable for something foundational. Presumably we do not change frameworks that often, since we are supposed to see them as akin to paradigms in science.

Friedman’s picture is very much like Carnap. I’m not sure why he is saddling it with the Kantian stuff. He presents Carnap as being quite the neo-Kantian, although I don’t think I get what that aspect adds to Carnap’s view as presented. (I’m also somewhat troubled by the seemingly uncritical wholesale adoption of Kuhn’s view of science. The presentation of Friedman’s view of the a priori here seems to depend on Kuhn’s picture of scientific development being right.)

The presentation of the relativized a priori was the positive part. The negative part consists of an argument against Quine’s epistemological holism. The arguments main thrust is that holism can’t account for the sort of dependence on, or presupposition of, different parts of math by different empirical laws. Friedman notes that Quine says that empirical content and evidence accrue to mathematical and logical statements as well as occurrence statements and empirical laws. Thus, the elements of the web of belief are all on an evidential (epistemic?) par, so we can treat the web as a big conjunction of statements. There are no asymmetric dependencies in a conjunction, so Quine’s view can’t account for the impossibility of, say, formulating Newtonian mechanics while rejecting (or merely lacking?) the presupposed math. In Friedman’s words, “Newton’s mechanics and gravitational physics are not happily viewed as symmetrically functioning elements of a larger conjunction: the former is rather a necessary part of the language or conceptual framework within which alone the latter makes empirical sense.” Friedman actually gives this argument twice, once applied to Newtonian mechanics and once applied to relativity theory. The arguments are virtually the same and are on consecutive pages. (Maybe it worked better in lecture form.) Quine’s view cannot account for the history of science, the parallel development of mathematical framework with empirical claims.

It seems like the Quinean could agree with Friedman. The view sketched flounders, but it is not Quine’s view either. It seems to me something of a strawman. Despite discussing some of Quine’s views on revising theory, Friedman concludes that Quine treats the elements of the web of belief, to continue using the metaphor, as parts of one big conjunction. This doesn’t seem like Quine’s view at all. It is important to Quine that certain things, such as math and logic, are less open to revision and rejection because they provide such utility and unificatory power. They are used in deriving consequences of theory and observation. It seems consistent with the Quinean view, I think because it was the Quinean view, that there be an asymmetry between the math that is needed in the framing of an empirical law and the empirical law. From what is presented, Friedman’s objection doesn’t cut against Quine.

In a way, this is too bad. The set up is perfect for really testing how Quine’s epistemological holism could deal with some hard cases, i.e. detailed case studies from the history of science. Unfortunately, these are used to dismiss the weird conjunctive picture of Quine’s holism, which is obviously bad. It would be informative to tell the Quinean story, in more detail, for what is going on with the dependence of Newton’s mechanics and gravitation on the calculus. I’m not going to do that now though.

In all, the positive part of the lecture was more convincing, although it was still a bit lacking. There is a follow up essay entitled “The Relativized A Priori” that would probably clear things up. I’m not sure if I’m going to read it though. It depends how lecture three goes.