Robert Brandom’s recent work aims to reconceive and pragmatist thought by on the one hand reconnecting it with its roots in the German Idealist tradition, and on the other hand synthesizing it with analytic philosophy of language, epistemology, and metaphysics. These lectures provide an overview of how he proposes to do that. A central figure in this reconceptualization of pragmatism and its history is the brilliant and notoriously difficult American philosopher Wilfrid Sellars. Brandom explains how Sellars’s ideas can form the basis for contemporary analytic pragmatist rethinkings of the Kantian idea of categories, the significance of modal vocabulary, and the metaphysics of universals. The lectures are drawn from Brandom’s most recent books Perspectives on Pragmatism: Classical, Recent, and Contemporary [Harvard University Press, 2011] and From Empiricism to Expressivism: Brandom Reads Sellars [Harvard University Press, forthcoming in 2014]. century
vocabulary. I will refer to this aspect of the analytic project as its commitment to ‘semantic logicism’. If we ask which were the vocabulary-kinds whose semantic relations it was thought to be important to investigate during this period, at least two core programs of classical analytic philosophy show up: empiricism and naturalism. These venerable modern philosophical traditions in epistemology and ontology respectively were transformed in the twentieth century, first by being transposed into a semantic key, and second by the application of the newly available logical vocabulary to the self-consciously semantic programs they then became. As base vocabularies, different species of empiricism appealed to phenomenal vocabulary, expressing how things appear, or to secondary-quality vocabulary, or, less demandingly, to observational vocabulary. Typical target vocabularies include objective vocabulary formulating claims about how things actually are (as opposed to how they merely appear), primary-quality vocabulary, theoretical vocabulary, and modal, normative, and semantic vocabularies. The generic challenge is to show how what is expressed by the use of such target vocabularies can be reconstructed from what is expressed by the base vocabulary, when it is elaborated by the use of logical vocabulary. As base vocabularies, different species of naturalism appealed to the vocabulary of fundamental physics, or to the vocabulary of the natural sciences (including the special sciences) more generally, or just to objective descriptive vocabulary, even when not regimented by incorporation into explicit scientific theories. Typical targets include normative, semantic, and intentional vocabularies. II. The Pragmatist Challenge
As a writer of the laughing Santa vocabulary, the task of the automaton is to produce only licit strings of that vocabulary, by a process that can produce any and all such strings. It begins in its initial state, State 1, and emits an ‘h’ (its only available move), changing to State 2. In this state, it can produce either an ‘a’ or an ‘o’—it selects one at random—and goes into State 3. In this state, it can either tack on an exclamation point, and move into its final state, State 4, finishing the process, or emit another ‘h’ and return to State 2 to repeat the process. In any case, whenever it reaches State 4 and halts, the string it has constructed will be a member of the laughing Santa vocabulary. I hope this brief rehearsal makes it clear how the constellation of nodes and arrows that makes up this directed graph represents the abilities to read and write (recognize and produce arbitrary strings of) the laughing Santa vocabulary. What it represents is abilities that are to deploy that vocabulary—that is, read and write it, in the attenuated sense appropriate to this purely syntactic case. And the digraph representation is itself a vocabulary that is to specify those vocabulary-deploying abilities. That is, the digraph representation of this finite-state automaton is a pragmatic metavocabulary for the laughing Santa vocabulary. The relation between the digraph vocabulary and the laughing Santa vocabulary is, then, a pragmatically mediated—not now semantic, but syntactic—relation between vocabularies. It may seem that I am stretching things by calling the digraph form of representation a ‘vocabulary’. It will be useful, as a way of introducing my final point in the vicinity, to consider a different form of pragmatic metavocabulary for the laughing Santa vocabulary. Besides the digraph representation of a finite-state automaton, we can also use a state-table representation. For the laughing Santa automaton this is: State 1 State 2 State 3
Context-Free A<anything> Push-Down Automaton Context-Sensitive c1Ac2c1<anything>c2 Linear Bounded Automaton Recursively Enumerable No Restrictions on Rules Turing Machine (= 2 Stack PDA) The point I want to make fortunately does not require us to delve very deeply into the information summarized in this table. A few basic points will suffice. The first thing to realize is that not all vocabularies in the syntactic sense we have been pursuing can be read and written by finite-state automata. For instance, it can be shown that no finite-state automaton is to deploy the vocabulary anbn, defined over the alphabet {a,b}, which consists of all strings of any arbitrary number of ‘a’s followed by the same number of ‘b’s. The idea behind the proof is that in order to tell whether the right number of ‘b’s follow the ‘a’s (when reading) or to produce the right number of ‘b’s (when writing), the automaton must somehow keep track of how many ‘a’s have been processed (read or written). The only way an FSA can store information is by being in one state rather than another. So, it could be in one state—or in one of a class of states—if one ‘a’ has been processed, another if two have, and so on. But by definition, a finite-state automaton only has a finite number of states, and that number is fixed in advance of receiving its input or producing its output. Whatever that number of states is, and whatever system it uses to code numbers into states (it need not be one-to-one—it could use a decimal coding, for instance), there will be some number of ‘a’s that is so large that the automaton runs out of states before it finishes counting. But the vocabulary in question consists of arbitrarily long strings of ‘a’s and ‘b’s. In fact, it is possible to say exactly which vocabularies finite-state automata (specifiable by digraphs and state-tables of the sort illustrated above) are capable of deploying. These are called the ‘regular’ vocabularies (or languages).
A further development of what I want to claim will be retrospectively recognizable as the same line of thought can be found in Frege. His use of Latin letters and his logical sign of generality (used in conjunction with the notation for hypotheticals) express relations between concepts. It has always been an embarrassment for the anachronistic extensional quantificational reading of this notation (due originally to Russell) that Frege says of it, when he first introduces it in the Begriffsschrift, that it is the right way to express causal relations of necessitation. For it is a commonplace of the later logistical tradition that merely quantificational relations between concepts cannot distinguish between contingent regularities and lawlike, necessary ones. For that, explicit modal operators must be applied to the quantified conditionals. But Frege deploys his notation so that the relations between concepts expressed by generalized conditionals already have modal force. Relations between concepts of the sort logic lets us express have consequences for relations between their extensions, of the sort our quantificational notation expresses, but his generality locutions (the use of Latin letters and the concavity with German ones) codify relations we think of as intensional. Fregean logical concepts are indeed second- and higher-order concepts, but more than that, the universality they express is rulish. They are in the first instance principles in accordance with which to reason, and only derivatively premises from which to reason. In addition to permitting the formulation of purely logical relations among logical concepts, Frege’s logical vocabulary permits us to assert necessary connections among empirical concepts that themselves can only be discovered empirically: physically or causally necessary connections. In the Preface to the Begriffsschrift, Frege says: It seems to me to be easier still to extend the domain of this concept-script [Begriffsschrift] to include geometry. We would only have to add a few signs for the intuitive relations that occur there…The transition to the pure theory of motion and then to mechanics and physics could follow at this point. The latter two fields, in which besides rational necessity [Denknotwendigkeit] natural necessity [Naturnotwendigkeit] asserts itself, are the first for which we can predict a further development of the notation as knowledge progresses.