“Induction, Conceptual Spaces, and Homotopy: A Response on Carnap’s Behalf”
Abstract: Despite logical empiricism falling out of favor in the second half of the 20th century, a resurgence of historical interest beginning in the 1980's has led to the recognition of the diversity of views within the movement and a reexamination of the objections mounted against its participants. This has led to a growing body of literature defending Carnap against several of his detractors and resuscitating much of his work, such as Awodey & Carus , Justus , and Price . This paper is a contribution to this Carnap revivalism, proposing a mathematically updated version of Carnap's inductive logic.
Goodman's new riddle of induction, one of the problems which plagued logical empiricism, continues to shape discourse in areas ranging from philosophy of science to artificial intelligence. It is argued in Gärdenfors  that the problem of projectability – that of delineating predicates such as "green" which can be used for inductive projections from those such as "grue" which cannot – is as much a problem for a computational theory of induction as it was for logical empiricism. According to Gärdenfors, the problem arises because of the use of solely linguistic or propositional formulations of projectible predicates which treat all predicates symmetrically, whereas what is needed is a formulation that does not preserve these symmetries. What he proposes is a non-linguistic formulation of natural properties based on conceptual spaces, where a property is taken to be a region of a conceptual space and that property is natural (i.e., projectible) if it is convex. While this provides a workable solution for a computational theory of induction, Gärdenfors claims that the logical empiricists could not make such a move to fend off Goodman's riddle.
However, Sznajder  has recently argued that the connection between Gärdenfors's conceptual spaces and Carnap's attribute spaces helps toward revitalizing Carnap's late inductive logic. Moreover, recent advances in the foundations of mathematics have led to an interpretation of Martin-Löf's dependent type theory, termed homotopy type theory, where types are interpreted as spaces using the notions of abstract homotopy theory. What I aim to do here is further this revitalization of Carnap's inductive logic by arguing that a type-theoretic explication of attribute spaces would be a step forward in developing a computational theory of induction. Along the way, I will address some potential objections by appealing to the features of homotopy type theory as well as Carnap's metaphilosophical standards, making my approach distinctively a defense of Carnap rather than one more generally of logical empiricism. Since Gärdenfors has framed the problem of projectability as a problem of knowledge representation, the upshot is two-fold: the response not only contributes to the Carnap literature, but additionally motivates a positive research program in inductive logic and artificial intelligence. I will conclude by discussing the potential benefits for philosophical practice and the work that remains to be done.
“Belief, Acceptance and Pragmatic Equivalence”
Abstract: The early twentieth century saw the rise of what can be labeled broadly as structuralist accounts of scientific representation, espoused by notable physicists and philosophers, such as Hertz, Boltzmann, Heisenberg, Russell, and Carnap. These accounts attempt a more metaphysically deflated view of what our scientific theories represent: through science we are only able to learn the structure of the world we investigate, and the key vehicle for representing this structure is mathematics. Numerous problems have plagued structuralist accounts, in particular the question of how our theories, being mathematical entities, come to have this representative relation with the target phenomena. In his 2008 book Scientific Representation: Paradoxes of Perspective, Bas C. van Fraassen dedicates a chapter to formulating an empiricist structuralism that evades these central problems. Crucial to his account are the notions of indexicality and pragmatic equivalence: he argues that from the standpoint of the scientist representing a phenomenon with a theoretical model, there is a pragmatic equivalence between asserting the model represents the data and the model represents the phenomena. This argument has come under some criticism. James Nguyen (2016) challenges the idea that this pragmatic equivalence holds, arguing that if a scientist believes that the theoretical model accurately represents the data, this does not doxastically or pragmatically commit her to holding that the model accurately represents the target phenomenon. I believe Nguyen’s criticism falls to the side due to his mischaracterization of van Fraassen’s argument. His mischaracterization, however, may be understandable as van Fraassen’s language surrounding epistemological terms like ‘belief’ is not always consistent, and thus belief’s relation to acceptance, another cognitive attitude van Fraassen makes use of, is not straightforward. I argue that by importing the conceptual distinction between belief and acceptance from J. L. Cohen (1989) can help clarify and strengthen van Fraassen’s empiricist structuralism. I suggest that the strongest version of van Fraassen’s argument makes use of the properties of the attitude Cohen labels as “acceptance” and which he holds to be the appropriate attitude in science. This view of ‘acceptance’ is not identical to van Fraassen’s own use of the term, but I argue that Cohen’s ‘acceptance’ serves van Fraassen’s constructive empiricism well. If we are to understand van Fraassen’s argument for empiricist structuralism as holding acceptance as indispensable from a scientist’s aims in producing empirically adequate scientific representations, then it becomes clear just how the scientist involved in representing incurs pragmatic commitments. I believe this recasting of van Fraassen’s argument, if not adequately reflecting his own aims, renders it unscathed by Nguyen’s criticisms and overall strengthens his formulation of empiricist structuralism.
“Carnap's Pragmatic Expressivism and the Syntactic-Semantic View of Theories”
Abstract: The syntactic-semantic dispute of scientific theories has recently come to a head, with the claim that it is a distinction without a formal difference (Sebastian Lutz, "What was the Syntactic-Semantic Debate in Philosophy of Science About?", Philosophy and Phenomenological Research, 2017). Even proponents of the syntactic view think the point of the debate has become unclear, and think that instead of focusing on what theories are, we should focus on what different explications of theories are good for different purposes (Hans Halvorson, Logic in Philosophy of Science, Cambridge University Press, 2019, p277). Thus the debate shifts from a debate over syntactic versus semantic interpretations of theories, to a debate over the pragmatic virtues of these interpretations for a given purpose. This shift is a return to the approach of a leading early proponent of the syntactic view, Rudolf Carnap. Carnap emphasized that the frameworks and logics we use are a pragmatic choice (Rudolf Carnap, Logical Syntax of Language, 1937, and "Empiricism, Semantics, and Ontology", 1956). Carnap's pragmatism about frameworks and logic is sometimes lost in opponents' rigid characterization of the syntactic view (Lutz, 2017). One worry is that emphasizing pragmatic features and norms maintains a rigid separation between the pragmatic aspects of a theory and its content. This risks favoring pragmatic interpretations against syntactic interpretations. I argue we can dispel this worry by construing theories expressively.
A recent paper argues Carnap was a proto-expressivist (Vera Flocke, "Carnap's Non-Cognitivism About Ontology", Nous, 2020). This interpretation takes Carnap's approach as analogous to Gibbard's norm expressivism, where frameworks are norm-world pairs for how to interpret sentences. Taking this approach for scientific theories, norms specify what is in the scientific theories, as well as how to interpret their logical and empirical content. We may take pragmatic features and scientific practices as supplying the norms for the interpretation of a scientific theory, as well as what the theory takes as its content. For instance, Carnap's preferred approach to the empirical criterion of meaningfulness is itself a pragmatic proposal, which we may include as a rule internal to the theory (Rudolf Carnap, "Methodological Character of Theoretical Concepts", 1956, and James Justus,"Carnap's Forgotten Criterion of Empirical Significance", Mind, 2014). Internal to the theory, there is no principled separation between the norms and the formal aspects of the theory. Externally there is a separation between norms and theories only insofar as we choose which norms we wish to include in the theory. This external selection is itself pragmatic. But pragmatic aspects favoring a theory's selection are compatible with those pragmatic aspects specifying which norms to include internal to the theory.