In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style ofPrincipia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics of (...) axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition and two proponents of the first-order tradition, we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory. (shrink)

Standard approaches to possible-world semantics allow us to define necessity and logical truth, but analyticity is considerably more difficult to account for. The source of this difficulty lies in the received model-theoretical conception of a language interpretation. In intuitive terms, analyticity amounts to truth in virtue of meaning alone, i.e. solely in virtue of the interpretation of linguistic expressions. In other words, an analytic sentence should remain true under all variations of ‘extralinguistic reality’ as long as the interpretation is kept (...) constant. However, the received conception of an interpretation as a mapping from language to a model frame hinders keeping the interpretation constant while varying other components of the model. To make room for analyticity, the concept of an interpretation should therefore be revised. The latter should be made richer in content than it has usually been assumed. As a by-product, this revision also gives us a one-dimensional analogue of the influential two-dimensional account of a priori. We are thus able to map out the network of formal connections between the notions of analyticity, apriority, logical truth and necessity. (shrink)

I. The function of models in the empirical sciencesII. Structure and purpose: conditions of a structural nature which models should satisfy in order to accomplish their function.III. Generalisation and specialisation of the classical definition of model, in view of the above requirements:the algebraic model conceptthe semantic model conceptthe syntactical model conceptIV. Attempt towards reunification: the concept of model on a pragmatic basis.

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

The sheer multitude of criteria of empirical significance has been taken as evidence that the pre-analytic notion being explicated is too vague to be useful. I show instead that a significant number of these criteria—by Ayer, Popper, Przełęcki, Suppes, and David Lewis, among others—not only form a coherent whole, but also connect directly to the theory of definition, the notion of empirical content as explicated by Ramsey sentences, and the theory of measurement; two criteria by Carnap and Sober are trivial, (...) but can be saved and connected to the other criteria by slight modifications. A corollary is that the ordinary language defense of Lewis, the conceptual arguments by Ayer and Popper, the theoretical considerations by Przełęcki, and the practical considerations by Suppes all apply to the same criterion or closely related criteria. Furthermore, the equivalence of some criteria allows for their individual justifications to be taken cumulatively and, together with the entailment relations between nonequivalent criteria, suggest criteria for general auxiliary assumptions, comparative criteria, and more liberal conceptions of observation. (shrink)

Marian Przełęcki’s semantics for the Received View is a good explication of Carnap’s position on the subject, anticipates many discussions and results from both proponents and opponents of the Received View, and can be the basis for a thriving research program.