Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued (...) that this assumption needs to be qualified and that Carnap was actually far from following Tarski when he decided to complement his syntactic method with a semantic one. Carnap and Tarski had different goals, divergent programs, and dissenting views on truth and semantics. After exploring several possible methods for the explication of logical concepts such as L-truth and L-implication, Carnap opted for definitions based on concepts he had found in Wittgenstein’s Tractatus and Waismann’s work on a logical interpretation of probability. Carnap’s reasons for taking a semantic turn are to be understood in the context of his principle of tolerance. He first hoped he could use Tarski’s technique to recover in the semantic setting the completeness result he had tried to establish in the Logical Syntax. His eventual adoption of non-Tarskian semantics can be accounted for by his program of a logical analysis of science—including empirical science—and his ambition to elaborate a unified logical framework for deductive, inductive, and modal logic, and for explicating analyticity. (shrink)

In this first paper of a series of works on the foundations of science, we examine the significance of logical and mathematical frameworks used in foundational studies. In particular, we emphasize the distinction between the order of a language and the order of a structure to prevent confusing models of scientific theories with first-order structures, and which are studied in standard model theory. All of us are, of course, bound to make abuses of language even in putatively precise contexts. This (...) is not a problem—in fact, it is part of scientific and philosophical practice. But it is important to be sensitive to the dierent uses that structure, model, and language have. In this paper, we examine these topics in the context of classical logic; only in the last section we touch upon briefly on non-classical ones. (shrink)

I offer a formal ontological theory where the basic building blocks of the world are timeless events. The composition of events results in processes. Spacetime emerges as the system of all events. Things are construed as bundles of processes. I maintain that such a view is in accord with General Relativity and offers interesting prospects for the foundations of classical and quantum gravity.

Dispositional essentialism maintains that all sparse properties are essentially powerful. Two conceptions of sparse properties appear compatible with dispositional essentialism: sparse properties as pure powers or as powerful qualities. This paper compares the two views, criticizes the powerful qualities view, and then develops a new theory of pure powers, termed Point Theory. This theory neutralizes the main advantage powerful qualities appear to possess over pure powers—explaining the existence of powers during latency periods. The paper discusses the relation between powers and (...) space-time points, whether pure powers need to occupy space, and how to account for the movement of pure powers through space-time. Given Point Theory, dispositional essentialists should maintain that sparse properties are pure powers. (shrink)

Temporal betweenness in space-time is defined solely in terms of light signals, using a signalling relation that does not distinguish between the sender and the receiver of a light signal. Special relativity and general relativity are considered separately, because the latter can be treated only locally. We conclude that the (local) coherence of time can be described if we know only which pairs of space-time points are light-connected. Other consequences in the case of special relativity: (1) a categorical axiom system (...) exists in terms of nondirected light connection alone, with neither particle nor time order as a primitive concept, though we do not actually present the axioms; (2) any concept definable by coordinates is also definable in terms of nondirected light signals if and only if it is invariant under Lorentz transformations, translations, dilations, space reflections, and time reflections; and (3) any transformation of space-time (not necessarily continuous) which preserves nondirected light connection is a product of transformations just listed above. The bulk of the paper is devoted to proving that the definitions we give correspond to their intended interpretations in the usual space-time continua. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field. Our approach was inspired by the work of Whitehead, though our (...) philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

Continuity is perhaps the most familiar characterization of the finitary character of the operations performed in computation. We sketch the historical and conceptual development of this notion by interpreting it as a unifying theme across three main varieties of semantical theories of programming: denotational, axiomatic and event-based. Our exploration spans the development of this notion from its origins in recursion theory to the forms it takes in the context of the more recent event-based analyses of sequential and concurrent computations, touching (...) upon the relations of continuity with non-determinism. (shrink)