This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

There are two principles which bear the name Frege''sprinciple: the principle of compositionality, and the contextprinciple. The aim of this contribution is to investigate whether thisis justified: did Frege accept both principles at the same time, did hehold the one principle but not the other, or did he, at some moment,change his opinion? The conclusion is as follows. There is a developmentin Frege''s position. In the period of Grundlagen he followed to a strict form of contextuality. He repeatedcontextuality in later (...) writings, but became less strict. From 1914 on,pushed by the needs of research, he comes close to compositionality. Buthe could never make the final step toward compositionality forprincipled reasons, therefore he always would reject compositionality. (shrink)

We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics (...) includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language. (shrink)

The paper argues that cognitive states of biological systems are inherently temporal. Three adequacy conditions for neuronal models of representation are vindicated: the compositionality of meaning, the compositionality of content, and the co-variation with content. Classicist and connectionist approaches are discussed and rejected. Based on recent neurobiological data, oscillatory networks are introduced as a third alternative. A mathematical description in a Hilbert space framework is developed. The states of this structure can be regarded as conceptual representations satisfying the three conditions.

In this essay I will consider two theses that are associated with Frege,and will investigate the extent to which Frege really believed them.Much of what I have to say will come as no surprise to scholars of thehistorical Frege. But Frege is not only a historical figure; he alsooccupies a site on the philosophical landscape that has allowed hisdoctrines to seep into the subconscious water table. And scholars in a widevariety of different scholarly establishments then sip from thesedoctrines. I believe (...) that some Frege-interested philosophers at various ofthese establishments might find my conclusions surprising.Some of these philosophical establishments have arisen from an educationalmilieu in which Frege is associated with some specific doctrine at theexpense of not even being aware of other milieux where other specificdoctrines are given sole prominence. The two theses which I will discussillustrate this point. Each of them is called Frege''s Principle, but byphilosophers from different milieux. By calling them milieux I do not want to convey the idea that they are each located at some specificsocio-politico-geographico-temporal location. Rather, it is a matter oftheir each being located at different places on the intellectuallandscape. For this reason one might (and I sometimes will) call them(interpretative) traditions. (shrink)