the logic of language language from within volume ii jan 2010

[...]... strictly mathematical perspective but also, and perhaps even more so, when seen in the context of human language and cognition In that 4 The Logic of Language context, the serene purity created by the mathematics of logic is drawn into the realm of the complexities of the human mind and the mundane needs served by human language But before we embark upon an investigation of the complexities and the mundane... long as the objects and the state of affairs 10 The Logic of Language involved remain the same, the predicates can do their entailment work We thus require of the relation of NATURAL ENTAILMENT from P to Q that it be subject to the condition that the preservation of truth rests on the meaning of the predicates in the entailing sentence P and on their structural position in P Henceforth, unless otherwise... thus also of entailment—as systematic consequences of certain logical constants Of course, the question arises of what motivates the particular selection of the logical constants involved and of the operations they allow for, given their semantic definition A good answer is that the choice of the relevant constants and of the operations on the expressions in which they occur is guided by the intuitive... investigation of the logic inherent in natural cognition and natural language will help clarify the hitherto opaque relation between logic on the one hand and language and cognition on the other (Ask any logician what this relation amounts to and you will get a curiously strange gamut of replies, all of them unsatisfactory.) This is, in itself, surprising 2 The Logic of Language because language and logic. .. propositional logic, though with occasional glances at multivalence and presuppositions But the reader will discover that, even within these limits, there is plenty of room for innovative uncluttering A further reason why logic is important for the study of language lies in the fact that the syntax of the formulae of the various predicate -logic systems considered is essentially the same as that of the semantic... seems to miss the point of the present study, which is the logical system of cognition and of the object language, the system that safeguards consistency through discourse Standard logic may provide a suitable descriptive metalanguage for the meanings of natural language logical operators (as for well-nigh anything else), but it does not provide a model for the logic of Logic and entailment 13 language. .. independence of any possible contingent situation In the actual practice of modern logic, logical entailments are taken to follow from the logical system in the logical language used And since this logical language consists of logical constants and variables, it is ultimately the constants that define the entailments But this is not quite the same as saying, as we do, that the entailments are due to the MEANING(S)... based on mathematics, in particular on standard Boolean set theory, whereas what is required for a proper understanding of the relations between logic, language, and thinking is a logic based on natural cognitive and linguistic intuitions We are in need of a ‘natural’ logic of language and cognition drawn from the facts not of mathematics but of language The first purpose of writing about logic in this... expressions in the logical language and the well-defined semantic properties of the logical constants 6 The Logic of Language When one accepts the dependency on the meanings of the logical constants involved, one may say that logic is an exercise in analytical necessity This basic adherence to the twentieth-century notion of what constitutes a logic is motivated not only by the fact that it is clear... by the consideration that it allows us to re-inspect the ‘peasant roots’ of logic, as found in the works of Aristotle and his ancient successors, from a novel point of view Traditional logicians only had natural intuitions of necessary consequence and consistency to fall back on for the construction of their logical systems, lacking as they did the sophisticated framework of modern mathematical set theory . bringing together the logical, the psychological, and the pragmatic; the empirical and the theoretical; the formalist and the empiricist; and situating it all in the context of two and a half millennia of. of two and a half millennia of language study. Volume I: Language in Cognition Volume II: The Logic of Language This page intentionally left blank The Logic of Language PIETER A. M. SEUREN 1 3 Great. these limits, there is plenty of room for innovative uncluttering. A further reason why logic is important for the study of language lies in the fact that the syntax of the formulae of the various