Chinese Research on Mathematical Logic and the Foundations of Mathematics

on the status of mixed methods research in applied linguistics

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Carnap on the Foundations of Logic and Mathematics

Throughout most of his philosophical career Carnap upheld and defended three distinctive philosophical positions: (1) The thesis that the truths of logic and mathematics are analytic and hence without content and purely formal. (2) The thesis that radical pluralism holds in pure mathematics in that any consistent system of postulates is equally legitimate and that there is no question of justif...

Second-order logic and foundations of mathematics

We discuss the differences between first-order set theory and secondorder logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if...

Second-Order Logic and Foundations of Mathematics

Mathematical Foundations of Logic and Functional Programming

As an introduction, we give some examples of logic programs and the intended semantics of them. A logic program is simply a (not necessarily finite!) set of program clauses. That is, there is no particular ordering of the clauses as in the case, say, imperative programs: a program here is just a set of constraints, a set of logical formulas describing the world in which the programming environm...