Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Logic, symbolic and mathematical. --- Mathematics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic.This book contains papers - many of them surveys by leading experts - of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7

Logic, Symbolic and mathematical --- Mathematics --- Math --- Science

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Logic, symbolic and mathematical. --- Reductionism. --- Cardinal numbers.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Fuzzy logic. --- Logic, Symbolic and mathematical.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal development of second‐ and higher‐order logic and an extended argument that higher‐order systems have an important role to play in the philosophy and foundations of mathematics. The development includes the languages, deductive systems, and model‐theoretic semantics for higher‐order languages, and the basic and advanced results in its meta‐theory: completeness, compactness, and the Löwenheim–Skolem theorems for Henkin semantics, and the failure of those results for standard semantics. Argues that second‐order theories and formalizations, with standard semantics, provide better models of important aspects of mathematics than their first‐order counterparts. Despite the fact that Quine is the main opponent of second‐order logic (arguing that second‐order logic is set‐theory in disguise), the present argument is broadly Quinean, proposing that there is no sharp line dividing mathematics from logic, especially the logic of mathematics. Also surveys the historical development in logic, tracing the emergence of first‐order logic as the de facto standard among logicians and philosophers. The connection between formal deduction and reasoning is related to Wittgensteinian issues concerning rule‐following. The book closes with an examination of several alternatives to second‐order logic: first‐order set theory, infinitary languages, and systems that are, in a sense, intermediate between first order and second order.

Logic --- Theory of knowledge --- Logic, Symbolic and mathematical. --- Logic, symbolic and mathematical