Logics and languages
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This chapter introduces the concepts of signature and structure, and describes the semantics for first- and second-order logic. We outline three different but extensionally equivalent treatments of quantifiers and variables (the Tarskian approach, the Robinsonian approach, and a hybrid approach) and discuss their philosophical merits concerning compositionality, and Fine’s antinomy of the variable. We also outline two extensionally distinct semantics for second-order logic (Henkin, full). The appendix to the chapter presents the formal definitions of some theories of arithmetic and set theory that we employ frequently throughout the remainder of the book.
2018 ◽
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2013 ◽
Vol 23
(6)
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pp. 1234-1256
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1997 ◽
Vol 7
(2)
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pp. 251-265
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2012 ◽
Vol 18
(1)
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pp. 91-121
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