David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Oxford University Press (1991)
The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today.
|Keywords||Logic, Symbolic and mathematical|
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|Call number||QA9.S48 1991|
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Christopher Menzel (2015). Logic, Essence, and Modality Bob Hale. Necessary Beings: An Essay on Ontology, Modality, & the Relations Between Them. Oxford University Press, 2013. ISBN: 978-0-19-966262-3 ; 978-0-19-874803-8 ; 978-0-19-164834-2 . Pp. Ix + 298. [REVIEW] Philosophia Mathematica 23 (3):407-428.
Theodore Sider (2013). Replies to Dorr, Fine, and Hirsch. Philosophy and Phenomenological Research 87 (3):733-754.
Salvatore Florio & Øystein Linnebo (2015). On the Innocence and Determinacy of Plural Quantification. Noûs 49 (1):1-19.
Fraser MacBride (2013). How Involved Do You Want to Be in a Non-Symmetric Relationship? Australasian Journal of Philosophy 92 (1):1-16.
Bradley Armour-Garb & James A. Woodbridge (2012). The Story About Propositions. Noûs 46 (4):635-674.
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