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Switch to: Citations
References in:
Properties and the Interpretation of Second-Order Logic
Philosophia Mathematica 21 (2):133-156 (2013)
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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 (...) |
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The classic, influential essay in 'descriptive metaphysics' by the distinguished English philosopher. |
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Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...) |
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This is a book about the concept of a physical thing and about how the names of things relate to the things they name. It questions the prevalent view that names 'refer to' or 'denote' the things they name. Instead it presents a new theory of proper names, according to which names express certain special properties that the things they name exhibit. This theory leads to some important conclusions about whether things have any of their properties as a matter of (...) |
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