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A Problem with the Dependence of Informal Proofs on Formal Proofs
Tanswell, F., 2015-09-22 14:46:19 PM
Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction.When Do Some Things Form a Set?
Hewitt, S., 2015-09-22 14:46:19 PM
This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle which pluralities form sets, the paper concludes by affirming a naturalistic approach to the philosophy of set theory.The Representational Foundations of Computation
Rescorla, M., 2015-09-22 14:46:19 PM
Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional enterprise: it studies entities as represented in certain ways, rather than entities detached from any means of representing them.Mathematical Structuralism, Modal Nominalism, and the Coherence Principle
Schwartz, J. S. J., 2015-09-22 14:46:19 PM
According to Stewart Shapiro's coherence principle, structures exist whenever they can be coherently described. I argue that Shapiro's attempts to justify this principle (along with his position, ante rem structuralism) are circular, as he relies on criticisms of modal nominalism which presuppose the coherence principle. I argue further that when the coherence principle is not presupposed, his reasoning more strongly supports modal nominalism than ante rem structuralism.Identity in Homotopy Type Theory, Part I: The Justification of Path Induction
Ladyman, J., Presnell, S., 2015-09-22 14:46:19 PM
Homotopy Type Theory (HoTT) is a proposed new language and foundation for mathematics, combining algebraic topology with logic. An important rule for the treatment of identity in HoTT is path induction, which is commonly explained by appeal to the homotopy interpretation of the theory's types, tokens, and identities as (respectively) spaces, points, and paths. However, if HoTT is to be an autonomous foundation then such an interpretation cannot play a fundamental role. In this paper we give a derivation of path induction, motivated from pre-mathematical considerations, without recourse to homotopy theory.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 (hbk); 978-0-19-874803-8 (pbk); 978-0-19-164834-2 (e-book). Pp. ix + 298
Menzel, C., 2015-09-22 14:46:19 PM
Bernard Bolzano. Theory of Science. Volumes I-IV. Paul Rusnock and Rolf George, trans. Oxford: Oxford University Press, 2014. ISBN: 978-0-19-968438-0. Pp. 2044.
Sebestik, J., 2015-09-22 14:46:19 PM
Pavel Pudlak. Logical Foundations of Mathematics and Computational Complexity: A Gentle Introduction. Springer Monographs in Mathematics. Springer, 2013. ISBN: 978-3-319-00118-0 (hbk); 978-3-319-00119-7 (ebook). Pp. xiv + 695
Urquhart, A., 2015-09-22 14:46:19 PM
Mark van Atten. Essays on Godel's Reception of Leibniz, Husserl, and Brouwer. Logic, Epistemology, and the Unity of Science; 35. Dordrecht: Springer, 2015. ISBN 978-3-319-10030-2 (hbk); 978-3-319-10031-9 (e-book). Pp. xiv + 328
2015-09-22 14:46:19 PM
Gabriele Lolli, Marco Panza, and Giorgio Venturi, eds. From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Boston Studies in the Philosophy and History of Science; 308. Springer, 2015. ISBN 978-3-319-10433-1 (hbk); 978-3-319-10434-8 (e-book). Pp. xix + 336
2015-09-22 14:46:19 PM
Author Index--Volume 23
2015-09-22 14:46:19 PM



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