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In a 2005 paper, John Burgess and Gideon Rosen offer a new argument against nominalism in the philosophy of mathematics. The argument proceeds from the thesis that mathematics is part of science, and that core existence theorems in mathematics are both accepted by mathematicians and acceptable by mathematical standards. David Liggins (2007) criticizes the argument on the grounds that no adequate interpretation of “acceptable by mathematical standards” can be given which preserves the soundness of the overall argument. In this discussion (...) 

Many contemporary philosophers rate error theories poorly. We identify the arguments these philosophers invoke, and expose their deficiencies. We thereby show that the prospects for error theory have been systematically underestimated. By undermining general arguments against all error theories, we leave it open whether any more particular arguments against particular error theories are more successful. The merits of error theories need to be settled on a casebycase basis: there is no good general argument against error theories. 

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 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. 