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Numbers and Propositions: Reply to Melia

Tim Crane

Analysis 52 (4):253-256 (1992)

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Chalmers and Semantics.Panu Raatikainen - 2021 - Theoria 87 (5):1193-1221.details David Chalmers’ two-dimensionalism is an ambitious philosophical program that aims to “ground” or “construct” Fregean meanings and restore “the golden triangle” of apriority, necessity, and meaning that Kripke seemingly broke. This paper aims to examine critically what Chalmers’ theory can in reality achieve. It is argued that the theory faces severe challenges. There are some gaps in the overall arguments, and the reasoning is in some places somewhat circular. Chalmers’ theory is effectively founded on certain strong philosophical assumptions. It is (...) Download Export citation Bookmark
Benacerraf’s revenge.Ben Caplan & Chris Tillman - 2013 - Philosophical Studies 166 (S1):111-129.details In a series of recent publications, Jeffrey King (The nature and structure of content, 2007; Proc Aristot Soc 109(3):257–277, 2009; Philos Stud, 2012) argues for a view on which propositions are facts. He also argues against views on which propositions are set-theoretical objects, in part because such views face Benacerraf problems. In this paper, we argue that, when it comes to Benacerraf problems, King’s view doesn’t fare any better than its set-theoretical rivals do. Finally, we argue that his view faces (...) Download Export citation Bookmark 11 citations
Propositions, numbers, and the problem of arbitrary identification.Joseph G. Moore - 1999 - Synthese 120 (2):229-263.details Those inclined to believe in the existence of propositions as traditionally conceived might seek to reduce them to some other type of entity. However, parsimonious propositionalists of this type are confronted with a choice of competing candidates – for example, sets of possible worlds, and various neo-Russellian and neo-Fregean constructions. It is argued that this choice is an arbitrary one, and that it closely resembles the type of problematic choice that, as Benacerraf pointed out, bedevils the attempt to reduce numbers (...) Download Export citation Bookmark 15 citations
Towards a Fictionalist Philosophy of Mathematics.Robert Knowles - 2015 - Dissertation, University of Manchesterdetails In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by (...) Download Export citation Bookmark

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