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Hilbertian reference

B. H. Slater

Noûs 22 (2):283-297 (1988)

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Arbitrary reference, numbers, and propositions.Michele Palmira - 2018 - European Journal of Philosophy 26 (3):1069-1085.details Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the problem by canvassing (...) Download Export citation Bookmark
Ramseying liars.Barry Hartley Slater - 2004 - Logic and Logical Philosophy 13:57-70.details Despite the volume of discussion on the Liar Paradox recently, there is one stream of largely British thought on the matter which is hardly represented in the wider literature. This paper points out salient aspects of the history of this tradition, from its origin in forms of propositional quantification found in Ramsey, through to more precise symbolisations which have emerged more recently. But its purpose is to exposit, with respect to a number of contested cases, the ensuing results. Thus it (...) Download Export citation Bookmark 5 citations
Routley’s formulation of transparency.B. H. Slater - 1992 - History and Philosophy of Logic 13 (2):215-224.details Routley?s Formula says, for instance, that if it is believed there is a man then there is something which is believed to be a man. In this paper I defend the formula; first directly, but then by looking at work by Gensler and Hintikka against it, and at the original work of Routley, Meyer and Goddard for it. The argument ultimately reduces to a central point about the extensionality of objects in Routley, Meyer and Goddard?s intensional system, i.e. in its (...) formulation of transparency. (shrink) Download Export citation Bookmark 1 citation
Grammar and sets.B. H. Slater - 2006 - Australasian Journal of Philosophy 84 (1):59 – 73.details 'Philosophy arises through misconceptions of grammar', said Wittgenstein. Few people have believed him, and probably none, therefore, working in the area of the philosophy of mathematics. Yet his assertion is most evidently the case in the philosophy of Set Theory, as this paper demonstrates (see also Rodych 2000). The motivation for twentieth century Set Theory has rested on the belief that everything in Mathematics can be defined in terms of sets [Maddy 1994: 4]. But not only are there notable items (...) Download Export citation Bookmark 1 citation
The Fallacy in Russell's Schema.Hartley Slater - 2002 - Russell: The Journal of Bertrand Russell Studies 22 (2).details An analysis of the paradoxes of self-reference, which Bertrand Russell initiated, exposes the common fallacy in them, and has consequences for some of Graham Priest's work. Notably it undermines his defence of the Domain Principle, and his consequent belief that there are true contradictions. Use of Hilbert's epsilon calculus shows, instead, that we must allow for indeterminacy of sense in connection with paradoxes of self-reference. Download Export citation Bookmark
The epsilon calculus' problematic.B. H. Slater - 1994 - Philosophical Papers 23 (3):217-242.details Download Export citation Bookmark 4 citations
De-mystieylng situations.B. H. Slater - 1997 - Philosophical Papers 26 (2):165-178.details Download Export citation Bookmark

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