Theories of Abstract Objects without Ad Hoc Restriction

Erkenntnis 74 (1):1-15 (2011)
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The ideas of fixed points (Kripke in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 53–81, 1975; Martin and Woodruff in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 47–51, 1984) and revision sequences (Gupta and Belnap in The revision theory of truth. MIT, London, 1993; Gupta in The Blackwell guide to philosophical logic. Blackwell, London, pp 90–114, 2001) have been exploited to provide solutions to the semantic paradox and have achieved admirable success. This happy situation naturally encourages one to look for other philosophical areas of their further applications where paradoxical results seem to follow from intuitively acceptable principles. In this paper, I propose to extend the use of these ideas to give two new treatments of abstract objects. Sections 1 and 2 below check several abstractionist theories and their main defects. Section 3 shows how the two ideas can be applied to generate consistent theories of abstract objects without any ad hoc restriction on any principle.



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Citations of this work

Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.
The revision theory of truth.Philip Kremer - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Recent essays on truth and the liar paradox.Robert Lazarus Martin (ed.) - 1984 - New York: Oxford University Press.
On representing ‘true-in-L’ in L.Robert L. Martin - 1975 - Philosophia 5 (3):213-217.

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