## Vagueness and Truth

### BibTeX

@MISC{Colyvan_vaguenessand,

author = {Mark Colyvan},

title = {Vagueness and Truth},

year = {}

}

### OpenURL

### Abstract

In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and consider reasons for subscribing to the principle of uniform solution. 1 Introducing the Principle of Uniform Solution It would be very odd to give different responses to two paradoxes depending on minor, seemingly-irrelevant details of their presentation. For example, it would be unacceptable to deal with the paradox of the heap by invoking a multi-valued logic, ̷L∞, say, and yet, when faced with the paradox of the bald man, invoke a supervaluational logic. Clearly these two paradoxes are of a kind—they are both instances of the sorites paradox. And whether the sorites paradox is couched in terms of heaps and grains of sand, or in terms of baldness and the number of hairs on the head, it is essentially the same problem and therefore must be solved by the same means. More generally, we might suggest that similar paradoxes should be resolved by similar means. This advice is sometimes elevated to the status of a principle, which usually goes by the name of the principle of uniform solution. This principle and its motivation will occupy us for much of the discussion in this paper. In particular, I will defend a rather general form of this principle. I will argue that two paradoxes can be thought to be of the same kind because (at a suitable level of abstraction) they share a similar internal structure, or because of external considerations such as the relationships of the paradoxes in question to other paradoxes in the vicinity, or the way they respond to proposed solutions. I will then use this reading of the principle of uniform solution to make a case for the sorites and the liar paradox being of a kind.

### Citations

58 |
The foundations of mathematics, in
- Ramsey
- 1926
(Show Context)
Citation Context ... between Russell and Ramsey about the liar and Russell’s paradoxes. 2 The Liar and Russell’s Paradoxes Russell and Ramsey disagreed about whether the liar and Russell’s paradox were of a kind. Ramsey =-=[20]-=- stressed that the liar, along with Grelling’s paradox, Berry’s paradox and other definability paradoxes, were linguistic, in that they relied upon thought or language. He argued that the “fault” was ... |

16 |
The Liar and Sorites paradoxes: Toward a unified treatment
- Tappenden
- 1993
(Show Context)
Citation Context ...nvelope paradox a St. Petersburg paradox [7]? Are the St. Petersburg and the Pasadena Paradoxes of a kind [4, 14]? And, as we will consider in the next section, are the sorites and the liar of a kind =-=[2, 8, 11, 12, 24]-=-? To answer these questions we need something more discriminating than the inclosure schema. This is not a failing of the inclosure schema, of course. It was never intended to answer such question. To... |

10 |
The Principles of Mathematics. George Allen and Unwin
- Russell
- 1903
(Show Context)
Citation Context ...e paradoxes of set theory as only relying on logical notions (such as set membership and number). 2 He thus saw two quite different kinds of paradox here: linguistic and logical/mathematical. Russell =-=[21]-=-, on the other hand, focussed more on the underlying structure of the paradoxes and saw them all as paradoxes of impredicativity. And we might add as a further consideration in favour of Russell, both... |

7 |
Prisoner’s dilemma is a Newcomb problem
- Lewis
- 1979
(Show Context)
Citation Context ...ggesting that those that fit the schema should be treated similarly. But we can reasonably ask about the similarity of paradoxes that do not fit the schema. Is the Prisoners Dilemma a Newcomb problem =-=[13]-=-? Is the two envelope paradox a St. Petersburg paradox [7]? Are the St. Petersburg and the Pasadena Paradoxes of a kind [4, 14]? And, as we will consider in the next section, are the sorites and the l... |

6 |
Paradox without self-reference', Analysis 53
- Yablo
- 1993
(Show Context)
Citation Context ... or cycles of reference. But the paradox is definitely liar like. Indeed, it is a kind of limiting case of longer and longer liar cycles. Why this paradox is so important is that if, as Stephen Yablo =-=[25]-=- originally suggested, 6 it is non self-referential yet liar like, then self reference does not seem to be the culprit after all. The source of the trouble in the so-called paradoxes of self-reference... |

4 |
The search for certainty: a philosophical account of foundations of mathematics
- Giaquinto
- 2002
(Show Context)
Citation Context ...liar paradoxes admit extended forms (cyclical liar and cyclical set theory paradoxes) that appear to be generated by the same formal feature: essentially the violation of the vicious circle principle =-=[9]-=-. 3 So on one way of looking at the liar and Russell’s paradox, we see a difference: one is about truth the other about set membership. But on another way of looking at them, they are of a kind: they ... |

4 | From heaps and gaps to heaps of gluts. Mind - Hyde - 1997 |

3 |
The St. Petersburg two-envelope paradox
- Chalmers
- 2002
(Show Context)
Citation Context ...imilarly. But we can reasonably ask about the similarity of paradoxes that do not fit the schema. Is the Prisoners Dilemma a Newcomb problem [13]? Is the two envelope paradox a St. Petersburg paradox =-=[7]-=-? Are the St. Petersburg and the Pasadena Paradoxes of a kind [4, 14]? And, as we will consider in the next section, are the sorites and the liar of a kind [2, 8, 11, 12, 24]? To answer these question... |

3 |
The structure of the paradoxes of self-reference. Mind
- Priest
- 1994
(Show Context)
Citation Context ...very least a set-theoretic analogue of the liar paradox. 8 There is also the substantial issue of the level of abstraction at which the structural similarities are revealed. See Smith [22] and Priest =-=[15, 17]-=- on this issue. 6s4 What Comes First, the Diagnosis or the Treatment? Let me return to the medical analogy that I used to motivate the principle of uniform solution: we want to treat the disease and n... |

3 |
Yablo's Paradox. Analysis 57
- Priest
- 1997
(Show Context)
Citation Context ... Yablo’s paradox is not circular, it fails to fit the inclosure schema and thus fails to be classified as a kind with the liar. But everyone agrees that this paradox is liar like. Some such as Priest =-=[16]-=- and Beall [1] suggest that, despite initial appearances, the paradox is self-referential because a fixed-point construction is required in the derivation of the paradoxical conclusion. They argue tha... |

3 |
Yablo's Paradox and Kindred Infinite Liars. Mind 107
- Sorensen
- 1998
(Show Context)
Citation Context ...n. There are many interesting points arising from this debate. First, those who argue that Yablo’s paradox is in fact circular, do so by invoking a quite 6 And more recently supported by Roy Sorensen =-=[23]-=- and Bueno and Colyvan [3]. 5sdifferent notion of circularity than the more intuitive notion, appealed to in liar cycles. After all, “requiring a fixed-point construction in the derivation of the para... |

2 |
Is Yablo’s paradox non-circular? Analysis 61(3):176–187
- Beall
- 2001
(Show Context)
Citation Context ...x is not circular, it fails to fit the inclosure schema and thus fails to be classified as a kind with the liar. But everyone agrees that this paradox is liar like. Some such as Priest [16] and Beall =-=[1]-=- suggest that, despite initial appearances, the paradox is self-referential because a fixed-point construction is required in the derivation of the paradoxical conclusion. They argue that the Yablo li... |

2 |
Relative Expectation Theory’, The Journal of Philosophy, forthcoming
- Colyvan
- 2008
(Show Context)
Citation Context ... also clear that this principle has broad applications, across all areas of philosophy where paradoxes arise: philosophy of logic, decision theory, ethics, philosophy of space and time and so on. See =-=[5]-=- for a recent implicit appeal to the principle to a family of paradoxes in decision theory. 2sof the bald man the same paradox? And what is the underlying pathology. Clearly both these paradoxes share... |

2 | Beyond the Limits of Thought, second edition - Priest - 2002 |

1 |
Reply to Beall and
- Hyde
(Show Context)
Citation Context ...nvelope paradox a St. Petersburg paradox [7]? Are the St. Petersburg and the Pasadena Paradoxes of a kind [4, 14]? And, as we will consider in the next section, are the sorites and the liar of a kind =-=[2, 8, 11, 12, 24]-=-? To answer these questions we need something more discriminating than the inclosure schema. This is not a failing of the inclosure schema, of course. It was never intended to answer such question. To... |

1 |
Are the Sorites and the Liar Paradox of a Kind
- Hyde
(Show Context)
Citation Context ...nvelope paradox a St. Petersburg paradox [7]? Are the St. Petersburg and the Pasadena Paradoxes of a kind [4, 14]? And, as we will consider in the next section, are the sorites and the liar of a kind =-=[2, 8, 11, 12, 24]-=-? To answer these questions we need something more discriminating than the inclosure schema. This is not a failing of the inclosure schema, of course. It was never intended to answer such question. To... |

1 |
Vexing Expectations’, Mind 113
- Nover, Hájek
- 2004
(Show Context)
Citation Context ...oxes that do not fit the schema. Is the Prisoners Dilemma a Newcomb problem [13]? Is the two envelope paradox a St. Petersburg paradox [7]? Are the St. Petersburg and the Pasadena Paradoxes of a kind =-=[4, 14]-=-? And, as we will consider in the next section, are the sorites and the liar of a kind [2, 8, 11, 12, 24]? To answer these questions we need something more discriminating than the inclosure schema. Th... |

1 | On the Principle of Uniform Solution: A Reply to Smith
- Priest
(Show Context)
Citation Context ...very least a set-theoretic analogue of the liar paradox. 8 There is also the substantial issue of the level of abstraction at which the structural similarities are revealed. See Smith [22] and Priest =-=[15, 17]-=- on this issue. 6s4 What Comes First, the Diagnosis or the Treatment? Let me return to the medical analogy that I used to motivate the principle of uniform solution: we want to treat the disease and n... |

1 |
The Principle of Uniform Solution (of the
- Smith
(Show Context)
Citation Context ...radox is at the very least a set-theoretic analogue of the liar paradox. 8 There is also the substantial issue of the level of abstraction at which the structural similarities are revealed. See Smith =-=[22]-=- and Priest [15, 17] on this issue. 6s4 What Comes First, the Diagnosis or the Treatment? Let me return to the medical analogy that I used to motivate the principle of uniform solution: we want to tre... |