Abstract
It is well-known that in combination with further premises that look less controversial, the tolerance principle – the constraint that if Pa holds, and a and b are similar in P-relevant respects, Pb holds as well – leads to contradiction, namely to the sorites paradox. According to many influential views of the sorites paradox (e.g. Williamson 1994), we therefore ought to reject the principle of tolerance as unsound.
Except for the last section, this paper is an abridged version of a longer paper entitled “The Tolerance Principle: Nontransitive Reasoning or Nonmonotonic Reasoning?”. We are indebted to two anonymous reviewers for helpful comments.
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Notes
- 1.
We assume here for convenience that each \(d \in D\) has a name \(\underline{d}\).
- 2.
- 3.
To be sure, we could make use of truth-makers as well to implement the analysis of similarity relation in (i). To do so, however, is somewhat involved, and we won’t go into that here.
- 4.
The point goes back at least to Grice (1967).
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Cobreros, P., Egré, P., Ripley, D., van Rooij, R. (2016). Comparing Some Substructural Strategies Dealing with Vagueness. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_14
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