Abstract
The Knowability Paradox is a logical argument showing that if all truths are knowable in principle, then all truths are, in fact, known. Many strategies have been suggested in order to avoid the paradoxical conclusion. A family of solutions—called logical revision—has been proposed to solve the paradox, revising the logic underneath, with an intuitionistic revision included. In this paper, we focus on so-called revisionary solutions to the paradox—solutions that put the blame on the underlying logic. Specifically, we analyse a possibile translation of the paradox into a modified intuitionistic fragment of a logic for pragmatics (KILP) inspired by Dalla Pozza and Garola [4]. Our aim is to understand if KILP is a candidate for the logical revision of the paradox and to compare it with the standard intuitionistic solution to the paradox.
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Notes
- 1.
See [15], Sect. II.1.
- 2.
An interesting analysis of the issue can be found in Dalla Pozza [3].
- 3.
“My argument for the law of excluded middle and against the definition of “truth” in terms of “verifiability” is not that it is impossible to construct a system on this basis, but rather that it is possible to construct a system on the opposite basis, and that this wider system, which embraces unverifiable truths, is necessary for the interpretation of beliefs which none of us, if we were sincere, are prepared to abandon” (p. 682).
- 4.
[18] points out that empirical and mathematical assertions can be justified by means of different grounds. He remarks that “a ground for the assertion of a numerical identity would be obtained by making a certain calculation, and outside of mathematics, a ground for asserting an observational sentence would be got by making an adequate observation”. Dummett [5], in fact, points out that: “The intuitionist theory of meaning applies only to mathematical statements, whereas a justificationist theory is intended to apply to the language as a whole. The fundamental difference between the two lies in the fact that, whereas a means of deciding a range of mathematical statements, or any other effective mathematical procedure, if available at all, is permanently available, the opportunity to decide whether or not an empirical statement holds good may be lost: what can be effectively decided now will no longer be effectively decidable next year, nor, perhaps, next week” (p. 42).
- 5.
See also Hand [9].
- 6.
From this perspective, notice that an assertion is a “purely logical entity” independent of the speaker’s intentions and beliefs. For a different perspective see [10].
- 7.
A similar intermediate logic has been developed in [1].
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Carrara, M., Chiffi, D. (2014). The Knowability Paradox in the Light of a Logic for Pragmatics. In: Ciuni, R., Wansing, H., Willkommen, C. (eds) Recent Trends in Philosophical Logic. Trends in Logic, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-06080-4_3
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