Abstract
The pragmatic logic of assertions shows a connection between ignorance and (informal) decidability. In it, we can express pragmatic factual ignorance and first-order ignorance as well as some of their variants. We also show how some pragmatic versions of second-order ignorance and of Rumsfeld-ignorance may be formulated. A specific variant of second-order ignorance is particularly relevant. This indicates a strong pragmatic version of ignorance of ignorance, irreducible to any previous form of ignorance, which defines limits to what can justifiably be asserted about higher-order ignorance. Finally, we relate the justified assertion of second-order ignorance (that cannot be known) with scientific assertions.
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Notes
This is the sense of uncertainty as used for instance by Keynes: “By ‘uncertain’ knowledge I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty [...] The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years [...] About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know”. (Keynes 1973, pp. 113–114). Uncertainty means incompleteness of knowledge or information, while ignorance is assumed to be the total absence of knowledge.
On this, see Van Der Hoek and Lomuscio (2004).
Notice that if K is considered as a \({{\mathbf {S}}}{{\mathbf {5}}}\) modality, then ignorance can be known in virtue of the epistemic version of the modal axiom 5.
From now on, we use \({\mathcal {L}}^{P}\) to refer both to the logic for pragmatics as well as to its extensions.
Take ‘observable universe’ as ‘all signals ever emitted following the inflationary epoch’.
“Modulation in the Periphery: What is the nose telling the Brain?” Stuart Firestein (Columbia), March 2019.
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Acknowledgements
We would like to thank the anonymous referees of Synthese for their comments that greatly contributed to improve the paper, as well as Lorenzo Magnani, and Selene Arfini. The work of Daniele Chiffi is supported by the Project PTDC/MHC-FIL/0521/2014 of the Portuguese Fundação para a Ciência e a Tecnologia and by the Dipartimento di Eccellenza project Fragilità Territoriali (MIUR 2018-2022). The work of Ahti-Veikko Pietarinen is supported in part by the Russian Academic Excellence Project ‘5-100’.
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Carrara, M., Chiffi, D., De Florio, C. et al. We don’t know we don’t know: asserting ignorance. Synthese 198, 3565–3580 (2021). https://doi.org/10.1007/s11229-019-02300-y
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DOI: https://doi.org/10.1007/s11229-019-02300-y