Published in Volume XXXV, Issue 1, 2025, pages 1-31, doi: 10.47743/SACS.2025.1.1
Author: J. A. Bergstra
Abstract
A relatively formal framework for the description of application of the precautionary principle is described, which we consider to provide a basic setup for precautionary logic, that is reasoning patterns making use of said precautionary principle. Probability is understood as subjective probability in the tradition requiring exact figures for subjective probabilities. Besides probability we need various related concepts, notably: proposition, proposition space, truth, falsity, certainty, uncertainty, ignorance, hazard, harm, and risk. We adopt a fairly simple and coherent picture of these notions. We suggest that precautionary logic involves the transfer of quantified ignorance in the form of an ignorance interval.
References
[1] Tobias Arnoldussen. Precautionary logic and a policy of moderation. Erasmus Law Review, 2(2):259–286, 2009. URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1498434
[2] Jan A. Bergstra. Adams conditioning and likelihood ratio transfer mediated inference. Scientific Annals of Computer Science, 29(1):1–58, 2019. doi:10.7561/SACS.2019.1.1.
[3] Jan A. Bergstra, Inge Bethke, and Alban Ponse. Equations for formally real meadows.Journal of Applied Logic, 13(2):1–23, 2015. doi:10.1016/J.JAL.2015.01.004.
[4] Jan A. Bergstra and Marcus Düwell. Promise Theory: Principles and Applications (Second Edition). χt Axis Press, 2019.
[5] Jan A. Bergstra and Marcus Düwell. Accusation theory. Transmathematica, 2021. doi:10.36285/tm.61.
[6] Jan A. Bergstra and Marcus Düuwell. Accusations in the context of computer programming. Transmathematica, 2022. doi:10.36285/tm.69.
[7] Jan A. Bergstra and John V. Tucker. Initial and final algebra semantics for data type specifications: Two characterization theorems. SIAM Journal on Computing, 12(2):366–387, 1983. doi:10.1137/0212024.
[8] Jan A. Bergstra and John V. Tucker. On defining expressions for entropy and cross-entropy: The entropic transreals and their fracterm calculus. Entropy, 27(1), 2025. doi:10.3390/e27010031.
[9] Deryck Beyleveld and Roger Brownsword and. Emerging technologies, extreme uncertainty, and the principle of rational precautionary reasoning. Law, Innovation and Technology, 4(1):35–65, 2012. doi:10.5235/175799612800650644.
[10] Deryck Beyleveld and Shaun Pattinson. Precautionary reasoning as a link to moral action. In Michael Boylan, editor, Medical Ethics, pages 39–53. Upper Saddle River New Jersey: Prentice-Hal, 2000.
[11] Enrico Cameron and Gian Francesco Peloso. Risk management and the precautionary principle: A fuzzy logic model. Risk Analysis, 25(4):901– 911, 2005. doi:10.1111/j.1539-6924.2005.00607.x.
[12] Nathan Dinneen. Precautionary discourse. Thinking through the distinction between the precautionary principle and the precautionary approach in theory and practice. Politics and the Life Sciences, 32(1):2–21, 2013. doi:10.2990/32_1_2.
[13] Myles Lavan. Epistemic uncertainty, subjective probability, and ancient history. The Journal of Interdisciplinary History, 50(1):91–111, 2019. doi:10.1162/jinh_a_01377.
[14] Roel Pieterman. Introduction: The many facets of precautionary logic. Erasmus Law Review, 2(2):7 pages, 2009. URL: https://ssrn.com/abstract=1498427.
[15] David B. Resnik. Is the precautionary principle unscientific? Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences, 34(2):329–344, 2003. doi:10.1016/S1369-8486(02)00074-2.
[16] David B. Resnik. Precautionary Reasoning in Environmental and Public Health Policy, volume 86 of The International Library of Bioethics. Springer International Publishing, 2021. doi:10.1007/978-3-030-70791-0.
[17] Derek W. Robinson. Entropy and uncertainty. Entropy, 10(4):493–506, 2008. doi:10.3390/e10040493.
[18] Agne Sirinskiene. The status of precautionary principle: Moving towards the rule of customary law. Jurisprudencija, 118(4):349–364, 2009.
[19] Richard B. Stewart. Administrative law in the twenty-first century. New York University Law Review, 78(2):437–460, 2003.
[20] Phil Torres. Existential risks: a philosophical analysis. Inquiry, 66(4):614–639, 2023. doi:10.1080/0020174X.2019.1658626.
[21] Arie Trouwborst. Prevention, precaution, logic and law: The relationship between the precautionary principle and the preventative principle. Erasmus Law Review, 2(2):23 pages, 2009. URL: https://ssrn.com/abstract=1498430.
[22] Marjolein B.. A. van Asselt and Ellen Vos. The precautionary principle and the uncertainty paradox. Journal of Risk Research, 9(4):313–336, 2006. doi:10.1080/13669870500175063.
[23] Kurt Weichselberger. The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning, 24(2-3):149–170, 2000. doi:10.1016/S0888-613X(00)00032-3.
Bibtex
@article{sacscuza:bergstra2025pliitmi,
title={Precautionary Logic and Ignorance Interval Transfer Mediated Inference},
author={J. A. Bergstra},
journal={Scientific Annals of Computer Science},
volume={35},
number={1},
organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
year={2025},
pages={1-31},
publisher={Alexandru Ioan Cuza University Press, Ia\c si},
doi={10.47743/SACS.2025.1.1}
}

