Formal approaches to inconsistent science

Federal University of Rio de Janeiro


George Washington University


Inconsistency toleration is the phenomenon of working with inconsistent information without threatening one's rationality. This tutorial aims at addressing the different ways in which formal tools help to scrutinize and explain cases of inconsistency toleration in the sciences. Two specific objectives of the tutorial are: (i) to provide a systematic overview of the different formal tools that have been used to explain the phenomenon of inconsistency toleration as well as to (ii) discuss some applications of these tools for two case studies.

In order to do so, the tutorial addresses three main questions: what is inconsistency toleration? which are the formal tools that are used to explain such a phenomenon? as well as, how satisfactory are them when confronted with specic instances of inconsistency toleration in the sciences? The tutorial is divided into three sessions.

1. Inconsistency toleration in the sciences.

  • Preliminaries. Contradiction, Principle of Explosion, logical triviality, scientic theory. (Martnez-Ordaz 2020; (Opt.) Vickers 2013: Chap. 1)

  • Case studies.

- The Early Calculus. Is there really a contradiction? Justication vs inferencial procedures. (Brown and Priest 2004; (Opt.) Bueno 2006; Vickers 2013: Chap. 6)

- The conflicting models of the atomic nucleus. Globally inconsistent procedures, locally consistent calculations. ((Opt.) Friend and Martnez-Ordaz 2018).

  • What to explain. Historical, methodological and logical approaches to inconsistency in science. The role of logic when explaining inconsistency toleration. (Martnez-Ordaz 2020; (Opt.) Bueno 2006, 2017)

2. Evaluating formal approaches to inconsistency toleration

  • Logic and evidence. Anti-exceptionalism about logic. Evidence and Strenght. ((Opt.) Hjortlan 2017)

  • Chunk and Permeate. What is Chunk and Permeate? (Brown and Priest 2004). Rights and wrongs (Friend and Martnez-Ordaz 2018).

3. Evaluating formal approaches to inconsistency toleration

  • Adaptive logics. What are adaptive logics? Rights and wrongs (Batens 2009; (Opt.) Batens 2014)

  • Partial structures. What are Partial structures? (Bueno 1997). Rights and wrongs (Bueno 1997; Martnez-Ordaz 2020).

  • Final Discussion.

Basic Readings

[1] Batens D. (2009) The Need for Adaptive Logics In Epistemology. In: Rahman S., Symons J., Gabbay D.M., Bendegem J.P.. (eds) Logic, Epistemology, and the Unity of Science. Logic, Epistemology, And The Unity Of Science, vol 1. Springer, Dordrecht.

[2] Brown, B. and Priest, G. (2004): Chunk and permeate, a paraconsistent inference strategy. part i: The innitesimal calculus. Journal of Philosophical Logic, 33(4):379{388.

[3] Bueno, O. (1997): Empirical adequacy: A partial structures approach. Studies in History and Philosophy of Science Part A, 28(4):585{610.

[4] Martnez-Ordaz, M. del R. (2020): The ignorance behind inconsistency toleration in S.I. Knowing the Unknown Synthese.

Complementary Readings

[1] Batens, D. (2014): The role of logic in philosophy of science, Routledge companion to philosophy of science: 59-69.

[2] Bueno, O. (2006): Why inconsistency is not hell: Making room for inconsistency in science. Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi: 70{86.

[3] Bueno, O. (2017): Scientic pluralism, consistency preservation, and inconsistency toleration. HUMANA. MENTE Journal of Philosophical Studies, 10(32):229{245.

[4] Friend, M. and M. del R. Martnez-Ordaz (2018): Keeping Globally Inconsistent Scientic Theories Locally Consistent, In: Carnielli W., Malinowski J. (eds) Contradictions, from Consistency to Inconsistency. Trends in Logic (Studia Logica Library), vol 47. Springer: 53-88.

[5] Hjortland, O.T. (2017): Anti-exceptionalism about logic. Philosophical Studies 174: 631{658.

[6] Vickers, P. (2013): Understanding inconsistent science, Oxford University Press.