Poincaré’s Classification of Hypotheses and Their Role in Natural Science

Abstract

In the introduction to his famous book, La Science et l’hypothèse, Poincaré remarks on the necessary role and legitimacy of hypotheses. He establishes a triple classification of hypotheses, dividing them into verifiable, useful, and apparent. However, in chapter 9, entitled ‘Les hypothèses en physique’, he gives a slightly different triadic classification: natural hypotheses, indifferent hypotheses, and real generalizations. The origin of this second classification is a lecture given at the International Congress of Physics, Paris, 1900. What are the similarities and differences between these two classifications? My main purpose is to provide a possible equivalence between the two classifications in order to clarify the role of hypotheses in Poincaré’s epistemology of natural science. The discussion will be based on the two fundamental texts mentioned above and on the contrast between Poincaré’s use of the notion of hypothesis and that of some of his contemporaries.

Acknowledgements

I am very grateful to David Stump and Fillipe Varela for insightful comments. I am also indebted to the editor and the anonymous referees of this journal for their contribution. I also thank the Fundação para a Ciência e a Tecnologia for a Ph.D. grant [SFRH/BD/4478/2008], during which part of this work was done at the Centre for Philosophy of Science at Lisbon University (CFCUL). I am indebted to the Institute of Mathematics at the Federal University of Rio de Janeiro (UFRJ), to the Programa de Ensino e História da Matemática e da Física, and to the Coordinação de Aperfeiçoamento de Pessoal de Ensino Superior for a postdoctoral fellowship during which I finished this work. I would like also to refer to my current institution, Department of Philosophy and Logic and Philosophy of Science of the University of Sevilla and the research project ‘The Genesis of Mathematical Knowledge: Cognition, History and Practices’ (P12-HUM-1216).

Notes

[1] I owe this remark to David Stump.

[2] Poincaré ([1902] 1968, 165) states that ‘every generalization is a hypothesis’.

[3] The origin of this text is a paper published in 1902 entitled ‘On the Objective Value of Science’. On the identification of this principle with the principle of physical induction, cf. also Heinzmann (2009), 184.

[4] This principle is mainly used for arithmetic and since it is not a hypothesis we are not going to discuss it.

[5] For example, Poincaré ([1902] 1968, 152–153) refers to the difference between conventions in geometry and conventions in mechanics. In fact, Poincaré never had to consider suspending a geometrical convention in the light of new experimental results. However, he reconsidered the classical principle of relative motion in the light of electromagnetism. A discussion of several different senses of the use of ‘convention’ in Poincaré is in Heinzmann (2010) and in de Paz (2014).

[6] Friedman (1996, 336) considers genuinely physical disciplines (namely, electromagnetism) ‘to be non-conventional’.

Additional information

Funding

I thank the Fundação para a Ciência e a Tecnologia for a Ph.D. grant [SFRH/BD/4478/2008], during which part of this work was done at the Centre for Philosophy of Science at Lisbon University (CFCUL).