Frappier Mélanie - Science and hypothesis: the complete text

Also available from Bloomsbury

The Bloomsbury Companion to the Philosophy of Science, edited by Steven French and Juha Saatsi

The History and Philosophy of Science: A Reader, edited by Daniel J. McKaughan and Holly Vande Wall

Philosophy of Science: Key Concepts, Steven French

With this new translation, we would like to reintroduce Poincar to a general audience. Science and Hypothesis was his first work aimed at such an audience and it was an immediate and continuing success. Even though this work is a collection of articles first published elsewhere, drawing them together created a whole with a sustained argument for the importance of hypotheses in mathematics and in physical science. Poincar saw the recognition of the role of hypotheses in science as an important alternative to both rationalism and empiricism. Of course, Kant had already presented an alternative to, and synthesis of, these two traditions, but Poincars view is different from Kants, even if he seems to side with Kant in his debate with the logicists later in his life. In Science and Hypothesis, his aim is to show that both in mathematics and in the physical sciences, scientists rely on hypotheses that are neither necessary first principles, as the rationalists claim, nor learned from experience, as the empiricists claim. These hypotheses fall into distinct classes, as presented in Chapter 9 and (somewhat differently) in the Introduction. There are natural hypotheses that seem to be obviously true and which are the last to be abandoned, though we may be forced to consider changing them because of new evidence. Indifferent hypotheses, by which he means, for example, the mechanical models that we develop to explain observed phenomena are the second kind of hypothesis. Poincar argues that these hypotheses are not to be taken literally as what is going on at the atomic level, but are rather just aides to our understanding. There are also real generalizations, which are empirically verified laws. Poincar includes them in the list of hypotheses in Chapter 9 and also in the Introduction, despite the fact that they are learned from experience. Finally, there are conventions, which Poincar sometimes describes as being merely linguistic a choice of language but which also include his famous thesis of the conventionality of metric geometry, which is more than just linguistic. The conventionality of metric geometry is the prime example of the abandonment of part of Kants synthetic a priori. Poincar will argue that metric geometry is not determined a priori, given that we know that there are consistent alternatives, nor determined empirically because of its role as a convention in physical theory. The central feature of Poincars view of science is that it makes essential use of conventions that are neither a priori nor empirical.

We have included the preface that Poincar wrote for the American edition of Science and Hypothesis (1905), translated by the mathematician George Bruce Halsted who was known for his advocacy of non-Euclidean geometry. It is not known if Poincar wrote the preface directly in English or if he wrote it in French and had it translated. Besides thanking the translator for his work, Poincar describes differences in national styles of doing science, arguing that while English and continental scientists use hypotheses of different sorts, the central thesis of Poincars book remains true namely that science requires hypotheses in a way that has often not been noticed. The preface to the American edition is also notable because here Poincar makes his strongest statement against Newtons absolute space, saying that space is only a word that we have believed a thing (xxix below). Poincar clearly had a relational view of space, though the details of his view remain rather unstudied.

Poincar opens his introduction to Science and Hypothesis by contrasting a nave realist view of science with his own view. He argues that hypotheses play an important role in both mathematics and in the physical sciences. Asking whether this does not lead to skepticism about science, he answers negatively; that a careful evaluation of the role of hypotheses will show that science is still objective, even if it does not fit the image of the nave realist. He warns against the danger of overgeneralizing the idea of conventions in science, calling those who do so nominalists. Poincar situates himself between the rationalists and the empiricists, that is, those who would found science on first principles and those who would found science on direct experience.

Poincar describes some of the frameworks that he will argue we create in order to describe nature; one such framework being the theory of mathematical magnitude and space. While these are created by us and are conventional, they are not arbitrary, given that Poincar argues that our constructions are guided by our experience. Furthermore, when we get to the physical sciences the situation changes. While there are still conventional elements in physical science, the principles and laws are founded directly on experiment through inductive argument. Poincar mentions how he will treat the problem of induction with probability theory, and gives some examples in the physical sciences.

Chapter 1 opens with the question of how mathematics can tell us anything new if it is a deductive science that is based on the principle of identity. Poincar shows that mathematics is also inductive; that is, it can make universal claims, even though it starts with particulars, by making use of mathematical induction. Through the example of elementary arithmetic, Poincar shows how we can make assertions about all of the numbers, while starting with a few simple definitions and using the principle of mathematical induction. In making claims about the infinite natural numbers, we go beyond any experience that we could possibly have, so we cannot base the principle of mathematical induction on experience. Therefore, Poincar claims that it is a genuine synthetic a priori judgment that presents itself to the mind as manifestly true.

In Chapter 2, Poincar introduces the continuum and the definitions of rational and irrational numbers. He notes that in physical cases, we can often distinguish quantity A from quantity C, even while we are unable to distinguish quantity A from quantity B or quantity B from quantity C. Thus, we are led to a contradiction, which we must overcome by inventing the mathematical continuum. As Poincar points out, we also need the real numbers to account for the intersection of some figures in geometry. He presents Dedekinds account of the real numbers in some detail.

Chapter 3 introduces non-Euclidean geometries and makes the preliminary case for the conventionalism of metric geometry, that is the thesis that each of these geometries is a more or less useful way of describing space and the things in it. None of the geometries are true or false. Ultimately, Poincar will argue that geometry is neither a priori nor empirical and, therefore, it is conventional. In this chapter, he focusses on the argument that the true metric geometry cannot be determined a priori, given that alternative geometries are logically consistent. Thus, we have no a priori method of favoring one over another. To prove this, Poincar introduces his famous dictionary that gives an interpretation of Lobachevskiis geometry. We would now say that he has given us a model showing the consistency of hyperbolic geometry, which is often called the Poincar or the BeltramiPoincar half plane model.