Premature deaths and long-term mortality effects of air pollution.

Sir—I read with great interest Sander Greenland’s article1 and wish to make a few remarks regarding its central issues. Greenland’s distinction between deductions and inductions recalls the classical separation of scientific statements into analytical and synthetical judgements. In a formal logic system, the truth of a judgement depends only on the correct use of deductive tools of that particular system (the ‘dictionary’, as it is commonly labelled). In empirical sciences, which are based on synthetical statements, syntactical tools must also be rigorous: in epidemiology, we need accurate definitions of risk or impact measurements. But this is not enough. We are also trying to say something about the real world, to make predictions. That is why empirical sciences, which are concerned (after Hume’s definition) with the ‘matters of fact’, go beyond the domain of formal language and its logically necessary conclusions. In physics, as well as in epidemiology, deductive reasoning is no more sufficient, even if it is still necessary. Since the 17th century scientific revolution, at least, the demarcation between analytical and synthetical judgements separates two different areas of science, each of them provided with its particular concept of truth. When David Hume affirmed that a statement like ‘the sun will rise tomorrow’ can by no means be demonstrated,2 he meant that the decision concerning the truth of this prediction does not belong to logic, but to experience. As a consequence, unlike Popper, the Scottish philosopher would not conclude that ‘induction does not exist’, but that logic (absolute) truth does not exist in the domains of experience. During the early decades of this century, the so-called ‘logical empirism’ developed the modern definition of a scientific theory as a structure in which two parts interact: (1i) A deductive system of symbols and definitions. (2i) An interpretation, i.e. a correspondence of part of the formal system and a group of empirical (observational) statements. The ‘translation’ is made possible by a rigorous rule manual. As a consequence, Carnap, Reichenbach, Hempel and other logical positivists deduced that a theory is always testable as a whole by valuing its operativity or its predictive power. The translation of formal statements into empirical ‘protocols’, i.e. into predictions, is precisely what is labelled as induction and what makes a theory work as a scientific explanation of facts. If I had to summarize Popper’s criticism against inductivism, I would choose two core points: (1P) Induction leads to indecidibility. No collection of observations can verify a theory. (2P) Inductive method leads to a search for highly probable hypotheses, while what science needs is highly informative (and least probable) conjectures, i.e. highly testable and falsifiable hypotheses. Popper’s conclusion is that the best result inductive rules can achieve is to support ad hoc hypotheses. It appears clear that, while point (1P) reflects an epistemological problem which seems to have been solved by the replacement of the concept of ‘verification’ by that of ‘testability’ of a theory, point (2P) focuses on a methodological question. I will, therefore, examine each criticism separately, even if both refer to the same misunderstanding of the nature of the inductive method. With respect to the first issue, my impression is that Popperian epidemiologists, following Popper, have in mind a simplistic idea of induction as a rule to reach certainty by proceeding from particular observations to general laws. Quite surprisingly, this point seems to be generally accepted and is not present at all in the current debate on inductive method:3,4 a basic and ‘semantic’ article from McLure,5 comparing refutationist and verificationist positions, defines inductivism by means of some core sentences like ‘Certainty is possible’, ‘Observation reveals truth’, ‘Recognition of facts precedes formulation of theories’ or ‘Induction is the logical foundation of science’. No doubt Popper’s criticisms to this position are successful: the point is that this is clearly not the definition of ‘inductive method’ given by logical positivism and which I have previously summarized. That induction leads to certainty, that it has a logical justification or that scientists develop theories by simply accumulating observations in their ‘tabula rasa’ minds are points of view which modern sciences definitively abandoned at the beginning of this century. The methodological question (2P) concerns Popper’s claim that scientific theories must be highly testable. It includes two aspects which appear very plausible and completely acceptable: a scientific theory must be rigorous, i.e. it must have a powerful formal system, and it must provide scientists with a relevant informative content, i.e. it must be able to explain new facts and predict them. To Popper, however, ‘testable’ necessarily means ‘falsifiable’ —it cannot mean ‘verifiable’—so his claim is that ‘highly falsifiable theories’ correspond to theories which are ‘rich in empirical content’. So far, this appears to be a strictly semantic question, and these lexical shifts could still be accepted. But Popper, and Popperians, come to conclusions which do not seem plausible in modern sciences. Given that the most highly informative theories are the least probable, because they explain many facts and make many falsifiable predictions, Popperians deduce that the most genuine scientific hypotheses are the most unlikely conjectures. Popper added6 that hypotheses generating is absolutely ‘free, neither justified nor justifiable’. In my opinion, points (IP) and (2P) reflect semantic questions which, in epistemology as well as in the daily practice of © International Epidemiological Association 1999 Printed in Great Britain