On theory and observation (1): The theoretician’s dilemma

Contemporary philosophy of science was, at least during its first decades (those of the glorious Vienna Circle), a kingdom of radically empiricist and positivist intellectuals: scientific knowledge had to be obtained and tested mainly through experiment, and everything that could not be robustly grounded on experimental observations was just dangerous speculation and metaphysics. The connections between scientific theories and empirical observation were, hence, one fundamental problem for people like Rudolf Carnap, Otto Neurath, Carl Hempel and the like (I have to confess that now it is not as hot a topic amongst the most recent discussions within philosophy of science as it used to be, not because the problems posed by and to the Logical Positivists were ‘conclusively solved’, but perhaps because my colleagues became a little bit bored of the subject and preferred to concentrate on cooler, more fashionable issues, assuming that ‘observation’ and ‘theory’ are just a couple of intrinsically vague terms for which no sharp definition can be worked out).

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For Logical Positivists, in any branch of science it should be possible to establish a relatively clear distinction between those concepts that were observational, in the sense that their applicability only depended on relatively easy, immediate and unproblematic empirical procedures of measurement, and those that were not, and that were named, in contraposition, theoretical concepts. Examples of observational concepts might be ‘position’, ‘time’, ‘temperature’, ‘colour’ (at least in simple circumstances); theoretical concepts would be ones like ‘force’, ‘electric charge’, ‘quantum spin’, etc. Of course, the easiness, immediacy and problematicity of the observations and measurements were certainly assumed to be context-dependent, nevertheless, and not absolute aspects of human perception: an astrophysicist might legitimately say things like that ‘we have observed the light spectre of such and such nebula, from which we infer its chemical composition’, though obviously you would never ‘observe’ such a thing by looking at the sky, nor even with a big telescope). Another important difference between theoretical and observational concepts was that the former appeared essentially in the context of theories, whereas observational terms only served (by themselves) to accumulate data and more data, i.e., observations or phenomena. Hence, theoretical concepts played some essential role in two of the main functions of scientific theories: establishing the systematic connections between apparently disconnected facts or empirical regularities, and helping to derive novel empirical predictions from those apparently disconnected facts or in unsuspected new empirical realms.

But, as Carl Hempel wrote in a momentous paper published in the fifties:

Why should science resort to the assumption of hypothetical entities when it is interested in establishing predictive and explanatory connections among observables? Would it not be sufficient for the purpose, and much less extravagant at that, to search for a system of general laws mentioning only observables, and thus expressed in terms of the observational vocabulary alone?

Stated in other words, if the only functions of theoretical concepts are, so to say, to order the “mess” in which our observations seem to consist when they are described only with the help of empirical terms, and to help us derive from them other observations (the predictions), which, obviously, have to be described only with observational terms in order to count as observations, doesn’t all this mean that theoretical terms are really superfluous with respect to their content? In more formal terms (those that the good old-fashioned Logical Empiricists enjoyed), imagine that we have a collection of empirical facts (observation sentences, O1, O2, …, On), describable just with the help of observational terms. To this we add a theory, which is a new set of sentences (much smaller and simple: let’s imagine that it is only one, T), that allows to make the following: in conjunction with O1, O2, …, On, it entails new observational sentences or facts (On+1, On+2, …) that we had not been able of deriving by using only our first set of observations. Simplifying still more, let’s call O the conjunction of all ‘previous’ observations, and P the conjunction of all ‘new’ observations (i.e., predictions). We have, then, the following:

O does not logically entail P

(O & T) logically entails P

But, taking this in mind, we may ask ‘what is the empirical content of T?’, i.e., what is what T allows to assert about the world, that we might not assert just with O alone? We can easily see that the ‘empirical content’ of T is exactly equivalent to the following sentence:

O → P

The logical equivalence between T and the proposition (O → P) is known as ‘Craig’s theorem’, and it reminds the classical empiricist argument from Georges Berkeley, according to which we don’t really have any idea about what do we literally mean when we use the concept of ‘matter’, if we understand by this something like ‘those real substances that are the cause of our sensations, but that don’t have in themselves the properties referred to by our sensations’ (and if we add the premise that all the content of our ideas has to derive from some sensations). To quote again Hempel’s own words:

The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and general principles of a theory serve their purpose, i.e, if they establish definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretative statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.

This can be expressed even more dramatically in the form of a logical dilemma:

If the terms and principles of a theory serve their purpose they are unnecessary, as just pointed out; and if they do not serve their purpose they are surely unnecessary. But given any theory, its terms and principles either serve their purpose or they do not. Hence: the terms and principles of any theory are unnecessary.

This is what Hempel named the theoretician’s dilemma: if theoretical concepts are useful, then they can (in principle) be dispensed with; if they are not useful, they of course must be dispensed with; hence, theoretical concepts are superfluous, at least regarding our aspiration to say something about the world that cannot be said even in principle if we limit ourselves to use only observational concepts. Note that this is not equivalent to saying that theoretical concepts are explicitly definable one by one with observational terms. It might be impossible (or requiring a formula infinitely long) to discover a sentence that says ‘a body has a positive electric charge of such and such units if and only if it happens that…’ (so that what follows after the points is everything that should happen if the body effectively had such an electric charge). But this has to do only with the practical applicability of theoretical terms, not with their semantic or scientific content: perhaps theoretical concepts and scientific theories are indispensable in practice (science would be impossibly complicated without them), but this does not entail that they say something about the world that it is not reducible to merely observational facts. Or, expressed in other words, perhaps the only value of scientific theories is their instrumental function. Empiricism seemed condemned, hence, to be some version of instrumentalism.


Hempel, C. G., ‘The Theoretician’s Dilemma: A Study in the Logic of Theory Construction’; chapter 8 of Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, The Free Press, New York, 1966 (originally published in 1958 in Minnesota Studies in the Philosophy of Science).

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