Carl Hempel – Laws and Their Role in Scientific Explanation Carl Hempel – Laws and Their Role in Scientific Explanation1 5.1 Two basic requirements for scientific explanations • The aim of the natural sciences is explanation insight rather than fact gathering. • Man’s concern for understanding is demonstrated by myths, metaphors, anthropomorphising, invocation of occult forces, God’s inscrutable plans or fate. • Such “answers”, while psychologically satisfying, are not scientifically adequate as they fall short of the two primary scientific requirements – explanatory relevance and testability. • Example of Francesco Sizi’s rejection of his contemporary Galileo’s discovery of the moons of Jupiter – a pseudo-logical argument for why there could only be seven heavenly bodies based on irrelevant “facts”, analogies and anthopocentric assumptions. • Contrast this with the scientific explanation of the rainbow. Even if we’d never seen one, the scientific account would be good grounds for their existence. This satisfies the criterion of explanatory relevance – that the phenomenon was to be expected under the relevant circumstances. • Relevance is necessary but not sufficient for explanation. We also need to know not just what happens, but why. • Empirical testability is our second requirement for explanation. Example of treating gravity as universal affinity analogous to love – no test implications, in contrast with the rainbow example. • Relevant explanations are testable, but not vice-versa. 5.2 Deductive-nomological explanation • Example of a scientific explanation (the variability with altitude of the height of mercury in a Torricelli apparatus). What is explained depends both on general laws expressing uniform empirical connections and particular facts. The effects are as they are because of particular laws of nature applying to particular circumstances, and are therefore to be expected. • What is to be explained is the explanandum; the explanation is the explanans. • Example : image formation by reflection in a spherical mirror. Explanandum is 1/u + 1/v = 2/r. Explanans is based on rectilinear propagation of light, geometry of spheres and the basic laws of reflection, from which the explanandum is deduced. • The standard for a deductive-nomological (D-N) explanation is :- Explanans L1, L2, … Ln, (Laws) C1, C2, …Cm (particular Circumstances) Explanandum E • The laws invoked in scientific explanation are called covering laws and the explanation subsumes the explanandum under these laws. • The explanandum may be a phenomenon taking place at a particular place and time (the height of a mercury column), a general natural phenomenon (rainbows), uniformities expressed in an empirical law (Keppler’s laws). The explanans will 1 Chapter 5 of Philosophy of Natural Science [email protected] Page 1 of 6 Carl Hempel – Laws and Their Role in Scientific Explanation include reference to laws of broader scope (Newton’s laws). Explanations of empirical laws rely on theoretical principles that make reference to structures and processes underlying the uniformities in question. • D-N explanations exhibit explanatory relevance in the strongest possible sense, offering logically conclusive grounds for occurrence of the explanandum. Testability is also satisfied as the explanans tells us under which conditions to expect the explanandum phenomenon. • The scientific explanations that follow the D-N model most closely are those using mathematical demonstrations from covering laws and initial conditions – as in the discovery of Neptune based on the expectations arising from anomalies (based on Newton’s laws) in the motions of Uranus that allowed the position and mass of the supposed perturbing body to be calculated. • Often, a D-N explanation omits to mention the covering laws, as in explaining the pavement’s remaining free of slush because of the application of salt. The explanans omits mention of the law that salt lowers the freezing point of water, and also conditions, such as that the temperature wasn’t so low as to make the salt ineffective. • Similar elliptical explanations of childbed fever. • General laws are presupposed when we invoke causation in the explanans. Same cause, same effect. Whenever an event of kind F (the cause) occurs, it is accompanied by an event of kind G (the effect). • The fact that an explanation relies on general laws doesn’t always mean that it depended on their discovery. The discovery may only be of a fact that relies on already-known laws to achieve the status of an explanans. Otherwise, both facts and laws may be known, and all that was required was the logical demonstration. • We cannot tell what kind of discovery is required from the problem itself. Irregularities in Mercury’s orbit did not succumb to the same sort of explanation as those of Uranus, as the proposed planet Vulcan was not discovered, but required a more radical explanation in terms of the new system of laws of general relativity. 5.3 Universal laws and accidental generalisations • The laws, Li, provide the link by which particular circumstances, the Cj, explain a given event. Or, where the explanandum is itself a uniformity, they explain it as a special case of more comprehensive uniformities. • As distinct from laws of probabilistic form, to be discussed later, the laws employed by D-N explanation assert uniform, exceptionless connections given the specified conditions. • Various examples of statements of universal form (eg. gas laws). Most of the laws of natural science are quantitative, asserting specific mathematical relationships between different quantitative characteristics of physical systems. • We only talk of laws if we have evidence to assume their truth. However, this truth has to be within certain limitations of approximation or circumstance, or few of our laws would count as such. • Not all true statements of the form “whenever conditions of kind F pertain, those of kind G pertain as well” are laws. There are accidental generalisations, such as “all rocks in this box contain iron” or “all bodies of pure gold weigh less than 100,000 kilograms”. [email protected] Page 2 of 6 Carl Hempel – Laws and Their Role in Scientific Explanation • So, being a true statement of universal form is a necessary but not sufficient condition for being a scientific law. So, what is the distinguishing feature ? • The important difference, noted by Nelson Goodman2 is that a law can support counterfactual conditional. We can say what would have happened if certain conditions had applied (but didn’t), whereas we can’t in the case of accidental generalisations (if we had put another rock in the box, this doesn’t imply that it would therefore have contained iron). Similarly, laws support subjective conditionals (“if A should happen, then so would B”) whereas accidental generalisations do not. • A closely-related difference is that laws provide explanations, whereas accidental generalisations do not. • Can the distinction be that laws refer to generalisations over a potentially infinite set, whereas accidental generalisations cover only finite sets (eg. {Rocki}) where the generalisation is short-hand for a finite conjunction (eg. Rock1 contains iron & Rock2 contains iron & …. ) ? Hempel thinks this is suggestive but inadequate, as the accidental set is not specifically enumerated and could even be infinite. • Additionally, a statement of universal form can be a law even if it applies to no instances (eg. if a body were of a certain mass, it’s gravitational field would be ..). • An accidental statement of universal form (eg. “all bodies of pure gold weigh less than 100,000 Kg”) cannot be used to make counterfactual or subjunctive conditionals (eg. “you can’t fuse two bodies of 60,000 Kg to form one of 120,000 Kg”). • What counts as a law depends in part on the physical theories of the time. This is not to say that we cannot have laws without theory (eg. Keppler’s laws were treated as such before Newton supplied the theory), but if the generalisation rules out certain occurrences that are allowed by present theory, as in the “gold” example above, it will not be treated as a law. 5.4 Probabilistic explanation : fundamentals • Not all scientific explanations are in the form of universal laws; some, like exposure to a contagious disease being given as an explanation of why someone has a disease, are of probabilistic form and are known as probabilistic laws. • So, such a probabilistic law is “exposure to a contagious disease results in contagion with high probability”. Combined with the circumstance that the person in question was exposed to the particular disease, the law forms the explanans. Note that the explanans does not imply the explanandum with deductive certainty, as for D-N explanations, but only with high3 probability. • The form of the argument is therefore very similar to that of D-N explanations :- Explanans L1, L2, … Ln, (probabilistic Laws) C1, C2, …Cm (particular Circumstances) Explanandum E The double-line means “makes more or less probable”, as distinct from the single-line of deductive validity in the D-N schema. 2 Chapter 1 of Fact, Fiction and Forecast (The Problem of Counterfactual Conditionals) 3 Or, I would say, even with low probability ! [email protected] Page 3 of 6 Carl Hempel – Laws and Their Role in Scientific Explanation • The criterion of explanatory relevance in the probabilistic explanation is met by the conclusion of the argument being a “practical certainty”. 5.5 Statistical probabilities and probabilistic laws • The two differentiating features of probabilistic explanations (as against deductive-nomological) are the invocation of probabilistic laws and the probabilistic implication connecting explanans with explanandum. • Hempel describes the standard sampling with replacement of coloured balls from an urn as an example of a random process or experiment U, each drawing being one performance of U and the colour of the ball drawn the result or outcome of that performance. • Hempel now introduces the probabilities of Urn-drawing P(W,U) = 0.6, of coin- tossing P(H, C) = 0.5 and die-rolling P(1, D) = 1/6.