Truthlikeness for deterministic and probabilistic laws

Abstract

Truthlikeness is a property of a theory or a proposition that represents its closeness, similarity or likeness to the truth. The notion allows to defend a middle position between infallibilism and scepticism, providing an optimistic understanding of a set of ideas regarding science that may seem to imply, prima facie, an instrumentalist or pessimistic view of scientific theories. In this sense, perhaps all scientific theories are strictly speaking false, but some may be closer to the truth than others; scientific progress is possible because of an increase in truthlikeness; truth might be said to be the aim of science in the sense of pursuing a better approximation to it; our best developed theories (including the unobservable parts) work because they are close to the truth; and finally, one may embrace fallibilism and still be able to estimate that some theories are closer to the truth than others. Since Popper’s failure to provide a satisfactory definition of truthlikeness, the notion has become a topic of intense discussion by philosophers of science and logicians. This gave rise to two main perspectives, the content-consequence and the similarity approach. This dissertation proposes a framework to define truthlikeness for deterministic and probabilistic laws within Niiniluoto’s version of the similarity approach. According to Niiniluoto, truthlikeness for quantitative deterministic laws can be defined by the Minkowski metric. We present some counter-examples to the definition and argue that it fails because it considers truthlikeness for quantitative deterministic laws to be just a function of “accuracy”, but an accurate law can be wrong about the actual “structure” or “behaviour” of the system it intends to describe. We develop a modification of Niiniluoto’s proposal that defines truthlikeness for quantitative deterministic laws as a function of two factors: accuracy and nomicity. The latter represents the qualitative behaviours implied by a law that are not captured by value comparison and can be measured by shape similarity, appealing to the Euclidean distance between the corresponding derivative functions. The final proposal solves the presented counter-examples and defines a new way of understanding scientific progress. The framework is expanded to cover probabilistic laws, which represent a relevant subset of actual scientific laws. When this research was developed, there were almost no proposals in the literature of truthlikeness to deal with probabilistic laws or probabilistic truths in general. In this way, we followed Niiniluoto’s suggestion to use the Kullback–Leibler divergence to define the distance between a probability law X and the true probability law T and we argue that the Kullback–Leibler divergence seems to be the best of the available probability distances to measure accuracy between probabilistic laws. However, as in the case of deterministic laws, we argue that accuracy represents a necessary but not sufficient condition, as two probabilistic laws may be equally accurate and still one may imply more true or truthlike probabilistic consequences, behaviours or facts about the system than the other. The final proposal defines truthlikeness for probabilistic laws again as a function of accuracy and nomicity, in intimate connexion with the proposal developed for deterministic laws.