Induction is a knowledge-expanding process that adds new facts based on existing information and observational evidence, but it also faces logical limits and justification problems. This course will cover the debates between Hume and Reichenbach, and the attempts of modern philosophers to overcome the limitations of induction through the problems of indeterminacy and probability theory.
Induction is the term used in modern logic for any reasoning that is not deductive, i.e., any reasoning in which the premises clearly support the conclusion. Induction is knowledge-expanding, adding new facts based on existing information or observational evidence. This characteristic has made induction the methodological foundation for the development of modern science, but it also leads to problems that point to its own logical limitations.
While induction has been at the center of philosophical discussions since the time of Aristotle, it was not until the Scientific Revolution of the 17th century that it became the methodology of modern science. Francis Bacon systematically developed induction and made it the foundation of scientific inquiry. His methodology, a process of deriving general laws from empirical observations, has become an important tool for scientists to understand and explain natural phenomena. However, Bacon’s method of induction still posed logical problems because it relied on empirical evidence.
First, Hume saw that for induction, which predicts the future based on past experience, to be a justifiable inference, it must assume the unity of nature, that is, that the future world is the same as the world we have experienced in the past. However, the unity of nature cannot be known a priori, but only in reliance on experience. In other words, the claim that “induction is a justifiable inference” presupposes another knowledge, “nature is unitary,” which in turn is an empirical knowledge that must be justified by induction, so the justification of induction falls into circular logic. This is the problem of justification by induction. Hume’s critique led to a deep skepticism about the foundations of scientific methodology, and it has been an important topic of discussion for philosophers and scientists ever since.
To defend induction as a method of science against the justification problem, Reichenbach offers a pragmatic solution to the problem. Reichenbach assumes that nature can be either quantitative or non-quantitative. First, if nature is quantitative, then he judges induction to be more successful than other methods, such as astrology or prophecy, based on our experience so far. If nature is not quantitative, then the logical conclusion that no method can systematically and consistently succeed in predicting the future affirms that induction is at least no worse than other methods. Reichenbach’s argument that induction is the right choice in situations where we don’t know whether nature is quantitative or not can be seen as an attempt to solve the problem of justifying induction on a practical level. Reichenbach’s approach moves beyond philosophical skepticism and emphasizes practical choices, contributing to the recognition of the practical utility of scientific inquiry.
As another logical limitation of induction, some modern philosophers point to the problem of indeterminacy. This problem is that we cannot decide which of several hypotheses is better based on observational evidence alone. For example, when a few points are found, the curve that passes through all of them is undecidable because there are multiple curves. The same is true for predictions. When predicting where the next point will be found, you can’t determine where the next point will appear based on the points that have already been found. No matter how many dots we add as observational evidence, it’s still impossible to determine that one prediction is better than another. This problem of indeterminacy emphasizes the uncertainty of scientific predictions, and it illustrates the tentative nature of scientific models and theories.
However, even with the problem of indeterminacy, most modern philosophers recognize induction as a method of science. Rather than trying to solve the problem of induction directly, they emphasize its characteristic of open-endedness by introducing probability. According to them, the degree to which the observational evidence supports a hypothesis, or the degree of plausibility between premises and conclusion, can be expressed in terms of probability. Furthermore, it is possible to determine on probabilistic grounds that one hypothesis is better than another, or that one prediction is better than another. This kind of probabilistic logic fits well with our everyday intuition. These attempts do not fundamentally solve the problem of induction, but they do show that induction still deserves its place as a scientific method.
In modern science, Bayes’ theorem is also used to discuss the probabilistic justification of inductive reasoning. Bayes’ theorem describes how beliefs about an initial hypothesis are updated by new evidence, and it serves as an important tool for inductive reasoning. Bayes’ theorem is a powerful tool for scientists to analyze data and test hypotheses, and it exemplifies the inductive nature of the scientific method. This approach can be seen as an attempt to maximize the usefulness of inductive reasoning while acknowledging its limitations.
In conclusion, despite its logical limitations, induction remains an important methodology in modern science. This is because induction plays an essential role in scientific inquiry, and scientists have recognized the limitations of inductive reasoning while exploring different methodological approaches to overcome them. Probability theory and Bayes’ theorem are part of this effort, and have contributed to better justifying inductive reasoning and increasing the efficiency of scientific inquiry. While the justification of induction and the problem of undecidability remain important topics of philosophical discussion, modern science is making progress in addressing these issues practically.
