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Charles Sanders Peirce plays a unique role in the history of modern American philosophy. The paper’s focus is on scientific discovery and explanation, i.e. two important issues of Peirce’s thinking. Many types of scientific reasoning have long been identified as supplying important methodologies for discovery and explanation in science, but many questions regarding their logical properties remain open in contemporary investigations in philosophy of science, methodology and logic. These styles of reasoning include induction, abduction, deduction, explanation or confirmation. The article offers alogical, or more exactly, methodeutical analysis of a particular type of scientific reasoning, namely abduction, i.e. reasoning from an observation to its possible explanations. There is no single logical method in scientific practice in general, and with respect to abduction in particular. Abduction is not a new form of inference, but belongs to the most important ways leading to scientific discovery.