## Medical Logic

The following logics are examined for application in medicine: classical logic, paraconsistent logic, alethic and deontic modal logics, probability logic, and fuzzy logic. The examples given demonstrate that the language of medicine has many syntactic and semantic particularities the most salient ones being that (i) as an extended natural language, it has a variety of modal operators and is thus a multimodal language; and (ii) is highly vague. Each of its peculiarities requires a suitable logic capable of handling the specific problems associated with that particularity. In consequence, medicine needs a variety of logics, as an all-embracing multilogic suitable for logical problems of any kind in medicine does not yet exist. So, just as any scientific domain is amenable to a variety of mathematical theories - from algebra to non-Euclidean geometries to stochastics to chaos theory -, medicine will remain a domain of application of many different types of logics. This is what we call *logical pluralism* in medicine. Simply put, there exists no 'one true logic'. However, because vagueness is ubiquitous in medicine, fuzzy logic is a promising candidate for wide-ranging use. A logic is applied in medicine whenever it is capable of assisting in practical problem-solving. It has only instrumental value. Fuzzy logic seems to have the highest instrumental value in medicine because it is both an inconsistency-tolerant method of reasoning and a powerful methodology.

To inquire into whether there is a specific medical logic, the concept of logic is explicated first. A logic is an inference system built around a particular implication operator. A bivalent implication operator may be distinguished from a multivalent, fuzzy one. The latter is general enough to also include the former. On this basis, a concept of implication structure is introduced. In order for medicine to have a specific logic, a specific medical implication operator, MIO, would be needed to render medical reasoning implication structures according to MIO. However, there is no such MIO. A variety of existing, non-medical logics each with their specific implication operators are, or may be, used in medicine. Logical pluralism and instrumentalism is the only 'medical logic' in the narrow sense of this term. It may be objected that in medicine the subject of reasoning consists in actions, not in statements. Thus, the physician has to justify why she acts in a particular way and not why she believes that something is the case. So, in discussing medical logic, inferential logics are irrelevant. This objection is not well-substantiated. First, medicine is something more than the physician’s actions. Second, in a clinical setting, the physician acts in a particular way because in the process of clinical decision-making she has decided to act in that way. Therefore, she needs to reason about this decision and not about the act itself. Why did she make the decision *A* and not the decision *B* to act? It is her preference of *A* over *B* that she has to justify. Justification of preference behavior is always practical reasoning on the basis of knowledge, data, and goals. And such reasoning requires a method of reasoning usually called logic. The common morality of medicine seems to provide such a specific medical logic.

This completes Part V consisting of 2 chapters and 101 pages.