A false dilemma, also referred to as false dichotomy, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives. For example, a false dilemma is committed when it is claimed that, "Stacey spoke out against capitalism; therefore, she must be a communist". One of the options excluded is that Stacey may be neither communist nor capitalist. False dilemmas often have the form of treating two contraries, which may both be false, as contradictories, of which one is necessarily true. Various inferential schemes are associated with false dilemmas, for example, the constructive dilemma, the destructive dilemma or the disjunctive syllogism. False dilemmas are usually discussed in terms of deductive arguments. But they can also occur as defeasible arguments. Our liability to commit false dilemmas may be due to the tendency to simplify reality by ordering it through either-or-statements, which is to some extent already built into our language. This may also be connected to the tendency to insist on clear distinction while denying the vagueness of many common expressions.
Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements (premises) to reach a logical conclusion.
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular premises to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.
A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences, i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. Most studied formal logics have a monotonic entailment relation, meaning that adding a formula to a theory never produces a pruning of its set of conclusions. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. A monotonic logic cannot handle various reasoning tasks such as reasoning by default, abductive reasoning, some important approaches to reasoning about knowledge, and similarly, belief revision.
Two kinds of logical reasoning are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or premise, a conclusion or logical consequence and a rule or material conditional that implies the conclusion given the precondition, one can explain the following.
- Deductive reasoning determines whether the truth of a conclusion can be determined for that rule, based solely on the truth of the premises. Example: "When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet." Mathematical logic and philosophical logic are commonly associated with this type of reasoning.
- Inductive reasoning attempts to support a determination of the rule. It hypothesizes a rule after numerous examples are taken to be a conclusion that follows from a precondition in terms of such a rule. Example: "The grass got wet numerous times when it rained, therefore: the grass always gets wet when it rains." This type of reasoning is commonly associated with generalization from empirical evidence. While they may be persuasive, these arguments are not deductively valid: see the problem of induction.
- Abductive reasoning, sometimes called inference to the best explanation, selects a cogent set of preconditions. Given a true conclusion and a rule, it attempts to select some possible premises that, if true also, can support the conclusion, though not uniquely. Example: "When it rains, the grass gets wet. The grass is wet. Therefore, it might have rained." This kind of reasoning can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data. Diagnosticians, detectives, and scientists often use this type of reasoning.
Secundum quid is a type of informal fallacy that occurs when the arguer fails to recognize the difference between rules of thumb and categorical propositions, rules that hold true universally.
Legal informatics is an area within information science.
In philosophical logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductively valid. It usually occurs when a rule is given, but there may be specific exceptions to the rule, or subclasses that are subject to a different rule. Defeasibility is found in literatures that are concerned with argument and the process of argument, or heuristic reasoning.
Defeasible logic is a non-monotonic logic proposed by Donald Nute to formalize defeasible reasoning. In defeasible logic, there are three different types of propositions:
F-logic is a knowledge representation and ontology language. F-logic combines the advantages of conceptual modeling with object-oriented, frame-based languages and offers a declarative, compact and simple syntax, as well as the well-defined semantics of a logic-based language.
Probabilistic argumentation refers to different formal frameworks pertaining to probabilistic logic. All share the idea that qualitative aspects can be captured by an underlying logic, while quantitative aspects of uncertainty can be accounted for by probabilistic measures.
In logic and philosophy, an argument is a series of statements, called the premises or premisses, intended to determine the degree of truth of another statement, the conclusion. The logical form of an argument in a natural language can be represented in a symbolic formal language, and independently of natural language formally defined "arguments" can be made in math and computer science.
A semantic reasoner, reasoning engine, rules engine, or simply a reasoner, is a piece of software able to infer logical consequences from a set of asserted facts or axioms. The notion of a semantic reasoner generalizes that of an inference engine, by providing a richer set of mechanisms to work with. The inference rules are commonly specified by means of an ontology language, and often a description logic language. Many reasoners use first-order predicate logic to perform reasoning; inference commonly proceeds by forward chaining and backward chaining. There are also examples of probabilistic reasoners, including non-axiomatic reasoning systems, and probabilistic logic networks.
John L. Pollock (1940–2009) was an American philosopher known for influential work in epistemology, philosophical logic, cognitive science, and artificial intelligence.
In information technology a reasoning system is a software system that generates conclusions from available knowledge using logical techniques such as deduction and induction. Reasoning systems play an important role in the implementation of artificial intelligence and knowledge-based systems.
Argument from analogy is a special type of inductive argument, whereby perceived similarities are used as a basis to infer some further similarity that has yet to be observed. Analogical reasoning is one of the most common methods by which human beings attempt to understand the world and make decisions. When a person has a bad experience with a product and decides not to buy anything further from the producer, this is often a case of analogical reasoning. It is also implicit in much of science; for instance, experiments on laboratory rats typically proceed on the basis that some physiological similarities between rats and humans entails some further similarity.
Formal scientists have attempted to combine logic and dialectic through formalisation. These attempts include pre-formal and partially formal treatises on argument and dialectic, systems based on defeasible reasoning, and systems based on game semantics and dialogical logic.
Rulelog is an expressive semantic rule-based knowledge representation and reasoning (KRR) language. It underlies knowledge representation languages used in systems such as Flora-2, SILK and others. It extends well-founded declarative logic programs with features for higher-order syntax, frame syntax, defeasibility, general quantified expressions both in the bodies of the rules and their heads, user-defined functions, and restraint bounded rationality.
In argumentation theory, an argumentation scheme or argument scheme is a template that represents a common type of argument used in ordinary conversation. Many different argumentation schemes have been identified. Each one has a name and presents a type of connection between premises and a conclusion in an argument, and this connection is expressed as a rule of inference. Argumentation schemes can include inferences based on different types of reasoning—deductive, inductive, abductive, probabilistic, etc.
