Logical reasoning

Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together, they form an argument. Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing. The main discipline studying logical reasoning is logic.

Distinct types of logical reasoning differ from each other concerning the norms they employ and the certainty of the conclusion they arrive at. Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true. Such an argument is called a valid argument, for example: all men are mortal; Socrates is a man; therefore, Socrates is mortal. For valid arguments, it is not important whether the premises are actually true but only that, if they were true, the conclusion could not be false. Valid arguments follow a rule of inference, such as modus ponens or modus tollens. Deductive reasoning plays a central role in formal logic and mathematics.

For non-deductive logical reasoning, the premises make their conclusion rationally convincing without ensuring its truth. This is often understood in terms of probability: the premises make it more likely that the conclusion is true and strong inferences make it very likely. Some uncertainty remains because the conclusion introduces new information not already found in the premises. Non-deductive reasoning plays a central role in everyday life and in most sciences. Often-discussed types are inductive, abductive, and analogical reasoning. Inductive reasoning is a form of generalization that infers a universal law from a pattern found in many individual cases. It can be used to conclude that "all ravens are black" based on many individual observations of black ravens. Abductive reasoning, also known as "inference to the best explanation", starts from an observation and reasons to the fact explaining this observation. An example is a doctor who examines the symptoms of their patient to make a diagnosis of the underlying cause. Analogical reasoning compares two similar systems. It observes that one of them has a feature and concludes that the other one also has this feature.

Arguments that fall short of the standards of logical reasoning are called fallacies. For formal fallacies, like affirming the consequent, the error lies in the logical form of the argument. For informal fallacies, like false dilemmas, the source of the faulty reasoning is usually found in the content or the context of the argument. Some theorists understand logical reasoning in a wide sense that is roughly equivalent to critical thinking. In this regard, it encompasses cognitive skills besides the ability to draw conclusions from premises. Examples are skills to generate and evaluate reasons and to assess the reliability of information. Further factors are to seek new information, to avoid inconsistencies, and to consider the advantages and disadvantages of different courses of action before making a decision.

Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion. It can be defined as "selecting and interpreting information from a given context, making connections, and verifying and drawing conclusions based on provided and interpreted information and the associated rules and processes." Logical reasoning is rigorous in the sense that it does not generate any conclusion but ensures that the premises support the conclusion and act as reasons for believing it. One central aspect is that this support is not restricted to a specific reasoner but that any rational person would find the conclusion convincing based on the premises. This way, logical reasoning plays a role in expanding knowledge.

The main discipline studying logical reasoning is called logic. It is divided into formal and informal logic, which study formal and informal logical reasoning. Traditionally, logical reasoning was primarily associated with deductive reasoning studied by formal logic. But in a wider sense, it also includes forms of non-deductive reasoning, such as inductive, abductive, and analogical reasoning.

The forms of logical reasoning have in common that they use premises to make inferences in a norm-governed way. As norm-governed practices, they aim at inter-subjective agreement about the application of the norms, i.e. agreement about whether and to what degree the premises support their conclusion. The types of logical reasoning differ concerning the exact norms they use as well as the certainty of the conclusion they arrive at. Deductive reasoning offers the strongest support and implies its conclusion with certainty, like mathematical proofs. For non-deductive reasoning, the premises make the conclusion more likely but do not ensure it. This support comes in degrees: strong arguments make the conclusion very likely, as is the case for well-researched issues in the empirical sciences. Some theorists give a very wide definition of logical reasoning that includes its role as a cognitive skill responsible for high-quality thinking. In this regard, it has roughly the same meaning as critical thinking.

A variety of basic concepts is used in the study and analysis of logical reasoning. Logical reasoning happens by inferring a conclusion from a set of premises. Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. For example, the sentence "The water is boiling." expresses a proposition since it can be true or false. The sentences "Is the water boiling?" or "Boil the water!", on the other hand, express no propositions since they are neither true nor false. The propositions used as the starting point of logical reasoning are called the premises. The proposition inferred from them is called the conclusion. For example, in the argument "all puppies are dogs; all dogs are animals; therefore all puppies are animals", the propositions "all puppies are dogs" and "all dogs are animals" act as premises while the proposition "all puppies are animals" is the conclusion.