Logical reasoning

Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing.

Distinct types of logical reasoning differ from each other concerning the norms they employ and the certainty of the conclusion they arrive at.

Inductive reasoning is a form of generalization that infers a universal law from a pattern found in many individual cases.

For informal fallacies, like false dilemmas, the source of the faulty reasoning is usually found in the content or the context of the argument.

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.

[5][6] 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 support comes in degrees: strong arguments make the conclusion very likely, as is the case for well-researched issues in the empirical sciences.

[1][16] Some theorists give a very wide definition of logical reasoning that includes its role as a cognitive skill responsible for high-quality thinking.

They include the law of excluded middle, the double negation elimination, the principle of explosion, and the bivalence of truth.

[50] So-called deviant logics reject some of these basic intuitions and propose alternative rules governing the validity of arguments.

For example, Peano arithmetic is based on a small set of axioms from which all essential properties of natural numbers can be inferred using deductive reasoning.

[65][66][67] Inductive reasoning starts from a set of individual instances and uses generalization to arrive at a universal law governing all cases.

[69][71][68] In the more narrow sense, it can be defined as "the process of inferring a general law or principle from the observations of particular instances.

In a slightly weaker form, induction can also be used to infer an individual conclusion about a single case, for example, that "the next raven I will see is black".

In this regard, the sample size should be large to guarantee that many individual cases were considered before drawing the conclusion.

For example, when making a generalization about human beings, the sample should include members of different races, genders, and age groups.

It plays an equally central role in the sciences, which often start with many particular observations and then apply the process of generalization to arrive at a universal law.

This problem was initially raised by David Hume, who holds that future events need not resemble past observations.

[83][81][84] Other central criteria for a good explanation are that it fits observed and commonly known facts and that it is relevant, precise, and not circular.

[85] Abductive reasoning is also common in medicine when a doctor examines the symptoms of their patient in order to arrive at a diagnosis of their underlying cause.

For example, the Bohr model explains the interactions of sub-atomic particles in analogy to how planets revolve around the sun.

Outside the field of logic, the term "fallacy" is sometimes used in a slightly different sense for a false belief or theory and not for an argument.

[107][108][109] Some theorists discuss logical reasoning in a very wide sense that includes its role as a broad skill responsible for high-quality thinking.

In this sense, it is roughly equivalent to critical thinking and includes the capacity to select and apply the appropriate rules of logic to specific situations.

Examples are to understand a position, to generate and evaluate reasons for and against it as well as to critically assess whether to accept or reject certain information.

It also includes the ability to consider different courses of action and compare the advantages and disadvantages of their consequences, to use common sense, and to avoid inconsistencies.

A central aspect concerns the abilities used to distinguish facts from mere opinions, like the process of finding and evaluating reasons for and against a position to come to one's own conclusion.

This matters for effective reasoning since it is often necessary to rely on information provided by other people instead of checking every single fact for oneself.

In such cases, logical reasoning includes weighing the potential benefits and drawbacks as well as considering their likelihood in order to arrive at a balanced all-things-considered decision.

during a baseball game the most logical response may be to blindly trust them and duck instead of demanding an explanation or investigating what might have prompted their exclamation.