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.
Definition[edit]
Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way.[1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion.[2][3] 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."[4] 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.[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.[6][1] This way, logical reasoning plays a role in expanding knowledge.[7]
The main discipline studying logical reasoning is called logic. It is divided into formal and informal logic, which study formal and informal logical reasoning.[8][9][10] Traditionally, logical reasoning was primarily associated with deductive reasoning studied by formal logic.[11] But in a wider sense, it also includes forms of non-deductive reasoning, such as inductive, abductive, and analogical reasoning.[12][13][14]
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.[1][15] 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.[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. In this regard, it has roughly the same meaning as critical thinking.[13][17]
Basic concepts[edit]
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.[3] 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.[18][19][3] 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.[20][3] The propositions used as the starting point of logical reasoning are called the premises. The proposition inferred from them is called the conclusion.[18][19] 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.[21][22]
A set of premises together with a conclusion is called an argument.[23][3] An inference is the mental process of reasoning that starts from the premises and arrives at the conclusion.[18][24] But the terms "argument" and "inference" are often used interchangeably in logic. The purpose of arguments is to convince a person that something is the case by providing reasons for this belief.[25][26] Many arguments in natural language do not explicitly state all the premises. Instead, the premises are often implicitly assumed, especially if they seem obvious and belong to common sense.[25][27] Some theorists distinguish between simple and complex arguments. A complex argument is made up of many sub-arguments. This way, a chain is formed in which the conclusions of earlier arguments act as premises for later arguments. Each link in this chain has to be successful for a complex argument to succeed.[18][25]
An argument is correct or incorrect depending on whether the premises offer support for the conclusion. This is often understood in terms of probability: if the premises of a correct argument are true, it raises the probability that its conclusion is also true. Forms of logical reasoning can be distinguished based on how the premises support the conclusion. Deductive arguments offer the strongest possible support. Non-deductive arguments are weaker but are nonetheless correct forms of reasoning.[28][29] The term "proof" is often used for deductive arguments or very strong non-deductive arguments.[30] Incorrect arguments offer no or not sufficient support and are called fallacies,[31][32] although the use of incorrect arguments does not mean their conclusions are incorrect.[33]
As a skill[edit]
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.[110] It encompasses a great variety of abilities besides drawing conclusions from premises. 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 is about making judgments and drawing conclusions after careful evaluation and contrasts in this regard with uncritical snap judgments and gut feelings.[17] Other core skills linked to logical reasoning are to assess reasons before accepting a claim and to search for new information if more is needed to reach a reliable conclusion. 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.[111][112] The skills responsible for logical reasoning can be learned, trained, and improved.[17][113]
Logical reasoning is relevant both on the theoretical and practical level.[114][115] On the theoretical level, it helps decrease the number of false beliefs. 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.[114] This includes being able to differentiate between reliable and unreliable sources of information. 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. [116][117] This way, logical reasoning can help the person avoid the effects of propaganda or being manipulated by others.[118][119] When important information is missing, it is often better to suspend judgment than to jump to conclusions.[118] In this regard, logical reasoning should be skeptical and open-minded at the same time.[120]
On the practical level, logical reasoning concerns the issue of making rational and effective decisions.[114][115] For many real-life decisions, various courses of action are available to the agent. For each possible action, there can be conflicting reasons, some in favor of it and others opposed to it. 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.[121][122] For example, when a person runs out of drinking water in the middle of a hiking trip, they could employ the skills associated with logical reasoning to decide whether to boil and drink water from a stream that might contain dangerous microorganisms rather than break off the trip and hike back to the parking lot. This could include considering factors like assessing how dangerous the microorganisms are and the likelihood that they survive the boiling procedure. It may also involve gathering relevant information to make these assessments, for example, by asking other hikers.[123]
Time also plays a central role in logical reasoning.[124] If one lacks important information, it is often better to delay a decision and look for new information before coming to a conclusion.[111] If the decision is time-sensitive, on the other hand, logical reasoning may imply making a fast decision based on the currently available evidence even if it is very limited. For example, if a friend yells "Duck!" 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.[124][125] Generally speaking, the less time there is, the more significant it is to trust intuitions and gut feelings. If there is more time, on the other hand, it becomes important to examine ambiguities and assess contradictory information.[126]