Logical reasoning - Knowledge (XXG)

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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. 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.

528:: 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. 1050:

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. 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

1023:, even involve correct deductive reasoning on the formal level. The content of an argument is the idea that is expressed in it. For example, a false dilemma is an informal fallacy that is based on an error in one of the premises. The faulty premise oversimplifies reality: it states that things are either one way or another way but ignore many other viable alternatives. False dilemmas are often used by politicians when they claim that either their proposal is accepted or there will be dire consequences. Such claims usually ignore that various alternatives exist to avoid those consequences, i.e. that their proposal is not the only viable solution. 853: 1082:

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. 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.

550:: 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. The term "proof" is often used for deductive arguments or very strong non-deductive arguments. Incorrect arguments offer no or not sufficient support and are called 786:

can be defined as "the process of inferring a general law or principle from the observations of particular instances." For example, starting from the empirical observation that "all ravens I have seen so far are black", inductive reasoning can be used to infer that "all ravens are black". 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". Inductive reasoning is closely related to

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usually that they believe it and have evidence for it. This form of abductive reasoning is relevant to why one normally trusts what other people say even though this inference is usually not drawn in an explicit way. Something similar happens when the speaker's statement is ambiguous and the audience tries to discover and explain what the speaker could have meant. Abductive reasoning is also common in medicine when a doctor examines the symptoms of their patient in order to arrive at a

387:. 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 434: 507:. 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 995:. This fallacy is committed, for example, when a person argues that "the burglars entered by the front door" based on the premises "the burglars forced the lock" and "if the burglars entered by the front door, then they forced the lock". This fallacy is similar to the valid rule of inference known as modus ponens. It is faulty because the first premise and the conclusion are switched around. Other well-known formal fallacies are 778: 736:

This means that if the premises are true, it makes it more likely but not certain that the conclusion is also true. So for a non-deductive argument, it is possible for all its premises to be true while its conclusion is still false. There are various types of non-deductive reasoning, like inductive, abductive, and analogical reasoning. Non-deductive reasoning is more common in everyday life than deductive reasoning.

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given feature of one object also characterizes the other object. Another factor concerns not just the degree of similarity but also its relevance. For example, an artificial strawberry made of plastic may be similar to a real strawberry in many respects, including its shape, color, and surface structure. But these similarities are irrelevant to whether the artificial strawberry tastes as sweet as the real one.

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example, when making a generalization about human beings, the sample should include members of different races, genders, and age groups. A lot of reasoning in everyday life is inductive. For example, when predicting how a person will react to a situation, inductive reasoning can be employed based on how the person reacted previously in similar circumstances. It plays an equally central role in the

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does not mean that the conclusion is false. Instead, it only means that some kind of error was committed on the way to reaching the conclusion. An argument can be a fallacy even if, by a fortuitous accident, the conclusion is true. 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.

763:. This means that one may have to withdraw a conclusion upon learning new information. For example, if all birds a person has seen so far can fly, this person is justified in reaching the inductive conclusion that all birds fly. This conclusion is defeasible because the reasoner may have to revise it upon learning that penguins are birds that do not fly. 756:

present in the premises without adding any additional information. So with non-deductive reasoning, one can learn something new that one did not know before. But the fact that new information is added means that this additional information may be false. This is why non-deductive reasoning is not as secure as deductive reasoning.

535:. An inference is the mental process of reasoning that starts from the premises and arrives at the conclusion. 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. Many arguments in 1037:, like the argument "(1) feathers are light; (2) light is opposed to darkness; (3) therefore feathers are opposed to darkness". The error is found in the ambiguous term "light", which has one meaning in the first premise ("not heavy") and a different meaning in the second premise ("visible electromagnetic radiation"). 1027:

this view. For example, an alcohol lobbyist may respond to the suggestion to ban alcohol advertisements on television by claiming that it is impossible to make people give up drinking alcohol. This is a strawman fallacy since the suggestion was merely to ban advertisements and not to stop all alcohol consumption.

543:. 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. 1062:

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. This way, logical reasoning can help the person avoid the effects of

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Time also plays a central role in logical reasoning. If one lacks important information, it is often better to delay a decision and look for new information before coming to a conclusion. If the decision is time-sensitive, on the other hand, logical reasoning may imply making a fast decision based on

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level. 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. This includes being able

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The more plausible the explanation is, the stronger it is supported by the premises. In this regard, it matters that the explanation is simple, i.e. does not include any unnecessary claims, and that it is consistent with established knowledge. Other central criteria for a good explanation are that it

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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

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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. It encompasses a great variety of abilities besides drawing conclusions from premises. Examples are

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Inductive reasoning starts from a set of individual instances and uses generalization to arrive at a universal law governing all cases. Some theorists use the term in a very wide sense to include any form of non-deductive reasoning, even if no generalization is involved. In the more narrow sense, it

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A fallacy is an incorrect argument or a faulty form of reasoning. This means that the premises provide no or not sufficient support for the conclusion. Fallacies often appear to be correct on the first impression and thereby seduce people into accepting and using them. In logic, the term "fallacy"

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that try to discover the relation between causes and effects. Abduction is also very common in everyday life. It is used there in a similar but less systematic form. This relates, for example, to the trust people put in what other people say. The best explanation of why a person asserts a claim is

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On the practical level, logical reasoning concerns the issue of making rational and effective decisions. 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

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The strawman fallacy is another informal fallacy. Its error happens on the level of the context. It consists in misrepresenting the view of an opponent and then refuting this view. The refutation itself is often correct but the error lies in the false assumption that the opponent actually defends

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Through analogical reasoning, knowledge can be transferred from one situation or domain to another. Arguments from analogy provide support for their conclusion but do not guarantee its truth. Their strength depends on various factors. The more similar the systems are, the more likely it is that a

794:. Like other forms of non-deductive reasoning, induction is not certain. This means that the premises support the conclusion by making it more probable but do not ensure its truth. In this regard, the conclusion of an inductive inference contains new information not already found in the premises. 735:

Non-deductive reasoning is an important form of logical reasoning besides deductive reasoning. It happens in the form of inferences drawn from premises to reach and support a conclusion, just like its deductive counterpart. The hallmark of non-deductive reasoning is that this support is fallible.

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if it is valid and all its premises are true. For example, inferring the conclusion "no cats are frogs" from the premises "all frogs are amphibians" and "no cats are amphibians" is a sound argument. But even arguments with false premises can be deductively valid, like inferring that "no cats are

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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

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Abductive reasoning is usually understood as an inference from an observation to a fact explaining this observation. Inferring that it has rained after seeing that the streets are wet is one example. Often, the expression "inference to the best explanation" is used as a synonym. This expression

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should be large to guarantee that many individual cases were considered before drawing the conclusion. An intimately connected factor is that the sample is random and representative. This means that it includes a fair and balanced selection of individuals with different key characteristics. For

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are used synonymously even though there are slight differences in their meaning. Non-deductive reasoning is ampliative in the sense that it arrives at information not already present in the premises. Deductive reasoning, by contrast, is non-ampliative since it only extracts information already

926:. Analogical reasoning can be used, for example, to infer information about humans from medical experiments on animals: (1) rats are similar to humans; (2) birth control pills affect the brain development of rats; (3) therefore they may also affect the brain development of humans. 335:

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

422:. 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 576:

inferences are the most reliable form of inference: it is impossible for their conclusion to be false if all the premises are true. This means that the truth of the premises ensures the truth of the conclusion. A deductive argument is

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Franks, Bridget A.; Therriault, David J.; Buhr, Miriam I.; Chiang, Evelyn S.; Gonzalez, Claire M.; Kwon, Heekyung K.; Schelble, Jenni L.; Wang, Xuesong (August 2013). "Looking back: reasoning and metacognition with narrative texts".

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Abductive reasoning plays a central role in science when researchers discover unexplained phenomena. In this case, they often resort to a form of guessing to come up with general principles that could explain the observations. The

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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

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Informal fallacies are expressed in natural language. Their main fault usually lies not in the form of the argument but has other sources, like its content or context. Some informal fallacies, like some instances of

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could also explain why the streets are wet but this is usually not the best explanation. As a form of non-deductive reasoning, abduction does not guarantee the truth of the conclusion even if the premises are true.

941:, and learning. It can be used both for simple physical characteristics and complex abstract ideas. In science, analogies are often used in models to understand complex phenomena in a simple way. For example, the 582:

frogs" from the premises "all frogs are mammals" and "no cats are mammals". In this regard, it only matters that the conclusion could not be false if the premises are true and not whether they actually are true.

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can be used to draw inferences about what happened before, during, and after an event. Classical logic and its extensions rest on a set of basic logical intuitions accepted by most logicians. They include the

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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

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stand for. For example, the argument "today is Sunday; if today is Sunday then I don't have to go to work today; therefore I don't have to go to work today" is deductively valid because it has the form of

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and covers many additional forms of inferences besides syllogisms. So-called extended logics are based on classical logic and introduce additional rules of inference for specific domains. For example,

418:, 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 331:

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

316:, 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 817:, who holds that future events need not resemble past observations. In this regard, inductive reasoning about future events seems to rest on the assumption that nature remains uniform. 975:

and usually belong to deductive reasoning. Their fault lies in the logical form of the argument, i.e. that it does not follow a valid rule of inference. A well-known formal fallacy is

4878: 2233: 898:. It starts from information about one system and infers information about another system based on the resemblance between the two systems. Expressed schematically, arguments from 704:, and the bivalence of truth. So-called deviant logics reject some of these basic intuitions and propose alternative rules governing the validity of arguments. For example, 367:: 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 4190: 2325: 1070:

by others. When important information is missing, it is often better to suspend judgment than to jump to conclusions. In this regard, logical reasoning should be

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Analogical reasoning can be used to transfer insights from animal experiments to humans, like in the case of research on obesity and hypertension performed on

3603: 2736: 813:. It concerns the question of whether or why anyone is justified in believing the conclusions of inductive inferences. This problem was initially raised by 3867:

Enyeart, Morris A.; Baker, Dale; Vanharlingen, Dave (May 1980). "Correlation of inductive and deductive logical reasoning to college physics achievement".

4493: 3427: 3394: 679:, like concluding that "Socrates is a mortal" from the premises "Socrates is a man" and "all men are mortal". The currently dominant system is known as 498:

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

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and vague expressions in natural language are often responsible for the faulty reasoning in informal fallacies. For example, this is the case for

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

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The rules governing deductive reasoning are often expressed formally as logical systems for assessing the correctness of deductive arguments.

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An argument is correct or incorrect depending on whether the premises offer support for the conclusion. This is often understood in terms of

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fits observed and commonly known facts and that it is relevant, precise, and not circular. Ideally, the explanation should be verifiable by

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do not explicitly state all the premises. Instead, the premises are often implicitly assumed, especially if they seem obvious and belong to

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is one of the earliest systems and was treated as the canon of logic in the Western world for over two thousand years. It is based on

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Logical reasoning is concerned with the correctness of arguments. A key distinction is between deductive and non-deductive arguments.

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Various aspects of the premises are important to ensure that they offer significant support to the conclusion. In this regard, the

5062: 5037: 806:, which often start with many particular observations and then apply the process of generalization to arrive at a universal law. 4656:

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underlines that there are usually many possible explanations of the same fact and that the reasoner should only infer the best

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719:. In mathematics, it is used to prove mathematical theorems based on a set of premises, usually called axioms. For example, 4173: 781:

Based on many individual observations of black ravens, inductive reasoning can be used to infer that all ravens are black.

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are then tested and compared to discover which one provides the best explanation. This pertains particularly to cases of

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person would find the conclusion convincing based on the premises. This way, logical reasoning plays a role in expanding

697: 479:, which study formal and informal logical reasoning. Traditionally, logical reasoning was primarily associated with 5318: 1106: 760: 359:

For non-deductive logical reasoning, the premises make their conclusion rationally convincing without ensuring its

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of the premises and the conclusion but not on their specific content. The most-discussed rule of inference is the

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Doctors use abductive reasoning when investigating the symptoms of a patient to determine their underlying cause.

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4300: 3697: 976: 407: 3411: 3378: 1772: 1506: 524:. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as 371:

not already found in the premises. Non-deductive reasoning plays a central role in everyday life and in most

895: 791: 426:, and to consider the advantages and disadvantages of different courses of action before making a decision. 395:

systems. It observes that one of them has a feature and concludes that the other one also has this feature.

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studied by formal logic. But in a wider sense, it also includes forms of non-deductive reasoning, such as

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Some theorists discuss logical reasoning in a very wide sense that includes its role as a broad

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that is concerned with arriving at a conclusion in a rigorous way. This happens in the form of

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by transforming the information present in a set of

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(1 December 2012). 4335:Johnson, Gregory (6 January 2017). 4086:Internet Encyclopedia of Philosophy 3799:Internet Encyclopedia of Philosophy 3779:Internet Encyclopedia of Philosophy 3759:Stanford Encyclopedia of Philosophy 3430:from the original on 8 January 2022 3413:The Oxford Dictionary of Philosophy 3397:from the original on 8 January 2022 1009:fallacy of the undistributed middle 963:Fallacies are usually divided into 712:reject the principle of explosion. 221: 178: 170: 162: 106: 63: 55: 48: 40: 33: 25: 5246:Walton, Douglas (26 August 2013). 5078:Sriram, Ram D. (6 December 2012). 4678:The Oxford Handbook of Rationality 4414:Kenny, Anthony (15 October 2018). 4399:. Simon and Schuster. p. 57. 4234:The Oxford Companion to Philosophy 4176:from the original on 29 March 2021 3661:Cottrell, Stella (14 March 2017). 3585:Introduction to Mathematical Logic 3299:"Analogy and Analogical Reasoning" 3284:from the original on 14 April 2021 1074:and open-minded at the same time. 14: 4061:Goswami, Usha (23 October 2013). 3545:Cellucci, Carlo (29 March 2017). 3255:Atwater, Lyman Hotchkiss (1867). 1168:, Logical Reasoning and Learning. 979:. It has the following form: (1) 5288:. World Scientific. p. 70. 4839:Nute, Donald (6 December 2012). 4566:Li, Ming; Vitányi, Paul (2019). 4289:. North Holland. pp. 1–12. 4063:Analogical Reasoning in Children 3830:. Wadsworth Publishing Company. 3566:Principles of Scientific Methods 3343:. Springer Nature. p. 110. 3259:. J. B. Lippincott. p. 167. 2306:Asher, Banks & Scheuren 2007 1725:Byrne, Evans & Newstead 2019 475:. It is divided into formal and 432: 5227:Walton, Douglas (15 May 2014). 5040:from the original on 3 May 1998 4767:. Nelson Thornes. p. 167. 4708:. Springer Nature. p. 83. 4500:. Routledge. pp. 366–382. 4452:Kohar, Richard (15 June 2016). 4002:Gambrill, Eileen (1 May 2012). 3987:. Broadview Press. p. 15. 3934:Flick, Uwe (10 December 2013). 3826:Dowden, Bradley Harris (1993). 3179:Amaya, Amalia (30 April 2015). 1966:Priest, Tanaka & Weber 2018 1907:Shapiro & Kouri Kissel 2021 1112:Transduction (machine learning) 447:Logical reasoning is a form of 296:way. It happens in the form of 4130:. Cambridge University Press. 3900:. Cambridge University Press. 3824:(for an earlier version, see: 3713:Demir, Imran (24 March 2017). 3358:Bird, Alexander (9 May 2006). 3270:. Cambridge University Press. 2098:Bertolaso & Sterpetti 2020 1: 5284:Weaver, Nik (22 April 2015). 4316:Jamieson, D. (9 March 2013). 4126:Haack, Susan (27 July 1978). 3753:Douven, Igor (9 March 2011). 2466:1.2 The ubiquity of abduction 2044:Magnani & Bertolotti 2017 1653:Arp, Barbone & Bruce 2018 1592:Copi, Cohen & Rodych 2018 1455:Copi, Cohen & Rodych 2018 902:have the following form: (1) 597:. It has the following form: 5208:Vleet, Jacob E. Van (2011). 4880:A Dictionary of Epidemiology 4803:Directions in Relevant Logic 3564:Chang, Mark (22 July 2014). 1275:, 1. 'Philosophy of logics'. 375:. Often-discussed types are 5265:Walton, Douglas N. (1987). 4943:. OUP Oxford. p. 192. 4921:"Induction, The Problem of" 4883:. Oxford University Press. 4687:10.1093/0195145399.001.0001 4580:10.1007/978-3-030-11298-1_5 4433:Kilcrease, Bethany (2021). 4237:. Oxford University Press. 3813:Dowden, Bradley H. (2020). 3608:. Oxford University Press. 2025:Anshakov & Gergely 2010 874:of their underlying cause. 698:double negation elimination 5337: 5172:. Routledge. p. 746. 5013:. 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Routledge. p. 59. 2130:Nadler & Shapiro 2021 1582:, p. 67-8, 432, 470. 1317:Formal and informal logic 1117:Transduction (psychology) 1059:theoretical and practical 226: 219: 196: 183: 176: 168: 160: 111: 104: 81: 68: 61: 53: 46: 38: 31: 5248:Methods of Argumentation 4980:Enzyklopädie Philosophie 4841:Defeasible Deontic Logic 4784:Handbook of Epistemology 4339:. MIT Press. p. 2. 4210:Henderson, Leah (2022). 3793:Dowden, Bradley (2021). 3773:Dowden, Bradley (2023). 3717:. Springer. p. 32. 2737:affirming the consequent 2248:, p. 432, 450, 470. 1879:Norman & Sylvan 2012 977:affirming the consequent 408:affirming the consequent 5286:Truth And Assertibility 4542:10.1161/01.HYP.13.6.896 4360:WIREs Cognitive Science 3583:Church, Alonzo (1996). 3004:Mele & Rawling 2004 792:probabilistic reasoning 745:non-deductive reasoning 743:. Sometimes, the terms 731:Non-deductive reasoning 4900:"Paraconsistent Logic" 4473:"Defeasible Reasoning" 4471:Koons, Robert (2022). 3889:10.1002/tea.3660170311 2904:Bronkhorst et al. 2020 2648:Ornek & Saleh 2012 2203:, Inductive Reasoning. 1701:8. Deductive reasoning 1568:Bronkhorst et al. 2020 1329:Bronkhorst et al. 2020 1211:Bronkhorst et al. 2020 1178:Bronkhorst et al. 2020 1035:fallacies of ambiguity 997:denying the antecedent 891: 857: 782: 702:principle of explosion 694:law of excluded middle 5193:Oxford Bibliographies 5189:"Inductive Reasoning" 5097:Tomić, Taeda (2013). 5053:Smith, Robin (2020). 4568:"Inductive Reasoning" 4506:10.4324/9781315725697 4356:"Deductive reasoning" 4164:Hansen, Hans (2020). 3938:. SAGE. p. 123. 3919:. Brill. p. 51. 3738:Oxford Bibliographies 3732:Douven, Igor (2022). 3644:Introduction to Logic 3511:. Wiley. p. 25. 3360:Philosophy Of Science 3318:Bartha, Paul (2022). 3297:Bartha, Paul (2019). 2600:Fasko & Fair 2020 2424:Explicating Abduction 2340:, p. 346-7, 432. 2197:Li & Vitányi 2019 1610:, p. 31-2, 67-8. 885: 855: 788:statistical reasoning 780: 710:paraconsistent logics 706:intuitionistic logics 650:disjunctive syllogism 5134:. SAGE. p. 75. 4962:. Cengage Learning. 4128:Philosophy of Logics 2632:Margolis et al. 1986 2509:Bunnin & Yu 2008 1942:Logic, Non-Classical 1775:, rule of inference. 1092:Argumentation theory 1001:affirming a disjunct 811:problem of induction 753:defeasible reasoning 749:ampliative reasoning 493:analogical reasoning 385:analogical reasoning 166:Non‑deductive 5229:Abductive Reasoning 5055:"Aristotle's Logic" 4862:. IAP. p. 82. 4535:(6_pt_2): 896–901. 4286:Philosophy of Logic 3881:1980JRScT..17..263E 3482:2020IJSME..18.1673B 3022:, p. 143, 172. 2234:Inductive Reasoning 2012:, p. 432, 470. 1443:philosophical logic 1424:Philosophy of logic 827:Abductive reasoning 773:Inductive reasoning 568:Deductive reasoning 562:Deductive reasoning 505:mathematical proofs 481:deductive reasoning 329:Deductive reasoning 4082:"Aristotle: Logic" 2968:Conati et al. 2015 2499:, p. 896–901. 1669:Johnson-Laird 2009 1346:, p. 263–267. 1226:Franks et al. 2013 1021:strawman fallacies 1005:denying a conjunct 969:informal fallacies 892: 858: 847:empirical evidence 783: 673:Aristotelian logic 412:informal fallacies 5319:Concepts in logic 5030:"Classical Logic" 3828:Logical Reasoning 3816:Logical Reasoning 3228:978-1-119-16580-4 2894:, p. 263–267 2447:, p. 519-20. 1570:, p. 1676-7. 1374:, p. 5, 432. 1331:, p. 1674-6. 836:. For example, a 587:rule of inference 509:critical thinking 420:critical thinking 338:rule of inference 286:Logical reasoning 283: 282: 273: 272: 264: 263: 255: 254: 246: 245: 237: 236: 207: 206: 149: 148: 140: 139: 131: 130: 122: 121: 92: 91: 5326: 5299: 5280: 5261: 5242: 5223: 5204: 5202: 5200: 5183: 5164: 5145: 5126: 5093: 5074: 5072: 5070: 5049: 5047: 5045: 5024: 5005: 5003: 5002: 4993:. 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3178: 3174: 3169: 3168: 3160: 3156: 3144: 3140: 3132: 3125: 3117: 3113: 3101: 3097: 3089: 3085: 3077: 3073: 3061: 3057: 3049: 3042: 3030: 3026: 3018: 3014: 3002: 2995: 2987: 2978: 2966: 2962: 2950: 2946: 2938: 2931: 2927: 2887: 2883: 2871: 2867: 2855: 2851: 2839: 2835: 2823: 2819: 2807: 2803: 2791: 2787: 2779: 2775: 2763: 2759: 2747: 2743: 2731: 2727: 2715: 2708: 2696: 2692: 2684: 2677: 2669: 2658: 2646: 2642: 2630: 2626: 2614: 2610: 2598: 2594: 2590: 2554: 2550: 2540:Sandkühler 2010 2538: 2534: 2526: 2519: 2507: 2503: 2495: 2491: 2479: 2472: 2460: 2451: 2443: 2430: 2418: 2414: 2402: 2398: 2390: 2383: 2375: 2368: 2360: 2356: 2348: 2344: 2336: 2332: 2320: 2316: 2304: 2300: 2288: 2284: 2272: 2268: 2256: 2252: 2244: 2240: 2228: 2224: 2216: 2207: 2195: 2184: 2172: 2168: 2156: 2152: 2144: 2140: 2128: 2124: 2112: 2108: 2096: 2089: 2077: 2073: 2065: 2054: 2042: 2035: 2023: 2016: 2008: 2004: 1992: 1988: 1976: 1972: 1964: 1960: 1952: 1948: 1936: 1929: 1917: 1913: 1905: 1901: 1893: 1889: 1877: 1873: 1861: 1857: 1849: 1845: 1837: 1833: 1821: 1814: 1802: 1798: 1786: 1779: 1767: 1763: 1751: 1747: 1739: 1735: 1723: 1719: 1711: 1707: 1695: 1691: 1683: 1679: 1667: 1663: 1651: 1647: 1639: 1630: 1618: 1614: 1606: 1602: 1590: 1586: 1578: 1574: 1566: 1562: 1550: 1546: 1542:, p. 67-8. 1538: 1529: 1517: 1513: 1501: 1497: 1485: 1481: 1469: 1465: 1453: 1449: 1437: 1430: 1418: 1407: 1399: 1390: 1382: 1378: 1370: 1366: 1354: 1350: 1342: 1335: 1327: 1323: 1311: 1307: 1295: 1291: 1283: 1279: 1267: 1263: 1251: 1247: 1239: 1232: 1224: 1217: 1213:, p. 1676. 1209: 1205: 1197: 1184: 1180:, p. 1675. 1176: 1172: 1160: 1135: 1130: 1125: 1088: 1052:inconsistencies 1043: 973:formal language 957: 951: 939:decision-making 935:problem-solving 880: 829: 823: 775: 769: 733: 725:natural numbers 681:classical logic 570: 564: 517: 445: 440: 439: 438: 437: 424:inconsistencies 274: 265: 256: 247: 238: 208: 150: 141: 132: 123: 93: 19: 12: 11: 5: 5334: 5333: 5330: 5322: 5321: 5316: 5306: 5305: 5301: 5300: 5294: 5281: 5275: 5262: 5256: 5243: 5237: 5224: 5218: 5205: 5184: 5178: 5165: 5159: 5146: 5140: 5127: 5109:(4): 347–368. 5094: 5088: 5075: 5050: 5025: 5019: 5006: 4989: 4974: 4969:978-1133711643 4968: 4955: 4949: 4936: 4916: 4895: 4889: 4874: 4868: 4855: 4849: 4836: 4830: 4817: 4811: 4798: 4792: 4779: 4773: 4760: 4754: 4741: 4720: 4714: 4701: 4695: 4672: 4666: 4653: 4647: 4634: 4628: 4613: 4607: 4594: 4588: 4563: 4520: 4514: 4489: 4468: 4462: 4449: 4443: 4430: 4424: 4411: 4405: 4392: 4372:10.1002/wcs.20 4351: 4345: 4332: 4326: 4313: 4295: 4280: 4274: 4261: 4243: 4228: 4207: 4201: 4186: 4161: 4155: 4142: 4136: 4123: 4117: 4102: 4077: 4071: 4058: 4037: 4031: 4018: 4012: 3999: 3993: 3980: 3950: 3944: 3931: 3925: 3912: 3906: 3893: 3875:(3): 263–267. 3864: 3858: 3843: 3836: 3810: 3790: 3770: 3750: 3729: 3723: 3710: 3692: 3677: 3671: 3658: 3652: 3639: 3633: 3620: 3614: 3599: 3593: 3580: 3574: 3561: 3555: 3542: 3536: 3523: 3517: 3504: 3461: 3455: 3440: 3422: 3407: 3389: 3374: 3368: 3355: 3349: 3336: 3315: 3294: 3276: 3261: 3252: 3246: 3233: 3227: 3214: 3208: 3195: 3189: 3175: 3173: 3170: 3167: 3166: 3154: 3138: 3123: 3121:, p. 2-5. 3111: 3103:Robertson 2009 3095: 3083: 3071: 3055: 3040: 3024: 3012: 2993: 2976: 2960: 2944: 2929: 2926: 2925: 2916: 2907: 2906:, p. 1674 2901: 2895: 2888: 2881: 2865: 2849: 2833: 2817: 2801: 2785: 2773: 2757: 2741: 2725: 2706: 2698:Kilcrease 2021 2690: 2688:, p. 290. 2675: 2656: 2640: 2624: 2608: 2592: 2589: 2588: 2579: 2570: 2565: 2555: 2548: 2532: 2517: 2501: 2489: 2470: 2449: 2428: 2412: 2396: 2392:Koslowski 2017 2381: 2366: 2354: 2350:Henderson 2022 2342: 2330: 2314: 2298: 2282: 2266: 2250: 2238: 2222: 2205: 2182: 2166: 2150: 2138: 2122: 2106: 2087: 2071: 2069:, p. 470. 2052: 2033: 2014: 2002: 1986: 1970: 1958: 1946: 1927: 1911: 1899: 1887: 1871: 1855: 1843: 1831: 1823:Jacquette 2006 1812: 1796: 1777: 1769:Blackburn 2016 1761: 1745: 1743:, p. 392. 1733: 1717: 1705: 1689: 1687:, p. 432. 1677: 1661: 1645: 1628: 1612: 1600: 1584: 1572: 1560: 1544: 1527: 1511: 1503:Blackburn 2008 1495: 1479: 1463: 1447: 1439:Honderich 2005 1428: 1405: 1388: 1376: 1364: 1348: 1333: 1321: 1305: 1289: 1287:, p. 355. 1277: 1261: 1245: 1230: 1228:, p. 146. 1215: 1203: 1182: 1170: 1132: 1131: 1129: 1126: 1124: 1121: 1120: 1119: 1114: 1109: 1104: 1099: 1094: 1087: 1084: 1042: 1039: 1017:false dilemmas 953:Main article: 950: 947: 906:is similar to 879: 876: 825:Main article: 822: 819: 771:Main article: 768: 765: 732: 729: 689:Temporal logic 566:Main article: 563: 560: 516: 515:Basic concepts 513: 477:informal logic 444: 441: 431: 430: 429: 428: 416:false dilemmas 281: 280: 276: 275: 271: 270: 267: 266: 262: 261: 258: 257: 253: 252: 249: 248: 244: 243: 240: 239: 235: 234: 231: 230: 225: 220: 218: 214: 213: 210: 209: 205: 204: 201: 200: 195: 192: 191: 188: 187: 182: 177: 175: 169: 167: 161: 159: 156: 155: 152: 151: 147: 146: 143: 142: 138: 137: 134: 133: 129: 128: 125: 124: 120: 119: 116: 115: 110: 105: 103: 99: 98: 95: 94: 90: 89: 86: 85: 80: 77: 76: 73: 72: 67: 62: 60: 54: 52: 47: 45: 39: 37: 32: 30: 24: 17: 13: 10: 9: 6: 4: 3: 2: 5332: 5331: 5320: 5317: 5315: 5312: 5311: 5309: 5297: 5295:9789814619981 5291: 5287: 5282: 5278: 5276:9789027250056 5272: 5268: 5263: 5259: 5257:9781107039308 5253: 5249: 5244: 5240: 5238:9780817357825 5234: 5230: 5225: 5221: 5219:9780761854333 5215: 5211: 5206: 5194: 5190: 5185: 5181: 5179:9781317330790 5175: 5171: 5166: 5162: 5160:9780521675994 5156: 5152: 5147: 5143: 5141:9781412909457 5137: 5133: 5128: 5124: 5120: 5116: 5112: 5108: 5104: 5103:Argumentation 5100: 5095: 5091: 5089:9781447106319 5085: 5081: 5076: 5064: 5060: 5056: 5051: 5039: 5035: 5031: 5026: 5022: 5020:9781433107801 5016: 5012: 5007: 4997:on 2021-03-11 4996: 4992: 4990:9783787319992 4986: 4982: 4981: 4975: 4971: 4965: 4961: 4956: 4952: 4950:9780191610219 4946: 4942: 4937: 4926: 4922: 4917: 4905: 4901: 4896: 4892: 4890:9780199976720 4886: 4882: 4881: 4875: 4871: 4869:9781617356100 4865: 4861: 4856: 4852: 4850:9789401588515 4846: 4842: 4837: 4833: 4831:9781441914279 4827: 4823: 4818: 4814: 4812:9789400910058 4808: 4804: 4799: 4795: 4793:9781402019852 4789: 4785: 4780: 4776: 4774:9780748792566 4770: 4766: 4761: 4757: 4755:9780691220086 4751: 4747: 4742: 4730: 4726: 4721: 4717: 4715:9783030580476 4711: 4707: 4702: 4698: 4696:9780195145397 4692: 4688: 4684: 4680: 4679: 4673: 4669: 4667:9789024732715 4663: 4659: 4654: 4650: 4648:9783319305264 4644: 4640: 4635: 4631: 4629:9780028657905 4625: 4622:. Macmillan. 4621: 4620: 4614: 4610: 4608:9781848263239 4604: 4600: 4595: 4591: 4589:9783030112981 4585: 4581: 4577: 4573: 4569: 4564: 4560: 4556: 4552: 4548: 4543: 4538: 4534: 4530: 4526: 4521: 4517: 4515:9781315725697 4511: 4507: 4503: 4499: 4495: 4490: 4478: 4474: 4469: 4465: 4463:9789814730419 4459: 4455: 4450: 4446: 4444:9781487588618 4440: 4436: 4431: 4427: 4425:9781119531173 4421: 4417: 4412: 4408: 4406:9781780741475 4402: 4398: 4393: 4389: 4385: 4381: 4377: 4373: 4369: 4365: 4361: 4357: 4352: 4348: 4346:9780262035255 4342: 4338: 4333: 4329: 4327:9789401583138 4323: 4319: 4314: 4302: 4298: 4296:9780444515414 4292: 4288: 4287: 4281: 4277: 4275:9780198841531 4271: 4267: 4262: 4250: 4246: 4244:9780199264797 4240: 4236: 4235: 4229: 4217: 4213: 4208: 4204: 4202:9780521856485 4198: 4194: 4193: 4187: 4175: 4171: 4167: 4162: 4158: 4156:9781317778370 4152: 4148: 4143: 4139: 4137:9780521293297 4133: 4129: 4124: 4120: 4118:9780226311333 4114: 4110: 4109: 4103: 4091: 4087: 4083: 4078: 4074: 4072:9781317775393 4068: 4064: 4059: 4047: 4043: 4038: 4034: 4032:9781482243147 4028: 4025:. CRC Press. 4024: 4019: 4015: 4013:9780470904381 4009: 4005: 4000: 3996: 3994:9781551114057 3990: 3986: 3981: 3977: 3973: 3969: 3965: 3961: 3957: 3951: 3947: 3945:9781446296691 3941: 3937: 3932: 3928: 3926:9789004444591 3922: 3918: 3913: 3909: 3907:9780521824170 3903: 3899: 3894: 3890: 3886: 3882: 3878: 3874: 3870: 3865: 3861: 3859:9781457695957 3855: 3851: 3850: 3844: 3839: 3837:9780534176884 3833: 3829: 3818: 3817: 3811: 3800: 3796: 3791: 3780: 3776: 3771: 3760: 3756: 3751: 3739: 3735: 3730: 3726: 3724:9783319526058 3720: 3716: 3711: 3699: 3695: 3693:9780415073103 3689: 3686:. Routledge. 3685: 3684: 3678: 3674: 3672:9781350314672 3668: 3664: 3659: 3655: 3653:9781351386975 3649: 3646:. Routledge. 3645: 3640: 3636: 3634:9783319197739 3630: 3626: 3621: 3617: 3615:9780199534067 3611: 3607: 3606: 3600: 3596: 3594:9780691029061 3590: 3586: 3581: 3577: 3575:9781482238099 3571: 3567: 3562: 3558: 3556:9783319532370 3552: 3548: 3543: 3539: 3537:9781317716266 3533: 3529: 3524: 3520: 3518:9780470997215 3514: 3510: 3505: 3501: 3497: 3492: 3487: 3483: 3479: 3475: 3471: 3467: 3462: 3458: 3456:9780028657905 3452: 3449:. Macmillan. 3448: 3447: 3441: 3429: 3425: 3423:9780199541430 3419: 3415: 3414: 3408: 3396: 3392: 3390:9780198735304 3386: 3382: 3381: 3375: 3371: 3369:9781135364236 3365: 3361: 3356: 3352: 3350:9783030250010 3346: 3342: 3337: 3325: 3321: 3316: 3304: 3300: 3295: 3283: 3279: 3277:9781107643796 3273: 3269: 3268: 3262: 3258: 3253: 3249: 3247:9780387728377 3243: 3239: 3234: 3230: 3224: 3220: 3215: 3211: 3209:9783540688754 3205: 3201: 3196: 3192: 3190:9781782255161 3186: 3182: 3177: 3176: 3171: 3164:, p. 10. 3163: 3158: 3155: 3151: 3147: 3142: 3139: 3135: 3130: 3128: 3124: 3120: 3115: 3112: 3108: 3104: 3099: 3096: 3092: 3087: 3084: 3081:, p. 19. 3080: 3075: 3072: 3068: 3064: 3063:Gambrill 2012 3059: 3056: 3052: 3047: 3045: 3041: 3037: 3033: 3032:Cottrell 2017 3028: 3025: 3021: 3016: 3013: 3009: 3005: 3000: 2998: 2994: 2990: 2985: 2983: 2981: 2977: 2973: 2969: 2964: 2961: 2957: 2953: 2948: 2945: 2942:, p. 18. 2941: 2936: 2934: 2930: 2924: 2920: 2917: 2915: 2911: 2908: 2905: 2902: 2899: 2896: 2893: 2890: 2889: 2885: 2882: 2878: 2874: 2869: 2866: 2862: 2858: 2853: 2850: 2846: 2842: 2837: 2834: 2830: 2826: 2821: 2818: 2814: 2810: 2805: 2802: 2798: 2794: 2789: 2786: 2782: 2777: 2774: 2770: 2766: 2761: 2758: 2754: 2750: 2745: 2742: 2738: 2734: 2729: 2726: 2722: 2718: 2713: 2711: 2707: 2703: 2699: 2694: 2691: 2687: 2682: 2680: 2676: 2672: 2667: 2665: 2663: 2661: 2657: 2653: 2649: 2644: 2641: 2637: 2633: 2628: 2625: 2621: 2617: 2612: 2609: 2605: 2601: 2596: 2593: 2587: 2583: 2580: 2578: 2574: 2571: 2569: 2566: 2564: 2560: 2557: 2556: 2552: 2549: 2545: 2541: 2536: 2533: 2529: 2524: 2522: 2518: 2514: 2510: 2505: 2502: 2498: 2493: 2490: 2486: 2482: 2477: 2475: 2471: 2467: 2463: 2458: 2456: 2454: 2450: 2446: 2441: 2439: 2437: 2435: 2433: 2429: 2425: 2421: 2416: 2413: 2409: 2405: 2400: 2397: 2393: 2388: 2386: 2382: 2378: 2373: 2371: 2367: 2363: 2358: 2355: 2351: 2346: 2343: 2339: 2334: 2331: 2327: 2323: 2318: 2315: 2311: 2307: 2302: 2299: 2295: 2291: 2286: 2283: 2279: 2275: 2270: 2267: 2263: 2259: 2254: 2251: 2247: 2242: 2239: 2235: 2231: 2226: 2223: 2219: 2214: 2212: 2210: 2206: 2202: 2198: 2193: 2191: 2189: 2187: 2183: 2179: 2175: 2170: 2167: 2163: 2159: 2154: 2151: 2147: 2142: 2139: 2135: 2131: 2126: 2123: 2119: 2115: 2114:Cellucci 2017 2110: 2107: 2103: 2099: 2094: 2092: 2088: 2084: 2080: 2075: 2072: 2068: 2063: 2061: 2059: 2057: 2053: 2049: 2045: 2040: 2038: 2034: 2030: 2026: 2021: 2019: 2015: 2011: 2006: 2003: 1999: 1995: 1990: 1987: 1983: 1979: 1974: 1971: 1967: 1962: 1959: 1955: 1950: 1947: 1943: 1939: 1938:Borchert 2006 1934: 1932: 1928: 1924: 1920: 1915: 1912: 1908: 1903: 1900: 1896: 1891: 1888: 1884: 1880: 1875: 1872: 1868: 1864: 1859: 1856: 1852: 1847: 1844: 1840: 1835: 1832: 1828: 1824: 1819: 1817: 1813: 1809: 1805: 1800: 1797: 1793: 1789: 1788:Velleman 2006 1784: 1782: 1778: 1774: 1770: 1765: 1762: 1758: 1754: 1753:Jamieson 2013 1749: 1746: 1742: 1737: 1734: 1730: 1726: 1721: 1718: 1714: 1709: 1706: 1702: 1698: 1693: 1690: 1686: 1681: 1678: 1674: 1670: 1665: 1662: 1658: 1654: 1649: 1646: 1642: 1637: 1635: 1633: 1629: 1625: 1621: 1616: 1613: 1609: 1604: 1601: 1597: 1593: 1588: 1585: 1581: 1576: 1573: 1569: 1564: 1561: 1557: 1553: 1548: 1545: 1541: 1536: 1534: 1532: 1528: 1524: 1520: 1515: 1512: 1508: 1504: 1499: 1496: 1492: 1488: 1483: 1480: 1476: 1472: 1467: 1464: 1460: 1456: 1451: 1448: 1444: 1440: 1435: 1433: 1429: 1425: 1421: 1416: 1414: 1412: 1410: 1406: 1402: 1397: 1395: 1393: 1389: 1385: 1380: 1377: 1373: 1368: 1365: 1361: 1357: 1352: 1349: 1345: 1340: 1338: 1334: 1330: 1325: 1322: 1318: 1314: 1309: 1306: 1302: 1298: 1293: 1290: 1286: 1281: 1278: 1274: 1270: 1265: 1262: 1258: 1254: 1249: 1246: 1242: 1237: 1235: 1231: 1227: 1222: 1220: 1216: 1212: 1207: 1204: 1201:, p. 24. 1200: 1195: 1193: 1191: 1189: 1187: 1183: 1179: 1174: 1171: 1167: 1163: 1158: 1156: 1154: 1152: 1150: 1148: 1146: 1144: 1142: 1140: 1138: 1134: 1127: 1122: 1118: 1115: 1113: 1110: 1108: 1105: 1103: 1100: 1098: 1095: 1093: 1090: 1089: 1085: 1083: 1079: 1075: 1073: 1069: 1065: 1060: 1055: 1053: 1048: 1040: 1038: 1036: 1032: 1028: 1024: 1022: 1018: 1012: 1010: 1006: 1002: 998: 994: 990: 986: 982: 978: 974: 970: 966: 961: 956: 948: 946: 944: 940: 936: 931: 927: 925: 921: 917: 913: 909: 905: 901: 897: 889: 884: 877: 875: 873: 868: 864: 854: 850: 848: 842: 839: 835: 828: 820: 818: 816: 812: 807: 805: 800: 795: 793: 789: 779: 774: 766: 764: 762: 761:non-monotonic 757: 754: 750: 746: 742: 737: 730: 728: 726: 722: 718: 713: 711: 707: 703: 699: 695: 690: 686: 682: 678: 674: 669: 667: 663: 659: 655: 651: 647: 643: 639: 635: 631: 630: 629:modus tollens 625: 620: 616: 612: 608: 604: 600: 596: 592: 588: 583: 580: 575: 569: 561: 559: 557: 553: 549: 544: 542: 538: 534: 529: 527: 526:truth-bearers 523: 514: 512: 510: 506: 501: 496: 494: 490: 486: 482: 478: 474: 469: 467: 463: 458: 454: 450: 442: 435: 427: 425: 421: 417: 413: 409: 405: 401: 396: 394: 390: 386: 382: 378: 374: 370: 366: 362: 357: 355: 351: 350: 349:modus tollens 345: 344: 339: 334: 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