Reasoning is the cognitive process of looking fson]], which cognitive and neural processes are engaged, how cultural factors affect the inferences people draw. The properties of logics which may be used to reason are studied in mathematical logic. The field of automated reasoning studies how reasoning may be modelled computationally. Lawyers also study reasoning.

History of reasoning

It is likely that humans have used reasoning to work out what they should believe or do for a very long time. However, some researchers have tried to determine when, in the history of human development, humans began using formal techniques of reasoning.

Babylonian reasoning

In Mesopotamia, Esagil-kin-apli's medical Diagnostic Handbook written in the 11th century BC was based on a logical set of axioms and assumptions, including the modern view that through the examination and inspection of the symptoms of a patient, it is possible to determine the patient's disease, its aetiology and future development, and the chances of the patient's recovery.¹

During the 8th and 7th centuries BC, Babylonian astronomers began employing an internal logic within their predictive planetary systems, which was an important contribution to logic and the philosophy of science.² Babylonian thought had a considerable influence on early Greek thought.³

Greek reasoning

The works of Homer, written in the eighth century BC, contain mythic stories that use gods to explain the formation of the world. However, only two centuries later, late in the sixth century BC, Xenophanes of Colophon began to question the Homeric accounts of the creation of nature and the gods. He wrote:

• “Homer and Hesiod attribute all things to the gods that among men are shame and a disgrace” (frag. 11).
• “God is one, greatest among gods and among men, in no way like men in form and thought” (frag. 23).
• “If oxen and horses and lions had hands or could paint and make things with their hands like men, then they would paint the forms of gods and make their bodies each according to their own shapes, horses like horses, oxen like oxen” (frag. 15).

According to David Furley, "the basis of [Xenophanes'] criticism appears to have been that he saw an inconsistency between the concept of god as something different from man, and the stories told about the gods, which made them behave as men do."⁴ In the same period, other Greek thinkers began to develop theories about the nature of the world that suggest that they believed that there were regularities in nature and that humans could use reasoning to develop a consistent story about the nature of the world. Thales of Miletus, c. 624 BC – c. 546 BC, proposed that all is water. Anaximenes of Miletus, c. 585 BC – c. 525 BC, claimed that air is the source of everything.⁴

Aristotle is, so far as we know, the first writer to give an extended, systematic treatment of the methods of human reasoning. He identified two major methods of reasoning, analysis and synthesis. In the first, we try to understand an object by looking at its component parts. In the second, we try to understand a class of objects by looking at the common properties of each object in that class.

Aristotle developed what is known as syllogistic logic, which makes it possible to analyse reasoning in a way that ignores the content of the argument and focuses on the form or structure of the argument.⁵ In the Prior Analytics, Aristotle begins by pointing out that:

"[If] no pleasure is a good, neither will any good be a pleasure."⁶

He then argues that this argument is an example of a rule of reasoning of the following form:

Premise: "Aristotle is Greek" and "All Greeks are human"

Conclusion: "Aristotle is Human"

Aristotle points out that by understanding the reasoning involved in this type of argument, we can know that whatever the As and Bs are, we can reach the same conclusion about the relationship between them. This is a simple and straightforward argument, but it is a sign of an amazing leap in understanding and research into reason and was the beginning of the development of formal logic.

Indian reasoning

Two of the six Indian schools of thought deal with logic: Nyaya and Vaisheshika. The Nyaya Sutras of Aksapada Gautama constitute the core texts of the Nyaya school, one of the six orthodox schools of Hindu philosophy. This realist school developed a rigid five-member schema of inference involving an initial premise, a reason, an example, an application and a conclusion. The idealist Buddhist philosophy became the chief opponent to the Naiyayikas. Nagarjuna, the founder of the Madhyamika "Middle Way" developed an analysis known as the "catuskoti" or tetralemma. This four-cornered argumentation systematically examined and rejected the affirmation of a proposition, its denial, the joint affirmation and denial, and finally, the rejection of its affirmation and denial. But it was with Dignaga and his successor Dharmakirti that Buddhist logic reached its height. Their analysis centered on the definition of necessary logical entailment, "vyapti", also known as invariable concomitance or pervasion. To this end a doctrine known as "apoha" or differentiation was developed. This involved what might be called inclusion and exclusion of defining properties. The difficulties involved in this enterprise, in part, stimulated the neo-scholastic school of Navya-Nyāya, which developed a formal analysis of inference in the 16th century.

Chinese reasoning

In China, a contemporary of Confucius, Mozi, "Master Mo", is credited with founding the Mohist school, whose canons dealt with issues relating to valid inference and the conditions of correct conclusions. In particular, one of the schools that grew out of Mohism, the Logicians, are credited by some scholars for their early investigation of formal logic. Unfortunately, due to the harsh rule of Legalism in the subsequent Qin Dynasty, this line of investigation disappeared in China until the introduction of Indian philosophy by Buddhists.

Islamic reasoning

For a time after prophet Muhammad's death, Islamic law placed importance on formulating standards of argument, which gave rise to a novel approach to logic in Kalam, but this approach was later influenced by ideas enistic philosophy]] with the rise of the Mu'tazili philosophers, who highly valued Aristotle's Organon. The works of Hellenistic-influenced Islamic philosophers were crucial in the reception of Aristotelian logic in medieval Europe, along with the commentaries on the Organon by Averroes. The works of al-Farabi, Avicenna, al-Ghazali and other Muslim logicians who often criticized and corrected Aristotelian logic and introduced their own forms of logic, also played a central role in the subsequent development of medieval European logic.

Islamic logic not only included the study of formal patterns of inference and their validity but also elements of the philosophy of language and elements of epistemology and metaphysics. Due to disputes with Arabic grammarians, Islamic philosophers were very interested in working out the relationship between logic and language, and they devoted much discussion to the question of the subject matter and aims of logic in relation to reasoning and speech. In the area of formal logical analysis, they elaborated upon the theory of terms, propositions and syllogisms. They considered the syllogism to be the form to which all rational argumentation could be reduced, and they regarded syllogistic theory as the focal point of logic. Even poetics was considered as a syllogistic art in some fashion by many major Islamic logicians.

Important developments made by Muslim logicians included the development of "Avicennian logic" as a replacement of Aristotelian logic. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism,⁷ temporal modal logic,⁸⁹ and inductive logic.¹⁰¹¹ Other important developments in Islamic philosophy include the development of a strict citation practice, the isnad or "backing", and the development of a scientific method of open inquiry to disprove claims, the ijtihad, which could be generally applied to many types of questions.

Reasoning methods and argumentation

One approach to the study of reasoning is to identify various forms of reasoning that may be used to support or justify conclusions. The main division between forms of reasoning that is made in philosophy is between deductive reasoning and inductive reasoning. Formal logic has been described as 'the science of deduction'.¹² The study of inductive reasoning is generally carried out within the field known as informal logic or critical thinking.

Deductive reasoning

Reasoning in an argument is valid if the argument's conclusion must be true when the premises (the reasons given to support that conclusion) are true. One classic example of deductive reasoning is that found in syllogisms like the following:

Premise 1: All humans are mortal.

Premise 2: Socrates is a human.

Conclusion: Socrates is mortal.

The reasoning in this argument is valid, because there is no way in which the premises, 1 and 2, could be true and the conclusion, 3, be false.

Validity is a property of the reasoning in the argument, not a property of the premises in the argument or the argument as a whole. In fact, the truth or falsity of the premises and the conclusion is irrelevant to the validity of the reasoning in the argument. The following argument, with a false premise and a false conclusion, is also valid, (it has the form of reasoning known as modus ponens).

Premise 1: If green is a color, then grass poisons cows.

Premise 2: Green is a color.

Conclusion: Grass poisons cows.

Again, if the premises in this argument were true, the reasoning is such that the conclusion would also have to be true.

In a deductive argument with valid reasoning the conclusion contains no more information than is contained in the premises. Therefore, deductive reasoning does not increase one's knowledge base, and so is said to be non-ampliative.

Within the field of formal logic, a variety of different forms of deductive reasoning have been developed. These involve abstract reasoning using symbols, logical operators and a set of rules that specify what processes may be followed to arrive at a conclusion. These forms of reasoning include Aristotelian logic, also known as syllogistic logic, propositional logic, predicate logic, and modal logic.

Inductive reasoning

Induction is a form of inference producing propositions about unobserved objects or types, either specifically or generally, based on previous observation. It is used to ascribe properties or relations to objects or types based on previous observations or experiences, or to formulate general statements or laws based on limited observations of recurring phenomenal patterns.

Inductive reasoning contrasts strongly with deductive reasoning in that, even in the best, or strongest, cases of inductive reasoning, the truth of the premises does not guarantee the truth of the conclusion. Instead, the conclusion of an inductive argument follows with some degree of probability. Relatedly, the conclusion of an inductive argument contains more information than is already contained in the premises. Thus, this method of reasoning is ampliative.

A classic example of inductive reasoning comes from the empiricist David Hume:

Premise: The sun has risen in the east every morning up until now.

Conclusion: The sun will also rise in the east tomorrow.

Abductive reasoning

Abductive reasoning, or argument to the best explanation, is a form of inductive reasoning, since the conclusion in an abductive argument does not follow with certainty from its premises and concerns something unobserved. What distinguishes abduction from the other forms of reasoning is an attempt to favor one conclusion above others, by attempting to falsify alternative explanations or by demonstrating the likelihood of the favored conclusion, given a set of more or less disputable assumptions. For example, when a patient displays certain symptoms, there might be various possible causes, but one of these is preferred above others as being more probable.

Analogical reasoning

Analogical reasoning is reasoning from the particular to the particular. An example follows:

Premise 1: Socrates is human and Socrates died.

Premise 2: Plato is human.

Conclusion: Plato will die.

Analogical reasoning can be viewed as a form of inductive reasoning, since the truth of the premises does not guarantee the truth of the conclusion. However, the traditional view is that inductive reasoning is reasoning from the particular to the general, and thus analogical reasoning is distinct from inductive reasoning.¹³ An example of inductive reasoning from the particular to the general follows:

Premise 1: Socrates is human and Socrates died.

Premise 2: Plato is human and Plato died.

Premise 3: Aristotle is human and Aristotle died.

Conclusion: All humans die.

It has been argued that deductive, inductive, and abductive reasoning are all based on a foundation of analogical reasoning.¹⁴

Fallacious reasoning

Flawed reasoning in arguments is known as fallacious reasoning. Reasoning within arguments can be bad because it commits either a formal fallacy or an informal fallacy.

Formal fallacies

Formal fallacies occur when there is a problem with the form, or structure, of the argument. The word 'formal' refers to this link to the form of the argument. An argument that contains a formal fallacy will always be invalid. Consider, for example, the following argument:

1. If a drink is made with boiling water, it will be hot.
2. This drink was not made with boiling water.
3. This drink is not hot.

The reasoning in this argument is bad, because the antecedent (first part) of the conditional (the 'if..., then...' statement) can be false without the consequent (second half) of the conditional being true. In this example, the drink could have been made with boiling milk, or heated in the microwave, and so be hot in spite of the truth of statement 2. This particular formal fallacy is known as denying the antecedent.

Informal fallacies

An informal fallacy is an error in reasoning that occurs due to a problem with the content, rather than mere structure, of the argument. Reasoning that commits an informal fallacy often occurs in an argument that is invalid, that is, contains a formal fallacy. One example of such reasoning is a red herring argument.

An argument can be valid, that is, contain no formal reasoning fallacies, and yet still contain an informal fallacy. The clearest examples of this occur when an argument contains circular reasoning, also known as begging the question.

Psychology

Scientific research into reasoning is carried out within the fields of psychology and cognitive science. Psychological research into reasoning falls into three general areas of research. First, the biological functioning of the brain is studied by neurophysiologists and neuropsychologists. Research in this area includes research into the structure and function of normally functioning brains, and of damaged or otherwise unusual brains. Second, psychologists carry out research on reasoning behaviour. Such research may focus, for example, on how people perform on tests of reasoning, such as intelligence or I.Q. tests, or on how well people's reasoning matches ideals set by logic (see, for example, the Wason test).¹⁵ Third, developmental psychologists investigate the development of reasoning from birth to adulthood. Piaget's theory of cognitive development was the first complete theory of reasoning development. Subsequently, several alternative theories were proposed, including the neo-Piagetian theories of cognitive development. ¹⁶ In addition to carrying out research into reasoning, some psychologists, for example, clinical psychologists and psychotherapists work to alter people's reasoning habits when they are unhelpful.

Cognitive science and artificial intelligence

Cognitive science sees reasoning by the analogy to a data processing, where relations between observed properties of reasoning are used in numerous models leading to evident logically correct conclusions in different circumstances.^{citation needed} The complexity and efficacy of reasoning is considered the critical indicator of cognitive intelligence.^{citation needed} Therefore it is the inevitable component of cognitive decision-making.

In artificial intelligence, philosophers and scientists study reasoning and machines, and consider such questions as whether a machine can properly be considered to reason or think, and, relatedly, what would count as a test for reasoning. (See, for example, the Turing test.)¹⁷

Legal reasoning

Legal reasoning is used when reflecting on the nature of existing laws or when reaching decisions about the relationship between laws and particular court cases.

Thorne McCarty did pioneering early work in the mechanization of legal reasoning for taxation using Micro Planner.¹⁸ More recent work on the formalization and mechanization of legal reasoning can be found in the proceedings of the International Conferences on Artificial Intelligence and Law ( most recently at Stanford in June 2007).

Footnotes

1. ^ H. F. J. Horstmanshoff, Marten Stol, Cornelis Tilburg (2004), Magic and Rationality in Ancient Near Eastern and Graeco-Roman Medicine, p. 99, Brill Publishers, ISBN 9004136665.
2. ^ D. Brown (2000), Mesopotamian Planetary Astronomy-Astrology , Styx Publications, ISBN 9056930362.
3. ^ Giorgio Buccellati (1981), "Wisdom and Not: The Case of Mesopotamia", Journal of the American Oriental Society 101 (1), p. 35-47 [43].
4. ^ ^{a b} Furley, David (1973). "Rationality among the Greeks and Romans". in Wiener, Philip P. Dictionary of the History of Ideas. Scribner. ISBN 0684132931. http://xtf.lib.virginia.edu/xtf/view?docId=DicHist/uvaGenText/tei/DicHist4.xml;chunk.id=dv4-07. Retrieved 2009-12-02. 
5. ^ Aristotle. 350 B.C. Robin Smith (transl.). 1989. Prior Analytics. Indianapolis, Indiana: Hackett Publishing.
6. ^ Aristotle. 350 B.C. Robin Smith (transl.). 1989. Prior Analytics. Indianapolis, Indiana: Hackett Publishing: A2:7
7. ^ Lenn Evan Goodman (2003), Islamic Humanism, p. 155, Oxford University Press, ISBN 0195135806.
8. ^ History of logic: Arabic logic, Encyclopædia Britannica.
9. ^ Dr. Lotfollah Nabavi, Sohrevardi's Theory of Decisive Necessity and kripke's QSS System, Journal of Faculty of Literature and Human Sciences.
10. ^ Science and Muslim Scientists, Islam Herald.
11. ^ Wael B. Hallaq (1993), Ibn Taymiyya Against the Greek Logicians, p. 48. Oxford University Press, ISBN 0198240430.
12. ^ Jeffrey, Richard. 1991. Formal logic: its scope and limits, (3rd ed.). New York: McGraw-Hill:1.
13. ^ Vickers, John, "The Problem of Induction", The Stanford Encyclopedia of Philosophy, 2009, http://plato.stanford.edu/entries/induction-problem/
14. ^ John F. Sowa and Arun K. Majumdar, Analogical Reasoning, in de Moor, Lex, Ganter, eds., Conceptual Structures for Knowledge Creation and Communication, Proceedings of ICCS 2003, LNAI 2746, Springer-Verlag, Berlin, 2003, pp. 16-36. http://www.jfsowa.com/pubs/analog.htm
15. ^ Manktelow, K.I. 1999. Reasoning and Thinking (Cognitive Psychology: Modular Course.). Hove, Sussex:Psychology Press
16. ^ Demetriou, A. (1998). Cognitive development. In A. Demetriou, W. Doise, K. F. M. van Lieshout (Eds.), Life-span developmental psychology (pp. 179-269). London: Wiley.
17. ^ Copeland, Jack. 1993. Artificial Intelligence:a philosophical introduction. Oxford: Blackwell.
18. ^ McCarty, L. Thorne. 1977. 'Reflections on TAXMAN: An Experiment on Artificial Intelligence and Legal Reasoning'. Harvard Law Review. Vol. 90, No. 5.

References

• Copeland, Jack. 1993. Artificial Intelligence:a philosophical introduction. Oxford: Blackwell.
• Furley, David (1973). "Rationality among the Greeks and Romans". in Wiener, Philip P. Dictionary of the History of Ideas. Scribner. ISBN 0684132931. http://xtf.lib.virginia.edu/xtf/view?docId=DicHist/uvaGenText/tei/DicHist4.xml;chunk.id=dv4-07. Retrieved 2009-12-02. 
• Jeffrey, Richard. 1991. Formal logic: its scope and limits, (3rd ed.). New York: McGraw-Hill.
• Kirwin, Christopher. 1995. 'Reasoning'. In Ted Honderich (ed.), The Oxford Companion to Philosophy. Oxford: Oxford University Press.
• Manktelow, K.I. 1999. Reasoning and Thinking (Cognitive Psychology: Modular Course.). Hove, Sussex:Psychology Press
• McCarty, L. Thorne. 1977. 'Reflections on TAXMAN: An Experiment on Artificial Intelligence and Legal Reasoning'. Harvard Law Review. Vol. 90, No. 5.
• Scriven, Michael. 1976. Reasoning. New York: McGraw-Hill. ISBN 0-07-055882-5

See also

Thinking portal

• Casuistry
• Categorical syllogism
• Critical thinking
• Defeasible reasoning
• Evidence
• Inference
• Logic
• Logical fallacy
• Logical reasoning
• Mill's Methods
• Practical reason
• Reason
• Recognition primed decision
• Retroduction
• Theoretical reason
• What the Tortoise Said to Achilles
• Rastafarian reasoning ceremony

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