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Encyclopedia > Reasoning

Reasoning is the mental (cognitive) process of looking for reasons to support beliefs, conclusions, actions or feelings.[1] Humans have the ability to engage in reasoning about their own reasoning using introspection. Different forms of such reflection on reasoning occur in different fields. In philosophy, the study of reasoning typically focuses on what makes reasoning efficient or inefficient, appropriate or inappropriate, good or bad. Philosophers do this by either examining the form or structure of the reasoning within arguments, or by considering the broader methods used to reach particular goals of reasoning. Psychologists and cognitive scientists, in contrast, tend to study how people reason, which brain processes are engaged, and how the reasoning is influenced by the structure of the brian. Specific forms of reasoning are also studied by mathematicians and lawyers. The term cognition is used in several different loosely related ways. ... For other uses, see Reason (disambiguation). ... This article is about the psychological process of introspecting. ... The philosopher Socrates about to take poison hemlock as ordered by the court. ... Psychology (from Greek: ψυχή, psukhē, spirit, soul; and λόγος, logos, knowledge) is both an academic and applied discipline involving the scientific study of mental processes and behavior. ... Cognitive science is usually defined as the scientific study either of mind or of intelligence (e. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ...

Contents

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 indeed. However, some researchers have tried to determine when, in the history of human development, humans have moved from using myths to describe the world to attempting to reason about the world, and when humans first began to reason about their own reasoning.


Greek development of reasoning

The works of Homer, written in the eighth century BCE, contain mythic stories that use gods to explain the formation of the world. However, only two centuries later, late in the sixth century BCE, Xenophanes of Colophon began to question the Homeric mythic accounts of the creation of the nature of the gods. He wrote: Homer (Greek: ) is the name given to the supposed unitary author of the early Greek poems the Iliad and the Odyssey. ... Xenophanes of Colophon (Greek: Ξενοφάνης, 570 BC-480 BC) was a Greek philosopher, poet, and social and religious critic. ...

  • “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."[2] 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 BCE – c. 546 BCE, proposed that all is water. Anaximenes of Miletus, c. 585 BCE – c. 525 BCE, claimed that air is the source of everything.[3] Thales of Miletos (, ca. ... Anaximenes was the name of several notable people in ancient Greece. ...


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'.[4] The study of inductive reasoning is generally carried out within the field known as informal logic or critical thinking. Deductive reasoning is the kind of reasoning where the conclusion is necessitated by previously known premises. ... Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. ... Informal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial (technical) or formal language (see formal logic). ... are you kiddin ? i was lookin for it for hours ...


Deductive reasoning

Main article: Deductive reasoning

Deductive arguments are intended to have reasoning that is valid. 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: Deductive reasoning is the kind of reasoning where the conclusion is necessitated by previously known premises. ... In psychology a conclusion is said to be valid, if and only if, it is based on true premises. ... A syllogism (Greek: — conclusion, inference), usually the categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. ...

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). The form or logical form of an argument is the representation of its sentences using the formal grammar and symbolism of a logical system to display its similarity with all other arguments of the same type. ... In logic, modus ponens (Latin: mode that affirms; often abbreviated MP) is a valid, simple argument form. ...

Premise 1: If green is a colour, then grass poisons cows.
Premise 2: Green is a colour.
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. Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. ... In logic, a logical connective or propositional operator is a syntactic operation on sentences, or the symbol for such an operation, that corresponds to a logical operation on the logical values of those sentences. ... Aristotelian logic, also known as syllogistic logic, is the particular type of logic created by Aristotle, primarily in his works Prior Analytics and De Interpretatione. ... Propositional logic or sentential logic is the logic of propositions, sentences, or clauses. ... ... In philosophical logic, a modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. ...


Inductive reasoning

Main article: Inductive reasoning

Inductive reasoning contrasts strongly with deductive reasoning. 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. Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ... Probability is the likelihood that something is the case or will happen. ...


A classical example of inductive reasoning comes from the empiricist David Hume: In philosophy generally, empiricism is a theory of knowledge emphasizing the role of experience in the formation of ideas, while discounting the notion of innate ideas. ... David Hume (April 26, 1711 – August 25, 1776)[1] was a Scottish philosopher, economist, and historian. ...

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

Main article: abductive reasoning

Abductive reasoning, or argument to the best explanation often involves both inductive and deductive arguments. However, as the conclusion in an abductive argument does not follow with certainty from its premises it is best thought of as a form of inductive reasoning. What separates 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. It has been suggested that Abductive validation be merged into this article or section. ... It has been suggested that Abductive validation be merged into this article or section. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ...


Argument from analogy

Argument from analogy is usually also a form of inductive reasoning. An argument from analogy has the following form: Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ...

A has characteristics x,y, and z
B has characteristics x and y
So, B has (or probably has) characteristic z

Reasoning by analogy goes from one particular thing, or category, to another particular thing, or category. As with other forms of inductive argument, even the best reasoning in an argument from analogy can only make the conclusion probable given the truth of the premises, not certain. The word characteristic has several meanings: In mathematics, see characteristic (algebra) characteristic function characteristic subgroup Euler characteristic method of characteristics In genetics, see characteristic (genetics). ...


Analogical reasoning is very frequent in common sense, science, philosophy and the humanities, but sometimes it is accepted only as an auxiliary method. A refined approach is case-based reasoning. For more information on inferences by analogy, see Juthe, 2005. This article or section does not cite its references or sources. ... Part of a scientific laboratory at the University of Cologne. ... The philosopher Socrates about to take poison hemlock as ordered by the court. ... The humanities are those academic disciplines which study the human condition using methods that are largely analytic, critical, or speculative, as distinguished from the mainly empirical approaches of the natural and social sciences. ... Case-based reasoning (CBR), broadly construed, is the process of solving new problems based on the solutions of similar past problems. ...


Fallacious reasoning

Main article: Logical fallacy

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. It has been suggested that this article or section be merged into Fallacy. ... It has been suggested that this article or section be merged into Fallacy. ... In philosophy, the term logical fallacy properly refers to a formal fallacy : a flaw in the structure of a deductive argument which renders the argument invalid. ... In Philosophical logic, an informal fallacy is a pattern of reasoning which is false due to the falsity of one or more of its premises. ...


Formal fallacies

Main article: Formal fallacy

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: In philosophy, the term logical fallacy properly refers to a formal fallacy : a flaw in the structure of a deductive argument which renders the argument invalid. ...

  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. An antecedent is a preceding phrase or word. ... Look up conditional in Wiktionary, the free dictionary. ... A consequent is the second half of a hypothetical proposition. ... Denying the antecedent (also known as vacuous implication) is a type of logical fallacy. ...


Informal fallacies

Main article: Informal fallacy

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. In Philosophical logic, an informal fallacy is a pattern of reasoning which is false due to the falsity of one or more of its premises. ... Ignoratio elenchi (also known as irrelevant conclusion or irrelevant thesis) is the formal fallacy of presenting an argument that may in itself be valid, but which proves or supports a different proposition than the one it is purporting to prove or support. ...


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. Begging the question, in modern popular usage, is often used synonymously for raising the question. However the original meaning is quite different: it described a type of logical fallacy (also called petitio principii) in which the evidence given for a proposition as much needs to be proved as the proposition... This article needs additional references or sources for verification. ...


Psychology

Scientific research into reasoning is carried out within the fields of psychology and cognitive science. Psychological research into reasoning falls into two 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).[5] 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. Psychology (from Greek: ψυχή, psukhē, spirit, soul; and λόγος, logos, knowledge) is both an academic and applied discipline involving the scientific study of mental processes and behavior. ... Cognitive science is usually defined as the scientific study either of mind or of intelligence (e. ... Neurophysiology is a part of physiology as a science, which is concerned with the study of the nervous system. ... Neuropsychology is a branch of psychology and neurology that aims to understand how the structure and function of the brain relate to specific psychological processes. ... IQ tests are designed to give approximately this Gaussian distribution. ... ... Named in honour of Peter Cathcart Wason, a Wason Test is a logical puzzle which is formally equivalent to the following question: A response which identifies a card which need not be inverted, or a response which fails to identify a card which needs to be inverted are both incorrect. ... The Greek letter Psi is often used as a symbol of psychology. ... Psychotherapy is an interpersonal, relational intervention used by trained psychotherapists to aid clients in problems of living. ...


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. Cognitive science is usually defined as the scientific study either of mind or of intelligence (e. ... Data processing is any computer process that converts data into information or knowledge. ... Complexity in general usage is the opposite of simplicity. ... Efficacy is the ability to produce a desired amount of a desired effect. ... A critic (derived from the ancient Greek word krites meaning a judge) is a person who offers a value judgement or an interpretation. ... Intelligence is a property of mind that encompasses many related abilities, such as the capacities to reason, plan, solve problems, think abstractly, comprehend ideas and language, and learn. ... Decision making is the cognitive process leading to the selection of a course of action among variations. ...


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.)[6] Garry Kasparov playing against Deep Blue, the first machine to win a chess game against a reigning world champion. ... Doctor Who novel named after the test, see The Turing Test. ...


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.[7] 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). Planner (often seen in publications as PLANNER) is a programming language designed by Carl Hewitt at MIT, and first published in 1969. ...


Footnotes

  1. ^ Kirwin, Christopher. 1995. 'Reasoning'. In Ted Honderich (ed.), The Oxford Companion to Philosophy. Oxford: Oxford University Press: p. 748
  2. ^ Furley, David. 2003. 'Rationality among the Greeks and Romans'. In The Gale Group, Dictionary of the history of ideas. University of Virginia Library. [1]
  3. ^ Furley, David. 2003. 'Rationality among the Greeks and Romans'. In The Gale Group, Dictionary of the history of ideas. University of Virginia Library. [2]
  4. ^ Jeffrey, Richard. 1991. Formal logic: its scope and limits, (3rd ed.). New York: McGraw-Hill:1.
  5. ^ Manktelow, K.I. 1999. Reasoning and Thinking (Cognitive Psychology: Modular Course.). Hove, Sussex:Psychology Press
  6. ^ Copeland, Jack. 1993. Artificial Intelligence:a philosophical introduction. Oxford: Blackwell.
  7. ^ McCarty, L. Thorne. 1977. 'Reflections on TAXMAN: An Experiment on Artificial Intelligence and Legal Reasoning'. Harvard Law Review. Vol. 90, No. 5.

The University of Virginia (also called U.Va. ... The University of Virginia (also called U.Va. ... B. Jack Copeland is Professor of Philosophy at the University of Canterbury, Christchurch, New Zealand. ...

References

  • Copeland, Jack. 1993. Artificial Intelligence:a philosophical introduction. Oxford: Blackwell.
  • Furley, David. 2003. 'Rationality among the Greeks and Romans'. In The Gale Group, Dictionary of the history of ideas. University of Virginia Library. [3]</
  • 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

B. Jack Copeland is Professor of Philosophy at the University of Canterbury, Christchurch, New Zealand. ... The University of Virginia (also called U.Va. ... Michael Scriven is an academic who has made significant contributions in the fields of philosophy, psychology, and perhaps most notably, educational evaluation. ...

See also

Logic Portal

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The limits within which reason may be used have been laid down differently in different churches and periods of thought: on the whole, modern Christianity, especially in the Protestant churches, tends to allow to reason a wide field, reserving, however, as the sphere of faith the ultimate (supernatural) truths of theology.
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