Reasoning

Reasoning is the mental (cognitive) process of looking for reasons for beliefs, conclusions, actions or feelings. 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 brain. Specific forms of reasoning are also studied by mathematicians and lawyers.

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 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 accounts of the creation of nature and the gods. He wrote: 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." 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.
 * “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).

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. In the Prior Analytics, Aristotle begins by pointing out that:
 * "[If] no pleasure is a good, neither will any good be a pleasure."

He then argues that this argument is an example of a rule of reasoning of the following form:
 * Premise:   "A belongs to none of the Bs"
 * Conclusion: "B [does not] belong to any of the As".

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.

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'. The study of inductive reasoning is generally carried out within the field known as informal logic or critical thinking.

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:
 * 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 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.

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.

A classical 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 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.

Argument from analogy
Argument from analogy is usually also a form of inductive reasoning. An argument from analogy has the following form:
 * 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.

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.

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:
 * If a drink is made with boiling water, it will be hot.
 * This drink was not made with boiling water.
 * 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 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). 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. The complexity and efficacy of reasoning is considered the critical indicator of cognitive intelligence. 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.)

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. 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).