Deductive reasoning is reasoning which uses deductive arguments to move from given statements (premises), which are assumed to be true, to conclusions, which must be true if the premises are true. Reasoning is the cognitive process of looking for Reasons for beliefs conclusions actions or feelings In Logic, an argument is a Set of one or more Declarative sentences (or "propositions") known as the Premises along In Discourse and Logic, a premise is a claim that is a reason (or element of a set of reasons for or objection against some other claim A conclusion is a Proposition, which is arrived at after the consideration of Evidence, Arguments or Premises Logic ^[1]

The classic example of deductive reasoning, given by Aristotle, is

• All men are mortal. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. (major premise)
• Socrates is a man. (minor premise)
• Socrates is mortal. (conclusion)

For a detailed treatment of deduction as it is understood in philosophy, see Logic. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language Logic is the study of the principles of valid demonstration and Inference. For a technical treatment of deduction as it is understood in mathematics, see mathematical logic. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic.

Deductive reasoning is often contrasted with inductive reasoning, which reasons from a large number of particular examples to a general rule. Induction or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed

Contents 1 Background 2 Deductive logic 3 Natural deduction 4 Cultural references 5 Further reading 6 References 7 See also

Background

Deductive reasoning was developed by Aristotle, Thales, Pythagoras, and other Greek philosophers of the Classical Period (600 to 300 B. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. Thales of Miletus According to Bertrand Russell, "Philosophy begins with Thales "Pythagoras of Samos" redirects here For the Samian statuary of the same name see Pythagoras (sculptor. C. ). Aristotle, for example, relates a story of how Thales used his skills to deduce that the next season's olive crop would be a very large one. He therefore bought all the olive presses and made a fortune when the bumper olive crop did indeed arrive. ^[2]

Deductive reasoning is dependent on its premises. That is, a false premise can possibly lead to a false result, and inconclusive premises will also yield an inconclusive conclusion. ^[3]

Alternative to deductive reasoning is inductive reasoning. Induction or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed The basic difference between the two can be summarized in the deductive dynamic of logically progressing from general evidence to a particular truth or conclusion; whereas with induction the logical dynamic is precisely the reverse. Inductive reasoning starts with a particular observation that is believed to be a demonstrative model for a truth or principle that is assumed to apply generally.

Deductive reasoning applies general principles to reach specific conclusions, whereas inductive reasoning examines specific information, perhaps many pieces of specific information, to impute a general principle. By thinking about phenomena such as how apples fall and how the planets move, Isaac Newton induced his theory of gravity. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass In the 19th century, Adams and LeVerrier applied Newton's theory (general principle) to deduce the existence, mass, position, and orbit of Neptune (specific conclusions) from perturbations in the observed orbit of Uranus (specific data). The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar The discovery of the planet Neptune remains notable because it resulted from theoretical prediction of the existence of a major solar-system body without having previously seen Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System.

Deductive logic

Deductive reasoning is supported by deductive logic

For example:

All apples are fruit.

All fruits grow on trees.

Therefore all apples grow on trees.

Or

All apples are fruit.

Some apples are red.

Therefore some fruits are red.

The first premise may be false yet anyone accepting the premises is compelled to accept the conclusion.

Natural deduction

Main article: Natural deduction

Deductive reasoning should be distinguished from the related concept of natural deduction, an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs. In Philosophical logic, natural deduction is an approach to Proof theory that attempts to provide a Deductive system which is a formal model of logical In Philosophical logic, natural deduction is an approach to Proof theory that attempts to provide a Deductive system which is a formal model of logical

Cultural references

Sherlock Holmes, the fictional detective created by Sir Arthur Conan Doyle, is well known for referring to deductive reasoning in numerous of Doyle's stories. Sherlock Holmes is a famous fictional detective of the late nineteenth and early twentieth centuries who first appeared in Publication in 1887 Sir Arthur Ignatius Conan Doyle, DL (22 May 1859 – 7 July 1930 was an Anglo-Scottish Author most noted for his stories about the

Further reading

• Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8

• Zarefsky, David, Argumentation: The Study of Effective Reasoning Parts I and II, The Teaching Company 2002

References

See also

Abductive reasoning Analogical reasoning Correspondence theory of truth Defeasible reasoning Hypothetico-deductive method Inquiry Inductive reasoning

Logical consequence Propositional calculus Retroductive reasoning Scientific method Soundness

Abduction, or inference to the best explanation, is a method of Reasoning in which one chooses the hypothesis that would if true best explain the relevant evidence Analogy is both the cognitive process of transferring Information from a particular subject (the analogue or source to another particular subject (the target and The correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i Defeasible reasoning is the study of forms of Reasoning that while convincing are not as formal and rigorous as Deductive reasoning. See also Falsifiability The hypothetico-deductive model, or method is a proposed description of Scientific method. Inquiry or enquiry is any process that has the aim of augmenting Knowledge, resolving Doubt, or solving a Problem. Induction or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed "Therefore" redirects here For the symbol see Therefore sign. This is a technical mathematical article about the area of mathematical logic variously known as "propositional calculus" or "propositional logic" Retroduction is similar to induction, but it is predicated on known or assumed relationary rules and observations that contain at least one of the predicates or Scientific method refers to bodies of Techniques for investigating phenomena In Mathematical logic, a Logical system has the soundness property If and only if its Inference rules prove only formulas that are

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