Deductive reasoning

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Deductive reasoning

Deductive reasoning, sometimes called deductive logic, is reasoning

Reasoning

Reasoning is the Cognition process of looking for reasons for beliefs, conclusions, actions or feelings. Although reasoning was once thought to be a uniquely human capability, other animals also engage in Animal_cognition#Reasoning_and_problem_solving....
which constructs or evaluates deductive arguments. In logic

Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
, an argument is said to be deductive when the truth of the conclusion is purported to follow necessarily or be a logical consequence

Logical consequence

Logical consequence is a fundamental concept in logic. It is the Relation that holds between a Set of Sentence and a sentence when the former Entailment the latter....
of the premises and (consequently) its corresponding conditional is a necessary truth. Deductive arguments are said to be valid or invalid, never true or false.

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Deductive logic

An argument is valid when it is impossible for its premises to be true and its conclusion to be false, or, to put it another way, if the premises were true the conclusion would have to be true, or again, the conclusion follows necessarily from the premises. An argument can be valid even though the premises are false. Note, for example, that the conclusion of the following argument would have to be true if the premises were true, (even though they are, in fact, false):

All fire-breathing rabbits live on Mars

All humans are fire-breathing rabbits

all humans live on Mars

The argument, however, is not sound
Soundness

In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formula that are valid with respect to its semantics....
. In order for a deductive argument to be sound, the premises must be true.

A theory of deductive reasoning known as categorical or term logic

Term logic

In philosophy, term logic, also known as traditional logic, is a loose name for the way of doing logic that began with Aristotle, and that was dominant until the advent of modern predicate logic in the late nineteenth century....
was developed by Aristotle

Aristotle

Aristotle was a Greeks philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, Poetics , theater, music, logic, rhetoric, politics, government, ethics, biology and zoology....
. This was later joined by propositional logic

Propositional calculus

In logic and mathematics, a propositional calculus or logic is a formal system in which formulae representing propositional formulas can be formed by combining atomic formula propositions using logical connectives, and a system of formal proof rules allows certain formul? to be established as "theorem"....
and then superseded by predicate logic

Predicate logic

In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic....
.

Deductive reasoning is often contrasted with inductive reasoning

Inductive reasoning

Isaac Newton

Sir Isaac Newton, Fellow of the Royal Society was an English people physicist, mathematician, Astronomy, Natural philosophy, Alchemy, and Theology and one of the the 100 in human history....
induced his theory of gravity

Newton's law of universal gravitation

Isaac Newton's law of universal gravitation is an empirical physical law describing the gravitational attraction between bodies with mass. It is a part of classical mechanics and was first formulated in Newton's work Philosophiae Naturalis Principia Mathematica, first published on July 5 1687....
. In the 19th century, Adams and LeVerrier

Discovery of Neptune

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 it....
applied Newton's theory (general principle) to deduce the existence, mass

Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
, position, and orbit

ORBit

ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
of Neptune

NEPTUNE

=Overview=The project, along with sister project, VENUS, offers a unique approach to ocean science. Traditionally, ocean scientists have relied on infrequent ship cruises or space-based satellites to carry out their research....
(specific conclusions) from perturbations in the observed orbit of Uranus

Uranus

Uranus is the seventh planet from the Sun and the third-largest and fourth most massive planet in the Solar System. It is named after the ancient Greek deity of the sky Uranus the father of Kronos and grandfather of Zeus ....
(specific data).

Natural deduction

Deductive reasoning should be distinguished from the related concept of natural deduction

Natural deduction

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 reasoning as it "naturally" occurs....
, an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs.

Deductive reasoning

Deductive logic

Natural deduction

Further reading

See also