Two kinds of logical reasoning are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or ''
premise
A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agre ...
'', a conclusion or ''
logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is on ...
'' and a rule or ''
material conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q is ...
'' that implies the ''conclusion'' given the ''precondition'', one can explain the following.
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Deductive reasoning
Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be fals ...
determines whether the truth of a ''conclusion'' can be determined for that ''rule'', based solely on the truth of the premises. Example: "When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet."
Mathematical logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...
and
philosophical logic
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical ...
are commonly associated with this type of reasoning.
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Inductive reasoning
Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' re ...
attempts to support a determination of the ''rule''. It hypothesizes a ''rule'' after numerous examples are taken to be a ''conclusion'' that follows from a ''precondition'' in terms of such a ''rule''. Example: "The grass got wet numerous times when it rained, therefore: the grass always gets wet when it rains." This type of reasoning is commonly associated with
generalization
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteri ...
from
empirical evidence
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
. While they may be persuasive, these arguments are not deductively valid: see the
problem of induction
First formulated by David Hume, the problem of induction questions our reasons for believing that the future will resemble the past, or more broadly it questions predictions about unobserved things based on previous observations. This inferen ...
.
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Abductive reasoning
Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th century ...
, sometimes called ''inference to the best explanation'', selects a
cogent The CoGeNT experiment has searched for dark matter. It uses a single germanium crystal (~100 grams) as a cryogenic detector for WIMP particles. CoGeNT has operated in the Soudan Underground Laboratory since 2009.
Results
Their first announ ...
set of ''preconditions''. Given a true ''conclusion'' and a ''rule'', it attempts to select some possible ''premises'' that, if true also, can support the ''conclusion'', though not uniquely. Example: "When it rains, the grass gets wet. The grass is wet. Therefore, it might have rained." This kind of reasoning can be used to develop a
hypothesis
A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obse ...
, which in turn can be tested by additional reasoning or data.
Diagnostician
Diagnosis is the identification of the nature and cause of a certain phenomenon. Diagnosis is used in many different disciplines, with variations in the use of logic, analytics, and experience, to determine " cause and effect". In systems engin ...
s,
detective
A detective is an investigator, usually a member of a law enforcement agency. They often collect information to solve crimes by talking to witnesses and informants, collecting physical evidence, or searching records in databases. This leads th ...
s, and
scientist
A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of the natural sciences.
In classical antiquity, there was no real ancient analog of a modern scientist. Instead, ...
s often use this type of reasoning.
Within the context of a
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
, these three kinds of reasoning can be described as follows. The construction/creation of the structure of the model is ''abduction''. Assigning values (or probability distributions) to the parameters of the model is ''induction''. Executing/running the model is ''deduction''.
Other kinds of reasoning beside the three common categories above are:
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Defeasible reasoning
In philosophical logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductively valid. It usually occurs when a rule is given, but there may be specific exceptions to the rule, or subclasses that are su ...
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Paraconsistent reasoning
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Probabilistic reasoning Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A diffic ...
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Statistical reasoning
See
Non-demonstrative reasoning
In philosophical logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductively valid. It usually occurs when a rule is given, but there may be specific exceptions to the rule, or subclasses that are ...
for a comparison of these other kinds of reasoning.
See also
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Analogy
Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject ( ...
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Argument
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectic ...
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Argumentation theory
Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory, incl ...
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Critical thinking
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Dialogical logic
Dialogical logic (also known as the logic of dialogues) was conceived as a pragmatic approach to the semantics of logic that resorts to concepts of game theory such as "winning a play" and that of "winning strategy".
Since dialogical logic was the ...
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Fallacy
A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument which may appear stronger than it really is if the fallacy is not spotted. The term in the Western intellectual tradition was intr ...
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Inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...
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Informal logic
Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements). However, the precise definition of "informal logic" is a matter of some dispute. Ralph H. ...
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Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
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Reason
Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, ...
References
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{{Authority control
Logic
Reasoning
Analogy
Arguments
Causal inference
Concepts in epistemology
Concepts in logic
Concepts in metaphysics
Critical thinking
Deductive reasoning
Empiricism
Epistemology of science
Inductive reasoning
Metaphilosophy
Philosophical logic
Philosophy of logic
Philosophy of mathematics
Problem solving skills
Rationalism
Thought
Truth
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