Inductive Reasoning - Wikipedia
Inductive Reasoning - Wikipedia
Inductive Reasoning - Wikipedia
org/wiki/Inductive_reasoning
Inductive reasoning
From Wikipedia, the free encyclopedia
Many dictionaries define inductive reasoning as the derivation of general principles from specific
observations, though some sources disagree with this usage.[2]
The philosophical definition of inductive reasoning is more nuanced than simple progression from
particular/individual instances to broader generalizations. Rather, the premises of an inductive
logical argument indicate some degree of support (inductive probability) for the conclusion but do
not entail it; that is, they suggest truth but do not ensure it. In this manner, there is the possibility of
moving from general statements to individual instances (for example, statistical syllogisms,
discussed below).
Contents
1 Description
2 Inductive vs. deductive reasoning
3 Criticism
3.1 Biases
4 Types
4.1 Generalization
4.2 Statistical syllogism
4.3 Simple induction
4.4 Argument from analogy
4.5 Causal inference
4.6 Prediction
5 Bayesian inference
6 Inductive inference
7 See also
8 References
9 Further reading
10 External links
Description
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Inductive reasoning is inherently uncertain. It only deals in degrees to which, given the premises,
the conclusion is credible according to some theory of evidence. Examples include a many-valued
logic, DempsterShafer theory, or probability theory with rules for inference such as Bayes' rule.
Unlike deductive reasoning, it does not rely on universals holding over a closed domain of
discourse to draw conclusions, so it can be applicable even in cases of epistemic uncertainty
(technical issues with this may arise however; for example, the second axiom of probability is a
closed-world assumption).[3]
All biological life forms that we know of depend on liquid water to exist.
Therefore, if we discover a new biological life form it will probably depend on liquid water to
exist.
This argument could have been made every time a new biological life form was found, and would
have been correct every time; however, it is still possible that in the future a biological life form not
requiring liquid water could be discovered.
All biological life forms that we know of depend on liquid water to exist.
All biological life probably depends on liquid water to exist.
Given that "if A is true then that would cause B, C, and D to be true", an example of deduction
would be "A is true therefore we can deduce that B, C, and D are true". An example of induction
would be "B, C, and D are observed to be true therefore A might be true". A is a reasonable
explanation for B, C, and D being true.
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For example:
A large enough asteroid impact would create a very large crater and cause a severe impact
winter that could drive the non-avian dinosaurs to extinction.
We observe that there is a very large crater in the Gulf of Mexico dating to very near the time
of the extinction of the non-avian dinosaurs
Therefore it is possible that this impact could explain why the non-avian dinosaurs became
extinct.
Note however that this is not necessarily the case. Other events also coincide with the extinction of
the non-avian dinosaurs. For example, the Deccan Traps in India.
The definition of inductive reasoning described in this article excludes mathematical induction,
which is a form of deductive reasoning that is used to strictly prove properties of recursively
defined sets.[7]
Criticism
Inductive reasoning has been criticized by thinkers as diverse as Sextus Empiricus[8] and Karl
Popper.[9]
The classic philosophical treatment of the problem of induction was given by the Scottish
philosopher David Hume.[10]
Although the use of inductive reasoning demonstrates considerable success, its application has been
questionable. Recognizing this, Hume highlighted the fact that our mind draws uncertain
conclusions from relatively limited experiences. In deduction, the truth value of the conclusion is
based on the truth of the premise. In induction, however, the dependence on the premise is always
uncertain. As an example, let's assume "all ravens are black." The fact that there are numerous
black ravens supports the assumption. However, the assumption becomes inconsistent with the fact
that there are white ravens. Therefore, the general rule of "all ravens are black" is inconsistent with
the existence of the white raven. Hume further argued that it is impossible to justify inductive
reasoning: specifically, that it cannot be justified deductively, so our only option is to justify it
inductively. Since this is circular he concluded that our use of induction is unjustifiable with the
help of Hume's Fork.[11]
However, Hume then stated that even if induction were proved unreliable, we would still have to
rely on it. So instead of a position of severe skepticism, Hume advocated a practical skepticism
based on common sense, where the inevitability of induction is accepted.[12]
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Bertrand Russell illustrated his skepticism in a story about a turkey, fed every morning without fail,
who following the laws of induction concludes this will continue, but then his throat is cut on
Thanksgiving day.[13]
Biases
Inductive reasoning is also known as hypothesis construction because any conclusions made are
based on current knowledge and predictions. As with deductive arguments, biases can distort the
proper application of inductive argument, thereby preventing the reasoner from forming the most
logical conclusion based on the clues. Examples of these biases include the availability heuristic,
confirmation bias, and the predictable-world bias.
The availability heuristic causes the reasoner to depend primarily upon information that is readily
available to him/her. People have a tendency to rely on information that is easily accessible in the
world around them. For example, in surveys, when people are asked to estimate the percentage of
people who died from various causes, most respondents would choose the causes that have been
most prevalent in the media such as terrorism, and murders, and airplane accidents rather than
causes such as disease and traffic accidents, which have been technically "less accessible" to the
individual since they are not emphasized as heavily in the world around him/her.
The confirmation bias is based on the natural tendency to confirm rather than to deny a current
hypothesis. Research has demonstrated that people are inclined to seek solutions to problems that
are more consistent with known hypotheses rather than attempt to refute those hypotheses. Often, in
experiments, subjects will ask questions that seek answers that fit established hypotheses, thus
confirming these hypotheses. For example, if it is hypothesized that Sally is a sociable individual,
subjects will naturally seek to confirm the premise by asking questions that would produce answers
confirming that Sally is in fact a sociable individual.
The predictable-world bias revolves around the inclination to perceive order where it has not been
proved to exist, either at all or at a particular level of abstraction. Gambling, for example, is one of
the most popular examples of predictable-world bias. Gamblers often begin to think that they see
simple and obvious patterns in the outcomes and, therefore, believe that they are able to predict
outcomes based upon what they have witnessed. In reality, however, the outcomes of these games
are difficult to predict and highly complex in nature. However, in general, people tend to seek some
type of simplistic order to explain or justify their beliefs and experiences, and it is often difficult for
them to realise that their perceptions of order may be entirely different from the truth.[14]
Types
Generalization
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Example
There are 20 ballseither black or whitein an urn. To estimate their respective numbers, you
draw a sample of four balls and find that three are black and one is white. A good inductive
generalization would be that there are 15 black and five white balls in the urn.
How much the premises support the conclusion depends upon (a) the number in the sample group,
(b) the number in the population, and (c) the degree to which the sample represents the population
(which may be achieved by taking a random sample). The hasty generalization and the biased
sample are generalization fallacies.
Statistical syllogism
The proportion in the first premise would be something like "3/5ths of", "all", "few", etc. Two dicto
simpliciter fallacies can occur in statistical syllogisms: "accident" and "converse accident".
Simple induction
Simple induction proceeds from a premise about a sample group to a conclusion about another
individual.
This is a combination of a generalization and a statistical syllogism, where the conclusion of the
generalization is also the first premise of the statistical syllogism.
The process of analogical inference involves noting the shared properties of two or more things,
and from this basis inferring that they also share some further property:[15]
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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.[16]
Causal inference
A causal inference draws a conclusion about a causal connection based on the conditions of the
occurrence of an effect. Premises about the correlation of two things can indicate a causal
relationship between them, but additional factors must be confirmed to establish the exact form of
the causal relationship.
Prediction
Bayesian inference
As a logic of induction rather than a theory of belief, Bayesian inference does not determine which
beliefs are a priori rational, but rather determines how we should rationally change the beliefs we
have when presented with evidence. We begin by committing to a prior probability for a hypothesis
based on logic or previous experience, and when faced with evidence, we adjust the strength of our
belief in that hypothesis in a precise manner using Bayesian logic.
Inductive inference
Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of
prediction based on observations; for example, predicting the next symbol based upon a given
series of symbols. This is a formal inductive framework that combines algorithmic information
theory with the Bayesian framework. Universal inductive inference is based on solid philosophical
foundations,[17] and can be considered as a mathematically formalized Occam's razor. Fundamental
ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity.
See also
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Abductive reasoning
Algorithmic information theory
Algorithmic probability
Analogy
Bayesian probability
Counterinduction
Deductive reasoning
Explanation
Failure mode and effects analysis
Falsifiability
Grammar induction
Inductive inference
Inductive logic programming
Inductive probability
Inductive programming
Inductive reasoning aptitude
Inquiry
Kolmogorov complexity
Lateral thinking
Laurence Jonathan Cohen
Logic
Logical positivism
Machine learning
Mathematical induction
Mill's Methods
Minimum description length
Minimum message length
Open world assumption
Raven paradox
Recursive Bayesian estimation
Retroduction
Solomonoff's theory of inductive inference
Statistical inference
Stephen Toulmin
Universal artificial intelligence
References
1. Copi, I. M.; Cohen, C.; Flage, D. E. (2007). Essentials of Logic (Second ed.). Upper Saddle River, NJ:
Pearson Education. ISBN 978-0-13-238034-8.
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2. "Deductive and Inductive Arguments", Internet Encyclopedia of Philosophy, "Some dictionaries define
"deduction" as reasoning from the general to specific and "induction" as reasoning from the specific to
the general. While this usage is still sometimes found even in philosophical and mathematical contexts,
for the most part, it is outdated."
3. Kosko, Bart (1990). "Fuzziness vs. Probability". International Journal of General Systems. 17 (1):
211240. doi:10.1080/03081079008935108.
4. John Vickers. The Problem of Induction (http://plato.stanford.edu/entries/induction-problem/). The
Stanford Encyclopedia of Philosophy.
5. Herms, D. "Logical Basis of Hypothesis Testing in Scientific Research" (pdf).
6. "Stanford Encyclopedia of Philosophy : Kant's account of reason".
7. Chowdhry, K.R. (January 2, 2015). Fundamentals of Discrete Mathematical Structures (3rd ed.). PHI
Learning Pvt. Ltd. p. 26. Retrieved 1 December 2016.
8. Sextus Empiricus, Outlines Of Pyrrhonism. Trans. R.G. Bury, Harvard University Press, Cambridge,
Massachusetts, 1933, p. 283.
9. Popper, Karl R.; Miller, David W. (1983). "A proof of the impossibility of inductive probability".
Nature. 302 (5910): 687688. doi:10.1038/302687a0.
10. David Hume (1910) [1748]. An Enquiry concerning Human Understanding. P.F. Collier & Son.
ISBN 0-19-825060-6.
11. Vickers, John. "The Problem of Induction" (http://plato.stanford.edu/entries/induction-problem
/#2HumIndJus) (Section 2). Stanford Encyclopedia of Philosophy. 21 June 2010
12. Vickers, John. "The Problem of Induction" (http://plato.stanford.edu/entries/induction-problem/#IndJus)
(Section 2.1). Stanford Encyclopedia of Philosophy. 21 June 2010.
13. The story by Russell is found in Alan Chalmers, What is this thing Called Science, Open University
Press, Milton Keynes, 1982, p. 14
14. Gray, Peter (2011). Psychology (Sixth ed.). New York: Worth. ISBN 978-1-4292-1947-1.
15. Baronett, Stan (2008). Logic. Upper Saddle River, NJ: Pearson Prentice Hall. pp. 321325.
16. For more information on inferences by analogy, see Juthe, 2005 (http://www.cs.hut.fi/Opinnot/T-93.850
/2005/Papers/juthe2005-analogy.pdf).
17. Rathmanner, Samuel; Hutter, Marcus (2011). "A Philosophical Treatise of Universal Induction".
Entropy. 13 (6): 10761136. doi:10.3390/e13061076.
Further reading
Cushan, Anna-Marie (1983/2014). Investigation into Facts and Values: Groundwork for a
theory of moral conflict resolution. [Thesis, Melbourne University], Ondwelle Publications
(online): Melbourne. [1] (http://www.ondwelle.com/ValueJudgements.pdf)
Herms, D. "Logical Basis of Hypothesis Testing in Scientific Research" (PDF).
Kemerling, G. (27 October 2001). "Causal Reasoning".
Holland, J. H.; Holyoak, K. J.; Nisbett, R. E.; Thagard, P. R. (1989). Induction: Processes of
Inference, Learning, and Discovery. Cambridge, MA, USA: MIT Press. ISBN 0-262-58096-9.
Holyoak, K.; Morrison, R. (2005). The Cambridge Handbook of Thinking and Reasoning.
New York: Cambridge University Press. ISBN 978-0-521-82417-0.
External links
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