Inductive reasoning is reasoning in which the premises seek to supply strong evidence
for the truth of the conclusion. While the conclusion of a deductive argument is supposed
to be certain, the truth of the conclusion of an inductive argument is supposed to be
probable, based upon the evidence given. The philosophical definition of inductive
reasoning is much 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 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. Many dictionaries define inductive reasoning
as reasoning that derives general principles from specific observations, though some sources
disagree with this usage.
Description 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, Dempster–Shafer 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.
A statistical syllogism is an example of inductive reasoning:
Almost all people are taller than 26 inches Gareth is a person
Therefore, Gareth is almost certainly taller than 26 inches
As a stronger example: 100% of 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 water could be discovered.
As a result, the argument may be stated less formally as:
All biological life forms that we know of depend on liquid water to exist.
All biological life probably depends on liquid water to exist.
Inductive vs. deductive reasoning Unlike deductive arguments, inductive reasoning
allows for the possibility that the conclusion is false, even if all of the premises are
true. Instead of being valid or invalid, inductive arguments are either strong or weak, which
describes how probable it is that the conclusion is true.
A classical example of an incorrect inductive argument was presented by John Vickers:
All of the swans we have seen are white. Therefore, all swans are white.
Note that this definition of inductive reasoning excludes mathematical induction, which is
a form of deductive reasoning. Criticism
Inductive reasoning has been criticized by thinkers as diverse as Sextus Empiricus and
Karl Popper. The classic philosophical treatment of the
problem of induction was given by the Scottish philosopher David Hume.
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".
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.
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. Types
Generalization A generalization proceeds from a premise about
a sample to a conclusion about the population. The proportion Q of the sample has attribute
A. Therefore:
The proportion Q of the population has attribute A.
Example There are 20 balls—either black or white—in
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 the number in the sample group, the number in the population, and the degree
to which the sample represents the population. The hasty generalization and the biased sample
are generalization fallacies. Statistical syllogism
A statistical syllogism proceeds from a generalization to a conclusion about an individual.
A proportion Q of population P has attribute A.
An individual X is a member of P. Therefore:
There is a probability which corresponds to Q that X has A.
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. Proportion Q of the known instances of population
P has attribute A. Individual I is another member of P.
Therefore: There is a probability corresponding to Q
that I has A. 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. Argument from analogy
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:
P and Q are similar in respect to properties a, b, and c.
Object P has been observed to have further property x.
Therefore, Q probably has property x also. 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. 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
A prediction draws a conclusion about a future individual from a past sample.
Proportion Q of observed members of group G have had attribute A.
Therefore: There is a probability corresponding to Q
that other members of group G will have attribute A when next observed.
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 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
Abductive reasoning Algorithmic information theory
Algorithmic probability Analogy
Bayesian probability Counterinduction
Deductive reasoning Explanation
Failure mode and effects analysis Falsifiability
Grammar induction 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
Universal artificial intelligence References
Further reading Cushan, Anna-Marie. Investigation into Facts
and Values: Groundwork for a theory of moral conflict resolution. [Thesis, Melbourne University],
Ondwelle Publications: Melbourne. [1] Herms, D. "Logical Basis of Hypothesis Testing
in Scientific Research". Kemerling, G.. "Causal Reasoning".
Holland, J. H.; Holyoak, K. J.; Nisbett, R. E.; Thagard, P. R.. Induction: Processes of
Inference, Learning, and Discovery. Cambridge, MA, USA: MIT Press. ISBN 0-262-58096-9.
Holyoak, K.; Morrison, R.. The Cambridge Handbook of Thinking and Reasoning. New York: Cambridge
University Press. ISBN 978-0-521-82417-0. External links
Confirmation and Induction entry in the Internet Encyclopedia of Philosophy
Inductive Logic entry in the Stanford Encyclopedia of Philosophy
Inductive reasoning at PhilPapers Inductive reasoning at the Indiana Philosophy
Ontology Project Four Varieties of Inductive Argument from
the Department of Philosophy, University of North Carolina at Greensboro.
Properties of Inductive Reasoning PDF (166 KiB), a psychological review by Evan Heit of the
University of California, Merced. The Mind, Limber An article which employs
the film The Big Lebowski to explain the value of inductive reasoning.
The Pragmatic Problem of Induction, by Thomas Bullemore