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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
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for t ...
beginning in the last third of the 19th century. It starts with an observation or set of observations and then seeks the simplest and most likely conclusion from the observations. This process, unlike
deductive reasoning, yields a plausible conclusion but does not positively verify it. Abductive conclusions are thus qualified as having a remnant of uncertainty or doubt, which is expressed in retreat terms such as "best available" or "most likely". One can understand abductive reasoning as inference to the best explanation, although not all usages of the terms ''abduction'' and ''inference to the best explanation'' are exactly equivalent.
In the 1990s, as computing power grew, the fields of law,
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
, and
artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech r ...
research
[For examples, see]
Abductive Inference in Reasoning and Perception
, John R. Josephson, Laboratory for Artificial Intelligence Research, Ohio State University, and ''Abduction, Reason, and Science. Processes of Discovery and Explanation'' by Lorenzo Magnani
Lorenzo Magnani (born 1952), is an Italian philosopher who teaches philosophy of science in the Department of Humanities, Philosophy Section, at the University of Pavia, where he is full professor and directs the Computational Philosophy Laborator ...
(Kluwer Academic/Plenum Publishers, New York, 2001). spurred renewed interest in the subject of abduction.
Diagnostic
expert systems frequently employ abduction.
Deduction, induction, and abduction
Deduction
Deductive reasoning allows deriving
from
only where
is a formal
logical consequence of
. In other words, deduction derives the consequences of the assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. For example, given that "Wikis can be edited by anyone" (
) and "Wikipedia is a wiki" (
), it follows that "Wikipedia can be edited by anyone" (
).
Induction
Inductive reasoning is the process of inferring some general principle
from a body of knowledge
, where
does not necessarily follow from
.
might give us very good reason to accept
, but does not ensure
. For example, if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. (Indeed, it turns out that
some swans are black.)
Abduction
Abductive reasoning allows inferring
as an explanation of
. As a result of this inference, abduction allows the precondition
to be abducted from the consequence
.
Deductive reasoning and abductive reasoning thus differ in which end, left or right, of the proposition "
entail
In English common law, fee tail or entail is a form of trust established by deed or settlement which restricts the sale or inheritance of an estate in real property and prevents the property from being sold, devised by will, or otherwise alien ...
s
" serves as conclusion.
As such, abduction is formally equivalent to the logical fallacy of
affirming the consequent
Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dar ...
because of multiple possible explanations for
. For example, in a billiard game, after glancing and seeing the ''eight'' ball moving towards us, we may abduce that the cue ball struck the eight ball. The strike of the cue ball would account for the movement of the eight ball. It serves as a hypothesis that explains our observation. Given the many possible explanations for the movement of the eight ball, our abduction does not leave us certain that the cue ball in fact struck the eight ball, but our abduction, still useful, can serve to orient us in our surroundings. Despite many possible explanations for any physical process that we observe, we tend to abduce a single explanation (or a few explanations) for this process in the expectation that we can better orient ourselves in our surroundings and disregard some possibilities. Properly used, abductive reasoning can be a useful source of
priors
Prior (or prioress) is an ecclesiastical title for a superior in some religious orders. The word is derived from the Latin for "earlier" or "first". Its earlier generic usage referred to any monastic superior. In abbeys, a prior would be ...
in
Bayesian statistics
Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...
.
Formalizations of abduction
Logic-based abduction
In
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 premise ...
,
explanation
An explanation is a set of statements usually constructed to describe a set of facts which clarifies the causes, context, and consequences of those facts. It may establish rules or laws, and may clarify the existing rules or laws in relatio ...
is accomplished through the use of a logical theory
representing a
domain and a set of observations
. Abduction is the process of deriving a set of explanations of
according to
and picking out one of those explanations. For
to be an explanation of
according to
, it should satisfy two conditions:
*
follows from
and
;
*
is consistent with
.
In formal logic,
and
are assumed to be sets of
literals. The two conditions for
being an explanation of
according to theory
are formalized as:
:
:
is consistent.
Among the possible explanations
satisfying these two conditions, some other condition of minimality is usually imposed to avoid irrelevant facts (not contributing to the entailment of
) being included in the explanations. Abduction is then the process that picks out some member of
. Criteria for picking out a member representing "the best" explanation include the
simplicity
Simplicity is the state or quality of being simple. Something easy to understand or explain seems simple, in contrast to something complicated. Alternatively, as Herbert A. Simon suggests, something is simple or complex depending on the way we ...
, the
prior probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into ...
, or the explanatory power of the explanation.
A
proof-theoretical abduction method for first order classical logic based on the
sequent calculus
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology i ...
and a dual one, based on semantic tableaux (
analytic tableaux
In proof theory, the semantic tableau (; plural: tableaux, also called truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure compu ...
) have been proposed. The methods are sound and complete and work for full first order logic, without requiring any preliminary reduction of formulae into normal forms. These methods have also been extended to
modal logic.
Abductive logic programming is a computational framework that extends normal
logic programming
Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic pro ...
with abduction. It separates the theory
into two components, one of which is a normal logic program, used to generate
by means of
backward reasoning
Backward chaining (or backward reasoning) is an inference method described colloquially as working backward from the goal. It is used in automated theorem provers, inference engines, proof assistants, and other artificial intelligence applicat ...
, the other of which is a set of integrity constraints, used to filter the set of candidate explanations.
Set-cover abduction
A different formalization of abduction is based on inverting the function that calculates the visible effects of the hypotheses. Formally, we are given a set of hypotheses
and a set of manifestations
; they are related by the domain knowledge, represented by a function
that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations. In other words, for every subset of the hypotheses
, their effects are known to be
.
Abduction is performed by finding a set
such that
. In other words, abduction is performed by finding a set of hypotheses
such that their effects
include all observations
.
A common assumption is that the effects of the hypotheses are independent, that is, for every
, it holds that
. If this condition is met, abduction can be seen as a form of
set covering.
Abductive validation
Abductive validation is the process of validating a given hypothesis through abductive reasoning. This can also be called reasoning through successive approximation. Under this principle, an explanation is valid if it is the best possible explanation of a set of known data. The best possible explanation is often defined in terms of simplicity and elegance (see
Occam's razor). Abductive validation is common practice in hypothesis formation in
science
Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earli ...
; moreover, Peirce claims that it is a ubiquitous aspect of thought:
It was Peirce's own maxim that "Facts cannot be explained by a hypothesis more extraordinary than these facts themselves; and of various hypotheses the least extraordinary must be adopted." After obtaining possible hypotheses that may explain the facts, abductive validation is a method for identifying the most likely hypothesis that should be adopted.
Subjective logic abduction
Subjective logic generalises
probabilistic logic 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 ...
by including degrees of epistemic
uncertainty
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...
in the input arguments, i.e. instead of probabilities, the analyst can express arguments as
subjective opinions. Abduction in subjective logic is thus a generalization of probabilistic abduction described above.
The input arguments in subjective logic are subjective opinions which can be binomial when the opinion applies to a binary variable or multinomial when it applies to an ''n''-ary variable. A subjective opinion thus applies to a state variable
which takes its values from a domain
(i.e. a state space of exhaustive and mutually disjoint state values
), and is denoted by the tuple
, where
is the belief mass distribution over
,
is the epistemic uncertainty mass, and
is the
base rate
In probability and statistics, the base rate (also known as prior probabilities) is the class of probabilities unconditional on "featural evidence" (likelihoods).
For example, if 1% of the population were medical professionals, and remaining ...
distribution over
. These parameters satisfy
and
as well as
.
Assume the domains
and
with respective variables
and
, the set of conditional opinions
(i.e. one conditional opinion for each value
), and the base rate distribution
. Based on these parameters, the subjective
Bayes' theorem denoted with the operator
produces the set of inverted conditionals
(i.e. one inverted conditional for each value
) expressed by:
:
.
Using these inverted conditionals together with the opinion
subjective
deduction denoted by the operator
can be used to abduce the marginal opinion
. The equality between the different expressions for subjective abduction is given below:
:
The symbolic notation for subjective abduction is "
", and the operator itself is denoted as "
". The operator for the subjective Bayes' theorem is denoted "
", and subjective deduction is denoted "
".
[A. Jøsang. ''Subjective Logic: A Formalism for Reasoning Under Uncertainty'', Springer 2016, ]
The advantage of using subjective logic abduction compared to probabilistic abduction is that both aleatoric and epistemic uncertainty about the input argument probabilities can be explicitly expressed and taken into account during the analysis. It is thus possible to perform abductive analysis in the presence of uncertain arguments, which naturally results in degrees of uncertainty in the output conclusions.
History
Introduction and development by Peirce
Overview
The American philosopher Charles Sanders Peirce introduced abduction into modern logic. Over the years he called such inference ''hypothesis'', ''abduction'', ''presumption'', and ''retroduction''. He considered it a topic in logic as a normative field in philosophy, not in purely formal or mathematical logic, and eventually as a topic also in economics of research.
As two stages of the development, extension, etc., of a hypothesis in scientific
inquiry, abduction and also
induction
Induction, Inducible or Inductive may refer to:
Biology and medicine
* Labor induction (birth/pregnancy)
* Induction chemotherapy, in medicine
* Induced stem cells, stem cells derived from somatic, reproductive, pluripotent or other cell t ...
are often collapsed into one overarching concept — the hypothesis. That is why, in the
scientific method
The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific ...
known from
Galileo and
Bacon, the abductive stage of hypothesis formation is conceptualized simply as induction. Thus, in the twentieth century this collapse was reinforced by
Karl Popper's explication of the
hypothetico-deductive model
The hypothetico-deductive model or method is a proposed description of the scientific method. According to it, scientific inquiry proceeds by formulating a hypothesis in a form that can be falsifiable, using a test on observable data where the ou ...
, where the hypothesis is considered to be just "a guess" (in the spirit of Peirce). However, when the formation of a hypothesis is considered the result of a process it becomes clear that this "guess" has already been tried and made more robust in thought as a necessary stage of its acquiring the status of hypothesis. Indeed, many abductions are rejected or heavily modified by subsequent abductions before they ever reach this stage.
Before 1900, Peirce treated abduction as the use of a known rule to explain an observation. For instance: it is a known rule that, if it rains, grass gets wet; so, to explain the fact that the grass on this lawn is wet, one ''abduces'' that it has rained. Abduction can lead to false conclusions if other rules that might explain the observation are not taken into accounte.g. the grass could be wet from
dew
Dew is water in the form of droplets that appears on thin, exposed objects in the morning or evening due to condensation.
As the exposed surface cools by radiating its heat, atmospheric moisture condenses at a rate greater than that at wh ...
. This remains the common use of the term "abduction" in the
social science
Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of so ...
s and in
artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech r ...
.
Peirce consistently characterized it as the kind of inference that originates a hypothesis by concluding in an explanation, though an unassured one, for some very curious or surprising (anomalous) observation stated in a premise. As early as 1865 he wrote that all conceptions of cause and force are reached through hypothetical inference; in the 1900s he wrote that all explanatory content of theories is reached through abduction. In other respects Peirce revised his view of abduction over the years.
In later years his view came to be:
* Abduction is guessing.
[Peirce, C. S.
* "On the Logic of drawing History from Ancient Documents especially from Testimonies" (1901), ''Collected Papers'' v. 7, paragraph 219.
* "PAP" Prolegomena to an Apology for Pragmatism" MS 293 c. 1906, ''New Elements of Mathematics'' v. 4, pp. 319–320.
* A Letter to F. A. Woods (1913), ''Collected Papers'' v. 8, paragraphs 385–388.
(See under]
Abduction
and
at ''Commens Dictionary of Peirce's Terms''.) It is "very little hampered" by rules of logic.
[Peirce, C. S. (1903), Harvard lectures on pragmatism, ''Collected Papers'' v. 5]
Even a well-prepared mind's individual guesses are more frequently wrong than right. But the success of our guesses far exceeds that of random luck and seems born of attunement to nature by instinct
[Peirce, C. S. (1908), "]A Neglected Argument for the Reality of God
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes' ...
", ''Hibbert Journal'' v. 7, pp. 90–112. See both part III and part IV. Reprinted, including originally unpublished portion, in ''Collected Papers'' v. 6, paragraphs 452–85, ''Essential Peirce'' v. 2, pp. 434–50, and elsewhere. (some speak of
intuition
Intuition is the ability to acquire knowledge without recourse to conscious reasoning. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledge; unconscious cognition; ...
in such contexts).
* Abduction guesses a new or outside idea so as to account in a plausible, instinctive, economical way for a surprising or very complicated phenomenon. That is its proximate aim.
* Its longer aim is to economize
inquiry itself. Its rationale is inductive: it works often enough, is the only source of new ideas, and has no substitute in expediting the discovery of new truths. Its rationale especially involves its role in coordination with other modes of inference in inquiry. It is inference to explanatory hypotheses for selection of those best worth trying.
*
Pragmatism
Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. ...
is the logic of abduction. Upon the generation of an explanation (which he came to regard as instinctively guided), the
pragmatic maxim {{C. S. Peirce articles, abbreviations=no
The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce. Serving as a normative recommendation or a regulative princ ...
gives the necessary and sufficient logical rule to abduction in general. The hypothesis, being insecure, needs to have conceivable implications for informed practice, so as to be testable
[Peirce, C. S., Carnegie Application (L75, 1902, ''New Elements of Mathematics'' v. 4, pp. 37–38. See under]
Abduction
at the ''Commens Dictionary of Peirce's Terms'': [Peirce, "Pragmatism as the Logic of Abduction" (Lecture VII of the 1903 Harvard lectures on pragmatism), see parts III and IV. Published in part in ''Collected Papers'' v. 5, paragraphs 180–212 (see 196–200]
and in full in ''Essential Peirce'' v. 2, pp. 226–241 (see sections III and IV). and, through its trials, to expedite and economize inquiry. The economy of research is what calls for abduction and governs its art.
[Peirce, C.S. (1902), application to the Carnegie Institution, see MS L75.329-330, fro]
of Memoir 27:
Writing in 1910, Peirce admits that "in almost everything I printed before the beginning of this century I more or less mixed up hypothesis and induction" and he traces the confusion of these two types of reasoning to logicians' too "narrow and formalistic a conception of inference, as necessarily having formulated judgments from its premises."
He started out in the 1860s treating hypothetical inference in a number of ways which he eventually peeled away as inessential or, in some cases, mistaken:
* as inferring the occurrence of a character (a characteristic) from the observed combined occurrence of multiple characters which its occurrence would necessarily involve;
[(1867), "On the Natural Classification of Arguments", ''Proceedings of the American Academy of Arts and Sciences'' v. 7, pp. 261–287. Presented April 9, 1867. See especially starting at p. 284in Part III §1. Reprinted in ''Collected Papers v. 2, paragraphs 461–516 and ''Writings'' v. 2, pp. 23–49.''] for example, if any occurrence of ''A'' is known to necessitate occurrence of ''B, C, D, E'', then the observation of ''B, C, D, E'' suggests by way of explanation the occurrence of ''A''. (But by 1878 he no longer regarded such multiplicity as common to all hypothetical inference.
[Peirce, C. S. (1878), "Deduction, Induction, and Hypothesis", ''Popular Science Monthly'', v. 13, pp. 470–82, see ]472
__NOTOC__
Year 472 ( CDLXXII) was a leap year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Festus and Marcianus (or, less frequently, year 1225 ''A ...
''Collected Papers'' 2.619–44, see 623.Wikisource
* as aiming for a more or less probable hypothesis (in 1867 and 1883 but not in 1878; anyway by 1900 the justification is not probability but the lack of alternatives to guessing and the fact that guessing is fruitful;[A letter to Langley, 1900, published in ''Historical Perspectives on Peirce's Logic of Science''. See excerpts under]
at the ''Commens Dictionary of Peirce's Terms''. by 1903 he speaks of the "likely" in the sense of nearing the truth in an "indefinite sense"; by 1908 he discusses ''plausibility'' as instinctive appeal.) In a paper dated by editors as ''circa'' 1901, he discusses "instinct" and "naturalness", along with the kind of considerations (low cost of testing, logical caution, breadth, and incomplexity) that he later calls methodeutical.
* as induction from characters (but as early as 1900 he characterized abduction as guessing)
* as citing a known rule in a premise rather than hypothesizing a rule in the conclusion (but by 1903 he allowed either approach[Peirce, C. S., "A Syllabus of Certain Topics of Logic" (1903), ''Essential Peirce'' v. 2, p. 287:
])
* as basically a transformation of a deductive categorical syllogism (but in 1903 he offered a variation on ''modus ponens'' instead, and by 1911 he was unconvinced that any one form covers all hypothetical inference[A Letter to J. H. Kehler (1911), ''New Elements of Mathematics'' v. 3, pp. 203–4, see under]
at ''Commens Dictionary of Peirce's Terms''.).
''The Natural Classification of Arguments'' (1867)
In 1867, Peirce's "On the Natural Classification of Arguments", hypothetical inference always deals with a cluster of characters (call them ''P′, P′′, P′′′,'' etc.) known to occur at least whenever a certain character (''M'') occurs. Note that categorical syllogisms have elements traditionally called middles, predicates, and subjects. For example: All ''men'' iddleare ''mortal'' redicate ''Socrates'' ubjectis a ''man'' iddle ergo ''Socrates'' ubjectis ''mortal'' redicate. Below, 'M' stands for a middle; 'P' for a predicate; 'S' for a subject. Peirce held that all deduction can be put into the form of the categorical syllogism Barbara (AAA-1).
''Deduction, Induction, and Hypothesis'' (1878)
In 1878, in "Deduction, Induction, and Hypothesis", there is no longer a need for multiple characters or predicates in order for an inference to be hypothetical, although it is still helpful. Moreover, Peirce no longer poses hypothetical inference as concluding in a ''probable'' hypothesis. In the forms themselves, it is understood but not explicit that induction involves random selection and that hypothetical inference involves response to a "very curious circumstance". The forms instead emphasize the modes of inference as rearrangements of one another's propositions (without the bracketed hints shown below).
''A Theory of Probable Inference'' (1883)
Peirce long treated abduction in terms of induction from characters or traits (weighed, not counted like objects), explicitly so in his influential 1883 "A theory of probable inference", in which he returns to involving probability in the hypothetical conclusion. Like "Deduction, Induction, and Hypothesis" in 1878, it was widely read (see the historical books on statistics by Stephen Stigler
Stephen Mack Stigler (born August 10, 1941) is Ernest DeWitt Burton Distinguished Service Professor at the Department of Statistics of the University of Chicago. He has authored several books on the history of statistics; he is the son of the e ...
), unlike his later amendments of his conception of abduction. Today abduction remains most commonly understood as induction from characters and extension of a known rule to cover unexplained circumstances.
Sherlock Holmes used this method of reasoning in the stories of Arthur Conan Doyle, although Holmes refers to it as " deductive reasoning".
''Minute Logic'' (1902) and after
In 1902 Peirce wrote that he now regarded the syllogistical forms and the doctrine of extension and comprehension (i.e., objects and characters as referenced by terms), as being less fundamental than he had earlier thought. In 1903 he offered the following form for abduction:
The hypothesis is framed, but not asserted, in a premise, then asserted as rationally suspectable in the conclusion. Thus, as in the earlier categorical syllogistic form, the conclusion is formulated from some premise(s). But all the same the hypothesis consists more clearly than ever in a new or outside idea beyond what is known or observed. Induction in a sense goes beyond observations already reported in the premises, but it merely amplifies ideas already known to represent occurrences, or tests an idea supplied by hypothesis; either way it requires previous abductions in order to get such ideas in the first place. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts.
Note that the hypothesis ("A") could be of a rule. It need not even be a rule strictly necessitating the surprising observation ("C"), which needs to follow only as a "matter of course"; or the "course" itself could amount to some known rule, merely alluded to, and also not necessarily a rule of strict necessity. In the same year, Peirce wrote that reaching a hypothesis may involve placing a surprising observation under either a newly hypothesized rule or a hypothesized combination of a known rule with a peculiar state of facts, so that the phenomenon would be not surprising but instead either necessarily implied or at least likely.
Peirce did not remain quite convinced about any such form as the categorical syllogistic form or the 1903 form. In 1911, he wrote, "I do not, at present, feel quite convinced that any logical form can be assigned that will cover all 'Retroductions'. For what I mean by a Retroduction is simply a conjecture which arises in the mind."
Pragmatism
In 1901 Peirce wrote, "There would be no logic in imposing rules, and saying that they ought to be followed, until it is made out that the purpose of hypothesis requires them." In 1903 Peirce called pragmatism
Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. ...
"the logic of abduction" and said that the pragmatic maxim {{C. S. Peirce articles, abbreviations=no
The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce. Serving as a normative recommendation or a regulative princ ...
gives the necessary and sufficient logical rule to abduction in general. The pragmatic maxim is:
It is a method for fruitful clarification of conceptions by equating the meaning of a conception with the conceivable practical implications of its object's conceived effects. Peirce held that that is precisely tailored to abduction's purpose in inquiry, the forming of an idea that could conceivably shape informed conduct. In various writings in the 1900s he said that the conduct of abduction (or retroduction) is governed by considerations of economy, belonging in particular to the economics of research. He regarded economics as a normative science whose analytic portion might be part of logical methodeutic (that is, theory of inquiry).
Three levels of logic about abduction
Peirce came over the years to divide (philosophical) logic into three departments:
# Stechiology, or speculative grammar, on the conditions for meaningfulness. Classification of signs (semblances, symptoms, symbols, etc.) and their combinations (as well as their objects and interpretants).
# Logical critic, or logic proper, on validity or justifiability of inference, the conditions for true representation. Critique of arguments in their various modes (deduction, induction, abduction).
# Methodeutic, or speculative rhetoric, on the conditions for determination of interpretations. Methodology of inquiry in its interplay of modes.
Peirce had, from the start, seen the modes of inference as being coordinated together in scientific inquiry and, by the 1900s, held that hypothetical inference in particular is inadequately treated at the level of critique of arguments. To increase the assurance of a hypothetical conclusion, one needs to deduce implications about evidence to be found, predictions which induction can test through observation so as to evaluate the hypothesis. That is Peirce's outline of the scientific method of inquiry, as covered in his inquiry methodology, which includes pragmatism
Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. ...
or, as he later called it, pragmaticism
"Pragmaticism" is a term used by Charles Sanders Peirce for his pragmatic philosophy starting in 1905, in order to distance himself and it from pragmatism, the original name, which had been used in a manner he did not approve of in the "literary ...
, the clarification of ideas in terms of their conceivable implications regarding informed practice.
=Classification of signs
=
As early as 1866, Peirce held that:
1. Hypothesis (abductive inference) is inference through an ''icon'' (also called a ''likeness'').
2. Induction is inference through an ''index'' (a sign by factual connection); a sample is an index of the totality from which it is drawn.
3. Deduction is inference through a ''symbol'' (a sign by interpretive habit irrespective of resemblance or connection to its object).
In 1902, Peirce wrote that, in abduction: "It is recognized that the phenomena are ''like'', i.e. constitute an Icon of, a replica of a general conception, or Symbol."
=Critique of arguments
=
At the critical level Peirce examined the forms of abductive arguments (as discussed above), and came to hold that the hypothesis should economize explanation for plausibility in terms of the feasible and natural. In 1908 Peirce described this plausibility in some detail. It involves not likeliness based on observations (which is instead the inductive evaluation of a hypothesis), but instead optimal simplicity in the sense of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity" (Peirce does not dismiss logical simplicity entirely but sees it in a subordinate role; taken to its logical extreme it would favor adding no explanation to the observation at all). Even a well-prepared mind guesses oftener wrong than right, but our guesses succeed better than random luck at reaching the truth or at least advancing the inquiry, and that indicates to Peirce that they are based in instinctive attunement to nature, an affinity between the mind's processes and the processes of the real, which would account for why appealingly "natural" guesses are the ones that oftenest (or least seldom) succeed; to which Peirce added the argument that such guesses are to be preferred since, without "a natural bent like nature's", people would have no hope of understanding nature. In 1910 Peirce made a three-way distinction between probability, verisimilitude, and plausibility, and defined plausibility with a normative "ought": "By plausibility, I mean the degree to which a theory ought to recommend itself to our belief independently of any kind of evidence other than our instinct urging us to regard it favorably." For Peirce, plausibility does not depend on observed frequencies or probabilities, or on verisimilitude, or even on testability, which is not a question of the critique of the hypothetical inference ''as'' an inference, but rather a question of the hypothesis's relation to the inquiry process.
The phrase "inference to the best explanation" (not used by Peirce but often applied to hypothetical inference) is not always understood as referring to the most simple and natural hypotheses (such as those with the fewest assumptions). However, in other senses of "best", such as "standing up best to tests", it is hard to know which is the best explanation to form, since one has not tested it yet. Still, for Peirce, any justification of an abductive inference as "good" is not completed upon its formation as an argument (unlike with induction and deduction) and instead depends also on its methodological role and promise (such as its testability) in advancing inquiry.
=Methodology of inquiry
=
At the methodeutical level Peirce held that a hypothesis is judged and selected for testing because it offers, via its trial, to expedite and economize the inquiry process itself toward new truths, first of all by being testable and also by further economies, in terms of cost, value, and relationships among guesses (hypotheses). Here, considerations such as probability, absent from the treatment of abduction at the critical level, come into play. For examples:
* Cost: A simple but low-odds guess, if low in cost to test for falsity, may belong first in line for testing, to get it out of the way. If surprisingly it stands up to tests, that is worth knowing early in the inquiry, which otherwise might have stayed long on a wrong though seemingly likelier track.
* Value: A guess is intrinsically worth testing if it has instinctual plausibility or reasoned objective probability, while subjective likelihood, though reasoned, can be treacherous.
* Interrelationships: Guesses can be chosen for trial strategically for their
** ''caution'', for which Peirce gave as an example the game of Twenty Questions,
** ''breadth'' of applicability to explain various phenomena, and
** ''incomplexity'', that of a hypothesis that seems too simple but whose trial "may give a good 'leave', as the billiard-players say", and be instructive for the pursuit of various and conflicting hypotheses that are less simple.[Peirce, "On the Logic of Drawing Ancient History from Documents", ''Essential Peirce'' v. 2, see pp. 107–9 and 113. On Twenty Questions, p. 109, Peirce has pointed out that if each question eliminates half the possibilities, twenty questions can choose from among 220 or 1,048,576 objects, and goes on to say: ]
Uberty
Peirce indicated that abductive reasoning is driven by the need for "economy in research"—the expected fact-based productivity of hypotheses, prior to deductive and inductive processes of verification. A key concept proposed by him in this regard is " uberty"—the expected fertility and pragmatic value of reasoning. This concept seems to be gaining support via association to the Free Energy Principle
The free energy principle is a mathematical principle in biophysics and cognitive science that provides a formal account of the representational capacities of physical systems: that is, why things that exist look as if they track properties of the ...
.
Gilbert Harman (1965)
Gilbert Harman is a professor of philosophy at Princeton University
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...
. Harman's 1965 account of the role of "inference to the best explanation" – inferring the existence of that which we need for the best explanation of observable phenomena – has been very influential.
Stephen Jay Gould (1995)
Stephen Jay Gould, in answering the Omphalos hypothesis
The Omphalos hypothesis is one attempt to reconcile the scientific evidence that the Earth is billions of years old with a literal interpretation of the Genesis creation narrative, which implies that the Earth is only a few thousand years old. ...
, claimed that only hypotheses that can be proved incorrect lie within the domain of science
Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earli ...
and only these hypotheses are good explanations of facts worth inferring to.
Applications
Artificial intelligence
Applications in artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech r ...
include fault diagnosis, belief revision Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational ag ...
, and automated planning
Automation describes a wide range of technologies that reduce human intervention in processes, namely by predetermining decision criteria, subprocess relationships, and related actions, as well as embodying those predeterminations in machines ...
. The most direct application of abduction is that of automatically detecting faults in systems: given a theory relating faults with their effects and a set of observed effects, abduction can be used to derive sets of faults that are likely to be the cause of the problem.
Medicine
In medicine
Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...
, abduction can be seen as a component of clinical evaluation and judgment.
Automated planning
Abduction can also be used to model automated planning
Automation describes a wide range of technologies that reduce human intervention in processes, namely by predetermining decision criteria, subprocess relationships, and related actions, as well as embodying those predeterminations in machines ...
. Given a logical theory relating action occurrences with their effects (for example, a formula of the event calculus The event calculus is a logical language for representing and reasoning about events and their effects first presented by Robert Kowalski and Marek Sergot in 1986. It was extended by Murray Shanahan and Rob Miller in the 1990s. Similar to other l ...
), the problem of finding a plan for reaching a state can be modeled as the problem of abducting a set of literals implying that the final state is the goal state.
Intelligence analysis
In intelligence analysis
Intelligence analysis is the application of individual and collective cognitive methods to weigh data and test hypotheses within a secret socio-cultural context. The descriptions are drawn from what may only be available in the form of deliberate ...
, analysis of competing hypotheses
The analysis of competing hypotheses (ACH) is a methodology for evaluating multiple competing hypotheses for observed data. It was developed by Richards (Dick) J. Heuer, Jr., a 45-year veteran of the Central Intelligence Agency, in the 1970s for ...
and Bayesian network
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bay ...
s, probabilistic abductive reasoning is used extensively. Similarly in medical diagnosis
Medical diagnosis (abbreviated Dx, Dx, or Ds) is the process of determining which disease or condition explains a person's symptoms and signs. It is most often referred to as diagnosis with the medical context being implicit. The information r ...
and legal reasoning, the same methods are being used, although there have been many examples of errors, especially caused by the base rate fallacy
The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (i.e., general prevalence) in favor of the individuating information (i.e., information pertaining only to a ...
and the prosecutor's fallacy
The prosecutor's fallacy is a fallacy of statistical reasoning involving a test for an occurrence, such as a DNA match. A positive result in the test may paradoxically be more likely to be an erroneous result than an actual occurrence, even i ...
.
Belief revision
Belief revision Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational ag ...
, the process of adapting beliefs in view of new information, is another field in which abduction has been applied. The main problem of belief revision is that the new information may be inconsistent with the prior web of belief
Web most often refers to:
* Spider web, a silken structure created by the animal
* World Wide Web or the Web, an Internet-based hypertext system
Web, WEB, or the Web may also refer to:
Computing
* WEB, a literate programming system created by ...
s, while the result of the incorporation cannot be inconsistent. The process of updating the web of beliefs can be done by the use of abduction: once an explanation for the observation has been found, integrating it does not generate inconsistency.
This use of abduction is not straightforward, as adding propositional formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional for ...
e to other propositional formulae can only make inconsistencies worse. Instead, abduction is done at the level of the ordering of preference of the possible world
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their me ...
s. Preference models use fuzzy logic or utility models.
Philosophy of science
In the philosophy of science
Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ult ...
, abduction has been the key inference method to support scientific realism
Scientific realism is the view that the universe described by science is real regardless of how it may be interpreted.
Within philosophy of science, this view is often an answer to the question "how is the success of science to be explained?" Th ...
, and much of the debate about scientific realism is focused on whether abduction is an acceptable method of inference.
Historical linguistics
In historical linguistics
Historical linguistics, also termed diachronic linguistics, is the scientific study of language change over time. Principal concerns of historical linguistics include:
# to describe and account for observed changes in particular languages
# ...
, abduction during language acquisition is often taken to be an essential part of processes of language change such as reanalysis and analogy.
Applied linguistics
In applied linguistics
Applied linguistics is an interdisciplinary field which identifies, investigates, and offers solutions to language-related real-life problems. Some of the academic fields related to applied linguistics are education, psychology, communication rese ...
research, abductive reasoning is starting to be used as an alternative explanation to inductive reasoning, in recognition of anticipated outcomes of qualitative inquiry playing a role in shaping the direction of analysis. It is defined as "The use of an unclear premise based on observations, pursuing theories to try to explain it" (Rose et al., 2020, p. 258)
Anthropology
In anthropology
Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of be ...
, Alfred Gell
Alfred Antony Francis Gell, (; June 12, 1945 – January 28, 1997) was a British social anthropologist whose most influential work concerned art, language, symbolism and ritual. He was trained by Edmund Leach (MPhil, Cambridge University) and R ...
in his influential book ''Art and Agency'' defined abduction (after Eco) as "a case of synthetic inference 'where we find some very curious circumstances, which would be explained by the supposition that it was a case of some general rule, and thereupon adopt that supposition. Gell criticizes existing "anthropological" studies of art for being too preoccupied with aesthetic value and not preoccupied enough with the central anthropological concern of uncovering "social relationships", specifically the social contexts in which artworks are produced, circulated, and received. Abduction is used as the mechanism for getting from art to agency. That is, abduction can explain how works of art inspire a ''sensus communis:'' the commonly held views shared by members that characterize a given society.[Whitney D. (2006) "Abduction the agency of art". Retrieved May 2009 from]
University of California, Berkeley
The question Gell asks in the book is, "how does it initially 'speak' to people?" He answers by saying that "No reasonable person could suppose that art-like relations between people and things do not involve at least some form of semiosis." However, he rejects any intimation that semiosis can be thought of as a language because then he would have to admit to some pre-established existence of the ''sensus communis'' that he wants to claim only emerges afterwards out of art. Abduction is the answer to this conundrum because the tentative nature of the abduction concept (Peirce likened it to guessing) means that not only can it operate outside of any pre-existing framework, but moreover, it can actually intimate the existence of a framework. As Gell reasons in his analysis, the physical existence of the artwork prompts the viewer to perform an abduction that imbues the artwork with intentionality. A statue of a goddess, for example, in some senses actually becomes the goddess in the mind of the beholder; and represents not only the form of the deity but also her intentions (which are adduced from the feeling of her very presence). Therefore, through abduction, Gell claims that art can have the kind of agency that plants the seeds that grow into cultural myths. The power of agency is the power to motivate actions and inspire ultimately the shared understanding that characterizes any given society.
Computer programming
In formal methods
In computer science, formal methods are mathematically rigorous techniques for the specification, development, and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the exp ...
logic is used to specify and prove properties of computer programs. Abduction has been used in mechanized reasoning tools to increase the level of automation of the proof activity.
A technique known as bi-abduction, which mixes abduction and the frame problem
In artificial intelligence, the frame problem describes an issue with using first-order logic (FOL) to express facts about a robot in the world. Representing the state of a robot with traditional FOL requires the use of many axioms that simply impl ...
, was used to scale reasoning techniques for memory properties to millions of lines of code; logic-based abduction was used to infer pre-conditions for individual functions in a program, relieving the human of the need to do so. It led to a program-proof startup company which was acquired by Facebook, and the Infer program analysis tool which led to thousands of bugs being prevented in industrial codebases.
In addition to inference of function preconditions, abduction has been used to automate inference of invariants for program loops, inference of specifications of unknown code, and in synthesis of the programs themselves.
See also
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Notes
References
* .
*Awbrey, Jon, and Awbrey, Susan (1995), "Interpretation as Action: The Risk of Inquiry", ''Inquiry: Critical Thinking Across the Disciplines'', 15, 40–52
Eprint
*Cialdea Mayer, Marta and Pirri, Fiora (1993) "First order abduction via tableau and sequent calculi" Logic Jnl IGPL 1993 1: 99–117;
Oxford Journals
*Cialdea Mayer, Marta and Pirri, Fiora (1995) "Propositional Abduction in Modal Logic", Logic Jnl IGPL 1995 3: 907–919;
Oxford Journals
*Edwards, Paul (1967, eds.), "The Encyclopedia of Philosophy," Macmillan Publishing Co, Inc. & The Free Press, New York. Collier Macmillan Publishers, London.
*, T., and Gottlob, G. (1995),
The Complexity of Logic-Based Abduction
''Journal of the ACM'', 42.1, 3–42.
*Hanson, N. R. (1958). ''Patterns of Discovery: An Inquiry into the Conceptual Foundations of Science'', Cambridge: Cambridge University Press. .
*
*Josephson, John R., and Josephson, Susan G. (1995, eds.),
Abductive Inference: Computation, Philosophy, Technology
', Cambridge University Press, Cambridge, UK.
*Lipton, Peter. (2001). ''Inference to the Best Explanation'', London: Routledge. .
* Magnani, Lorenzo (2014), "Understanding abduction", ''Model-Based Reasoning in Science and Technology: Theoretical and Cognitive Issues'' (editor—Magnani L.) Springer, p. 173-205.
*McKaughan, Daniel J. (2008), "From Ugly Duckling to Swan: C. S. Peirce, Abduction, and the Pursuit of Scientific Theories", ''Transactions of the Charles S. Peirce Society'', v. 44, no. 3 (summer), 446–468.
*
*Queiroz, Joao & Merrell, Floyd (guest eds.). (2005). "Abduction - between subjectivity and objectivity". (special issue on abductive inference) ''Semiotica
''Semiotica'' is an academic journal covering semiotics. It is the official journal of the International Association for Semiotic Studies.
Publication
Since 2000, the journal publishes five issues per year. It is published in English and French.
...
'' 153 (1/4)
*Santaella, Lucia (1997) "The Development of Peirce's Three Types of Reasoning: Abduction, Deduction, and Induction", 6th Congress of the IASS
Eprint
*Sebeok, T. (1981) "You Know My Method". In Sebeok, T. "The Play of Musement". Indiana. Bloomington, IA.
*Yu, Chong Ho (1994), "Is There a Logic of Exploratory Data Analysis?", ''Annual Meeting of American Educational Research Association'', New Orleans, LA, April, 1994
External links
*
*
*
(once there, scroll down), John R. Josephson, Laboratory for Artificial Intelligence Research, Ohio State University.
via the Wayback Machine.)
Deduction, Induction, and Abduction
, Chapter 3 in article
Charles Sanders Peirce
by Robert Burch, 2001 and 2006, in th
Stanford Encyclopedia of Philosophy
, links to articles and websites on abductive inference
International Research Group on Abductive Inference
Uwe Wirth and Alexander Roesler, eds. Uses frames. Click on link at bottom of its home page for English. Wirth moved to U. of Gießen, Germany, and set u
Abduktionsforschung
home page not in English but see Artikel section there
(1981), by Thomas Sebeok
Thomas Albert Sebeok ( hu, Sebők Tamás, ; 1920–2001) was a Hungarian-born American polymath,Cobley, Paul; Deely, John; Kull, Kalevi; Petrilli, Susan (eds.) (2011). Semiotics Continues to Astonish: Thomas A. Sebeok and the Doctrine of Signs'. ...
with Jean Umiker-Sebeok, from ''The Play of Musement'', Thomas Sebeok, Bloomington, Indiana: Indiana University Press, pp. 17–52.
Commens Dictionary of Peirce's Terms
Mats Bergman and Sami Paavola, editors, Helsinki U. Peirce's own definitions, often many per term across the decades. There, see "Hypothesis s a form of reasoning
S, or s, is the nineteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ess'' (pronounced ), plural ''esses''.
History ...
, "Abduction", "Retroduction", and "Presumption s a form of reasoning
S, or s, is the nineteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ess'' (pronounced ), plural ''esses''.
History ...
.
{{DEFAULTSORT:Abductive Reasoning
Belief revision
Bayesian statistics
Epistemology
Reasoning
Charles Sanders Peirce