Ho constatato che sorge talora confusione sul concetto di IBE, allorquando essa viene associata 1:1 al metodo scientifico classicamente inteso, da cui incomprensibili accostamenti a scientismo o positivismo, da ricondurre unicamente alla mancata comprensione o conoscenza tout court di tale processo inferenziale. Oltre al Nr. 40 propongo quindi questa ottima presentazione (che potete facilmente reperire sul web come pdf, unitamente alle illustrazioni che non ho potuto qui riportare), che sperů servirŗ a chiarire le basilari differenze e quindi le modalitŗ di applicazione. Molto bella la sintesi finale ďFrom wonder to understandingĒ. (Volentieri farů una traduzione per coloro che non hanno dimestichezza con l'inglese).
Computation, Philosophy, Technology
John R. Josephson and Susan G. Josephson
© Cambridge University Press, 1996
Chapter 1 Conceptual analysis of abduction
This chapter was written by John R. Josephson, except the second section on
diagnosis, which was written by Michael C. Tanner and John R. Josephson.
What is abduction?
Abduction, or inference to the best explanation, is a form of inference that
goes from data describing something to a hypothesis that best explains or
accounts for the data. Thus abduction is a kind of theory-forming or
interpretive inference. The philosopher and logician Charles Sanders Peirce
(1839-1914) contended that there occurs in science and in everyday life a
distinctive pattern of reasoning wherein explanatory hypotheses are formed and
accepted. He called this kind of reasoning “abduction.”
In their popular textbook on artificial intelligence (AI), Charniak and
McDermott (1985) characterize abduction variously as modus ponens turned
backward, inferring the cause of something, generation of explanations for what
we see around us, and inference to the best explanation. They write that
medical diagnosis, story understanding, vision, and understanding natural
language are all abductive processes. Philosophers have written of “inference
to the best explanation” (Harman, 1965) and “the explanatory inference”
(Lycan, 1988). Psychologists have found “explanation-based” evidence
evaluation in the decision-making processes of juries in law courts (Pennington
& Hastie, 1988).
We take abduction to be a distinctive kind of inference that follows this
pattern pretty nearly:1
D is a collection of data (facts, observations, givens).
H explains D (would, if true, explain D ).
No other hypothesis can explain D as well as H does.
Therefore, H is probably true.
The core idea is that a body of data provides evidence for a hypothesis that
satisfactorily explains or accounts for that data (or at least it provides evidence
if the hypothesis is better than explanatory alternatives).
Abductions appear everywhere in the un-self-conscious reasonings,
interpretations, and perceivings of ordinary life and in the more critically selfaware
reasonings upon which scientific theories are based. Sometimes
abductions are deliberate, such as when the physician, or the mechanic, or the
scientist, or the detective forms hypotheses explicitly and evaluates them to find
the best explanation. Sometimes abductions are more perceptual, such as when
we separate foreground from background planes in a scene, thereby making
sense of the disparities between the images formed from the two eyes, or when
we understand the meaning of a sentence and thereby explain the presence and
order of the words.
Abduction in ordinary life
Abductive reasoning is quite ordinary and commonsensical. For example, as
Harman (1965) pointed out, when we infer from a person’s behavior to some
fact about her mental state, we are inferring that the fact explains the behavior
better than some other competing explanation does. Consider this specimen of
JOE: Why are you pulling into the filling station?
TIDMARSH: Because the gas tank is nearly empty.
JOE: What makes you think so?
TIDMARSH: Because the gas gauge indicates nearly empty. Also, I have no
reason to think that the gauge is broken, and it has been a long time since
I filled the tank.
Under the circumstances, the nearly empty gas tank is the best available
explanation for the gauge indication. Tidmarsh’s other remarks can be
understood as being directed to ruling out a possible competing explanation
(broken gauge) and supporting the plausibility of the preferred explanation.
Consider another example of abductive reasoning: Imagine that one day
you are driving your car, and you notice the car behind you because of its
peculiar shade of bright yellow. You make two turns along your accustomed
path homeward and then notice that the yellow car is still behind you, but now
it is a little farther away. Suddenly, you remember something that you left at
the office and decide to turn around and go back for it. You execute several
complicated maneuvers to reverse your direction and return to the office. A few
minutes later you notice the same yellow car behind you. You conceive the
hypothesis that you are being followed, but you cannot imagine any reason why
this should be so that seems to have any significant degree of likelihood. So,
you again reverse direction, and observe that the yellow car is still behind you.
You conclude that you are indeed being followed (reasons unknown) by the
person in the dark glasses in the yellow car. There is no other plausible way to
explain why the car remains continually behind you. The results of your
experiment of reversing direction a second time served to rule out alternative
explanations, such as that the other driver’s first reversal of direction was a
coincidence of changing plans at the same time.
Harman (1965) gave a strikingly insightful analysis of law court
testimony, which argues that when we infer that a witness is telling the truth,
we are using best-explanation reasoning. According to Harman our inference
goes as follows:
(i) We infer that he says what he does because he believes it.
(ii) We infer that he believes what he does because he actually did witness
the situation which he describes.
Our confidence in the testimony is based on our conclusions about the
most plausible explanation for that testimony. Our confidence fails if we come
to think that there is some other plausible explanation for his testimony - for
example, that he stands to gain from our believing him. Here, too, we see the
same pattern of reasoning from observations to a hypothesis that explains those
observations - not simply to a possible explanation, but to the best explanation
for the observations in contrast with alternatives.
In Winnie-the-Pooh (Milne, 1926) Pooh says:
It had HUNNY written on it, but, just to make sure, he took off the
paper cover and looked at it, and it looked just like honey. “But
you never can tell,” said Pooh. “I remember my uncle saying once
that he had seen cheese just this colour.” So he put his tongue in,
and took a large lick. (pp. 61-62)
Pooh’s hypothesis is that the substance in the jar is honey, and he has two
pieces of evidence to substantiate his hypothesis: It looks like honey, and
“hunny” is written on the jar. How can this be explained except by supposing
that the substance is honey? He considers an alternative hypothesis: It might be
cheese. Cheese has been observed to have this color, so the cheese hypothesis
offers another explanation for the color of the substance in the jar. So, Pooh
(conveniently dismissing the evidence of the label) actively seeks evidence that
would distinguish between the hypotheses. He performs a test, a crucial
experiment. He takes a sample.
The characteristic reasoning processes of fictional detectives have also
been characterized as abduction (Sebeok & Umiker-Sebeok, 1983). To use
another example from Harman (1965), when a detective puts the evidence
together and decides that the culprit must have been the butler, the detective is
reasoning that no other explanation that accounts for all the facts is plausible
enough or simple enough to be accepted. Truzzi (1983) alleges that at least 217
abductions can be found in the Sherlock Holmes canon.
“There is no great mystery in this matter,” he said, taking the cup
of tea which I had poured out for him; “the facts appear to admit of
only one explanation.”
- Sherlock Holmes (Doyle, 1890, p. 620)
Abduction in science
Abductions are common in scientific reasoning on large and small scales.2 The
persuasiveness of Newton’s theory of gravitation was enhanced by its ability to
explain not only the motion of the planets, but also the occurrence of the tides.
In On the Origin of Species by Means of Natural Selection Darwin presented
what amounts to an extended argument for natural selection as the best
hypothesis for explaining the biological and fossil evidence at hand. Harman
(1965) again: when a scientist infers the existence of atoms and subatomic
particles, she is inferring the truth of an explanation for her various data.
Science News (Peterson, 1990) reported the attempts of astronomers to explain
a spectacular burst of X rays from the globular cluster M15 on the edge of the
Milky Way. In this case the inability of the scientists to come up with a
satisfactory explanation cast doubt on how well astronomers understand what
happens when a neutron star accretes matter from an orbiting companion star.
Science News (Monastersky, 1990) reported attempts to explain certain
irregular blocks of black rock containing fossilized plant matter. The best
explanation appears to be that they are dinosaur feces.
Abduction and history
Knowledge of the historical past also rests on abductions. Peirce (quoted
in Fann, 1970) cites one example:
Numberless documents refer to a conqueror called Napoleon
Bonaparte. Though we have not seen the man, yet we cannot
explain what we have seen, namely, all those documents and
monuments without supposing that he really existed. (p. 21)
Abduction and language
Language understanding is another process of forming and accepting
explanatory hypotheses. Consider the written sentence, “The man sew the rat
eating the corn.” The conclusion seems inescapable that there has been some
sort of mistake in the third word “sew” and that somehow the “e” has
improperly replaced an “a.” If we are poor at spelling, or if we read the
sentence rapidly, we may leap to the “saw” reading without even noticing that
we have not dealt with the fact of the “e.” Taking the “saw” reading demands
our acceptance so strongly that it can cause us to overturn the direct evidence of
the letters on the page, and to append a hypothesis of a mistake, rather than
accept the hypothesis of a nonsense sentence.
The process of abduction
Sometimes a distinction has been made between an initial process of coming up
with explanatorily useful hypothesis alternatives and a subsequent process of
critical evaluation wherein a decision is made as to which explanation is best.
Sometimes the term “abduction” has been restricted to the hypothesisgeneration
phase. In this book, we use the term for the whole process of
generation, criticism, and acceptance of explanatory hypotheses. One reason is
that although the explanatory hypotheses in abduction can be simple, more
typically they are composite, multipart hypotheses. A scientific theory is
typically a composite with many separate parts holding together in various
ways,3 and so is our understanding of a sentence and our judgment of a law
case. However, no feasible information-processing strategy can afford to
explicitly consider all possible combinations of potentially usable theory parts,
since the number of combinations grows exponentially with the number of parts
available (see chapter 7). Reasonably sized problems would take cosmological
amounts of time. So, one must typically adopt a strategy that avoids generating
all possible explainers. Prescreening theory fragments to remove those that are
implausible under the circumstances makes it possible to radically restrict the
potential combinations that can be generated, and thus goes a long way towards
taming the combinatorial explosion. However, because such a strategy mixes
critical evaluation into the hypothesis-generation process, this strategy does not
allow a clear separation between the process of coming up with explanatory
hypotheses and the process of acceptance. Thus, computationally, it seems best
not to neatly separate generation and acceptance. We take abduction to include
the whole process of generation, criticism, and possible acceptance of
Diagnosis and abductive justification
In this section we show by example how the abductive inference pattern can be
used simply and directly to describe diagnostic reasoning and its justifications.
In AI, diagnosis is often described as an abduction problem (e.g., Peng &
Reggia, 1990). Diagnosis can be viewed as producing an explanation that best
accounts for the patient’s (or device’s) symptoms. The idea is that the task of a
diagnostic reasoner is to come up with a best explanation for the symptoms,
which are typically those findings for the case that show abnormal values. The
explanatory hypotheses appropriate for diagnosis are malfunction hypotheses:
typically disease hypotheses for plants and animals and broken-part hypotheses
for mechanical systems.
The diagnostic task is to find a malfunction, or set of malfunctions, that
best explains the symptoms. More specifically, a diagnostic conclusion should
explain the symptoms, it should be plausible, and it should be significantly
better than alternative explanations. (The terms “explain,” “plausible,” and
“better” remain undefined for now.)
Taking diagnosis as abduction determines the classes of questions that
are fair to ask of a diagnostician. It also suggests that computer-based
diagnostic systems should be designed to make answering such questions
Consider the example of liver disease diagnosis given by Harvey and
Bordley (1972, pp. 299-302). In this case the physician organized the
differential (the set of alternative hypotheses) around hepatomegaly (enlarged
liver), giving five categories of possible causes of hepatomegaly: venous
congestion of the liver, obstruction of the common duct, infection of the liver,
diffuse hepatomegaly without infection, and neoplasm (tumor) of the liver. He
then proceeded to describe the evidence for and against each hypothesis.
Venous congestion of the liver was ruled out because none of its important
symptoms were present. Obstruction of the common duct was judged to be
unlikely because it would not explain certain important findings, and many
expected symptoms were not present. Various liver infections were judged to
be explanatorily irrelevant because certain important findings could not be
explained this way. Other liver infections were ruled out because expected
consequences failed to appear, although one type of infection seemed somewhat
plausible. Diffuse hepatomegaly without infection was considered
explanatorily irrelevant because, by itself, it would not be sufficient to explain
the degree of liver enlargement. Neoplasm was considered to be plausible and
would adequately explain all the important findings. Finally, the physician
concluded the following:
The real choice here seems to lie between an infection of the liver
and neoplasm of the liver. It seems to me that the course of the
illness is compatible with a massive hepatoma [neoplasm of the
liver] and that the hepatomegaly, coupled with the biochemical
findings, including the moderate degree of jaundice, are best
explained by this diagnosis.
Notice the form of the argument:
1. There is a finding that must be explained (hepatomegaly).
2. The finding might be explained in a number of ways (venous congestion
of the liver, obstruction of the common duct, infection of the liver,
diffuse hepatomegaly without infection, and neoplasm of the liver).
3. Some of these ways are judged to be implausible because expected
consequences do not appear (venous congestion of the liver).
4. Some ways are judged to be irrelevant or implausible because they do
not explain important findings (obstruction of the common duct, diffuse
hepatomegaly without infection).
5. Of the plausible explanations that remain (infection of the liver,
neoplasm of the liver), the best (neoplasm of the liver) is the diagnostic
The argument is an abductive justification for the diagnostic conclusion.
Suppose the conclusion turned out to be wrong. What could have
happened to the true answer? That is, why was the true, or correct, answer not
the best explanation? This could only have happened for one or more of the
1. There was something wrong with the data such that it really did not need
to be explained. In this case, hepatomegaly might not have actually been
2. The differential was not broad enough. There might be causes of
hepatomegaly that were unknown to the physician, or that were
overlooked by him.
3. Hypotheses were incorrectly judged to be implausible. Perhaps venous
congestion should have been considered more plausible than it was, due
to faulty knowledge or missing evidence.
4a. Hypotheses were incorrectly thought not to explain important findings.
For example, obstruction might explain findings that the physician
thought it could not, possibly because the physician had faulty
4b. The diagnostic conclusion was incorrectly thought to explain the
findings. Neoplasm might not explain the findings, due to faulty
knowledge or to overlooking important findings.
5a. The diagnostic conclusion was incorrectly thought to be better than it
was. Neoplasm might have been overrated, due to faulty knowledge or
5b. The true answer was underrated, due to faulty knowledge or missing
Many questions to the diagnostician can be seen as indicating ways in
which the answer may be wrong, each question suggesting an error of a
particular type. An answer to such a question should convince the questioner
that the diagnosis is not mistaken in that way.
Returning to the example, if the physician were asked, “What makes
venous congestion implausible?” he might answer:
This patient exhibited no evidence of circulatory congestion or
obstruction of the hepatic veins or vena cava. . . .
thus trying to convince the questioner that venous congestion was correctly
ruled out. If asked, “Why not consider some toxic hepatic injury?” the
physician could reply:
[It would not] seem to compete with a large hepatoma in
explaining the massive hepatomegaly, the hypoglycemia, and the
manifestations suggestive of infection.
thus trying to convince the questioner that the differential is broad enough.
Interestingly, in this case Bordleyís diagnosis was wrong. Autopsy
revealed that the patient actually had cancer of the pancreas. (To be fair, the
autopsy also found tumors in the liver, but pancreatic cancer was considered the
primary illness.) One significant finding in the case was elevated amylase,
which is not explained by neoplasm of the liver. So, if we asked the physician,
“How do you account for the sharply elevated amylase?” his only possible reply
The diagnosis was inadequate because it failed to account for all the important
findings (item 4b in the previous numbered list).
This analysis tells us that if we build an expert system and claim that it
does diagnosis, we can expect it to be asked certain questions. These are the
only questions that are fair to ask simply because it is a diagnostic system.
Other questions would not be about diagnosis per se. These other questions
might include requests for definitions of terms, exam-like questions that check
the system’s knowledge about some important fact, and questions about the
implications of the diagnostic conclusion for treatment. Thus, the idea of
abductive justification gives rise to a model of dialogue between the
diagnostician and the client. It defines a set of questions that any person, or
machine, claiming to do diagnosis should be prepared to answer.
One power of this analysis lies in controlling for error, in making explicit
the ways in which the conclusion can be wrong. A challenging question implies
that the questioner thinks that the answer might be wrong and that the
questioner needs to be convinced that it is not. A proper answer will reassure
the questioner that the suspected error has not occurred.
Doubt and certainty
Inference and logic
Inferences are movements of thought within the sphere of belief.4 The function
of inference is the acceptance (or sometimes rejection) of propositions on the
basis of purported evidence. Yet, inferences are not wholly or merely
psychological; there may be objective relationships of evidential support (or its
absence) between propositions that have nothing much to do with whether
anyone thinks of them. Thus a science of evidential relationships is possible
that has very little to do with empirical psychology. This science is logic in the
Deduction and abduction
Deductions support their conclusions in such a way that the conclusions must
be true, given true premises; they convey conclusive evidence. Other forms of
evidential support are not so strong, and though significant support for a
conclusion may be given, a possibility of error remains. Abductions are of this
kind; they are fallible inferences.
Consider the following logical form, commonly called disjunctive
P or Q or R or S or . . .
But not-Q, not-R, not-S, . . .
This form is deductively valid. Moreover, the support for an abductive
conclusion fits this form if we assert that we have exhaustively enumerated all
possible explanations for the data and that all but one of the alternative
explanations has been decisively ruled out. Typically, however, we will have
reasons to believe that we have considered all plausible explanations (i.e., those
that have a significant chance of being true), but these reasons stop short of
being conclusive. We may have struggled to formulate a wide variety of
possible explanations but cannot be sure that we have covered all plausibles.
Under these circumstances we can assert a proposition of the form of the first
premise of the syllogism, but assert it only with a kind of qualified confidence.
Typically, too, alternative explanations can be discounted for one reason or
another but not decisively ruled out. Thus abductive inferences, in a way, rely
on this particular deductively valid inference form, but abductions are
conclusive only in the limit.
Of course disjunctive syllogism fits any decision by enumeration of
alternatives and exclusion, not just abductions (where explanatory alternatives
are considered). From this it can be seen that abduction cannot be identified
with disjunctive syllogism.
Like inductive generalizations, abductions are ampliative inferences; that is, at
the end of an abductive process, having accepted a best explanation, we may
have more information than we had before. The abduction transcends the
information of its premises and generates new information that was not
previously encoded there at all. This can be contrasted with deductions, which
can be thought of as extracting, explicitly in their conclusions, information that
was already implicitly contained in the premises. Deductions are truth
preserving, whereas successful abductions may be said to be truth producing.
This ampliative reasoning is sometimes done by introducing new
vocabulary in the conclusion. For example, when we abduce that the patient
has hepatitis because hepatitis is the only plausible way to explain the jaundice,
we have introduced into the conclusion a new term, “hepatitis,” which is from
the vocabulary of diseases and not part of the vocabulary of symptoms. By
introducing this term, we make conceptual connections with the typical
progress of the disease, and ways to treat it, that were unavailable before.
Whereas valid deductive inferences cannot contain terms in their conclusions
that do not occur in their premises, abductions can “interpret” the given data in
a new vocabulary. Abductions can thus make the leap from “observation
language” to “theory language.”
Doubt and hesitation
An abductive process aims at a satisfactory explanation, one that can be
confidently accepted. However it may be accompanied in the end with some
explicit qualification, for example, some explicit degree of assurance or some
doubt. One main form of doubt is just hesitation from being aware of the
possibility of alternative explanations. Classically, this is just how Descartes
generates doubts about knowledge from the senses: Alternative explanations to
the usual interpretations of sensory information are that we are dreaming or that
we are being deceived by a very powerful and evil demon (Descartes, 1641).
Since low-plausibility alternative explanations can be generated indefinitely,
doubt cannot be completely eliminated.
On the way to a satisfactory explanation, an abductive process might seek
further information beyond that given in the data initially to be explained. For
example, there may be a need to distinguish between explanatory alternatives;
for help in forming hypotheses; or for help in evaluating them. Often abductive
processes are not immediately concluded, but are suspended to wait for answers
from information-seeking processes. Such suspensions of processing can last a
very long time. Years later, someone may say, “So that’s why she never told
me. I was always puzzled about that.” Centuries later we may say, “So that’s
the secret of inheritance. It’s based on making copies of long molecules that
encode hereditary information.”
Abductive conclusions: likelihood and acceptance
As we said earlier, abductions follow approximately this pattern:
D is a collection of data.
H explains D.
No other hypothesis can explain D as well as H does.
Therefore, H is probably true.
The judgment of likelihood associated with an abductive conclusion
should depend on the following considerations (as it typically does in the
inferences we actually make):
1. how decisively H surpasses the alternatives5
2. how good H is by itself, independently of considering the alternatives
(we should be cautious about accepting a hypothesis, even if it is clearly
the best one we have, if it is not sufficiently plausible in itself)
3. judgments of the reliability of the data
4. how much confidence there is that all plausible explanations have been
considered (how thorough was the search for alternative explanations ).6
Beyond the judgment of its likelihood, willingness to accept the
conclusion should (and typically does) depend on:
1. pragmatic considerations, including the costs of being wrong and the
benefits of being right
2. how strong the need is to come to a conclusion at all, especially
considering the possibility of seeking further evidence before deciding.
This theory of abduction is an evaluative theory, offering standards for
judging reasoning patterns. It is also a descriptive and explanatory theory for
human and computer reasoning processes that provides a way of analyzing
these processes in functional terms, of showing what they accomplish, of
showing how they manifest good reasoning (i.e., intelligence).
Best explanation: compared with what?
There is some ambiguity in the abductive inference pattern as we have
described it. What is the set of explanatory hypotheses of which H is the best?
Perhaps this premise should say, “No other available hypothesis can explain D
as well as H does.”7 The set of alternatives might be thought of so narrowly as
to include just those hypotheses that one thinks of immediately, or so broadly as
to include all the hypotheses that can in principle be formulated. Construed
broadly, it would include the true explanation, which would of course be best,
but then the whole inference form would seem to be trivial.
Yet it appears that the force of the abductive inference depends on an
evaluation that ranges over all possible hypotheses, or at least a set of them
large enough to guarantee that it includes the true one. If we think that there is
a significant chance that there is a better explanation, even one that we have not
thought of, that we cannot think of, or that is completely unavailable to us, then
we should not make the inference and normally would not. After all, an
unavailable hypothesis might be the true one. It is quite unpersuasive for me to
try to justify a conclusion by saying, “It is likely to be true because I couldnít
think of a better explanation.” That I could not think of a better explanation is
some evidence that there is no better explanation, depending on how we judge
my powers of imagination and my powers of evaluating hypotheses, but these
are just evidential considerations in making the judgment that there is not
(anywhere) a better explanation. We should (and do) make the inferential leap
when we judge that “no other hypothesis can explain D as well as H does.”
In one sense the best explanation is the true one. But, having no
independent access to which explanatory hypothesis is true, the reasoner can
only assert judgments of best based on considerations such as plausibility and
explanatory power. The reasoner is, in effect, presuming that the best
explanation based on these considerations is the one most likely to be true. If
we challenge an abductive justification by asking what the grounds are for
judging that a particular hypothesis is best, then we properly get an answer in
terms of what is wrong with alternative explanations and what is the evidence
that all plausible explanations have been considered (all those with a significant
chance of being true). The inference schema as stated in this chapter is not
trivial, even though it ranges over all possible relevant hypotheses, because best
is not directly a judgment of truth but instead a summary judgment of accessible
Abductions often display emergent certainty ; that is, the conclusion of an
abduction can have, and be deserving of, more certainty than any of its
premises. This is unlike a deduction, which is no stronger than the weakest of
its links (although separate deductions can converge for parallel support). For
example, I may be more sure of the bear’s hostile intent than of any of the
details of its hostile gestures; I may be more sure of the meaning of the sentence
than of my initial identifications of any of the words; I may be more sure of the
overall theory than of the reliability of any single experiment on which it is
based. Patterns emerge from individual points where no single point is essential
to recognizing the pattern. A signal extracted and reconstructed from a noisy
channel may lead to a message, the wording of which, or even more, the intent
of which, is more certain than any of its parts.
This can be contrasted with traditional empiricist epistemology, which
does not allow for anything to be more certain than the observations (except
maybe tautologies) since everything is supposedly built up from the
observations by deduction and inductive generalization. But a pure
generalization is always somewhat risky, and its conclusion is less certain than
its premises. “All goats are smelly” is less certain than any given “This goat is
smelly.” With only deductive logic and generalization available, empirical
knowledge appears as a pyramid whose base is particular experiments or sense
perceptions, and where the farther up you go, the more general you get, and the
less certain. Thus, without some form of certainty-increasing inference, such as
abduction, traditional empiricist epistemology is unavoidably committed to a
high degree of skepticism about all general theories of science.
Knowledge without certainty
The conclusion of an abduction is “logically justified” by the force of the
abductive argument. If the abductive argument is strong, and if one is
persuaded by the argument to accept the conclusion, and if, beyond that, the
conclusion turns out to be correct, then one has attained justified, true, belief,
the classical philosophical conditions of knowledge, that date back to Plato.8
Thus abductions are knowledge producing inferences despite their fallibility.
Although we can never be entirely sure of an abductive conclusion, if the
conclusion is indeed true, we may be said to “know” that conclusion. Of
course, without independent knowledge that the conclusion is true, we do not
“know that we know,” but that is the usual state of our knowledge.
Summary: Abductions are fallible, and doubt cannot be completely
eliminated. Nevertheless, by the aid of abductive inferences, knowledge is
possible even in the face of uncertainty.
Explanations give causes
There have been two main traditional attempts to analyze explanations as
deductive proofs, neither attempt particularly successful. Aristotle maintained
that an explanation is a syllogism of a certain form (Aristotle c. 350 B.C.) that
also satisfies various informal conditions, one of which is that the “middle
term” of the syllogism is the cause of the thing being explained. (B is the
middle term of “All A are B ; All B are C ; Therefore, All A are C .”) More
recently (considerably) Hempel (1965) modernized the logic and proposed the
“covering law” or “deductive nomological” model of explanation.9 The main
difficulty with these accounts (besides Hempel’s confounding the question of
what makes an ideally good explanation with the question of what it is to
explain at all) is that being a deductive proof is neither necessary nor sufficient
for being an explanation. Consider the following:
QUESTION: Why does he have burns on his hand?
EXPLANATION: He sneezed while cooking pasta and upset the pot.
The point of this example is that an explanation is given but no deductive
proof, and although it could be turned into a deductive proof by including
additional propositions, this would amount to gratuitously completing what is
on the face of it an incomplete explanation. Under the circumstances
(incompletely specified) sneezing and upsetting the pot were presumably
causally sufficient for the effect, but this is quite different from being logically
The case that explanations are not necessarily deductive proofs becomes
even stronger if we consider psychological explanations and explanations that
are fundamentally statistical (e.g., where quantum phenomena are involved). In
these cases it is clear that causal determinism cannot be assumed, so the
antecedent conditions cannot be assumed to be even causally sufficient for the
effects. Conversely, many deductive proofs fail to be explanations of anything.
For example classical mechanics is deterministic and time reversible, so an
earlier state of a system can be deduced from a later state, but the earlier state
cannot be said to be explained thereby. Also, q can be deduced from “p and q
” but is not thereby explained.
Thus, we conclude that explanations are not deductive proofs in any
particularly interesting sense. Although they can often be presented in the form
of deductive proofs, doing so does not succeed in capturing anything essential
or especially useful and tends to confuse causation with logical implication.
An alternative view is that an explanation is an assignment of causal
responsibility; it tells a causal story. Finding possible explanations is finding
possible causes of the thing to be explained. It follows that abduction, as a
process of reasoning to an explanation, is a process of reasoning from effect to
Cause for abduction may be understood somewhat more broadly than its
usual senses of mechanical or efficient or event-event causation.10 To get some
idea of a more expanded view of causation, consider the four kinds of causes
according to Aristotle: efficient cause, material cause, final cause, and formal
cause (Aristotle, Physics , bk. 2, chap. 3). Let us take the example of my coffee
mug. The efficient cause is the process by which the mug was manufactured
and helps explain such things as why there are ripples on the surface of the
bottom. The material cause is the ceramic and glaze, which compose the mug
and cause it to have certain gross properties such as hardness. The final cause
is the end or purpose, in this case to serve as a container for liquids and as a
means of conveyance for drinking. A final-cause explanation is needed to
explain the presence and shape of the handle. Formal cause is somewhat more
mysterious - Aristotle is hard to interpret here - but it is perhaps something like
the mathematical properties of the shape, which impose constraints resulting in
certain specific other properties. That the cross-section of the mug, viewed
from above, is approximately a circle, explains why the length and width of the
cross-section are approximately equal. The causal story told by an abductive
explanation might rely on any of these four types of causation.11
When we conclude that a finding f is explained by hypothesis H , we say
more than just that H is a cause of f in the case at hand. We conclude that
among all the vast causal ancestry of f we will assign responsibility to H .
Typically, our reasons for focusing on H are pragmatic and connected rather
directly with goals of production or prevention. We blame the heart attack on
the blood clot in the coronary artery or on the high-fat diet, depending on our
interests. Perhaps we should explain the patient’s death by pointing out that the
patient was born, so what else can you expect but eventual death? We can
blame the disease on the invading organism, on the weakened immune system
that permitted the invasion, or on the wound that provided the route of entry
into the body. We can blame the fire on the presence of the combustibles, on
the presence of the spark, or even on the presence of the oxygen, depending on
which we think is the most remarkable. I suggest that it comes down to this:
The things that will satisfy us as accounting for f will depend on why we are
trying to account for f ; but the only things that count as candidates are parts of
what we take to be the causal ancestry of f .
Peirce’s view was that induction, deduction, and abduction are three distinct
types of inference, although as his views developed, the boundaries shifted
somewhat, and he occasionally introduced hybrid forms such as “abductive
induction” (Peirce, 1903). In this section I hope to clear up the confusion about
the relationship of abduction to induction. First I argue that inductive
generalizations can be insightfully analyzed as special cases of abductions. I
also argue that predictions are a distinctive form of inference, that they are not
abductions, and that they are sometimes deductive, but typically not. The result
is a new classification of basic inference types.
Harman (1965) argued that “inference to the best explanation” (i.e.,
abduction) is the basic form of nondeductive inference, subsuming
“enumerative induction” and all other forms of nondeductive inferences as
special cases. Harman argued quite convincingly that abduction subsumes
sample-to-population inferences (i.e., inductive generalizations [this is my way
of putting the matter]). The weakness of his overall argument was that other
forms of nondeductive inference are not seemingly subsumed by abduction,
most notably population-to-sample inferences, a kind of prediction. The main
problem is that the conclusion of a prediction does not explain anything, so the
inference cannot be an inference to a best explanation.
This last point, and others, were taken up by Ennis (1968). In his reply to
Ennis, instead of treating predictions as deductive, or admitting them as a
distinctive form of inference not reducible to abduction, Harman took the
dubious path of trying to absorb predictions, along with a quite reasonable idea
of abductions, into the larger, vaguer, and less reasonable notion of
“maximizing explanatory coherence” (Harman, 1968). In this I think Harman
made a big mistake, and it will be my job to repair and defend Harman’s
original arguments, which were basically sound, although they proved
somewhat less than he thought.
First, I will argue that it is possible to treat every good (i.e., reasonable, valid)
inductive generalization as an instance of abduction. An inductive
generalization is an inference that goes from the characteristics of some
observed sample of individuals to a conclusion about the distribution of those
characteristics in some larger population. As Harman pointed out, it is useful to
describe inductive generalizations as abductions because it helps to make clear
when the inferences are warranted. Consider the following inference:
All observed A ís are B ís
Therefore All A ís are B ís
This inference is warranted, Harman (1965) writes, “. . . whenever the
hypothesis that all A ís are B ís is (in the light of all the evidence) a better,
simpler, more plausible (and so forth) hypothesis than is the hypothesis, say,
that someone is biasing the observed sample in order to make us think that all
Aís are Bís. On the other hand, as soon as the total evidence makes some other
competing hypothesis plausible, one may not infer from the past correlation in
the observed sample to a complete correlation in the total population.”
If this is indeed an abductive inference, then “All A ís are B ís” should
explain “All observed A ís are B ís.” But, “All A ís are B ís” does not seem to
explain why “This A is a B ,” or why A and B are regularly associated (as
pointed out by Ennis, 1968). Furthermore, I suggested earlier that explanations
give causes, but it is hard to see how a general fact could explain its instances,
because it does not seem in any way to cause them.
The story becomes much clearer if we distinguish between an event of
observing some fact and the fact observed. What the general statement in the
conclusion explains is the events of observing, not the facts observed. For
example, suppose I choose a ball at random (arbitrarily) from a large hat
containing colored balls. The ball I choose is red. Does the fact that all of the
balls in the hat are red explain why this particular ball is red? No. But it does
explain why, when I chose a ball at random, it turned out to be a red one
(because they all are). “All A ís are B ís” cannot explain why “This A is a B ”
because it does not say anything at all about how its being an A is connected
with its being a B . The information that “they all are” does not tell me
anything about why this one is, except it suggests that if I want to know why
this one is, I would do well to figure out why they all are.
A generalization helps to explain the events of observing its instances,
but it does not explain the instances themselves. That the cloudless, daytime
sky is blue helps explain why, when I look up, I see the sky to be blue (but it
doesnít explain why the sky is blue). The truth of “Theodore reads ethics books
a lot” helps to explain why, so often when I have seen him, he has been reading
an ethics book (but it doesnít explain why he was reading ethics books on those
occasions). Seen this way, inductive generalization does have the form of an
inference whose conclusion explains its premises.
Generally, we can say that the frequencies in the larger population,
together with the frequency-relevant characteristics of the method for drawing a
sample, explain the frequencies in the observed sample. In particular, “A ís are
mostly B ís” together with “This sample of A ís was drawn without regard to
whether or not they were B ís” explain why the Aís that were drawn were mostly
Why were 61% of the chosen balls yellow?
Because the balls were chosen more or less randomly from a population
that was two thirds yellow (the difference from 2/3 in the sample being
due to chance).
Alternative explanation for the same observation:
Because the balls were chosen by a selector with a bias for large balls from
a population that was only one third yellow but where yellow balls tend
to be larger than non yellow ones.
How do these explain? By giving a causal story.
What is explained is (always) some aspect of an event/being/state, not a
whole event/being/state itself. In this example just the frequency of
characteristics in the sample is explained, not why these particular balls are
yellow or why the experiment was conducted on Tuesday. The explanation
explains why the sample frequency was the way it was, rather than having some
markedly different value. In general, if there is a deviation in the sample from
what you would expect, given the population and the sampling method, then
you have to throw some Chance into the explanation (which is more or less
plausible depending on how much chance you have to suppose).12
The objects of explanation - what explanations explain - are facts about
the world (more precisely, always an aspect of a fact, under a description).
Observations are facts; that is, an observation having the characteristics that it
does is a fact. When you explain observed samples, an interesting thing is to
explain the frequencies. A proper explanation will give a causal story of how
the frequencies came to be the way they were and will typically refer both to the
population frequency and the method of drawing the samples.
Unbiased sampling processes tend to produce representative outcomes;
biased sampling processes tend to produce unrepresentative outcomes. This
“tending to produce” is causal and supports explanation and prediction. A
peculiarity is that characterizing a sample as “representative” is characterizing
the effect (sample frequency) by reference to part of its cause (population
frequency). Straight inductive generalization is equivalent to concluding that a
sample is representative, which is a conclusion about its cause. This inference
depends partly on evidence or presumption that the sampling process is (close
enough to) unbiased. The unbiased sampling process is part of the explanation
of the sample frequency, and any independent evidence for or against unbiased
sampling bears on its plausibility as part of the explanation.
If we do not think of inductive generalization as abduction, we are at a
loss to explain why such an inference is made stronger or more warranted, if in
collecting data we make a systematic search for counter-instances and cannot
find any, than it would be if we just take the observations passively. Why is the
generalization made stronger by making an effort to examine a wide variety of
types of A ís? The inference is made stronger because the failure of the active
search for counter-instances tends to rule out various hypotheses about ways in
which the sample might be biased.
In fact the whole notion of a “controlled experiment” is covertly based on
abduction. What is being “controlled for” is always an alternative way of
explaining the outcome. For example a placebo-controlled test of the efficiency
of a drug is designed to make it possible to rule out purely psychological
explanations for any favorable outcome.
Even the question of sample size for inductive generalization can be seen
clearly from an abductive perspective. Suppose that on each of the only two
occasions when Konrad ate pizza at Marioís Pizza Shop, he had a stomachache
the next morning. In general, Konrad has a stomachache occasionally but not
frequently. What may we conclude about the relationship between the pizza
and the stomachache? What may we reasonably predict about the outcome of
Konradís next visit to Marioís? Nothing. The sample is not a large enough.
Now suppose that Konrad continues patronizing Marioís and that after every
one of 79 subsequent trips he has a stomach ache within 12 hours. What may
we conclude about the relationship between Marioís pizza and Konradís
stomachache? That Marioís pizza makes Konrad have stomachaches. We may
predict that Konrad will have a stomachache after his next visit, too.
A good way to understand what is occurring in this example is by way of
abduction. After Konradís first two visits we could not conclude anything
because we did not have enough evidence to distinguish between the two
competing general hypotheses:
1. The eating pizza - stomachache correlation was accidental (i.e., merely
coincidental or spurious [say, for example, that on the first visit the
stomach ache was caused by a virus contracted elsewhere and that on the
second visit it was caused by an argument with his mother]).
2. There is some connection between eating pizza and the subsequent
stomach ache (i.e., there is some causal explanation of why he gets a
stomach ache after eating the pizza [e.g., Konrad is allergic to the snake
oil in Marioís Special Sauce]).
By the time we note the outcome of Konradís 79th visit, we are able to
decide in favor of the second hypothesis. The best explanation of the
correlation has become the hypothesis of a causal connection because
explaining the correlation as accidental becomes rapidly less and less plausible
the longer the association continues.
Another inference form that has often been called “induction” is given by the
All observed Aís are Bís.
Therefore, the next A will be a B.
Let us call this inference form an inductive projection. Such an inference
can be analyzed as an inductive generalization followed by a prediction, as
Observations ----> All Aís are Bís ----> The next A will be a B.
Predictions have traditionally been thought of as deductive inferences.
However, something is wrong with this analysis. To see this, consider the
alternative analysis of inductive projections, as follows:
Observations -> At least generally Aís are Bís -> The next A will be a B.
This inference is stronger in that it establishes its conclusion with more
certainty, which it does by hedging the generalization and thus making it more
plausible, more likely to be true. It could be made stronger yet by hedging the
temporal extent of the generalization:
Observations --> At least generally Aís are Bís, at least for the recent past and
the immediate future --> The next A will be a B.
The analyses of inductive projection with the hedged generalizations are
better than the first analysis because they are better at making sense of the
inference, which they do by being better at showing the sense in it (i.e., they are
better at showing how, and when, and why the inference is justified - or
“rational” or “intelligent”). Reasonable generalizations are hedged. Generally
the best way to analyze “Aís are Bís” is not “All Aís are Bís,” as we are taught in
logic class, but as “Generally Aís are Bís,” using the neutral, hedged, universal
quantifier of ordinary life.13
We have analyzed inductive projections as inductive generalizations
followed by predictions. The inductive generalizations are really abductions, as
was argued before. But, what kind of inferences are predictions? One thing
seems clear: Predictions from hedged generalizations are not deductions.
Predictions from hedged generalizations belong to the same family as
statistical syllogisms which have forms like these:14
m/n of the Aís are Bís (where m/n > 1/2).
Therefore, the next A will be a B.
m/n of the Aís are Bís.
Therefore, approximately m/n of the Aís in the next sample will be Bís.
These are also related to the following forms:
Generally Aís are Bís.
S is an A.
Therefore, S is a B.
A typical, normal X does Y.
Therefore, this X will do Y.
None of these inferences appear to be deductions. One can, of course, turn
them into deductions by including a missing premise like “this X is normal,”
but unless there is independent evidence for the assumption, this adds nothing
to the analysis.
Furthermore, consider an inference of this form:
P has high probability.
Such an inference (whatever the probability is taken to mean) will have to allow
for the possibility of the conclusion being false while the premise is true. This
being so, such an inference cannot possibly be deductive.
Thus it seems that some of our most warranted inductive projections,
those mediated by various kinds of hedged generalizations, do not rely on
deduction for the final predictive step. These predictions, including statistical
syllogisms, are not deductions, and they do not seem to be abductions. That is,
sometimes the thing predicted is also explained, but note that the conclusions in
abductions do the explaining, whereas for predictions, if anything, the
conclusions are what is explained. Thus the predictive forms related to
statistical syllogism are in general nondeductive and nonabductive as well.
If predictions are not abductions, what then is the relationship between
prediction and explanation? The idea that they are closely related has a fairly
elaborate history in the philosophy of science. Some authors have proposed
that explanations and predictions have the same logical form. Typically this is
given as the form of a proof whereby the thing to be explained or predicted is
the conclusion, and causation enters in to the premises somehow, either as a
causal law or in some other way.
The idea seems to be that to explain something is to be in a position to
have predicted it, and to predict something puts one in a position to explain it, if
it actually occurs. This bridges the apparent basic asymmetry that arises
because what you explain is more or less a given (i.e., has happened or does
happen), whereas what you predict is an expectation and (usually) has not
Despite its apparent plausibility, this thesis is fundamentally flawed.
There is no necessary connection between explanation and prediction of this
sort. Consider the following two counterexamples.
Example 1. George-did-it explanations. Why is there mud on the carpet?
Explanation: George did it (presumably, but not explicitly, by tracking it into
the house stuck to his shoes, or something similar). Knowing that George came
into the room puts me in a position to predict mud on the carpet only if I assume
many questionable auxiliary assumptions about George’s path and the adhesive
properties of mud, and so forth. If I had an ideally complete explanation of the
mud on the carpet, some sort of complete causal story, then, perhaps, I would
be in a position to predict the last line of the story, given all the rest; but this is
an unrealistic representation of what normal explanation is like. George-did-it
explanations can be perfectly explanatory without any pretensions of
completeness. This shows that one can explain without being in a position to
predict. Many other examples can be given where explanation is ex post facto,
but where knowledge of a system is not complete enough to license prediction.
Why did the dice come up double 6s? Because of throwing the dice, and
chance. We are often in a position to explain a fact without being in a position
to have predicted it - specifically, when our explanation is not complete, which
is typical, or when the explanation does not posit a deterministic mechanism,
which is also typical.
Example 2. Predictions based on trust. Suppose that a mechanic, whom I have
good reason to trust, says that my car will soon lose its generator belt. On this
basis I predict that the car will lose its generator belt (on a long drive home,
say). Here I have made a prediction, and on perfectly good grounds, too, but I
am not in a position to give an explanation (I have no idea what has weakened
the belt). This example, weather predictions, and similar examples of
predictions based on authority show that one can be in a position to predict
without being in a position to explain.
I believe that explanations are causal, and that predictions are commonly
founded on projecting consequences based on our causal understanding of
things. Thus, commonly, an explanation of some event E refers to its causes,
and a prediction of E is based on its causes, and both the explanation and the
prediction suppose the causal connections. However, I believe that the
symmetry between explanation and prediction goes no further.
When a prediction fails, it casts doubt on the general premises on which
it is based. This is part of the logical underpinnings of scientific reasoning.
The view presented here is similar to what has been called the “hypotheticodeductive
” model of scientific reasoning, except in insisting that hypotheses
must be explanatory, and in denying that predictions are always deductive.
Predictions, then, are neither abductions nor (typically) deductions. This
is contrary, both to the view that predictions are deductions and to Harmanís
view that all nondeductive inferences are abductions. Rather, predictions and
abductions are two distinct kinds of plausible inference. Abductions go from
data to explanatory hypothesis; predictions go from hypothesis to expected data.
(See Figure 1.1.)
Jerry Hobbs has suggested (verbally) that, “The mind is a big abduction
machine.” In contrast Eugene Charniak has suggested (verbally) that there are
two fundamental operations of mind: abduction and planning. The view
presented in this chapter, while close to that of Hobbs in its enthusiasm for
abduction, is actually closer to Charniak’s. It elaborates that view, however, by
adding that planning depends on prediction (to anticipate consequences of
actions), and it is prediction that is inferentially fundamental. Planning is
choosing actions based on expected outcomes. So planning is “reasoning” all
right, but it is not “inference,” since planning decides action rather than belief.
While asserting that abduction and prediction are inferentially distinct,
we note that they are often entangled as processes. Sometimes an abduction
will use prediction as a subtask (e.g., for testing a hypothesis), and sometimes a
prediction will use abduction as a subtask (e.g., for assessing the situation).
e x p l a n a t o r y h y p o t h e s i s s p a c e
a b d u c t i o n
p r e d i c t i o n
d a t a s p a c e
F i g u r e 1 . 1 . A b d u c t i o n a n d p r e d i c t i o n .
Probabilities and abductions
It has been suggested that we should use mathematical probabilities to help us
choose among explanatory hypotheses. (Bayesís Theorem itself can be viewed
as a way of describing how simple alternative causal hypotheses can be
weighed.) If suitable knowledge of probabilities is available, the mathematical
theory of probabilities can, in principle, guide our abductive evaluation of
explanatory hypotheses to determine which is best. However, in practice it
seems that rough qualitative confidence levels on the hypotheses are enough to
support abductions, which then produce rough qualitative confidence levels for
their conclusions. It is certainly possible to model these confidences as
numbers from a continuum, and on rare occasions one can actually get
knowledge of numerical confidences (e.g., for playing blackjack). However,
for the most part numerical confidence estimates are unavailable and
unnecessary for reasoning. People are good abductive reasoners without close
estimates of confidence. In fact it can be argued that, if confidences need to be
estimated closely, then it must be that the best hypothesis is not much better
than the next best, in which case no conclusion can be confidently drawn
because the confidence of an abductive conclusion depends on how decisively
the best explanation surpasses the alternatives. Thus it seems that confident
abductions are possible only if confidences for hypotheses do not need to be
Moreover, it appears that accurate knowledge of probabilities is not
commonly available because the probability associated with a possible event is
not very well defined. There is almost always a certain arbitrariness about
which reference class is chosen as a base for the probabilities; the larger the
reference class, the more reliable the statistics, but the less relevant they are;
whereas the more specific the reference class, the more relevant, but the less
reliable. (See Salmon, 1967, p. 92.) Is the likelihood that the next patient has
the flu best estimated based on the frequency in all the people in the world over
the entire history of medicine? It seems better at least to control for the season
and to narrow the class to include people at just this particular time of the year.
(Notice that causal understanding is starting to creep into the considerations.)
Furthermore, each flu season is somewhat different, so we would do better to
narrow to considering people just this year. Then, of course, the average
patient is not the same as the average person, and so forth, so the class should
probably be narrowed further to something such as this: people of this particular
age, race, gender, and social status who have come lately to doctors of this sort.
Now the only way the doctor can have statistics this specific is to rely on his or
her own most recent experience, which allows for only rough estimates of
likelihood because the sample is so small. There is a Heisenberg-like
uncertainty about the whole thing; the closer you try to measure the likelihoods,
the more approximate the numbers become. In the complex natural world the
long-run statistics are often overwhelmed by the short-term trends, which
render the notion of a precise prior probability of an event inapplicable to most
Taxonomy of basic inference types
Considering its apparent ubiquity, it is remarkable how overlooked and
underanalyzed abduction is by almost 2,400 years of logic and philosophy.
According to the analysis given here, the distinction between abduction and
deduction is a distinction between different dimensions, so to speak, of
inference. Along one dimension inference can be distinguished into deductive
and nondeductive inference; along another dimension inferences can be
distinguished as abductive and predictive (and mixed) sorts of inferences.
Abduction absorbs inductive generalization as a subclass and leaves the
predictive aspect of induction as a separate kind of inference. Statistical
syllogism is a kind of prediction. This categorization of inferences is
summarized in Figure 1.2.
From wonder to understanding
Learning is the acquisition of knowledge. One main form of learning starts
with wonder and ends in understanding. To understand something is to grasp
an explanation of it. (To explain something to somebody is to package up an
understanding and communicate it.) Thus knowledge is built up of explanatory
hypotheses, which are put in place in memory as a result of processes set in
motion by wondering “Why?” That is, one main form of knowledge consists of
answers to explanation-seeking why questions.
An explanation-seeking why question rests on a Given, a presupposition
upon which the question is based. For example, “Why is the child sneezing?”
presupposes that the child is indeed sneezing. This Given is not absolutely
firm, even though it is accepted at the outset, for in the end we may be happy to
throw it away, as in, “Oh, those werenít sneezes at all. She was trying to keep a
feather in the air by blowing.” Usually, perhaps always, along with the Given
some contrasting possibility is held in mind, some imagined way that the Given
could have been different (Bromberger, 1966). Thus, behind the G in a “Why
G ?” usually there appears an “. . . as opposed to H ” discernible in the
Abduction is a process of going from some Given to a best explanation
for that (or related) given. Describing a computational process as abduction
says what it accomplishes - namely, generation, criticism, and acceptance of an
explanation - but superficially it says nothing about how it is accomplished (for
example, how hypotheses are generated or how generation interacts with
An explanation is an assignment of causal responsibility; it tells a causal
story (at least this is the sense of “explanation” relevant to abduction). Thus,
finding possible explanations is finding possible causes of the thing to be
explained, and so abduction is essentially a process of reasoning from effect to
A large part of knowledge consists of causal understanding. Abductions
produce knowledge, both in science and in ordinary life.