The Problem of Enthymemes: Is
There Help on the Way from AI?
Douglas Walton
CRRAR Talk, Oct. 13, 2011
University of Windsor, Ontario
CRRAR
Historical Funny Business
• This meaning of the term ‘enthymeme’
supposedly derives from Aristotle, and has been
accepted by nearly everybody who writes on the
subject (with some notable exceptions, like Sir
William Hamilton), but as Burnyeat (1994)
showed, it may be a historical misnomer.
CRRAR
Starting Definition
• An enthymeme is an incomplete argument
found in a text of discourse.
• In many cases, the missing assumption is a
premise, but sometimes it is a conclusion.
• In still other cases, there is chain of arguments
in which the conclusion of one argument also
functions as a premise in the next one. In these
cases the missing statement can be a premise as
well as a conclusion.
Classic Example
• The classic example is the argument: all men are
mortal; therefore Socrates is mortal.
• As pointed out in logic textbooks, you need to
insert the premise that Socrates is a man to
make the argument into a valid syllogism.
• But what are the grounds for inserting this
proposition as a premise if it was not explicitly
stated by the proponent?
How Useful is Deductive Logic?
• The possibility remains that we might think that
we could deal with enthymemes by only using
deductive logic, like syllogistic, to fill in missing
premises in an incomplete argument.
• This possibility has been argued against by van
Eemeren and Grootendorst (1984, p. 127) using
the familiar example of the argument that John
is English therefore John is brave.
Defeasible Generalizations
• This is a textbook, so don’t expect any jokes.
• According to Johnson and Blair (1983, 14), the
missing premise is a generalization, ‘Textbooks
don’t usually contain jokes’.
• This statement is a defeasible generalization.
• So deductive logic is not that useful.
• We need to use defeasible argumentation
schemes and generalizations.
Circumlocution Avoidance
• Mostly we are concerned with cases where the
missing assumption is a premise.
• Hence we will often speak this way, even
though we know that there is a possibility that
the case could be one of a missing conclusion.
• This prevents excessive repetition of the
qualification ‘or the conclusion’, and makes
things easier for the reader to grasp.
The Straw Man Problem
• The problem (Burke, 1985; Gough and Tindale,
1985; Hitchcock, 1985) is that if a critic is
allowed to fill in any proposition needed to
make the argument valid, she may be inserting
assumptions that were not meant by the
proponent to be part of his or her argument.
• There is the danger of committing the straw
man fallacy by attributing a premise that
distorts the argument in order to make it easier
to refute (Scriven, 1976, pp. 85-86).
Needed and Used Assumptions
• Ennis (1982, pp. 63-66) drew a distinction
between needed and used assumptions.
• A needed assumption in an argument is a
missing proposition such that (1) the argument
is not structurally correct as it stands, but (2)
when it is inserted, the argument becomes
structurally correct (e.g. deductively valid).
• A used assumption is really meant to be part of
the argument by the speaker.
Using Schemes to Find Missing Bits
• Needed assumptions can be found by using
argumentation schemes.
• My doctor says I need vitamin D, therefore I
need vitamin D.
• The missing assumption is that my doctor is an
expert in the relevant field (medicine).
• You can find the missing premise by using the
scheme for argument from expert opinion.
• Scheme for Argument from Expert Opinion



Major Premise: Source E is an expert in field F
containing proposition A.
Minor Premise: E asserts that proposition A (in field F)
is true (false).
Conclusion: A may plausibly be taken to be true
(false).
CRRAR
Finding Used Assumptions
• Finding used assumptions is much harder,
because it depends on that the arguer means.
• To do this we have to determine, based on the
evidence we have, whether the implicit
proposition is a commitment of the arguer.
• This can be a hard task to compute, because we
may have to draw inferences from the record of
what the arguer said.
Three Tools
• Here we can use three additional tools.
• The first of them is Gricean implicature.
• The second is the notion of commitment in
dialogue (Walton and Krabbe, 1995), used with
the dialogue system CBVK (Walton, 2008).
• Another is the notion of common knowledge.
Govier and Freeman
• Govier (1992, p. 120), categorized a proposition
as a matter of common knowledge if it states
something known by virtually everyone.
• She used the examples ‘Human beings have
hearts’ and ‘Many millions of civilians have been
killed in twentieth-century wars’ (p. 120).
• Freeman (1995, p. 269) categorized a
proposition as common knowledge if many,
most, or all people accept it.
OMCS Common Sense System
• The open mind common sense system
(OMCS)includes the following statements
(Singh, Lin, Mueller, Lim, Perkins and Zhu, 2002,
p. 3) under the category of common knowledge.
• People generally sleep at night.
• If you hold a knife by its blade then it may cut
you.
• People pay taxi drivers to drive them places.
Frames
• Common knowledge can be represented in
computing by what is called a frame, a data
structure for representing a stereotyped
situation, like going to a child’s birthday party
(Minsky, 1974, p. 2).
• The power of this theory lies in its inclusion of
expectations and other kinds of presumptions.
• A frame can be a source of common knowledge
used to fill in gaps in an enthymeme.
Scripts
• According to Schank and Abelson (1977),
common knowledge is based on a script, a body
of knowledge shared by language users
concerning what typically happens in certain
kinds of stereotypical situations, and which
enables a language user to fill in gaps in
inferences not explicitly stated in a text.
• Schank and Abelson used the restaurant story as
an example.
Jackson and Jacobs
• According to Jackson and Jacobs (1980, p. 263),
in order for rules of conversation to allow
participants to engage in collaborative
argumentation, there is a need to base many
implicit assumptions on commonly shared
knowledge.
• These might be assumptions like, ‘Snow is
white’, or ‘Los Angeles is in California’.
Free Animals Example
• This argument that was found in a web site
called “Animal Freedom”
(http://www.animalfreedom
.org/english/opinion/argument/ignoring.html).
• Animals in captivity are freer than in nature
because there are no natural predators to kill
them.
The Animals Diagram
Abductive Reasoning
• Abductive reasoning goes backward from a
given conclusion to search in a knowledge base
for premises that could prove a conclusion.
• The knowledge base can include explicitly stated
common knowledge statements.
• A knowledge-based system can search to find
additional premises that that are needed to fit
into argumentation schemes that can be used to
prove the conclusion.
The Carneades System
• The Carneades argumentation system can
perform abductive reasoning to find missing
premises needed to prove a conclusion.
• Carneades models critical questions as implicit
premises of an argumentation scheme.
• In addition to the ordinary premises of the
scheme, there can be assumptions and
exceptions.
The Global Warming Example
• Climate scientist Bruce, whose research is not
funded by industries that have financial
interests at stake, says that it is doubtful that
climate change is caused by carbon emissions.
• It is an exception that Bruce is not biased.
• The implicit premise that Bruce is not biased is
supported by the claim that his research is not
funded by industries with financial interests.
Six Basic Critical Questions for
Argument from Expert Opinion
Expertise Question: How credible is E as an expert
source?
Field Question: Is E an expert in the field F that A is in?
Opinion Question: What did E assert that implies A?
Trustworthiness Question: Is E personally reliable as a
source?
Consistency Question: Is A consistent with what other
experts assert?
Backup Evidence Question: Is E’s assertion based on
evidence?
Walton and Gordon (2005)
•
•
•
•
•
•
•
•
Ordinary Premise: E is an expert.
Ordinary Premise: E asserts that A.
Ordinary Premise: A is within F.
Assumption: It is assumed to be true that E is a
knowledgeable expert.
Assumption: It is assumed to be true that what E says is
based on evidence in field F.
Exception: E is not trustworthy.
Exception: What E asserts is not consistent with what
other experts in field F say.
Conclusion: A is true.
Global Warming Example Visualized
in Carneades Argument Map
The Yogurt Example
• The ad called “In Soviet Georgia”, designed by the
Burson ad agency, was run from 1975 to 1978 on TV
and in magazines like Time and Newsweek.
• The commercials presented shots of elderly Georgian
farmers and the announcer said, “In Soviet Georgia,
where they eat a lot of yogurt, a lot of people live past
100”.
• Advertising Age ranked In Soviet Georgia as number 89
on its list of the best of 100 greatest advertising
campaigns.
Four Implicit Parts
• Explicit Premise: In Soviet Georgia, they eat a lot of
yogurt.
• Explicit Premise: In Soviet Georgia, a lot of people live
past 100.
• Implicit premise: The eating of the yogurt is causing the
people in Soviet Georgia to live past 100.
• Implicit conclusion: If you want to live longer, you
should eat yogurt.
• Implicit premise: You want to live longer.
• Implicit Conclusion: You should eat yogurt.
The Yogurt Diagram
Enthymematic Chaining
• The analysis of this case it is interesting because it
shows not only an ad with an implicit conclusion, but
one with an implicit subconclusion used to link one
part of the argument with another.
• Also, two argumentation schemes can be applied to
the structure of the chain of argumentation.
• We essentially have to chain two arguments connected
to each other because an implicit conclusion of the one
argument functions as a premise supporting the one
premise in the other argument.
Post Hoc Fallacy?
• An interesting discussion point in this example is
whether the argument commits the post hoc fallacy,
the error of leaping prematurely from a correlation to a
causal conclusion.
• There are good grounds for concluding, on the analysis
above, that the argumentation in this case does
commit the post hoc fallacy.
• The analysis shown in the diagram along with the
scheme and critical questions provide the right kind of
evidence needed to support such a criticism.
Exploiting Common Knowledge
• This ad was successful during the days when people
were aware of the longevity of the farmers in Georgia.
• It was widely thought to be a remarkable phenomenon
because they appeared to be no explanation of it.
• The ad exploited this common knowledge successfully
by allowing the reader to jump to an explanation that
served the marketers of yogurt products.
• The same ad would not work today, as commonly held
opinions about aging and nutrition have changed.
The Signal Light Example
• The witness said he saw the signal light flashing
on Bob's car just before the car turned.
•
• Therefore Bob signaled his turn.
Missing Premises
• Pushing the turn signal indicator is the normal way to signal a turn.
• If the signal light is flashing on a car, and normally means that the driver has
pushed the turn signal indicator.
• If a witness makes an assertion, then the proposition that is asserted is true.
• Assumption: The witness is telling the truth.
• The signal light was flashing on Bob's car just before the car turned.
• If the red signal light was flashing on Bob's car just before the car turned, Bob
must have pushed the turn signal indicator before he turned.
• Action sequence [script]: Bob moved his hand, Bob pushed the turn signal
indicator, Bob activated the mechanism to make the signal light on this car
flash, Bob signaled his turn.
Scheme for Argument from Witness
Testimony
• Position to Know Premise: Witness W is in a
position to know whether A is true or not.
• Truth Telling Premise: Witness W is telling the
truth (as W knows it).
• Statement Premise: Witness W states that A is
true (false).
• Conclusion: Therefore (defeasibly) A is true
(false).
Critical Questions for Witness
Testimony Scheme
• Internal Consistency Question: Is what the witness said internally consistent?
• Factual Consistency Question: Is what the witness said consistent with the
known facts of the case (based on evidence apart from what the witness
testified to)?
• Consistency with Other Witnesses Question: Is what the witness said
consistent with what other witnesses have (independently) testified to?
• Trustworthiness Question: Is the witness personally reliable as a source?
• Plausibility Question: How plausible is the statement A asserted by the
witness? Exception if what the witness says is implausible.
• Bias Question: Is there some kind of bias that can be attributed to the
account given by the witness?
• Witness Testimony Evidence: Argumentation, Artificial Intelligence and Law,
Cambridge, Cambridge University Press, 2008, p. 60.
Some References
M. F. Burnyeat, Enthymeme: Aristotle on the Logic of Persuasion, Aristotle’s Rhetoric: Philosophical Essays, ed. David J. Furley and
Alexander Nehemas, Princeton, Princeton University Press, 1994, 3-55.
R. H. Ennis, Identifying Implicit Assumptions, Synthese, 51, 1982, 61-86.
J. B. Freeman, The Appeal to Popularity and Presumption by Common Knowledge,'Fallacies: Classical and Contemporary Readings,
ed. Hans V. Hansen and Robert C. Pinto, University Park, Pa., The Pennsylvania State University Press, 1995, 263-273.
J. Gough and C. Tindale, Hidden or Missing Premises, Informal Logic, 7, 1985, 99-106.
T. Govier, A Practical Study of Argument, 3rd ed., Belmont, Wadsworth, 1992.
J. P. Grice, Logic and Conversation, The Logic of Grammar, ed. D. Davidson and G. Harman, Encino, California, 1975, 64-75.
D. Hitchcock, Enthymematic Arguments, Informal Logic, 7, 1985, 83-97.
S. Jackson and S. Jacobs, Pragmatic Bases for the Enthymeme, Quarterly Journal of Speech, 66, 1980, 251-165.
R. H. Johnson and J. A. Blair, Logical Self-Defense, 2nd ed., Toronto, McGraw-Hill Ryerson, 1983.
M. Minsky, A Framework for Representing Knowledge, reprinted in The Psychology of Computer Vision, P. Winston, ed., McGraw Hill,
1975: available at http://web.media.mit.edu/~minsky/papers/Frames/frames.html
R. C. Schank and Robert P. Abelson, Scripts, Plans, Goals and Understanding, Hillsdale, N. J., Erlbaum, 1977.
M. Scriven, Reasoning, New York, McGraw-Hill, 1976.
P. Singh et al., Open Mind Common Sense: Knowledge Acquisition form the General Public, Proceedings of the First International
Conference on Ontologies, Databases, and Applications of Semantics for Large Scale Information Systems, Lecture Notes in
Computer Science, Heidelberg, Springer Verlag, 2002.
F. H. van Eemeren and R. Grootendorst, Speech Acts in Argumentative Discussions, Dordrecht, Foris, 1984.
D. Walton, The Three Bases for the Enthymeme: A Dialogical Theory, Journal of Applied Logic, 6, 2008, 361-379 .
D. Walton and E. C. W. Krabbe, Commitment in Dialogue, Albany, SUNY Press, 1995.