While there is wide disagreement among philosophers and
logicians about a precise definition for the term fallacy,[1]
it is generally agreed that fallacies are mistakes in reasoning that involve
ambiguity and vagueness.[2]
A fallacy can be a type of error in an argument, a type of error in reasoning
(such as arguing, defining, and explaining), a false belief, or a rhetorical
technique that causes any of these errors.[3]
For present purposes, fallacy refers either to errors in the substance of
arguments (as opposed to errors in the arguer’s thinking) or to the rhetorical
tools that cause these errors.
Fallacies are also described as being either formal or
informal. Formal fallacies are
concerned with highly technical errors in the logical structure of the argument.[4] Legal arguments rarely[5] contain formal fallacies.[6]
Informal fallacies are concerned not with the form
but with the content (and possibly the intent) of the reasoning.[7] They
are “proofs that appear at first glance to be sound but are fatally flawed in
their reasoning or construction.”[8]
And from a psychology perspective, “a fallacy is often defined as a mistake in
reasoning used for deceptive purposes.”[9]
While this certainly is not categorically true of all informal fallacies, “many
of the informal fallacies are often used in the manipulation of opinion.”[10]
Informal fallacies can also be difficult to identify. For instance, a
slippery-slope argument often straddles the line between being persuasively
plausible and fallaciously exaggerated.[11]
For present purposes, a fallacious argument is either inductively very weak, or
contains an unjustified premise, or ignores relevant, available evidence that
the arguer should know about, and the argument can be used to persuade.[12]
One such informal fallacy is the fallacy
of equivocation: “the illegitimate switching of the meaning of
a term during the reasoning.”[13]
Salary
data show that the vast majority of lawyers earn relatively
high salaries. According to the U.S. Census Bureau, lawyers boast the fourth
highest median salary behind medical doctors, dentists and CEOs
(some of whom have law degrees). While the majority of
occupations have median salaries between
$20,000 and $49,999, the median for lawyers in 2010
was almost $113,000. Again, this was the median — the
actual midpoint — which means the majority of lawyers made
six-figures.
The
problem here is that majority and median are
equivocal words, or words that are subject to two or more interpretations and
are usually used to mislead or confuse. The author equivocates because he uses
the same words twice but changes the meaning of the words. Here is a breakdown
showing the connotation of each phrase that uses majority or median.
Equivocal Words
§ vast
majority of lawyers = most lawyers
§ majority
of occupations = most occupations
§ median
salaries = average salaries
§ median
[salary] for lawyers = average salary
§ median = the actual midpoint salary with equal numbers of salaries that are higher
and lower
§ majority
of lawyers = a literal majority, or a number equaling more than half of the
total (at least 50.1%)
The main, implicit conclusion
that the author likely hoped his reader would draw might be something along
these lines:
The vast majority of lawyers
made at least $113,000 in 2010.
But this conclusion just doesn't
follow from the premises. The more genuine argument leads to a different
conclusion: a literal majority of
lawyers earned a relatively high salary in 2010.
1. Relatively high salary means
more than $99,999.99
2. Lawyers have the
fourth-highest median salary
3. Most occupations had a
median salary between $20k and $50k in 2010
4. Lawyers had a median salary
of $113k in 2010
5. Median is the midpoint on a
range of salaries
6. Only 50% of lawyers earned
at least $113k in 2010
7. But some lawyers also earned
between $100k and $113k in 2010
8. At least 50.1% of lawyers
earned more than $99,999.99 in 2010; thus,
A literal majority of lawyers
earned a relatively high salary in 2010.
Sketching out the argument in
this way reveals its real weakness. Regardless of whether the argument actually
commits the fallacy of equivocation, we should still reject its persuasiveness
because the premises lead to an equally troubling conclusion:
1. It is also true
that 50% of lawyers earned less than $113k in 2010;
2. And a proportionately large
minority of lawyers earned less than $99,999.99; thus,
A large minority of lawyers
did not earn a relatively high salary in 2010.
** These first three paragraphs come from a
paper I published during my third-year of law school. Cory S. Clements,
Comment, Perception and Persuasion in
Legal Argumentation: Using Informal Fallacies and Cognitive Biases to Win the
War of Words, 2013 BYU L. Rev. 319, 331–33 & nn.61–72, available at http://ssrn.com/abstract=2236669.
[1]. The Internet is rich with information
about the various types of logical fallacies. See Bradley Dowden, Fallacies, Internet
Encyc. Phil., http://www.iep.utm.edu/fallacy (last updated Dec. 31,
2010) (content may also be accessed through an alternate domain, dewsberry.com, http://dewsberry.com/content/es/content/reference/fallacies/fallacies.htm); Charles Ess, Informal Fallacies, Drury.edu, http://www.drury.edu/ess/Logic/Informal/Overview.html (last visited Feb. 3,
2013); Logical
Fallacies, http://www.logicalfallacies.info (last visited Feb. 3,
2013); Taxonomy of the Logical
Fallacies, Fallacy Files, http://www.fallacyfiles.org/taxonomy.html
(last
visited Feb. 3, 2013).
[2]. Dowden, supra note 1 (“The term ‘fallacy’ is not a precise
term. One reason is that it is ambiguous.”).
[4]. Id. Formal fallacies are typically
studied as part of a course on categorical, statement, and predicate logic. See generally Frances Howard-Snyder, Daniel Howard-Snyder
& Ryan Wasserman, The Power of Logic (5th ed. 2012).
[5]. Though rare, legal arguments
containing formal fallacies do appear from time to time—even in judicial
opinions. See, e.g., Cory S. Clements, Note, Judicial Takings in Vandevere v. Lloyd, 2012 BYU
L. Rev. 423, 438–39 &
n.117, available at http://lawreview.byu.edu/articles/1341676891_04clements.fin.pdf (construing Vandevere
v. Lloyd, 644 F.3d 957, 966–67 (9th Cir. 2011)).
[T]he Ninth Circuit’s reasoning .
. . is a non-sequitur. Logically speaking, the argument is invalid because it
denies the antecedent, taking the following form: If (A), then (B). (Not-A). So, (not-B). To make sense of how
the court’s reasoning is faulty, one must supply the implicit premises, (A) and (B),
because the court’s argument made explicit only the contrapositives, (Not-A) and (Not-B).
Thus, the argument with its implicit premises reads as follows:
If (A) Lucas’s remand order concerned
the extent of the property interest, then (B) the extent of the property interest is
not a matter of state law. (Not-A) Lucas’s remand order “did not
concern the extent of the property interest.” So, (not-B) “the extent of the property interest”
“is a matter of state law.”
Id. (footnote omitted)
(“[T]he Court’s quarrel with the state supreme court did not concern the extent of the property interest in the beachfront land, which the
Court’s remand order firmly suggests is a matter of state law but, rather,
concerned the extent to which
the state could invade a
property interest without providing just compensation, which is a matter of
federal law.” (quoting Vandevere,
644 F.3d at 964)).
For an in-depth
explanation of how to recognize legal arguments that commit the fallacy of
denying the antecedent, see Stephen M. Rice, Conventional
Logic: Using the Logical Fallacy of Denying the Antecedent as a Litigation Tool,
79 Miss. L.J. 669,
683 (2010) (“[W]here the rules of logic are not observed, the argument takes
the form of a fallacy. The Fallacy of Denying the Antecedent is one fallacy
that results from failure to observe the logical rules. Where the argument
denies the antecedent term of the hypothetical syllogism, it violates the rule
that requires the antecedent term be affirmed. Accordingly, when the antecedent
term is denied, the argument commits the Fallacy of Denying the Antecedent and
is logically invalid.”).
[6]. This is because formal fallacies are
easier to spot than informal fallacies. E.g.,
Stephen M. Rice, Indiscernible
Logic: Using the Logical Fallacies of the Illicit Major Term and the Illicit
Minor Term as Litigation Tools, 47 Willamette L. Rev. 101, 107 (2010) (“These
illogical arguments, called fallacies, can be identified by the pattern of an
argument’s form, which makes them easy to identify, describe, and discredit.”).
Judge Aldisert defines formal fallacy as follows:
A formal fallacy is any violation of any of the six rules of the
categorical syllogism or the rules of the hypothetical or disjunctive
-alternative syllogism. It is an argument whose conclusion could be false even
if all its premises are true. It can be detected merely by examining the form (hence its name) or structure of the
argument.
[7]. William
F. Lawhead, The Philosophical Journey app. A-9 (3d ed. 2006)
(stating that informal fallacies are “a type of bad reasoning that can only be
detected by examining the content of the argument”).
[9]. Introduction to Logic: Informal
Fallacies, P.L.E., http://philosophy.lander.edu/logic/fall
acy_topics.html (last visited Nov. 14, 2012).
[11]. E.g., Mitchell F. Park,
Comment, Defining One’s Own
Concept of Existence and the Meaning of the Universe: The Presumption of
Liberty in Lawrence v. Texas,
2006 BYU L. Rev. 837,
881 n.191 (“Suppose someone claims that a first step (in a chain of causes and
effects, or a chain of reasoning) will probably lead to a second step that in
turn will probably lead to another step and so on until a final step ends in
trouble. If the likelihood of the trouble occurring is exaggerated, the
slippery slope fallacy is committed.” (quoting Dowden, supra note 1)).
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