On the Limitations of Language and Logic

1

Tom Gally
The University of Tokyo
While most types of writing are expected to be clear and logical, theseproperties are demanded especially of academic writing. As a result, theteaching of writing for scholarship and research often emphasizes precise
language and critical thinking. However, as this paper endeavors to show,
language is inherently complex and difficult to tame and traditional logic fails
to encompass the actual reasoning methods used in academic discourse.
Pedagogies that emphasize the teaching and application of specific principles
and rules of language and logic are therefore insufficient for making young
scholars adequate writers of research papers. Better results might be obtained,
this paper suggests, by focusing on methods that embrace the social aspects oflanguage and logic.
1. Education and Writing
Education prefers clarity.
If knowledge and skills are to be learned, it is believed, the relevant facts, principles, andprocesses need to be conveyed to students with definiteness and precision. Terms must be
well defined, textbooks must be logically organized, and teachers must speak distinctly.
Testing, in particular, usually demands extraordinary exactness—statements are to be marked
either true or false, multiple-choice questions have unique answers, blanks can be filled in in
only one way. And students’ learning is rated on linear scales with unambiguous letters andnumbers.
One reason for this focus on clarity, of course, is that both teachers and students havefound clarity to be useful and necessary for many types of learning. Vague language andsloppy presentation do not help students learn algebra, anatomy, or the Armenian alphabet.
But the need for exactness is also driven by institutional imperatives, because the granting of
grades and diplomas, and of the concomitant social status, requires fairness and accountability.
The result can be an excessive focus on clarity and precision even with subjects that, in theiressence, are nebulous and ill-defined.
One such subject is writing. The act of writing, whether of novels, term papers, or user
manuals, is inherently the creation of something new; a person who reproduces a previously
written text is a copyist, typesetter, or plagiarist, not a writer. When writing is taught, thestudents are therefore expected to produce original texts, texts that have never been written
before, texts that therefore cannot be said to be correct or incorrect. But despite theindeterminacy of this creative act, the teaching of writing frequently succumbs to theeducational demand for precision. From the formatting of the printed page and thepunctuation of citations and references to the roles of sentences in paragraphs and ofparagraphs in longer texts, writing is often taught to students as if it were nothing more than1This paper is an expanded version of half of a lecture that I gave on February 16, 2013, at the 1st International
Symposium on Academic Writing & Critical Thinking, held at Nagoya University. The title of that talk was“Integrating Writing with Critical Thinking: First-Year Undergraduate Writing Programs at the University ofTokyo”; the programs referred to in that title were described in the other half of the talk, which is not covered
here.
NU Ideas Volume 2, issue 2. 2013. Nagoya University Institute of Liberal Arts & Sciences
Special issue: Proceedings of the First International Symposium on Academic Writing and Critical Thinking© 2013 by Tom GallyOn the Limitations of Language and Logic
the assembly of the pieces of a puzzle or the combination of the ingredients of a recipe.
Accustomed to being taught other subjects in the same way, students rarely object to thisprescriptive, procedure-based teaching. In fact, they often welcome it; after all, it is clear. The
fact that it distorts the nature of writing, and is insufficient to make students proficient writers,
is rarely noticed.
2. Language Is Lousy for Critical Thinking
The limitations of cooking-recipe approaches to the teaching of writing become even more
apparent when one remembers that writing is a form of language and that language is fiercely
resistant to clear, comprehensive description. Take, as just one example, the fluidity of themeanings of individual words. The entries in dictionaries for nearly all commonly used words
contain multiple senses: back can denote a location, a direction, a body area; blue is a color, amood, or a kind of butterfly. And dictionaries, constrained by the limitations of space andeditorial resources, indicate only the most common senses of words. A close examination of
any particular word in multiple contexts will reveal meanings and nuances not captured byany dictionary. In fact, as the lexicographer Allen Walker Read once noted, the meaning of aword is different every time it is used (Stacey 1989, 62).
A case in point is the word critical. Consider the following four instances, taken fromacademic writing, of its adverbial form, critically:(1) I decided to take him aside for 20 minutes to see if I could uncover why asuccessful team leader had such problems with presentations.... He said heseemed to derail in his presentations when he perceived the audience as blankand disengaged, and felt they were thinking critically about him.... (Lee 2003,
102)(2) In early adolescence, contemporary problem novels and wish fulfillment stories
provide an opportunity for the reader to “find oneself” through literature and to
begin thinking critically about it, which parallels a burgeoning critical view ofthe world. (Knickerbocker and Rycik 2002, 199)
(3) Thinking critically is an ability which is to be developed in the EFL [English
as a foreign language] class as a result of the generalized process ofglobalization, immigration and poverty. It is essential for teachers to be awareof the fact that tolerance, dialogue among cultures and deconstruction of texts
need to be exercised so that students can dissect dominant discourses and allow
for diversity knocking down stereotypes. (Farralelli 2009, 26)(4) The overall aim was to create a more explicit and methodical induction ofincoming students into the disciplinary academic practices of reading, thinking
critically, and writing in the appropriate forms. (Clarence 2012, 131)
Although those citations are all from academic texts, the phrase thinking critically has adifferent meaning in each. In (1), thinking critically means thinking disparaging thoughts
about another person; this is probably the most common meaning of critical, and it is used
often in everyday speech and writing. In (2), the phrase refers to the analysis andinterpretation of literary works, a more academic though still widely known sense. The phrase
in (3) refers to a particular approach to social issues, one that emphasizes awareness of power
relations and active attempts to overcome injustice; this meaning of critical, which has been
associated with the writings of Paulo Freire, Henry Giroux, and others, is used often by someacademics and political activists, but it is much less common in general contexts. Finally, in(4) the phrase refers to thinking clearly, logically, and analytically—the meaning in which it isused most often with regard to the teaching of academic writing.

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While these four senses overlap somewhat, they are largely distinct. One can thinkcritically as in (1) based solely on a subjective, emotional reaction to another person’s
appearance or behavior; that thinking does not need to be literary, political, or logical.
Similarly, critical thinking as in (2) need not share any of the main characteristics of (1), (3),or (4). And (3) is different from the others, as is (4). Thus the same word, critically, used insimilar collocations, can take on vastly different meanings depending on the context.
Furthermore, even a well-read, educated reader might not recognize the intended meaning;
this writer, for example, has more than once initially interpreted critical or critically to mean(1), (2), or (4) but later realized that the author or speaker had in fact meant (3). Similarly,
scholars and activists for whom (3) is an everyday sense might expect that, say, speakers at a
symposium on academic writing and critical thinking will be discussing issues such as global
capitalism and neoliberalism rather than the logic and structure of academic papers.
The word critical is far from unique in the diversity and fluidity of its meanings. Other
words essential to academic discourse—whether culture, society, knowledge, or truth—are
equally difficult to corral into definite semantic boundaries. One consequence of this fluidity
is that it hinders educational approaches that emphasize precision. It would be very difficult,for example, to include on a multiple-choice vocabulary test of English a question todetermine whether the test-takers understand the meanings of critical, as the question would
have to focus on only one of the meanings—most likely (1) for a general-purpose language
test, maybe (2) or (4) for a test of academic English—at the expense of the others (including
senses not discussed here).
A more significant problem is that language’s fluidity makes it a poor tool for—in thesense of (4)—critical thinking. If we wish to convey our arguments clearly and convincingly
to others, it is essential that our words be interpreted as we intend them to be. But with themeanings of words constantly shifting, and with every reader’s and listener’s understanding of
language somewhat different from others’, interpretations can be only partially faithful.
A medium more precise than language for thinking clearly and logically does exist. In
higher mathematics, terms are defined with a rigor and precision that makes them nearly
invulnerable to misinterpretation. Expressions such as complex number, Galois field, andtopological space are defined completely and uniquely, and mathematicians are rarely
confused about what any term means in any particular context. Special symbols, to which
specific meanings are assigned unambiguously, are frequently used to reduce the possibility of
misunderstanding even more.
Unfortunately, outside of physics, chemistry, and some other fields of the physical sciences,precise definitions and symbolic representations in the style of mathematics are of very
limited use. Most entities studied in the social sciences and humanities, in particular, are toocomplex, too diverse, too numerous to be precisely defined, and attempts to use mathematicslike formalities to advance knowledge in such fields have rarely been successful. To thinkcritically about most subjects that involve human beings, we are stuck with language. But
language is lousy for critical thinking.
3. Logic Is Limited, Too
The type of critical thinking being considered here depends in part on logic, that is, theprocess of drawing conclusions from assumptions. A classic example of logic is deductive
reasoning, such as in the following syllogism:
John is a bachelor.
All bachelors are male.
Therefore John is male.

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On the Limitations of Language and Logic
In order for such reasoning to work, each of the premises must have a binary truth value, thatis, it must be either completely true or completely false. In fact, statements like “John is abachelor” are chosen for examples of logical reasoning precisely because, at first glance, they
seem in the real world to indeed be either true or false. If John, it is assumed, has never signed
a marriage certificate that has also been signed by a woman and certified by a competent legal
authority—an act that, it would seem, either has happened or hasn’t—or if all of his previous
marriages have been dissolved in equally well-defined ways (divorce, annulment, death of a
spouse, etc.), then the statement “John is a bachelor” must be true; otherwise, it is false. The
truth value of “All bachelors are male” seems similarly binary; in fact, it is supposed to be
regarded as invariably true because the word bachelor is assumed to mean “an unmarried
male person.”Suppose, however, that the time is April 2013 and that John is a gay man living in the stateof Delaware in the United States. John has been in a committed relationship with another man,
Steve, for the past fifteen years. Delaware does not allow same-sex marriage, but in July 2007,
while on a vacation in Canada, which does allow same-sex marriage, John and Steve (who isa Canadian citizen) got married under the laws of Canada. That marriage is not recognizedunder the current laws of Delaware, where John and Steve live, but a bill has been submitted
to the Delaware legislature to legalize same-sex marriage. The bill seems likely to pass, but it
is not yet known when it will take effect or whether, in the bill’s final form, John and Steve’s
Canadian marriage will be recognized in Delaware.
In such a situation, what is the truth value of “John is a bachelor”? Even if the wordbachelor is interpreted according to legal definitions, the statement’s truth value is uncertain.
A court decision would probably be necessary to determine whether or not John’s Canadianmarriage means that he is also married in Delaware, and, with legislation pending, Delaware
courts in April 2013 might hesitate to rule on such a case. The truth value is even more
uncertain if we consider how the word bachelor is understood not legally but in general: somepeople, such as those opposed to same-sex marriage for religious reasons, might consider“John is a bachelor” to be true; others, such as John and Steve and their friends, might
consider it false; and others, including this writer, would be unsure.
If the truth value of such a simple statement can be uncertain,2 then there is little hope thatthe statements that are made in real discourses—even careful, formal, academic writing—will
have binary truth values. Consider, for example, the following sentence taken from anacademic paper:This paper argues that the traditional definition of the scope and practice ofmanagement control which was developed in the mid 1960s is now too
restrictive as it is based on a context of large, hierarchically structured
organizations which are now in relative decline. (Otley 1994, 289)
As this is the paper’s thesis statement, the author is arguing in favor of the stated proposition.
While it is completely reasonable to argue for such a complex proposition in an academic
paper, such a proposition cannot be assessed as being merely true or false.
For example, the word “too,” in “too restrictive,” is normally meant to be interpreted witha considerable degree of subjectivity. An author could, one supposes, assign numerical values
to “too restrictive” and “not too restrictive” so that the distinction between them becomes
clear and unambiguous. However, such everyday words are rarely defined in academic
writing; if they were, academic papers would become nearly incomprehensible.

2

The statements “All bachelors are male” and “John is male” are nearly as problematic from a truth-value
perspective. Explaining the fuzzy boundaries of the word male in the 21st century is left as an exercise for thereader.

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Symposium on Academic Writing and Critical Thinking
Furthermore, the main clause (“the traditional definition ... is too restrictive”) is modified
by propositions in subordinate clauses, specifically that “[the traditional definition] is basedon a context of large, hierarchically structured organizations” and that those organizations“are now in relative decline.” The validity of those propositions affects that of the entire
sentence in subtle ways. If, for example, large, hierarchically structured organizations are infact not in relative decline (suppose, instead, that all organizations, including small,egalitarian ones, are in similar decline), then the thesis statement might become weakerwithout becoming false.
In the following thesis statement, from another paper, the central assertion hinges on theword “should”:
This paper argues that policy makers should make CPRs [common property
resources] an important component of rural development, especially in suchareas as India’s dry region. (Jodha 1992)
It is difficult to imagine that such a statement—common in fields like political science andeconomic policy studies—could be assessed as “true” or “false.” This sentence is more apolicy recommendation as a factual claim, and policy recommendations—which are based on
moral, ethical, economic, and political considerations—do not emerge convincingly throughpurely logical arguments.
The point of these two examples—which could be extended to the thousands by a simple
search at Google Scholar for the phrase “this paper argues that”—is that arguments in serious
discourse are often expressed through statements that cannot be assessed as being simply trueor false. As a result, the tools of traditional logic, which depend on such binary truth values,
are of limited use when teaching young scholars to write more effectively.3
4. The Social Basis of Reasoning
The distinctive forms of both language and reasoning emerge through interactions amongpeople of particular social groups. For language, this process is clear to anyone who has
examined how people actually talk and write. Language, after all, varies in pronunciation,
grammar, and the meanings of words according to country, region, social class, age, and othercriteria by which people form groups. The members of each group interact with each otherfrequently, so the language they use with each other gradually takes on distinctive
characteristics.
The reasoning methods used by different groups of people can also be different. One
example is the sorts of evidence that members of any particular group accept as the basis forarguments. An extreme case is theological arguments: a believer in a religion might take asassumed without question—as statements of Eternal Truth—the assertions of the religion’s
fundamental teachings and therefore accept any argument that clearly follows from those
assertions; a non-devotee scholar studying the same religion might approach those teachings
with an open mind, neither accepting nor doubting; and a follower of another religion might
reject those teachings out of hand. Some academic fields, while perhaps not quite as dogmatic
as literalist religions, exhibit similar acceptance of foundational texts, with scholars in
psychoanalysis citing Freud, in deconstructionist literary theory Derrida, and in generativegrammar Chomsky as evidence in support of their arguments.
3

Another example of the limitations of traditional logic is shown in a statement that I recall the mathematician
Paul Halmos (1916–2006) attributing to George Boole (1815–64) in a class on mathematical logic that I tookfrom Halmos in the 1970s: something to the effect that “Although the development of formal logic has continued
for more than two thousand years since Aristotle, it is still not possible to prove the truth of the statement ‘If ahorse is an animal, then a horse’s head is an animal’s head.’ ” I might very well be misremembering from whom
I heard this statement or to whom it was attributed, but the point seems valid: Traditional logic captures only asubset—perhaps even a small subset—of all commonly accepted reasoning processes.

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On the Limitations of Language and Logic
Scholars in different fields use not only different assumptions but different reasoning
processes as well. In mainstream pure mathematics, for example, it is accepted that, for every
well-formed statement, either the statement is true or its negation is true. Thus, if “A is B” isfalse, then “A is not B” is true. This “principle of excluded middle” makes possible arguments
such as the following:
If n is a prime number greater than 2, then n is odd. Therefore, if n is not odd,
then n is not a prime number greater than 2.
Such arguments do not work in fields where the truth values of statements are not black orwhite. The following argument, for example, is unlikely to be accepted by scholars ofliterature:
Shakespeare’s plays contain complex renderings of the human condition, so
they deserve to be studied for generations to come. Consequently, because theplays of Neil Simon are of only temporary interest, they do not containcomplex renderings of the human condition.4
Such differences in reasoning methods can create deep rifts between academic communities.
Mathematicians and physicists, in particular, accustomed to tight mathematical arguments,
can be disparaging of the looser argumentation of the humanities. (Scholars in the humanities,
in contrast, usually do not understand enough higher mathematics to judge its methods ofargumentation.)
As fields of study evolve, new ways of reasoning can be born. An example from the fieldof linguistics is the methodology that was developed in the 1950s and 1960s for making
arguments about sentence structure in the context of generative grammar. This syntactic
argumentation generally accepts native speakers’ intuition as evidence for whether any
particular string of words forms a grammatical sentence. Generative grammarians’ arguments
also frequently rely on deep generalizations about linguistic phenomena.5 In contrast, linguists
in areas such as corpus analysis prefer more empirical descriptions based on spontaneous
language use. Thus even within the same field, linguistics, scholars can differ both about whatsorts of evidence to accept and how to reason with the evidence that is accepted.
I mention specifically the reasoning methods of mathematics and linguistics because thesehappen to be two fields with which I am familiar. But it is apparent that other academic fields
also possess their own standards—sometimes explicit, often merely understood—about how
arguments should be made. In fact, those differences in reasoning methods—together withdifferences in the objects of study—play an important role in distinguishing between different
academic fields. In other words, people are organic chemists or cognitive psychologists orsocial historians not only because they study carbon-based compounds or mental processes orthe experiences of ordinary people in the past; they have also learned to reason and argue likeother scholars in the same field.
5. What Can Be Done
By recognizing that, like languages, methods of reasoning differ among groups and thatthose differences emerge and are reinforced through intragroup interactions, we can see how
we might try to overcome the limitations of language and logic when teaching academic
writing and critical thinking. Rather than striving for unobtainable clarity and precision—for
meanings that cannot be misinterpreted, for rules that should never be violated, and forarguments that cannot be countered—we should continue to create structures and processes
4This argument is, of course, not completely parallel to the mathematical argument immediately above, because
the forms and terms of literary arguments are not as precisely defined and regulated as those of mathematics.
5

For an extensive account of syntactic argumentation, see Aarts 2001.

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that replicate the actual contexts and social interactions in which scholars learn the language
and logic of their fields. By intelligently guiding our students through those structures andprocesses, using methods that we already have—tutorials, peer review, discussion, debates,
collaborative writing, etc.—and by constantly refining and improving those methods, we canhelp our students learn through those interactive processes how to think and write more
effectively.
References
Aarts, Bas. 2001. English Syntax and Argumentation, 2nd edition. Basingstoke, Hampshire:
Palgrave.
Clarence, Sherran. 2012. “Making Inter-disciplinary Spaces for Talk about and Change inStudent Writing and Literacy Development.” Teaching in Higher Education. 17, 2: 127–
137.
Farralelli, Mariana. 2009. “Using a Critical Literacy Approach in the EFL Class.” Journal of
NELTA. 14: 26-31.
Jodha, N. S. 1992. “Common Property Resources: A Missing Dimension of Development
Strategies.” World Bank Technical Paper 1992, No. 169. http://www.cabdirect.org/
abstracts/19921801752.html
Knickerbocker, Joan L. and James Rycik. 2002. “Growing into Literature: Adolescents’
Literary Interpretation and Appreciation.” Journal of Adolescent & Adult Literacy. 46,
3: 196–208.
Lee, Graham. 2003. Leadership Coaching: From Personal Insight to Organisational
Performance. London: Chartered Institute of Personnel and Development.
Otley, David. 1994. “Management Control in Contemporary Organizations: Towards a Wider
Framework.” Management Accounting Research. 5: 289–299.
Stacey, Michelle. 1989. “At Play in the Language.” The New Yorker, September 4.

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