Logical fallacies are often aptly named—hasty generalization, faulty assumption, straw man, false analogy, begging the question, red herring, etc. Aristotle, to whom we are indebted for codifying them, subdivided the slippery concept into two parts. Formal fallacies derive from the structure of the syllogism, the underlying argument in its finished form: I think; therefore, I am. A full blown syllogism subsidizing Descartes dictum might go ‘thinking creatures are—I am a thinking creature—therefore, I am, too,’ wherein we find a major premise, a minor premise, and a conclusion. Onlookers searching for a way to break the argument must attack the content, not the form of the argument. Object. Raise your voice. What do you mean by ‘thinking creature?’ Have you read your Shakespeare? What is this quintessence of dust? Informal fallacies are inconsistencies or weaknesses in either the content of the argument or the language used to communicate it, the White whale. Post hoc ergo propter hoc.
***
During the middle of the interminable medieval period Thomas Aquinas scoured Aristotle’s writings, all of it, in his quest for logical proof of the existence of God. According to Pasnau (2023), Aquinas’ systematic reworking of Aristotle reshaped Western philosophy, not to mention theology, and spawned centuries of elaborations and disputations. Aquinas wrote an important book about his theory of analogy, which inserted a novel language flexibility into the machine-like syllogism to stretch it beyond its Earthly applications. Analogy was a gift to humankind because it explains how language can be applied meaningfully and logically to God without equivocation or univocal predication, both of which demean and reduce the significance of the God question.
Univocal predication vs equivocal predication is a hidden pitfall of language in anyone’s attempts to ferret out faulty arguments. I’m going to make up an example. Take the word “flow.” Does it share the same literal meaning in each use?
The river flows to the sea.
The water flows from the faucet.
The image is altered beyond recognition as you shift between the two, but the fundamental sense of “flows” remains the same, hence, univocal. What about these uses? Univocal?
Electricity flows through wires.
Words flow from her pen.
God’s love flows from heaven.
Clearly, “flow” in this set of sentences is more nuanced than in the water sentences. One immediate difficulty arises from tacit or systematic knowledge of electricity. Is electricity more like water flowing than God’s love flowing is like water? Aquinas argued in essence that God and electricity share enough literal meaning to qualify as a strong analogous relationship. Aquinas would look closely at “words flow” and find a metaphorical relationship with electricity, a figurative one, as he found his way toward proof of God. (He knew nothing of electricity and circuit breakers.) But in no meaningful way are “words flowing” literally like water from rivers and faucets, or like electricity, water and electricity being closely linked physical phenomena. Nor are “words flowing” like God’s love flowing. Can love flow regardless of its source? It seems logical to argue that the action of a physical matter or force flowing in streams, faucets, or wires is a use of “flow” in univocal predication—same meaning, different context. “Words flowing” is an equivocal use, different meaning, different context.
Aquinas argued that attributes of God are like electricity in a way that ‘words’ are not, despite ‘words’ being mental objects and ‘God’ being a spiritual presence sharing the status of non-physical existence. God cannot light up a light bulb like electricity, but God can light up a life. In the way that the flow of electricity is analogous to the flow of water, the flow of God’s love is analogous to electricity. For this reason, the theory of analogy, the existence of God is a question fit for logical argument. Furthermore, Aquinas argued using another analogy as proof. Try to object logically to this argument:
Visualize a row of dominoes standing upright. If you want the dominoes to fall over, you need to push the first one, which causes it to fall onto the next, and that one onto the next, and so on, until all the dominoes have fallen. But here's the question: Who pushed the first domino? Logically speaking, some force began the chain reaction. Visualize yourself as a domino. Who placed you in the row? The analogy moves the ball back to you in a fair and reasonable, if analogous, play.
Equivocation is, of course, an infamous informal fallacy. No one can have it both ways—usually. Allegedly, upon threat of the Inquisition, Galileo equivocated in his recantation of the heliocentric model of the universe, reportedly muttering, "And yet it moves," after an official denial. The U.S. Constitution's Three-Fifths Compromise defined enslaved African-Americans as three-fifths of a person for legislative representation and taxation. Logically, one can never have one’s cake and eat it, too, especially not after one speaks with forked tongue out of two faces. Is it possible to be three-fifths free, two-fifths enslaved? “God’s love” has meaning by way of analogical reasoning far more compelling than “three-fifths of a person” comparing a human life to, what, a pizza? This compromise was as flawed logically and analogically as it was ethically.
***
.In the 19th and 20th centuries, intellectuals and academics like Gottlob Frege, Bertrand Russell, and Ludwig Wittgenstein made significant forward progress in the development of symbolic logic. To clarify the foundations of mathematics, Frege introduced a notation for logic permitting the construction of arguments with greater clarity in a more consistent and structured manner. Russell expanded on Frege’s ideas, working to resolve paradoxes arising in naive set theory.
I’ve used ChatGPT to create an example of a notation system for logic; here is the bot’s output. Note that I commanded the bot to explain as if it were chatting with a five-year-old:
Let's imagine we have a secret code where we use symbols ☺ for "happy" and ☁ for "outside." Now, we want to say "If it's sunny, then I'm happy to be outside." In our secret code, we can use the sun symbol ☀ to mean "sunny."
So, our special sentence looks like this: ☀ ➡ ☺+☁. This means, if we see the ☀, then expect to find me happy (☺) and outside (☁)!
In this symbolic logic example, the ➡ symbol is like saying "then" or "leads to." It connects the sunny part with being happy and outside. It's like a magical rule that shows what happens (being happy and outside) when something else happens first (it's sunny).
Symbolic logic is like using a secret code or special symbols to tell stories or make rules about what happens in certain situations, and it helps us make sure we don't get mixed up about what we mean!
***
My post title, The Conceptual Fallacy, offers an original term as far as I know for a new type of informal fallacy for practicing teachers to apply with particular significance for bridging the distance between literacy pedagogical research and practice. This fallacy occurs when a concept like, say, ‘comprehension,’ under the assumption of univocality, is actually equivocal.
Thomas Aquinas succeeded in evoking a paradigm shift in theology by constructing a theory of analogical reasoning which moved the issue of the reality of God in the human world from the realm of magic and supernaturalism into the domain of logic and reason by analyzing the inner workings of the language we use to talk about God, distinguishing between mythical and mystical utterances of faith eliminated logically by linguistic evidence of equivocation or univocal predication and sound analogical reasoning ground in language related as water and electricity are related to flow.
Much educational research into practical problems or questions about schooling is carried out at a macro conceptual level that routinely confronts equivocation and conceptual ambiguity in making an argument. For example, Hirschl and Smith (2023)1 studied a notion they called “Advanced AP Gatekeeping” in relation to racialized tracking with an interest in uncovering the degree to which course gatekeeping, i.e., limiting access to AP courses, is a racial sorting mechanism. After discussing ambiguity surrounding canonical definitions of “electivity” as a crucial concept in the AP protocol, they stipulate a definition: “We define electivity as the realized ‘contribution’ of student choice to course placements given the set of constraints imposed by school policies (e.g., prerequisites, teacher recommendations).” In an effort to avoid equivocation within their study, the authors ineluctably contribute to the larger problem by creating yet another definition to befuddle practitioners unaccustomed to dancing on the head of a pin. In theoretical readings of research, keeping close track of nuanced and stipulated definitions for salient concepts is a norm. The focus of cognition is on concepts as listed and defined in the text, not on living and breathing children.
To diminish distortion caused by the conceptual fallacy, think about a concept in an argument by examining the words of the writer for univocal predication between the reader and the writer. When a writer identifies the concept “writing,” are they referencing the same concept I as reader understand—or some version of it? Hirschl and Smith (2023) provided an example of researcher diligence in locating and defining “electivity” with enough precision that practitioners who take the time to unpack it can distinguish between its meaning in the following two sentences. In the context of Hirschl and Smith, Sandra’s ‘elect’ is significantly different from Horace’s, equivocally different, and Horace may have been a victim of racialized tracking. Yet the school could have an official policy affirming the right of student election to take AP courses and a formal statement against racialized tracking.
Sandra elected not to enroll in an AP calculus course after considering the heavy workload of her other courses next semester.
Horace elected not to enroll in AP History because his teacher told him about how hard the class is for kids like him.
The research on literacy pedagogy is especially prone to instances of the conceptual fallacy. When an independent variable in a study is labeled “phonics” or “writing” or “comprehension,” a common assumption is that we agree on what we are talking about. When we act individually or collectively on this assumption without deeper inspection, it’s questionable that we are acting on any collectively meaningful basis even though we speak the same words. The field of education is riddled with conceptual fallacies regarding many central concepts—socioeconomic status, teacher, principal, parent, test, curriculum, formative assessment, narrative, paragraph, on and on. Within the profession, local faculties nested within regional professional organizations could rectify this situation over a period of years—far less time than it took to get in this mess. Given the earth shaking import of AI in literacy pedagogy destined to change schools for good or for bad, yesterday wouldn’t be soon enough.
*
BOTUAL CODA in BEEF LAT
ME: Give me five humorous examples of equivocation.
BOT: Equivocation can lead to some humorous misunderstandings or puns, as it plays on the different meanings of a word. Here are five playful examples:
1. **After hours of waiting for the bowling alley to open, we finally got the ball rolling.**
- Here, "got the ball rolling" equivocates between starting an activity and literally starting a game of bowling.
2. **"I'm reading a book on anti-gravity. It's impossible to put down!"**
- "Impossible to put down" equivocates between the figurative sense of a book being very engaging and the literal idea of anti-gravity preventing you from placing it down.
3. **"I used to be a baker because I kneaded dough."**
- "Kneaded dough" plays on the dual meanings of "kneading" dough to make bread and "needing" money (dough being a slang term).
4. **"Is the new cat movie good?" "It's purr-fect for a quick catnap!"**
- "Purr-fect" equivocates on being perfect for viewing and being so dull it induces sleep, with "catnap" reinforcing the pun on sleep and its feline theme.
5. **"Why don't we trust atoms anymore? They make up everything!"**
- "Make up everything" has a double meaning: atoms being the fundamental building blocks of all matter and the figurative sense of fabricating lies.
Equivocation in these examples creates humorous wordplay by exploiting the different meanings a single word or phrase can have.
ME: Give me two examples of sentences demonstrating univocal predication.
BOT: Sure, univocal predication occurs when a term is used with exactly the same meaning in different contexts. Here are two examples to illustrate this:
1. The biologist observed the cell under a microscope.
2. The engineer inspected the cell of the lithium-ion battery.
[ME—The biologist observed the cell under the microscope. The guard observed the cell on the monitor.]
In these sentences, "cell" is not an example of univocal predication because it refers to two different concepts: a biological cell in the first sentence and an electrical cell (battery cell) in the second. My mistake for providing a misleading example. Let's correct that with proper examples of univocal predication:
1. The oak tree adds beauty to the landscape.
2. The maple tree adds beauty to the landscape.
In these corrected examples, the term "adds beauty to the landscape" is used univocally in both sentences, indicating the same process of enhancing aesthetic appeal, regardless of whether it's an oak tree or a maple tree doing so.
[ME: The oak tree adds beauty to the landscape. The sprinklers add efficiency to the lawn.]
3. The software developer wrote a new program.
4. The novelist wrote a new book.
Upon further review, my second attempt also missed the mark, as "wrote" does not strictly represent univocal predication due to its application to different objects (a program vs. a book) which might imply different senses of writing.
[ME: How would you rewrite the two wrote sentences?]
Hirschl and Smith (2023), Advanced placement gatekeeping and racialized tracking, Sociology of Education, Vol. 96(3) 190–21
Excellent observation: “The research on literacy pedagogy is especially prone to instances of the conceptual fallacy. When an independent variable in a study is labeled “phonics” or “writing” or “comprehension,” a common assumption is that we agree on what we are talking about. When we act individually or collectively on this assumption without deeper inspection, it’s questionable that we are acting on any collectively meaningful basis even though we speak the same words. The field of education is riddled with conceptual fallacies regarding many central concepts—socioeconomic status, teacher, principal, parent, test, curriculum, formative assessment, narrative, paragraph, on and on. Within the profession, local faculties nested within regional professional organizations could rectify this situation over a period of years—far less time than it took to get in this mess. Given the earth shaking import of AI in literacy pedagogy destined to change schools for good or for bad, yesterday wouldn’t be soon enough.”
All language is based in simple physical metaphors. All philosophy is ultimately linguistic.