Informal Fallacies & Language

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Informal Fallacies & Language

Introduction to Fallacies: Formal versus Informal
– Vague & Ambiguous Language
– An Argument’s “Matter”
Informal Fallacies Due to Language (according to Aristotle)
– Fallacy of Equivocation
– Fallacy of Amphiboly
– Fallacy of Composition
– Fallacy of Division
– Fallacy of Accent
– Fallacy of Figure of Speech

Introduction to Fallacies

Any fallacy engages in poor reasoning.

Remember. . .
– An argument consists of form and matter.
– Its form is the “structure” or “pattern” of the argument.
– Its matter is the content of the argument.

Example: “All men are mortal. Socrates is a man. Thus, Socrates is mortal.”
Its form is AAA-1. Its matter consists of men, mortality, and Socrates.

This distinction between an argument’s form and matter provides us a precise way to classify a fallacy as formal or informal. A formal fallacy is an invalid argument due to the argument’s very structure. That structure is fatally flawed. An EEE-1 syllogism is invalid, for example, no matter what its “matter” is. Whatever its content, it’s just bad.

An informal fallacy concerns the matter of an argument! It thereby deals with its given content. It can also depend upon the context of the argument.

A formal fallacy is formal precisely because it technically doesn’t do either.

While we don’t need to know the meaning of the terms used in the EEE-1 syllogism to know that the EEE-1 is invalid, an argument that commits an informal fallacy is spotted by knowing the meaning of the terms used.

Indeed, many informal fallacies are due to the use of imprecise language.

http://classics.mit.edu/Aristotle/sophist_refut.html

As noted elsewhere, Aristotle’s “On Sophistical Refutations” argues against the sophists and covers informal fallacies.

Aristotle has two basic divisions:
(A) Informal fallacies due to language.
(B) Informal fallacies not due to language.

The first includes (1) equivocation, (2) amphiboly, (3) composition, (4) division, (5) accent, and (6) figure of speech.

Vague & Ambiguous Language

How often do two people talk past each other? It happens a lot, particularly when the discussion has turned into a debate. Two people might be using terms in different ways.

It’s vital to have clear and unambiguous terms – as best as possible.

Can we remove all vagueness from language 100%? Probably not.

“Natural language” used in daily life has a degree of vagueness. Precision in terms, other things being equal, is best. That precision must meet the needs of the argument or context in which it facilitates a meaningful dialogue with everyone on the “same page.”

Ambiguity will never disappear entirely. That’s because language uses arbitrary signs or symbols based on societal conventions. Language develops through time with people who may impose new meanings on already established signs. A language has a “living” history!

Advances in science refine. “Scientific” terms usually have less vagueness and ambiguity than other terms. Greater distinctions between terms occurs. This can make terms that were once not vague turn into something vaguer according to the new refinements.

For instance, with more “specialized” terms, extension tends to decrease and intension tends to increase. (Review “Concepts, Signs, & Names.”)

It’s a characteristic of our “rational nature” to make fine distinctions.
Our world is filled with distinct things!

By the way, is “vagueness” the same thing as “ambiguity”?

No! Vagueness is a lack of precise meaning. Ambiguity is a lack of one meaning. Hence, something can be vague but not ambiguous.

An Argument’s Matter

An argument is about something.
It will contain premises that lead to a conclusion.

Recall, a true conclusion will be reached provided:
(1) all premises are true
(2) the argument is valid

Let’s think about the premises. They contain terms.
All terms must be clear!
And all terms must be used in a consistent way!

Think about it… Not only should the premises be true, the terms should be clear and used in a consistent way. All premises might be true, for example, but the terms could be used in an inconsistent way. If that happens, the argument is bad and the conclusion is not necessarily true.

Therefore, we should add a third rule:
(3) all terms are clear and used in a consistent way

Traditional logic has the upper hand.

Good argumentation will engage in all three acts of the mind:
(1) simple apprehension, (2) judgment, and (3) reasoning.

Formal logic “dematerializes” an argument to its form alone. It allows us to evaluate the inferential process. (This has to do with the third act of the mind.) Knowing the form, though, is not sufficient to determine if we have a good argument.

Judgement is what allows us to create propositions and is used in evaluating their individual truth or falsity. A proposition is a judgement in words, since it declares a subject to have (or not have) an attribute.

And simple apprehension is what allows us to form concepts and then terms.

These are the three basic building blocks in an argument. An argument is no good if we don’t know what we are talking about! We need clear and consistent terms.

Good “matter” must be worked with.

Fallacy of Equivocation

**Example 0:** “*Who’s on First?*“
https://www.youtube.com/watch?v=kTcRRaXV-fg

In the course of argumentation, when a term or phrase is used in two different ways, the Fallacy of Equivocation is present. The argument is thereby unsound or invalid.

There is a shift in meaning.
It’s thereby semantic.

Example 1:
“All metals are elements.”
“Brass is metal.”
“Therefore, brass is an element.”

(Allow me to reuse this example.)

Jevons’ example above is pretty good, since it may not be obvious that the term “metal” is being used in two different senses. It’s first being used the way a chemist defines metal. Then it’s defined in a loose sense found in the arts. Brass is not a metal in the first sense, as it’s an alloy (of copper and zinc) and thus not an element. Usually, when you open up your standard logic textbook, the examples given would fool no man – or almost no man!

Who would be fooled with this Wikipedia example?

Example 2:
“Only man is rational, and no woman is a man.”
“That’s why no woman is rational.”

The term “man” is being used equivocally. It’s used to describe a human person, regardless of sex, and then it’s used to denote sex. So, the conclusion doesn’t follow.

Equivocation fools us when things are more subtle, like in Jevons’ example.

It’s also a part of comedy. We find equivocation, a playful use of words in contradictory ways, funny. “Example 0” comes from an Abbott and Costello routine. “Who’s On First?”

David Gordon*, a polymath intellectual hero of mine, has given this (harder) example:

Example 3:
Tom Palmer: “Sir Karl Popper has pointed out that the idea that one can predict one’s future knowledge … is philosophically incoherent: if one could predict one’s future knowledge, then one would already know it.”

The ambiguity is in “future knowledge.”

Either it means (1) knowledge we lack presently but will have in the future or (2) knowledge we have presently and will have in the future. Thus, to predict your “future knowledge,” what is predicted couldn’t be knowledge in the first sense, i.e., it would be in the second sense.

In other words, if I do know something, then it is not “future knowledge” in the first sense.
The argument is a tautology – and, therefore, doesn’t limit predictions at all.
It’s a “tautology” because it doesn’t give us any new information.

So, it doesn’t provide any new philosophical insights.

*[This is “inside baseball” humor: Dr. Gordon’s legendary humor — e.g., equivocation with the expression “carried away” — can be found in the beginning of this lecture.]

Fallacy of Amphiboly

Equivocation deals with semantics.
— That is, the meaning of terms or phrases.
Amphiboly deals with syntax.
— That is, the organization of words in a sentence or its grammatical structure.

The only difference this has to the Fallacy of Equivocation is that, in the Fallacy of Amphiboly, the syntax may be interpreted in two different ways. Some proposition may be stated in an ambiguous way, but the conclusion is inferred from a false interpretation of that ambiguous proposition.

Example 1. . .
The brilliant philosopher William Vallicella gives this example on his blog:

There are two different ways to look at the expression “pretty bad girls.”
Hence, the ambiguity.

There’s no argument here. But a sentence can be an example of an amphiboly.

Advertisements and news headlines are notorious for grammatical ambiguity.
Sometimes they are so with the intent to deceive.

Example 2. . .
Here’s an example from the prolific author Peter Kreeft:

Not a “profound” example, but very amusing nonetheless.

This is from Dr. Kreeft’s Socratic Logic on page 74.
Once upon a time The New Yorker collected these “humorous amphibolies.”

Example 3. . .
Peter Kreeft gives, perhaps, a more “profound” example dealing with philosophy:

As Dr. Kreeft summarizes, George Berkeley argued against the material world. Everything that exists is, rather, immaterial. “Is it not a great contradiction to think a thing exists when you do not think it?” Thus, so the argument goes, all of reality is mind dependent (ibid).

What’s ambiguous is “when you do not think it.”
Does this apply to “think” or “exists”?

(1) If to “think,” we get something like:
it is impossible that I think of X and nobody thinks of X

That really is a contradiction!
The problem, however, is that Berkeley argues something else.

(2) If to “exists,” we get something like this:
it is impossible that X exists if nobody thinks of X

This doesn’t lead to any contradiction. Berkeley, therefore, hasn’t proven that it’s impossible for something to exist independently from a mind.

Ambiguous “scope distinction” is another cause of amphiboly.
Example 4. . .

wikipedia.org/wiki/Mary,_mother_of_Jesus

“Every man loves a woman.”

Perhaps not the best example, but it will do. Good logicians, wanting precision, have pointed out that propositions like this can be interpreted two different ways. It’s based on what has “wide scope” and what has “narrow scope.”

What can this proposition mean?

(1) For all men there is some woman out there that he loves?
For every man x, there exists a woman y such that x loves y.
This starts with “wide scope” (i.e, “for every”).

(2) There is a woman out there that every man loves?
(For example, “a woman” such as Mary in particular that all men love?)
There exists a woman y, such that for every man x, x loves y.
This starts with “narrow scope” (i.e., “there exists a”).

In (mathematical) predicate logic, we can formulate this distinction.
(1) ∀x [Mx → ∃y (Wy & Lxy)]
(2) ∃y [Wy & ∀x (Mx → Lxy)]

Fallacy of Composition

The Fallacy of Composition is considered a “fallacy of grammatical analogy.” There is a part-to-whole reasoning that is fallacious. We can often view it as a case of equivocation, since a collective term (a.k.a. “collective predicate”) is confused with a general term (a.k.a. “distributive predicate”).

(Review the last section in “Concepts, Signs, & Names.”)

– A collective predicate makes a claim about a group as a whole.
– A distributive predicate makes a claim about individuals.

Example A:
“A Euclidean triangle’s angles are less than a straight angle.”
Example B:
“A Euclidean triangle’s angles are equal to a straight angle.”

Both examples are grammatically ambiguous. (As a criticism, that’s totally fair!)
This leads to a paradox: less than a straight angle and equal to a straight angle.

But Example A is only true if interpreted with distributive predication.
And Example B is only true if interpreted with collective predication.

Example B is better written as. . .
“The sum of a Euclidean triangle’s angles are equal to a straight angle.”

Example 1:
“The book’s pages have few words on it; so, the book has few words.”

A clear-cut example of fallacious part-to-whole reasoning.

It may be that each page individually has few words on it, though that doesn’t entail that the book as a whole has few words. We have the Fallacy of Composition!

Example 2:
“These trades benefit from protective duties; ergo, protective duties are good for the economy [as a whole].”

This example is borrowed from Jevons once again. Read his Elementary Lessons in Logic. One or several trades might benefit from a tariff, but it doesn’t follow that all trades will benefit; indeed, “this is impossible, because the protection of one trade by raising prices injures all others” (p. 174).

Henry Hazlitt, in his book Economics in One Lesson, made famous the “Broken Window Fallacy.” This fallacy traces back to the French economist Frédéric Bastiat. Read Bastiat’s 1850 “That Which Is Seen, and That Which Is Not Seen.”

Example 3:
“A young hoodlum, say, heaves a brick through the window of a baker’s shop,” writes Henry Hazlitt (p. 23).

“After a while the crowd feels the need for philosophic reflection. … How much does a new plate glass window cost? … That will be quite the sum. The glazier will have $250 more to spend with other merchants, and these in turn will have $250 more to spend with still other merchants, and so ad infinitum” (ibid).

“The logical conclusion from all this would be … that the little hoodlum who threw the brick, far from being a public menace, was a public benefactor” (ibid).

Warning! Not all examples of the “Broken Window Fallacy” can be interpreted as a Fallacy of Composition. I think, however, Example 3 allows us to.

A glazier will gain more money by that act of destruction.
That doesn’t mean that the economy as a whole is better.

What about the baker? He didn’t gain! True, the glazier has more money. Yet, again, what about the baker? He would have had $250. Maybe he would have spent that money on a new suit or invested it. There’s no net gain to the economy by acts of vandalism. In fact, destruction of property causes a loss. Resources were diverted to fix that destruction.

The “Broken Window Fallacy,” in general, happens when drawing a conclusion about how an action, policy, or procedure supposedly benefits a specific group without considering the impact on others outside that group.

It is reasoning that, e.g., ignores the total costs involved.

Alternatively, this fallacy has been committed when only thinking about the short-term economic consequences without considering long-term economic consequences.

A favorite target of George Joyce’s logic textbook, Principles of Logic, is John Stewart Mill.
Joyce gives this example starting on page 271.

Example 4:
John Stuart Mill: “Each person … desires his own happiness. This being a fact, we have all the proof which the case admits of … that each person’s happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of persons.”
(From Mill’s Utilitarianism, chapter four.)

A lot has been written about Mill’s arguments for utilitarianism. Even if one accepts a utilitarian ethics, you still should recognize that Mill’s argument here doesn’t work. From the fact that each man recognizes that his own happiness is a good thing, it doesn’t mean you have to believe there is a good to the aggregate of all persons.

Hence, there seems to be a Fallacy of Composition!

Warning! Are all part-to-whole reasonings bad? No, obviously not.

Judgement is called for to determine when it is.

“All Lego pieces to build the castle are red; ergo, the castle is red.”
“Each circuit component is off; ergo, the entire circuit is off.”
“All things in the universe are contingent; ergo, the universe as a whole is.”

Fallacy of Division

Fallacious whole-to-part reasoning occurs in the Fallacy of Division.
It’s the converse of the Fallacy of Composition.

Example 1:
“I love my library of books; ergo, I love this specific book by Marx in my library.”

This is pretty clear-cut as an example of the fallacy.

It may be that I love my collection of books as a whole, though that doesn’t entail that I must love each book individually. Some of those individual books I can do away with. A few books by Marx are a good reference for me to have, but I don’t love any of them. As a whole, however, I do love my collection of books. (They are awesome!)

Example 2:
“My doctor told me that ten cups of coffee are bad for me; so, it must be that one cup of coffee is bad for me, as well.”

Example 3:
“This has been a wonderful week; ergo, every second of it must have been wonderful.”

Warning! Are all whole-to-part reasonings bad? No, obviously not.
Just like the Fallacy of Composition, it depends upon the “material” context.

A good syllogism, for example, that applies a more general principle to something more particular has nothing to do with the Fallacy of Division.

Here there is no confusion between a collective predicate and a distributive predicate.

The dictum de omni et nullo (the maxim of all and none) is good!

Fallacy of Accent

The Fallacy of Accent concerns statements that are ambiguous from voice inflection, emphasis, or what is called “prosodic stress.” We might have a word in a statement that’s given a confusing or misleading emphasis or “stress” causing an ambiguity.

It’s another source for good comedy.
Both Jevons (p. 174) and Kreeft (p. 76) give the following example.

Example 1:
“And he spake to his sons, saying, Saddle me the ass. And they saddled him.”
(1 Kings 13:27.)

The King James Bible has the word him in italics. We might think that was done for emphasis. That’s a mistake. Most of the time italics suggests emphasis; however, the King James Bible does it for words not literally in the original.

What makes this funny is (1) equivocation with the word “ass” and (2) accent with the word “him.” So, a misreading suggests he was saddled in the butt.

Example 2:
“I won’t go to New York City.”
“I won’t go to New York City.”

Emphasis is being shifted around.
It suggests different meanings.

Take the first statement: “I won’t go to New York City.”
This may suggest that someone else is going.

Or this: “I won’t go to New York City.”
This may suggest that I’m going somewhere else.

The next example I found on Twitter (“X”).
Unfortunately, I don’t know the exact source for it. (My apologies!)

Example 3:

Did you read those out loud?
Quite a difference, right?!

Fallacy of Figure of Speech

“Form of expression” is Aristotle’s designation of what’s often called a “figure of speech.” Controversy surrounds this fallacy as logicians have debated its proper scope and interpretation. It’s rare to find it referenced in a contemporary logic textbook.

It’s a subset of equivocation. First, like equivocation, there is a shift in meaning in some word or expression. Second, and this is peculiar to “figure of speech,” the shift in meaning concerns a word’s inflection or structure. It’s not a shift in the entire grammatical structure of a sentence, however, as then we would have an amphiboly.

George Joyce (p. 273) shows how John Stewart Mill commits this fallacy.
“No better example can be given. . .”

Example 1:
John Stuart Mill: “The only proof capable of being given that an object is visible, is that people actually see it. The only proof that a sound is audible is that people hear it … in a like manner, I apprehend, the sole evidence it is possible to prove anything is desirable, is that people do actually desire it.”
(From Mill’s Utilitarianism, chapter four.)

The words “visible,” “audible,” and “desirable” are similar, but Mill’s argument shifts from what is or can be visible, audible, and/or desirable to what ought to be desirable.

The similar structure of the three words with “- able” misleads the reader and Mill. There’s a peculiar equivocation with “desire.” Mill shows that we are capable of desire, like we are capable of seeing and hearing, but that allows no inference to what we ought to desire.

Mill proved nothing about what ought to be desired; hence, the argument totally fails.

[N.B.: proofreading of this page was provided by a friend. Thank you, Keith!]