Confusion

•Confusion sometimes comes from the sloppy way we put our words together. This is grammatical confusion. This kind of confusion must be corrected by using better grammar. For example, a story-teller recounts the following: “While the salesman made his pitch, the lawyer reached for his wallet.” Is the lawyer about to buy something or steal something? The poor grammar of the sentence does not allow us to say, even though the speaker may be very clear whose wallet the lawyer is about to grab. It is unlikely that the story-teller is going to get confused by his mistake, though his listeners will not be sure what is happening in the story. •In other cases, confusion results from our sloppy thinking. This is logical confusion, and it is the logician’s job to be on guard for it, and to try to remove it. Logical confusion frequently will confuse not only the listener, but also the speaker, unless he is careful to sort out the mess in his own mind and lay out his ideas in an orderly fashion.•This slideshow will look at a few sources of logical confusion, namely, equivocation, and vagueness of meaning. appellation, and supposition.

SUMMARY: SOURCES OF LOGICAL CONFUSION

LOGICAL CONFUSION

CONFUSION OF THE WORD IN COMBINATION

WITH OTHER WORDS

INDISTINCT MEANING

CONFUSED APPELLATION

PURE EQUI-VOCATION

CONFUSED SUPPOSITION

CONFUSED APPELLANT

CONFUSION OF THE WORD

ALONE

ANALOGICAL EQUIVOCATION

“TYPE” CONFUSION

MULTIPLE MEANINGS

EXISTENTIAL CONFUSION

TEMPORAL CONFUSION

MULTIPLE APPELLATES

PROPER/ IMPROPER

CONFUSION

MATERIAL/ FORMAL

CONFUSION

INDIVIDUAL/ COLLECTIVE CONFUSION

Logical Confusion of Names in Isolation

I. Logical confusion in a word can be of two kinds:A. A word can cause confusion alone,

1. either because the idea it signifies is indistinct (vague name), 2. or because what idea it signifies is unclear (equivocal name);

B. Or a word can be confusing in the way it combines with other words. When a word is confusing because of the way it combined with other words, this can have two reasons:

1. Either because the way the word modifies other words is unclear (confusing appellation);

2. Or because the referents of the word are unclear (confusing supposition).

We will first look at the kinds of confusion found in isolation.

Vagueness of MeaningSometimes the idea that a word stands for is not well defined. This is different from equivocation, where a word may have more than one idea connected to it. In vagueness, the word may be assigned to just one idea, but the idea itself may not have precision. Is fire alive? It feeds, grows, and reproduces, but it does not seem to be “alive”. Is a virus alive? It seems more like an organism than fire does, and yet it does not feed or grow. What is “life”? The idea is not well defined. This is not a logical problem, but a philosophical or biological one.

When a little black paint is mixed in with white, the white looses its brilliance, but we still call it white. If more black paint is slowly added, the white eventually turns gray, and then black. But when does a less brilliant white “officially” turn gray? When does a dark gray “officially” turn black? White, gray, and black certainly are meaningful terms, and yet we do not have precise boundaries laid out between the middle and the extremes. This is not a logical problem, but a semantic one. In other words, we merely have not stipulated as a society a precise boundary in our definitions. Such vagueness is actually in a way more accurate, since it reflects the continuity in the colors themselves. An arbitrary, precise division would actually suggest a division in the shades that does not really exist.

Vagueness of MeaningSometimes, however, vagueness presents logical problems. If we are arguing over an expensive job creation bill, and someone claims that the expense is not worth it since “the unemployment rate is low,” the vagueness of the words “expensive” and “low” are problematic. “Low” implies that the rate is such that the expense of a job creation program is not worth putting more people to work. Such a definition begs the question: isn’t that the very thing under dispute? We might instead define the word “low” precisely as “below the historical average,” but then what is low will change over time as more economic history is made and more historical data is accumulated and the average moves one way or the other. Sometimes, vagueness means a line of argument needs to be totally abandoned because of the difficulty of establishing the desired precision to the idea behind the argument.

It should be remembered that vague words communicate vague ideas. Sometimes, there is nothing wrong with that. If I say that Joe is strong, that communicates to you an idea that I have vaguely so that you also have it vaguely. That may be good enough for our needs. It is actually more illogical to demand mathematical precision in a non-mathematical field. Vagueness is only a problem when the field itself demands greater precision, or when a vague idea masquerades as a precise one, and deceives the speaker or listener into thinking that they are being more precise than they really are.

Vagueness of MeaningDuring the election of 2012, President Barack Obama kept saying, “The rich need to pay their fair share of taxes.” But because this claim has two vague words, the claim is almost worthless as a way to advance a logical discussion of the issue, though it certainly was a slogan which had great rhetorical effect upon those who were swayed by it.

Take a survey of the class, and have each student complete the following statement: “An American is rich when he earns an annual salary of more than _______ dollars, but not rich when he earns less than this.” Have students right down their answer anonymously. Then see what are the highest and lowest number.

Another vague word is “fair”. Some think fair means “equal”, but does that mean equal dollar amounts, or an equal percentage of income? Some think that “fair” means those with higher incomes pay a higher dollar amount but less percentage wise. Some think that it is fair that those who contribute in substantial ways to society through charities or services or investments should be relieved of all or most income taxes. Some people think that those who earn most should shoulder the whole burden of funding the government. Some think income tax, by its very nature, is unfair, and government should only be funded through tariffs, business taxes, or other means.

Of course, everyone should contribute what is fair, but what is fair?

Univocal Names

•If two names have the same sound and the same meaning, then they are called “univocal.”

•Your wet dog got my sofa wet.•Beef is cattle meat, but venison is deer meat.•The house is white, but not as white as snow.

•In each of the above examples, the bold word has the very same meaning each time it is used. For example, even though beef and venison are different kinds of meat, nevertheless, the word meat means the same thing in both uses, namely, animal flesh which is food. Therefore, meat is used univocally.

Equivocal Names•If two names have the same sound (homophones) or the same spelling (homonyms), but different meanings, then they are called “equivocal.”

•PURELY EQUIVOCAL NAMES: Equivocal names whose meanings are unrelated.

•The patient surgeon cut open the wound of his patient.•As I was cleaning the attic, I found a bat in the rafters.

•ANALOGICAL NAMES: Equivocal names whose meanings are related to one another.

•The bright student studied under a bright light. •A baseball player uses a bat to bat balls.•Elmer was glued to the television screen.

•Can you explain the examples given in each sentence.

HOW IS A MICROBIOLOGIST LIKE A JAILER?

THEY BOTH WATCH CELLS.

FUN WITH EQUIVOCATION

HOW IS A JAILER DIFFERENT FROM A JEWELER?

ONE WATCHES CELLS...

THE OTHER SELLS WATCHES.

FUN WITH EQUIVOCATION

FUN WITH EQUIVOCATIONPoint out the equivocation. Try to say the two definitions. Is the equivocation pure or analogical?

•On a frozen food package: “Tender pieces of battered chicken.”•After Thanksgiving dinner at the taxidermist’s house, all the guests were stuffed.•Heard at the airport: “Welcome to Vatican Airlines. All confirmed passengers please report to Gate Seven.”•When we arrived at the novelist’s house, we found him on the third story.•Green house slogan: “Our business is growing!”•The fashion photographer drove a car of an older model.•Captain Hook demanded that the conquered sailors surrender their arms.•Sign on the epileptic tailor’s shop: “Come in for a great fit.”•Upon digging up the corpse, the coroner realized he had made a grave mistake.•In order to scare away the angry ram, the mountain climber blew on his horn.•The senile widow claimed that the tardy gentleman was her late husband.•Although he was only a corporal, the deserter knew he was in major trouble.•Mr. Lincoln was said to be so honest he would not even lie in his bed.•After too many sick leaves, the orchard owner fired his botanist.•The baseball coach angrily threw his glass to the floor, saying it was time to look for a new pitcher.•The Italian ophthamologist hung the Venetian blind over his window.

Removing the Problem of Equivocation

One can remove the problem of equivocation by adding in the definition when the context does not

make it clear.“I found a bat (that is, a wooden cylinder for striking

balls) in my attic.”

Logical Confusion of Names in Combination

I. Logical confusion in a word can be of two kinds:A. A word can cause confusion alone,

1. either because the idea it signifies is indistinct (vagueness), 2. or because what idea it signifies is unclear (equivocation);

B. Or a word can be confusing in the way it combines with other words. When a word is confusing because of the way it combined with other words, this can have two reasons:

1. Either because the way the word modifies other words is unclear (confusing appellation);

2. Or because the way the meaning of the word is used in unclear (confusing supposition).

We will now look at the kinds of confusion found in word combinations.

Appellation of Names•When a name is assigned to anything it can sometimes name the subject in more than one way. How it modifies our understanding of the thing named is the name’s appellation.•“The rabbit’s eyes are red.” Red may denominate the color of the whole eye, or just the color of the iris. •“The carpenter was very good.” Good could denominate the carpenter’s skill or his moral character. •If the appellation of a name is unclear, or if it changes in the middle of a conversation, it should be made explicit. Otherwise, misunderstandings and errors are likely.

•My pastor reported that the plumber, Mr. Wrench, is the best in the business. But to be the best in the business, you would have to be very good. So Mr. Wrench must be very good. Now those who are good do not cheat others. Therefore, based on my pastor’s recommendation, I need not worry that Mr. Wrench will cheat me.

Appellants and Appellates•The name is called the “appellant”, the thing named is called the “appellate”.

•E.g. A poor (appellant) student (appellate).•If the name “poor” signifies the students study habits, then the name “poor” is called a “formal appellant”. If it signifies anything else about the student (e.g. the student’s financial status), then it is called a “material appellant”.•“The doctor’s hammer” This is either material or formal appellation. Is the hammer for building houses, or for testing a patient’s reflexes? •“Poor students were a burden to the college.” What does this mean if “poor” is a formal appellant? What does it mean if it is a material appellant?•Sometimes, the appellate, that is, what the name is supposed to be naming, is unclear.

•“Joe is an African elephant rider.” What does it mean if the appellate of African is “elephant”? What if the appellate is “rider”?•“Marge is a fat lion tamer.” So what’s the appellate of fat?

Removing Confusion of Appellation

•In written prose, commas can be used to make the appellate clear. In speech, pauses or stress in the voice might do the same thing.

•“Joe is an African, elephant rider.”•A better way to removing unclear appellates, whether in speech or writing, is to use prepositional phrases or subordinating clauses.

•E.g. “Marge is a tamer of fat lions.” •“Marge is a fat person who tames lions.”

•Sometimes one can rephrase the statement to remove ambiguity concerning formal and material appellation

•“The medical hammer” •“The doctor’s hammer for carpentry”•“Low-income students were a burden to the college.”•“Students with poor study habits were a burden to the college.”

Supposition

Supposition is the way that a word or phrase in a sentence refers to a thing.

Every word has a meaning, an idea that it calls to mind. This is the words “signification”. But when a word is used in a sentence, it also intends to refer

that meaning to something more, something called a “supposita”. Supposition is how a words refers to its intended reference

(its supposita).

FOR EXAMPLE: “Man” signifies “rational animal”, but in a given sentence, it may refer to just the concept of man, or to every man, or to a grouping of men, or to a

particular man, or even to a fictitious man. The relation between a word in a given sentence and its intended reference is

the word’s supposition.

TEMPORAL SUPPOSITION

SUPPOSITION

TYPICAL SUPPOSITION

EXISTENTIAL SUPPOSITION

Modes in Supposition

FOR CONVENIENCE, WE WILL GROUP SUPPOSITION INTO THREE MODES, AND THEN DIVIDE UP EACH OF THESE MODES

INDIVIDUALLY. LET’S CALL THE THREE MODES EXISTENTIAL, TEMPORAL, AND TYPICAL.

TEMPORAL SUPPOSITION

REALSUPPOSITION

IMAGINARYSUPPOSITION

CONCEPTUALSUPPOSITION

SUPPOSITION

TYPICAL SUPPOSITION

EXISTENTIAL SUPPOSITION

Existential SuppositionEvery word in a sentence must stand for something which exists in some way. Roughly, we can say there are three ways a supposita can exist, that is, the thing that substitutes for a word in a given sentence either really exists, or it exists in the imagination, or it exists only in our mind. This gives us a word’s “existential supposition.”

Usually, when we speak, we are using real supposition. All this means is that we intend the words to stand for something existing as a real being.

“The largest mammals are whales.” “(Real) Unicorns don’t exist (in reality).”“Abraham Lincoln was the sixteenth President.”

Sometimes, a word has only imaginary supposition. All this means is that we intend the word to stand for something existing in the imagination.

“Hobbits have large, hairy feet.” “Unicorns do exist (in the imagination).”“Tom Sawyer was friends with Huckleberry Finn.”

Other times, words have only conceptual supposition. This means that we intend the words to stand for something existing in the mind alone.

“Nothing is nowhere.”“A species is contained in a genus.”

Division of Existential Supposition

TEMPORAL SUPPOSITION

REALSUPPOSITION

IMAGINARYSUPPOSITION

CONCEPTUALSUPPOSITION

SUPPOSITION

TYPICAL SUPPOSITION

EXISTENTIAL SUPPOSITION

Temporal SuppositionNo matter how a name is supposited, it must also be supposited according to time. This is the name’s “temporal supposition”. Temporal supposition is the time frame in which the word or phrase is intended to be imposed. This is normally signified by the verb in the sentence where the word is used, or by the context in which it is used. There are roughly three time frames: past, present, and future.

Past supposition: “Romans ruled most of Europe.”Present supposition: “Romans are electing a new mayor.”Future supposition: “Romans will riot after the election.”

Eternal supposition: Sometimes, the time frame is unlimited, meaning, the statement is meant to signify something without time constraints, as when we say, “Triangles have at least two acute angles.”

TEMPORAL SUPPOSITION

LIMITED TIMESUPPOSITION

ETERNALSUPPOSITION

PASTSUPPOSITION

PRESENTSUPPOSITION

FUTURESUPPOSITION

SUPPOSITION

TYPICAL SUPPOSITION

EXISTENTIAL SUPPOSITION

Division of Temporal Supposition

Division of Typical Supposition

TEMPORAL SUPPOSITION

MATERIALSUPPOSITION

FORMALSUPPOSITION

PROPERSUPPOSITION

IMPROPERSUPPOSITION

SIMPLESUPPOSITION

COLLECTIVESUPPOSITION

INDIVIDUALSUPPOSITION

SUPPOSITION

EXISTENTIAL SUPPOSITION

TYPICAL SUPPOSITION

Other Kinds of Supposition(Division of Typical Supposition)All the other kinds of supposition we can call “typical.” This is a complex group, but the first division of the group is fairly straight forward.

Formal supposition: When a word stands for the idea it signifies.

“Man has the largest brain in the animal kingdom.”

Material supposition: When a word stands for the word itself.“Man has a single syllable.”

“Man rhymes with can.”

Inigo begins with a vowel.

Fezzik is very large.

What kind of supposition is being used with the highlighted words below? (Fezzik and Inigo are two characters from the novel “Princess Bride”.)

Fezzik rhymes with Inigo.

• What kind of supposition is used above with the name “Fezzik”?

Although formal and material supposition are rarely confused, sometimes, confusion can happen…

What consonant does “Moby Dick” start with?M or C?

How many words are there in “War and Peace”?More than 400 thousand or less?

Sometimes, there is no way to tell whether the supposition of a subject is material or formal without knowing the speaker’s intention. Here are two riddles that play on this confusion:

What does each of these questions mean when the supposition of the bold phrase is material? What do they mean when it is formal?

Sam rhymes with Pam.

Riddle: William haz too eyes, Timothy haz ownly won eye, but each man haz know

eyes.

The riddle is a vocal one – it is purposely misspelled because it does not work when

written out; so say it to yourself and see whether you can figure out what it is saying. The ultimate

trick works by confusing formal and material supposition and using equivocation as well.

CONFUSING FORMAL & MATERIAL SUPPOSITION

Removing the Confusion of Material Supposition

One can remove the problem of confusing material and formal supposition by adding phrases to make

the supposition clear.The title “Moby Dick” has just two words.

The book “Moby Dick” has over ten thousand words.Scare-quotes are generally used to indicate that

material supposition is intended, though it may not always do the job.

“Sam” rhymes with “Pam”.

Types of Formal Supposition

Proper supposition: A kind of formal supposition in which a word or phrase stands for the idea in its proper sense.

“A horse is as strong as an ox.”“I had lamb for dinner.”

Improper supposition: A kind of formal supposition in which a word or phrase stands for an idea applied through a figure of speech.

“My father is as strong as an ox.”“My sister is a lamb.”

Removing the Problem of Confusing Proper and Improper Supposition

One can remove the problem of confusing supposition by adding adverbs to make the supposition clear.

“I am hungry enough to eat a whole chicken, properly speaking, but figuratively, I could eat a horse.”

(Beware the adverb “literally,” which will not remove the ambiguity since it can appropriately be used as an intensifier in a figure of speech. In this way, one

can truly say, “I could literally eat a horse!”)

Two Types of Proper SuppositionINDIVIDUAL SUPPOSITION: A kind of proper supposition in which a word or phrase stands for an individual having that nature.

“Birds have feathers.”“The apostles were chosen by Jesus to follow him.”

“Football players practiced in the soccer field.”(Note: you intend the words to mean not just the nature signified, but also

individual birds or apostles or players.)

COLLECTIVE SUPPOSITION: A kind of proper supposition in which a word or phrase stands for a collection as a group, but not the elements of the collection.

“Birds inhabit every continent on the earth.”“The apostles evangelized every region of the Roman Empire.”

“Football players filled the locker room.”(Note: you do not intend the words to mean individual birds or apostles or

players, but intend the whole list of individuals together as a group.)

Test for Individual SuppositionINDIVIDUAL SUPPOSITION: A kind of proper supposition in which a word or phrase stands for an individual having that nature.

Try to substitute the name of an individual to see whether it changes the intended sense of the sentence. If it does not, as in these examples, then it is individual supposition.

“Birds have feathers.” Is the claim that individual birds like Polly have feathers?

“The apostles were chosen by Jesus to follow him.” Is the claim that individual apostles like Simon Peter were chosen by Jesus to follow him?

“Football players build up their strength with free weights.” Is the claim that individual football players like Tom Brady build up their strength with free weights?

Try to substitute the name of an individual to see whether it changes the intended sense of the statement. If it does, as in these examples, then it is not individual supposition.

“Birds inhabit every continent on the earth.”Is the claim that an individual bird like Polly inhabits every continent on the earth?

“The apostles evangelized every region of the Roman Empire.”Is the claim that an individual apostle like Simon Peter evangelized every region of the Roman

Empire?“Football players filled the locker room.”

Is the claim that an individual football player like Tom Brady filled the locker room?

Test for Collective SuppositionCOLLECTIVE SUPPOSITION: A kind of proper supposition in which a word or phrase stands for a collection as a group, but not the elements of the collection.

If you have shown it is not individual supposition, you then need to test to see whether it is collective supposition. Try to substitute the names of all the individuals to see whether it changes the intended sense of the statement. If it does not, as in these examples, then it is collective supposition.

“Birds inhabit every continent on the earth.”Is the claim that birds together, not alone but as a group, inhabit every continent on

the earth?“The apostles evangelized every region of the Roman Empire.”

Is the claim that no single apostle, but Peter, John, James, Phillip, Simon, James, Matthew, Thomas, Jude, Thaddeus, Bartholomew, Mathias, and Paul, together as a

group, evangelized every region of the Roman Empire?“Football players filled the locker room.”

Is the claim that not any single football player, but all of them together as a group, filled the locker room?

Removing the Problem of Individual and Collective Supposition

One can remove the problem of confusing supposition by adding adverbs to make the supposition clear.

“Individually, birds have feathers, and collectively, birds inhabit every continent on the Earth.”

“Collectively, the three students weigh over 400 pounds, but individually, the three students each weighs under 150 pounds.

A Third Type of Proper Supposition

INDIVIDUAL SUPPOSITION uses a name to stand for individuals. COLLECTIVE SUPPOSITION uses a name, not to stand for individuals, but only for a collection of individuals. There is a third type of Proper Supposition, where a word stands for neither the individuals, nor the collection. It is called “Simple Supposition” because the name stands for only the idea, or nature, that the word signifies. SIMPLE SUPPOSITION: A kind of proper supposition in which a word or phrase stands for only the nature, but not the individuals taken by themselves nor the collection of individuals taken together as a group.

“Birds are a species of vertebrate.”“An apostle is a kind of disciple.”

“Football players are a type of athlete.”

Test for Simple SuppositionSIMPLE SUPPOSITION: A kind of proper supposition in which a word or phrase stands for only the nature, but not the individuals taken by themselves nor the collection of individuals taken together as a group.

If you have shown it is not individual supposition or collective supposition, then it is probably simple.

“Birds are a species of vertebrate.”Is the claim that that individually this or that bird is a species of vertebrate?

Is the claim that this bird, that bird, and all the other birds as a group is a species of vertebrate?Or is the claim that, conceptually, it is the nature of a bird be to be a species of vertebrate?

“An apostle is a kind of disciple.”Is the claim that that individually this or that apostle is a kind of disciple?

Is the claim that this apostle, that apostle, and all the apostles together as a group is a kind of disciple?Or is the claim that, conceptually, it is the nature of an apostle to be a kind of disciple?

“Football players are a type of athlete.” Is the claim that that individually this or that player is a kind of athlete?

Is the claim that this player, that player, and all the other players together as a group is a kind of athlete?Or is the claim that, conceptually, it is the nature of an football player to be a kind of athlete?

“Animal is a kingdom of organisms.” Is the claim that individually this or that animal is a kingdom of organisms?

Is the claim that all worms, insects, fish, amphibians, reptiles, birds, and mammals together as a population is a kingdom of organisms?

Or is the claim that, conceptually, it is the nature of animal to be a kingdom of organisms?

Division of Typical SuppositionSUPPOSITION

TEMPORAL SUPPOSITION

MATERIALSUPPOSITION

FORMALSUPPOSITION

PROPERSUPPOSITION

IMPROPERSUPPOSITION

SIMPLESUPPOSITION

COLLECTIVESUPPOSITION

INDIVIDUALSUPPOSITION

EXISTENTIAL SUPPOSITION

TYPICAL SUPPOSITION

SOURCES OF LOGICAL CONFUSIONLOGICAL

CONFUSION

CONFUSION OF THE WORD IN COMBINATION

WITH OTHER WORDS

INDISTINCT MEANING

CONFUSED APPELLATION

PURE EQUI-VOCATION

CONFUSED SUPPOSITION

CONFUSED APPELLANT

CONFUSION OF THE WORD

ALONE

ANALOGICAL EQUIVOCATION

TYPE CONFUSION

MULTIPLE MEANINGS

EXISTENTIAL CONFUSION

TEMPORAL CONFUSION

MULTIPLE APPELLATES

PROPER/ IMPROPER

CONFUSION

MATERIAL/ FORMAL

CONFUSION

INDIVIDUAL/ COLLECTIVE CONFUSION