Errors in Concept Development, Copyright © 1998 Art Lightstone

A Guide to Standard Errors in Concept Development Art Lightstone

As students progress through my courses, they will invariably encounter a variety of icons presented on their tests, papers, or projects as part of my evaluation and feedback. Most difficulties in concept development can often be attributed to a few standard errors. I have outlined and described these errors below. I have also presented the icons that I typically use within my marking in order to quickly identify these errors to my student's.

	Broken Link		Circular Argument
	Non-Linear Argument		Narrow Argument
	Contradiction		Unfalsifiable Hypothesis
	Poetic Argument		Direction of Causality (Post Hoc Fallacy, False Cause)
	Third Variable		Vague Argument
	Tautology		Composition Error

Icon Explanation Example

Broken Link: A sequence of concepts that are broken by an unexpressed or insufficiently explained element. "The corporation's profits increased, causing the price of the stock to increase." In this case, two concepts are broken by a missing element. The corporation's increase in profits would cause an increase in demand for it's stock, and it is this increase in demand for the stock that would actually cause the price of the stock to increase.

Circular Argument: An argument supported exclusively by the very assumptions that it provides. "Criminal laws outline criminal acts, and criminal acts are deemed to be any acts which violate criminal laws."

Non-Linear Argument: Several disjointed ideas which may, in-of-themselves, be correct, but they lack a linear progression towards a logical conclusion. "Inflation cannot continue indefinitely. Markets must fluctuate, as stocks rise and fall."

Narrow Argument: The concept is described or defined in terms that are too narrow. Correct points may be present, but they fail to express the "defining" elements of the argument. "A teacher is someone who works with children." This may be true, but doctors, coaches, and even lawyers also work with children. Thus, the truly defining element is missing from the above explanation.

Contradiction: Two or more points presented within the argument contradict each other. "Young offenders are just as capable of committing criminal acts as adults, therefore they should be provided special considerations under the law."

Unfalsifiable Hypothesis: An argument constructed in such a manner that it eliminates any possible means of proving or disproving its fundamental assumption. "The fact that we can find no evidence of their plot against us just serves to prove the lengths they will go to in order to conceal their conspiracy."

Poetic Argument: An argument that presents an elegant sounding phrase or expression, but fails to present the substance necessary to allow one to challenge its fundamental assumption. "What goes up, must come down."

Direction of Causality (Post Hoc Fallacy, False Cause): An argument that presents a correlation between two variables, but fails to establish which variable is responding to the other. "Students achieve greater results in subjects they enjoy." In this case, the two variables may very well be correlated. However, the argument does not establish whether students achieve greater results because they enjoy a subject, or if students enjoy subjects because they do well in them.

Third Variable (Also Post Hoc Fallacy): An argument that presents a correlation between two variables, but fails to explore a third variable that may in fact be responsible for this correlation. "High Canadian interest rates increase Canadian exports." In this case, the two variables may very well be correlated. However, the argument does not acknowledge the third variable - namely, a low Canadian dollar, that is in fact responsible for both the high interest rates and the high exports.

Vague Argument: An argument presented in terms that are so general and ambiguous that it could equally apply to many other concepts. "Systemic discrimination is against the law and causes many people to suffer as a result." Although this statement is correct, it is vague enough that it would be just as true if said about almost any form of legal infraction.

Tautology: An unnecessary and usually unintentional repetition of meaning. "unsolved mystery," "first introduced," "new innovation," etc.

Composition Error: An error in logic wherein one mistakenly assumes that what is true for a part is true for the whole. As a mathematical example, we can see how a composition error could occur if one were to associate the dimensions of a square with the area of a square. One might assume that if we doubled the dimensions of a square (ex. 10 feet by 10 feet) then we would also double the area of the square (100 feet). However, this is clearly untrue. If the dimensions of the square doubled to 20 feet by 20 feet, the area of the square actually quadruples to 400 square feet. In economics, we would see a composition error if we were to assume that the demand curve for ALL goods and services slopes down and to the left for the same reason that the demand curve for a given market slopes down and to the left. In fact, the factors (or "effects") influencing the demand for ALL goods are entirely different than the factors influencing the demand for any particular good.

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Icon	Explanation	Example
	Broken Link: A sequence of concepts that are broken by an unexpressed or insufficiently explained element.	"The corporation's profits increased, causing the price of the stock to increase." In this case, two concepts are broken by a missing element. The corporation's increase in profits would cause an increase in demand for it's stock, and it is this increase in demand for the stock that would actually cause the price of the stock to increase.
	Circular Argument: An argument supported exclusively by the very assumptions that it provides.	"Criminal laws outline criminal acts, and criminal acts are deemed to be any acts which violate criminal laws."
	Non-Linear Argument: Several disjointed ideas which may, in-of-themselves, be correct, but they lack a linear progression towards a logical conclusion.	"Inflation cannot continue indefinitely. Markets must fluctuate, as stocks rise and fall."
	Narrow Argument: The concept is described or defined in terms that are too narrow. Correct points may be present, but they fail to express the "defining" elements of the argument.	"A teacher is someone who works with children." This may be true, but doctors, coaches, and even lawyers also work with children. Thus, the truly defining element is missing from the above explanation.
	Contradiction: Two or more points presented within the argument contradict each other.	"Young offenders are just as capable of committing criminal acts as adults, therefore they should be provided special considerations under the law."
	Unfalsifiable Hypothesis: An argument constructed in such a manner that it eliminates any possible means of proving or disproving its fundamental assumption.	"The fact that we can find no evidence of their plot against us just serves to prove the lengths they will go to in order to conceal their conspiracy."
	Poetic Argument: An argument that presents an elegant sounding phrase or expression, but fails to present the substance necessary to allow one to challenge its fundamental assumption.	"What goes up, must come down."
	Direction of Causality (Post Hoc Fallacy, False Cause): An argument that presents a correlation between two variables, but fails to establish which variable is responding to the other.	"Students achieve greater results in subjects they enjoy." In this case, the two variables may very well be correlated. However, the argument does not establish whether students achieve greater results because they enjoy a subject, or if students enjoy subjects because they do well in them.
	Third Variable (Also Post Hoc Fallacy): An argument that presents a correlation between two variables, but fails to explore a third variable that may in fact be responsible for this correlation.	"High Canadian interest rates increase Canadian exports." In this case, the two variables may very well be correlated. However, the argument does not acknowledge the third variable - namely, a low Canadian dollar, that is in fact responsible for both the high interest rates and the high exports.
	Vague Argument: An argument presented in terms that are so general and ambiguous that it could equally apply to many other concepts.	"Systemic discrimination is against the law and causes many people to suffer as a result." Although this statement is correct, it is vague enough that it would be just as true if said about almost any form of legal infraction.
	Tautology: An unnecessary and usually unintentional repetition of meaning.	"unsolved mystery," "first introduced," "new innovation," etc.
	Composition Error: An error in logic wherein one mistakenly assumes that what is true for a part is true for the whole.	As a mathematical example, we can see how a composition error could occur if one were to associate the dimensions of a square with the area of a square. One might assume that if we doubled the dimensions of a square (ex. 10 feet by 10 feet) then we would also double the area of the square (100 feet). However, this is clearly untrue. If the dimensions of the square doubled to 20 feet by 20 feet, the area of the square actually quadruples to 400 square feet. In economics, we would see a composition error if we were to assume that the demand curve for ALL goods and services slopes down and to the left for the same reason that the demand curve for a given market slopes down and to the left. In fact, the factors (or "effects") influencing the demand for ALL goods are entirely different than the factors influencing the demand for any particular good.