Logic and Argumentation

This page explores the basics of logic and argumentation. Please also view the page on the different types of evidence used in arguments.

Argumentation is the staple of most, if not all, academic writing as well as everyday discussions, debates, and RDTs.* Given the importance of argumentation, a writer should test and make certain that the point being argued is solid and well-founded rather than an unsupported statement, easily torn to shreds by a professor or colleague.

Ideally, a decent argument will be both valid and sound.

A valid argument is one where if all the premises are true, so that the conclusion necessarily follows. A non-valid argument is one where even if the premises are true, the conclusion does not necessarily follow. A sound argument is a valid argument with true premises, whereas an unsound argument has at least one false premise.

Example of a valid, sound argument:

All fish have gills. All goldfish are fish. All goldfish have gills.

Example of a valid, unsound argument:

Example of a non-valid argument:

If Dr. Litfin were Catholic, he would pray in chapel. Dr. Litfin does pray in chapel. Therefore, Dr. Litfin is Catholic.

The second argument is clearly not the case even though the line of argument makes logical sense. As for the third, the President of Wheaton College could have a great number of motivations for praying in chapel, including the one put forth in the non-valid argument, but this does not make him Catholic. Invalidity and unsoundness are often difficult to spot at first glance.

Logical Fallacies

Logical fallacies are logical mistakes made frequently and systematically enough to be formalized and given an official name. In order to make a sound, coherent argument, avoid them. Here is a (non-exhaustive) list of commonly occurring fallacies:

Begging the Question: the conclusion assumes or restates what is explicitly stated in the premise.

We know God exists because the Bible says he does, and we know the Bible is true because God wrote it.

Appeal to Authority: citing the opinion of a person, usually a celebrity, who has no special expertise on the subject as a way of proving a point.

Billy Graham likes to use Macs more than PCs, so Macs must be the better choice.

Appeal to the Populace: mentioning popular opinion as a way of convincing a reader instead of actually arguing.

Billions of people over the last two thousand years have believed in Christ. This shows us the power and truth of the Gospel.

Vagueness: using terms unclearly in a sentence or argument.

“The OSU research failed to find any significant difference between people who survive a heart attack and those who die from one” (Columbus Dispatch).

Equivocation: using a term in multiple ways in the same context.

I have faith that your faith can withstand questioning.

Appeal to Ignorance: argues that, since a certain statement or point has not been shown to be false, it must be true—or vice versa.

No one has proven God does not exist; therefore, he does.” or “no one has proved God does exist; therefore, he does not.

Composition and Division: assuming that either the characteristics of one part define the whole or that a characteristic of the whole defines each individual part.

A candle isn’t very bright, so a trillion candles wouldn’t be very bright.

Our football team is the best in Illinois, so our quarterback must also be the best in Illinois.

False Dilemma: reducing the options to two extremes.

Either you’ll willingly go to evening worship on Sunday or you aren’t a Christian.

Suppressed Evidence: making a conclusion without being aware of important background information.

You were gone all Friday night and came back in the morning with a headache. You must have been out drinking.

Slippery Slope: claiming that one event will inevitably lead to a disastrous chain of consequences.

If you skip class today, you’ll get used to skipping, and then never go to class, and then flunk out of school, fail to get a job, live on the street, and get killed by a hobo in downtown Chicago.

Conjunction: assuming that, since events A and B frequently occur together, they are the cause of one another.

Every time I eat chicken for lunch I do really well in English class.

Straw Man: intentional or unintentional misrepresentation of an opponent’s argument to make it an easier target to defeat.

All evolutionists believe that ooze popped up out of the ground somewhere, got zapped by something and turned into a fish, then it stepped on land, grew legs and became a person.

Red Herring: diverting attention from the real point of an argument to something unrelated.

It’s true that the volcano would kill us all if it erupted, but it would also increase property value for the surviving island estates.

* RDTs: Relationship Defining Talks, for those uninitiated.

This page explores the basics of logic and argumentation. Please also view the page on the different types of evidence used in arguments.

Argumentation is the staple of most, if not all, academic writing as well as everyday discussions, debates, and RDTs.* Given the importance of argumentation, a writer should test and make certain that the point being argued is solid and well-founded rather than an unsupported statement, easily torn to shreds by a professor or colleague.

Ideally, a decent argument will be both valid and sound.

A valid argument is one where if all the premises are true, so that the conclusion necessarily follows. A non-valid argument is one where even if the premises are true, the conclusion does not necessarily follow. A sound argument is a valid argument with true premises, whereas an unsound argument has at least one false premise.

Example of a valid, sound argument:

All fish have gills. All goldfish are fish. All goldfish have gills.

Example of a valid, unsound argument:

Example of a non-valid argument:

If Dr. Litfin were Catholic, he would pray in chapel. Dr. Litfin does pray in chapel. Therefore, Dr. Litfin is Catholic.

The second argument is clearly not the case even though the line of argument makes logical sense. As for the third, the President of Wheaton College could have a great number of motivations for praying in chapel, including the one put forth in the non-valid argument, but this does not make him Catholic. Invalidity and unsoundness are often difficult to spot at first glance.

Logical Fallacies

Logical fallacies are logical mistakes made frequently and systematically enough to be formalized and given an official name. In order to make a sound, coherent argument, avoid them. Here is a (non-exhaustive) list of commonly occurring fallacies:

Begging the Question: the conclusion assumes or restates what is explicitly stated in the premise.

We know God exists because the Bible says he does, and we know the Bible is true because God wrote it.

Appeal to Authority: citing the opinion of a person, usually a celebrity, who has no special expertise on the subject as a way of proving a point.

Billy Graham likes to use Macs more than PCs, so Macs must be the better choice.

Appeal to the Populace: mentioning popular opinion as a way of convincing a reader instead of actually arguing.

Billions of people over the last two thousand years have believed in Christ. This shows us the power and truth of the Gospel.

Vagueness: using terms unclearly in a sentence or argument.

“The OSU research failed to find any significant difference between people who survive a heart attack and those who die from one” (Columbus Dispatch).

Equivocation: using a term in multiple ways in the same context.

I have faith that your faith can withstand questioning.

Appeal to Ignorance: argues that, since a certain statement or point has not been shown to be false, it must be true—or vice versa.

No one has proven God does not exist; therefore, he does.” or “no one has proved God does exist; therefore, he does not.

Composition and Division: assuming that either the characteristics of one part define the whole or that a characteristic of the whole defines each individual part.

A candle isn’t very bright, so a trillion candles wouldn’t be very bright.

Our football team is the best in Illinois, so our quarterback must also be the best in Illinois.

False Dilemma: reducing the options to two extremes.

Either you’ll willingly go to evening worship on Sunday or you aren’t a Christian.

Suppressed Evidence: making a conclusion without being aware of important background information.

You were gone all Friday night and came back in the morning with a headache. You must have been out drinking.

Slippery Slope: claiming that one event will inevitably lead to a disastrous chain of consequences.

If you skip class today, you’ll get used to skipping, and then never go to class, and then flunk out of school, fail to get a job, live on the street, and get killed by a hobo in downtown Chicago.

Conjunction: assuming that, since events A and B frequently occur together, they are the cause of one another.

Every time I eat chicken for lunch I do really well in English class.

Straw Man: intentional or unintentional misrepresentation of an opponent’s argument to make it an easier target to defeat.

All evolutionists believe that ooze popped up out of the ground somewhere, got zapped by something and turned into a fish, then it stepped on land, grew legs and became a person.

Red Herring: diverting attention from the real point of an argument to something unrelated.

It’s true that the volcano would kill us all if it erupted, but it would also increase property value for the surviving island estates.

* RDTs: Relationship Defining Talks, for those uninitiated.