Intro to Logic: Fallacies

by Luke Muehlhauser on August 3, 2009 in Intro to Logic

Welcome to my course Intro to Logic (index). Here, we learn the basic skills of good thinking and their benefits in real life.

An argument can fail in two ways. An argument can fail if it contains a false premise, or if the premises do not actually provide support for the conclusion.

The first failure is a factual error. Premises can be about any subject, so establishing their truth may be the subject of science or philosophy or history or other fields.

The second failure is a logical error. The task of the logician is to determine whether an argument’s premises do or do not provide the required degree of support for its conclusion. In this course, we are learning to be logicians. We are learning how to distinguish good arguments from bad arguments.

What do I mean by “the required degree of support”? Last time, we learned about deductive and inductive arguments. These two types of argument claim to provide different degrees of support for their conclusions. A deductive argument claims that if its premises are true, its conclusion must be true. An inductive  argument claims only that if its premises are true, its conclusion is only probably true.

So, a deductive argument commits a logical error if its premises fail to provide conclusive support for the conclusion. If there is any way – no matter how remote – for its premises to be true but the conclusion false, then the deductive argument fails.

An inductive argument commits a logical error if its premises fail to provide even probable support for the conclusion. If the conclusion is still not probably true after accepting the premises, then the argument is a bad inductive argument.

A logical error is often called a fallacy. If an argument fails, it is said to be fallacious. Here is a fallacious deductive argument:

  1. If Portland is the capital of Maine, then it is in Maine.
  2. Portland is in Maine.
  3. Therefore, Portland is the capital of Maine.

The premises are true, but the argument is fallacious because the premises do not conclusively support the conclusion. (And in fact, the conclusion is false.)

And here is a fallacious inductive argument:

  1. Having just arrived in Kentucky, I saw two white squirrels.
  2. Therefore, all squirrels in Kentucky are white.

Not only does the premise fail to conclusively support the conclusion, it does not even make the conclusion probable. This is a bad (fallacious) inductive argument.

A Taxonomy of Fallacies

fallacy_detectiveLogicians have identified dozens of fallacies, though some are more common than others. For convenience, I’ll organize these fallacies into four groups.

The first group contains the formal fallacies, which represent technical errors of structure in an argument. You can see a formal fallacy merely by analyzing the structure of the propositions, without knowing their content at all. Consider:

  1. If it is raining then the streets are wet.
  2. The streets are wet.
  3. Therefore it is raining.

To see the argument’s structure more clearly, we can replace “it is raining” with p and “the streets are wet” with q. Now the argument is:

  1. If p then q.
  2. q.
  3. Therefore p.

This is an invalid argument. A common way to show that an argument form fails is to provide an argument of the exact same form that clearly fails. For example, let p = “it is snowing” and q = “the streets are covered with snow”. Now the argument becomes:

  1. If it is snowing then the streets are covered with snow.
  2. The streets are covered with snow.
  3. Therefore it is snowing.

This argument has the exact same form as the argument about raining above, but it is clearly invalid. The streets could be covered with snow even if it is not snowing. For example, the snow could have come from from last night, or from a snow machine. Given this counter example, we know that all arguments of this form are invalid.

The other three groups below contain informal fallacies, which represent other kinds of disconnect from premises to conclusion. With an informal fallacy, we can’t just look at the argument’s structure to see that it fails. We must also look at the content. For example:

  1. All b are r.
  2. Therefore the b where I deposit my money is r.

This argument structure is clearly valid. If all b are r, then any b I name is r, including the b specified in the conclusion. But now, let’s look at the content of the argument I had in mind:

  1. All banks are next to a river.
  2. Therefore the bank where I deposit my money is next to a river.

But this is clearly false, because two different meanings of the word bank are being used. It’s true that all banks (riversides) are next to a river, but that doesn’t mean that the bank (financial institution) where I deposit my money is next to a river.

Since we had to look at the content of the propositions in the argument to see the logical error, the above argument commits an informal fallacy.

Below I will keep a linked index of all fallacies as I write about them:

  1. Formal Fallacies (failure of technical structure)
    1. Ad hominem and appeal to the people
    2. Genetic fallacy
    3. Affirming the consequent
  2. Fallacies of Faulty Generalization
  3. Distraction Fallacies
  4. Other Informal Fallacies

Also see:

Michael C. LabossiereMichael C. Labossiere

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{ 9 comments… read them below or add one }

Taranu August 3, 2009 at 9:32 am

1. Luke, when you say the conclusion of an inductive argument must be probable do you mean that, statistically speaking, it’s probability must be higher than .5?
2. Can a cumulative argument be made from deductive arguments or only from inductive arguments (p-inductive) like the ones Swinburne mentions?

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lukeprog August 3, 2009 at 2:15 pm

Taranu,

1. Yes, I mean .5. But there are varying strengths of inductive arguments. Some are stronger than others.
2. It depends what you mean by cumulative. Clearly, you can string deductive arguments together to make a cumulative deductive argument. And you can do something similar with inductive arguments, but the probability of the ultimate conclusion gets lower with each less-than-100%-probable sub-argument.

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Dace August 3, 2009 at 4:41 pm

“here is a fallacious inductive argument:
 

Having just arrived in Kentucky, I saw two white squirrels.
Therefore, all squirrels in Kentucky are white.”

A question: why not treat this as a fallacious deductive argument? According to your definition, “an inductive argument claims that its premises make the conclusion probable”, this argument says nothing about probability, and so it must be deductive, right?
 
Perhaps you have some other criteria, but you’ll need to tell your readers what it is, otherwise you haven’t told them how to recognize inductive arguments at all.  (Very probably you are using interpretive charity: a deductive interpretation would be a miserable failure).
 
 

All banks are next to a river.
Therefore the bank where I deposit my money is next to a river.

 
Here too, I think you’re using interpretative charity without signalling it to your readers. After all, there is an interpretation on which equivocation does not happen, so it’s not as straightforward as you’re describing it. Also, you shouldn’t call the equivocative argument “clearly false”, as you have said that arguments cannot be false, but only valid or invalid.

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Taranu August 3, 2009 at 9:44 pm

“the probability of the ultimate conclusion gets lower with each less-than-100%-probable sub-argument”
 
I thought the whole thing with cumulative arguments was that sub-arguments with low probability can end up making a case with high probability. Isn’t this why Craig says in his debates on the existence of God that the 5 arguments he usually gives make a cumulative case?
 

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Lorkas August 4, 2009 at 6:30 am

Taranu: I thought the whole thing with cumulative arguments was that sub-arguments with low probability can end up making a case with high probability.

There’s two different things going on here. If you have propositions with a certain probability, then the more you have, the less probable your conclusion. It’s like saying, the more coins you flip, the less likely it is that they’re all heads:
1 flip = 50%
2 flips = 25%
3 flips = 12.5%
etc.
 
Some arguments are like this. If all of the supporting arguments have to be correct for the final conclusion to be correct (Z if and only if A AND B AND C AND …), then the probability of the final conclusion goes down the more supporting arguments are needed.
 
However, if the supporting arguments are all inductions to the same conclusion, but they don’t all have to be true for the conclusion to be true, then the probability of the final conclusion goes up with the number of sound inductive arguments you make.
 
A good example of this is the evidence for evolution: we have arguments from fossils, DNA, microbiology, developmental biology, comparitive anatomy, biogeography, and more. Now, even if one of those lines of evidence didn’t exist (for example, if there were no fossils at all), we could still reasonably conclude that biological evolution occurs. Not all of the lines of evidence have to be available for us to reach the conclusion, so the more lines of evidence we have, the higher the probability that our conclusion is correct.

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Taranu August 4, 2009 at 8:58 pm

Lorkas, thanks.

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Rhys Wilkins March 21, 2010 at 10:07 pm

Hey Luke,

Was wondering if you had thought about doing an article on the “Bloated Conclusions” fallacy? I think it is particularly relevant to philosophy of religion since Christian apologists commit this fallacy all the freaking time and they don’t even realize it. I heard Walter Sinnott-Armstrong mention it in his debate with Craig, and ever since then I have been seeing it everywhere!

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lukeprog March 21, 2010 at 11:44 pm

Rhys,

Yup, I’ll be writing quite a lot on that.

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sara December 16, 2010 at 3:27 pm

how to figure this out what are the fallacies?

The doctor must think I’m someone else. She referred to me as “John’s son” but my father’s name is “Mike”. I just turned in all of my paperwork. My father is listed as my emergency contact. You can’t miss it! What’s worse is that I printed my name clear as day right on the font: Charles M. Johnson. Whether the doctor can’t read or if she picked up someone else’s paperwork, I’m never coming back here again. If they can’t keep my name straight, I’m hesitant to trust them with my bloodwork or to give me the right vaccinations!

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