What Is Modus Tollens?


Modus tollens is a valid argument form. Because the form is deductive and has two premises and a conclusion, modus tollens is an example of a syllogism. (A syllogism is any  deductive argument with two premises and a conclusion.)

The Latin phrase ‘modus tollens‘, translated literally, means ‘mode of denying’.

Shown schematically, this form of argument looks like this:

Premise 1: If A then B.

Premise 2: Not-B.

Conclusion: Therefore, not-A.

Arguments of this form are produced by substituting statements in English for A and for B. For example, suppose A = ‘Casey is a dog’ and B = ‘Casey has four legs.’ We can substitute as follows, for a valid argument:

Premise 1: If Casey is a dog, then Casey has four legs.

Premise 2: Casey does not have four legs.

Conclusion: Therefore, Casey is not a dog.

Any argument of this form is valid. But not every argument of this form is sound. For an argument to be sound, it must meet two requirements. First, it must be valid; second, it must have true premises. The above argument about Casey is valid, but it’s not sound. Why? Because the first premise is false. It implies that all dogs have four legs. But this generalization, unfortunately, is not true. (It also turns out that Casey does have four legs; so premise 2 is false, also.)

Because modus tollens arguments are always valid, we may extrapolate from this argument form a rule of inference as follows:

“Always infer not-A from the conjunction of two premises, if one premise is a conditional statement of the form ‘If A, then B,’ and the other premise denies B.” (The order of the premises doesn’t matter.)

Caveat:

Be careful not to confuse modus ponens with modus tolendo ponens. Modus tolendo ponens is an argument of the following form:

Premise 1: Either A or B.

Premise 2: Not-A.

Therefore, B.

See also “What Is What Is Modus Ponens?”

What Is Modus Ponens?


Modus ponens is a valid argument form. Because the form is deductive and has two premises and a conclusion, modus pones is an example of a syllogism. (A syllogism is any  deductive argument with two premises and a conclusion.)

The Latin phrase ‘modus ponens‘, translated literally, means ‘mode of affirming’.

Shown schematically, this form of argument looks like this:

Premise 1: If A then B.

Premise 2: A.

Conclusion: Therefore, B.

Arguments of this form are produced by substituting statements in English for A and for B. For example, suppose A = ‘Casey is a dog’ and B = ‘Casey has four legs.’ We can substitute as follows, for a valid argument:

Premise 1: If Casey is a dog, then Casey has four legs.

Premise 2: Casey is a dog.

Conclusion: Therefore, Casey has four legs.

Any argument of this form is valid. But not every argument of this form is sound. For an argument to be sound, it must meet two requirements. First, it must be valid; second, it must have true premises. The above argument about Casey is valid, but it’s not sound. Why? Because the first premise is false. It implies that all dogs have four legs. But this generalization, unfortunately, is not true.

Because modus ponens arguments are always valid, we may extrapolate from this argument form a rule of inference as follows:

“Always infer B from the conjunction of two premises, if one premise is a conditional statement of the form ‘If A, then B,’ and the other premise affirms A.” (The order of the premises doesn’t matter.)

Caveat:

Be careful not to confuse modus ponens with modus tolendo ponens. Modus tolendo ponens is an argument of the following form:

Premise 1: Either A or B.

Premise 2: Not-A.

Therefore, B.

See also “What Is Modus Tollens?”

Teaching Logic & Critical Thinking to Your Kids


Cover of

Cover of Being Logical: A Guide to Good Thinking

It’s pleasing to know that parents are taking a more proactive role in the education of their children, whether or not they are homeschooling. I’ve been asked if I can recommend tools that could be used to teach children the elements of logic and critical thinking.

  1. My first suggestion is that the best way to teach children how to think critically is to be a visible model of critical thinking. Children have a far greater aptitude for critical thinking than adults credit them for. They tend to be good at inferential reasoning. Their powers are limited in part by their limited storehouse of information from which to make inferences.
  2. Modeling excellence in critical thinking presupposes skill in critical thinking. So parents need to be students of logic and critical thinking themselves. Unfortunately, most have not had the opportunity for formal education in these skills. But there are accessible books to consider. I’ll add a list of recommendations at the end of this post.
  3. If your children see you making the attempt to sharpen your skills in reasoning, this will itself be a good example to them. You can tell them what you’re learning.
  4. Learn the names of basic inferential moves (for example modus ponens, modus tollens) and use these labels with your children when they demonstrate their own ability to make such moves. This should reinforce their awareness of the significance of their mental powers, and affirm them in the use of their powers.
  5. Encourage your children to think about the implications of something they have said or heard. You’ll have to be alert to opportunities for this. But once you’ve been at it for awhile, you’ll get into a natural groove. It will eventually become a part of your routine interaction with your kids. How to do this? I’ll save that for another post sometime.
  6. Get your children reading at their grade level (or above!) books that exemplify and encourage critical thinking. Mystery and suspense novels, carefully selected for their sophistication and interest, can be useful. I read the Hardy Boys as a kid. I also liked the stories of the Sugar Creek Gang.
  7. If you’re home schooling (or not), you can include in the curriculum some materials that teach critical thinking. The Fallacy Detective is a good source for this. (See below.)

Recommendations:

So, here are a few of the many resources available. I’m recommending those that provide a good place to start. Each title is linked to its Amazon page.

Books that inspire parents and other educators to teach children these skills:

Books for self-education in logic and critical thinking:

With adequate preparation in the early years, children in junior high and high school may be ready to work through these books themselves. They don’t provide a complete education in logic, but they are satisfactory for pre-college preparation. For more rigorous study in high school, I recommend using one of two textbooks:

Like most textbooks, Copi and Hurley are pricey. So you may want to settle for a second-hand copy. The illustrations and exposition of old editions will be dated, but the logic will be the same! I shop for second-hand books at AbeBooks.com.

For grade school and up:

Fiction classics for youth:

This post is cross-referenced in an interesting post here.

Related Posts by Doug Geivett:

Did Rahm or Rush Use the R-word?


The word “retarded” is not the commonplace it once was. Today we rightly refer to people with mental disabilities in other ways. One severe problem with “retarded” as a noun (i.e., the collective noun “the retarded”) is that it is easily used too generally as a label for those with mental disabilities—as if having a disability is their essential attribute, the feature that defines them as human beings. Read more of this post

Critical Thinking—Best Book in This Category


Amazon

Amazon

I teach philosophy to graduate students. Many of these men and women are married. Wives of the married men often invite me to speak to their group. Some have told me how much they desire to understand what their husbands are studying, and, frankly, to be able to hold their own in argument when their husbands, by dint of their occupation, have a seeming advantage.

There’s one book I’ve been recommending to them. It’s an excellent general introduction to the skills we all need—both for gentle sparring and for serious debate, but also just for organizing our beliefs into cogent perspectives.

Written by D. Q. McInerny, it’s called Being Logical: A Guide to Good Thinking (2005). (I see that it’s also now available in a Kindle edition.)

Charles Osgood offers this poetic endorsement:

Given the shortage of logical thinking,

And the fact that mankind is adrift, if not sinking,

It is vital that all of us learn to think straight.

And this small book by D.Q. McInerny is great.

It follows therefore since we so badly need it,

Everybody should not only buy it, but read it.

That Bookshop in Portland

That Bookshop in Portland

* * *

What Others Are Saying:

BlogLogic—Rumors of Sarah Palin’s Affiliation with the Alaska Independence Party


It’s been interesting to see how things have unfolded on the Mudflats blog, which purports to be “tiptoeing through the muck of Alaskan politics.”

The host goes by the handle “AKMuckraker.” Today she published a post titled “Palin – Republican Party Infiltrator? Damning Video.” With a title like that, you hardly need to read further to know what’s up:

There’s a video that incriminates Sarah Palin by showing her past ties to the Alaska Independence Party (AIP) and her secret plan to advance that party’s aims by infiltrating the Republican party.

That’s the muckraker’s thesis.

If you want to know what’s so damning about the video, or whether it’s damning at all, then you might want to read the post. The muckraker connects the dots that lead to her conclusion. And she’s remarkably confident of her conclusion.

The only problem is, her evidence doesn’t support her conclusion. Her argument is fallacious. If it’s not a specimen of conscious bias against Palin, it’s at least a case of wishful thinking gone awry.

The video features a small gathering of crazies scheming about how best to achieve the secessionist goals of the Alaska Independence Party. So we’re told. We have to take the muckraker’s word for it that this video is not a setup. We’ll give her the benefit of the doubt here. We’re also told that a key participant seen and heard on the video is Dexter Clark, vice chairman of the Independence party. Fine. We’ll go with that.

The muckraker then provides transcripts of bits of the video. Since these are the portions she uses to make her argument, let’s assume that they are the most damning evidence in support of the muckraker’s conclusion.

The first excerpt shows Dexter Clark estimating the number of American soldiers and dependents who “could be eligible to vote” for Alaska “Statehood.” Of course, Alaska has been a state since 1959. Ah, but it isn’t yet a “State,” as in “independent nation state.” The excerpt doesn’t disambiguate for us, but I take it that Clark is referring to the independent-nation-state kind of state, and he’s calculating the number of votes his party might be able to count on in a referendum on Statehood.

OK?

Well, maybe not. The ensuing paragraph, where the muckraker explains things for us, leaves us in greater suspense. How is “Statehood” really being used here? It isn’t easy to tell.

It might not matter. The basic idea seems to be that the Independence party was shafted by a rigged vote about Alaska Statehood, and the desired result of the AIP went down in smoke.

We come, then, to the next excert, what the muckraker calls “the good part.” Here Clark lauds the election of Sarah Palin to become Alaska’s governor, even though she did so as a Republican. Clark explains why this is good news for his Independence party. Palin had once been a member of the party. The only reason she switched parties and became a Republican was to “get along and go along” (Clark’s words).

At this point, vagueness corrupts the argument. What does Clark mean by “get along and go along”? Presumably, he’s suggesting that at the time of Sarah Palin’s move to the Republican party, she was still an Independence party member at heart and that her new role as a town mayor might work out better if she had the appearance of being a Republican. She couldn’t have been much of a Republican, suggests Dexter Clark, since she discovered that “she all kinds of problems with their ethics.” This is clearly the message that muckraker gleans from Clark’s musings.

The joy in seeing Sarah Palin become governor of Alaska is rooted in Dexter Clark’s perception that Palin remains sympathetic with the AIP cause. And this is based on two things, Palin’s prior membership in the AIP, and Clark’s perception that Palin isn’t a sincere Republican. Clark’s perception that Palin isn’t a sincere Republican is itself based, in part, on Palin’s past association with the AIP. Clark’s perception of Palin’s continued affinities for the AIP is reinforced by his perception of a clash between Sarah Palin and the Republican party over the ethics of the party.

The net effect is supposed to be that Alaskans now have an AIP governor, disguised as a Republican, who can be counted on to reintroduce the issue of Statehood and perhaps facilitate the achievement of the AIP’s primary objective. What makes the whole thing really rich is that, because governor Palin is such a popular figure in her state, many Alaskans would probably vote with the AIP and everything turn out hunky-dory for the AIP.

So strategists in the AIP propose to infiltrate the two mainstream parties, get these pseudo-members elected to municipal and state offices, and watch them use their positions—synchronizing their efforts, of course—to bring about independence for Alaska.

This seems to be the basic trajectory of Clark’s reasoning process.

And the muckraker is floored by this. The video excerpts are so unbelievably damning that the muckraker thinks her readers might want to sit down before they are presented with the evidence she presents.

What’s truly unbelievable is that the muckraker finds the argument so compelling. Indeed, to sort it out you might need to sit down for a spell.

Here’s the argument:

  1. Dexter Clark is the vice chairman of the Alaska Independence Party (AIP). [Fact]
  2. If Dexter Clark is the vice chairman of the AIP, then his proposed strategy for achieving independence has been adopted by the AIP and its members. [Assumption]
  3. Dexter Clark’s strategy for achieving independence has been adopted by the AIP and its members. [MP, 1 and 2]
  4. Dexter Clark’s strategy for achieving independence is for members of the AIP to switch to one of the two main parties, get elected to government positions, and use their new authority to sponsor independence for Alaska.
  5. Members of the AIP agree to switch to one of the two main parties, get elected to government positions, and use their new authority to sponsor independence for Alaska. [Conjunction of 3 and 4]
  6. No member of the AIP ever leaves the AIP except in pursuit of Dexter Clark’s strategy for achieving independence. [Assumption]
  7. If a person who was once a member of the AIP and is now officially a member of the Republican party, then that person has left the AIP and inflitrated the GOP in order to advocate for independence. [Direct implication of 6]
  8. Sarah Palin was once a member of the AIP and is now officially a member of the Republican party. [Assumption or fact, as the case may be; that depends on the truth value of the first conjunct; we can safely believe that the second conjunct is true]
  9. Sarah Palin has left the AIP and inflitrated the GOP in order to advocate for independence. [MP, 7 and 8]
  10. If Sarah Palin has infiltrated the GOP in order to advocate for independence, then Sarah Palin is not a genuine Republican. [Direct implication of 7]
  11. Sarah Palin is not a genuine Republican. [MA, 9 and 10]
  12. If Sarah Palin is not a genuine Republican, then Sarah Palin is unfit to become Vice President of the United State. [Assumption]
  13. Sarah Palin is unfit to become Vice President of the United States. [MP, 11 and 12]
  14. If Sarah Palin is unfit to become Vice President of the United States, then we should not vote for John McCain in this year’s presidential election. [Assumption]
  15. We should not vote for John McCain in this year’s presidential election. [MP, 13 and 14]

Statements 10-15 do not appear in the muckraker’s post. They are gleaned from the tone and content of this and other posts at her blog, and my suspicion that she does not want John McCain to be the next President of the United States. In any case, we can dispense with them here.

The above argument can be simplified by extracting three of the numbered statements, 7-9. The resulting argument is as follows:

  1. If a person was once a member of the AIP and is now officially a member of the Republican party, then that person has left the AIP and inflitrated the GOP in order to advocate for the independence of Alaska. [Assumption]
  2. Sarah Palin was once a member of the AIP and is now officially a member of the Republican party. [Assumption or fact, as the case may be; that depends on the truth value of the first conjunct; we can safely believe that the second conjunct is true]
  3. Sarah Palin has left the AIP and inflitrated the GOP in order to advocate for the independence of Alaska. [MP, 1 and 2]

Notice three things about statement number 1.

First, it is an assumption that is never actually stated in the argument.

Second, it is crucial to the argument, since the muckraker never so much as hints that Sarah Palin was in the room when the video was shot, or even that Sarah Palin has unequivocally embraced Dexter Clark’s strategy for achieving Alaska’s independence.

Third, it isn’t true.

How’s that for a specimen of BlogLogic?

* * *

Why have I written this post?

One should not infer from what I’ve said here that I support the McCain/Palin ticket. That would require another instance of specious reasoning.

I have two reasons for writing this post.

First, Sarah Palin should be defended against arguments that violate the principles of sound reasoning. So should any other candidate. But Palin has been the target of incessant, vicious attack with arguments constructed on manufactured evidence. This seems to be the current number one priority of the muckraker. (Again, that’s what muckrakers do.)

Second, I can at least hope that exposing the barrenness of a BlogArgument—or Blogument, if you will—is a contribution to the common good, as a call to sound reasoning in the public square.

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