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:

400th Anniversary of the King James Version of the Bible


The first page of the Book of Genesis from the...

Image via Wikipedia

The world’s best-selling book of all time, the King James Version of the Bible, is 400 years old this year. Introduced in 1611, this elegant English translation has a storied history, and an influence on Western culture beyond that of any person or object.

Today, a friend and colleague of mine gave a brief presentation on the history and influence of the KJV to the faculty at my university. Dr. Clinton Arnold is a New Testament scholar with numerous books to his credit. For a beautiful book that surveys the history of the English Bible, I recommend his neatly organized and amply illustrated book How We Got Our Bible.

If you want to read up on the King James Bible, I recommend two books:

The general topic matters for two basic reasons:

  1. Some uninformed critics think that the existence of diverse English translations counts against the divine origin of the original manuscripts of the Bible.
  2. Many, believers and nonbelievers, are not familiar with the history of the “canon” of the Bible. They do not know how the various books of the Bible, written by many individuals over a period of centuries, came to be regarded together as the written word of God.

Whether or not you use the King James Version, whether or not you read the Bible, I encourage you to commemorate this anniversary of the KJV with a little study of the history of the Bible. Here are some sources for that purpose:

Related:

Protesting Governor Scott Walker May Backfire on Liberals


Wisconsin Budget Repair Bill Protest: Scott Wa...

Image by mrbula via Flickr

There’s turmoil in Madison, Wisconsin, as some public school teachers and others protest the efforts of Governor Scott Walker to curtail excessive state spending on state employee benefits. From a distance, this looks like a bad play by liberal Democrats.

  • Teachers who have left their jobs to protest at the state’s capitol may be breaking the law and may pay a price for doing so.
  • 14 Democrat legislators who have left the state in order to prevent a vote on the Governor’s proposals may not last long in their elected positions.
  • The antics of protesters in Wisconsin have brought national attention to the debacle, and these protesters are at risk of a backlash in public sentiment across the nation.
  • With the substantial visibility of Governor Walker’s boldness, and the prospects for his success, other states in fiscal trouble may be emboldened to adopt similar measures.

These probably would not be welcome effects of the protest movement in Wisconsin, among those actually protesting. But there is an even more significant possibility they may not have anticipated.

  • Governor Scott Walker has been propelled to national attention and has become a symbol of broad national support for greater fiscal responsibility and bolder leadership to achieve that end. Protesters have generated greater interest in Governor Walker as an icon of conservative politics. A figure who was unknown outside Wisconsin only a week ago is now a national icon. If he succeeds in Wisconsin, he may be a compelling candidate for national leadership. He may even be scrutinized as possible presidential timber. Imagine that! With every ounce of continued protest, the governor’s critics run a greater risk of showcasing the governor’s achievement if he prevails.

If the governor of Wisconsin prevails, his example may galvanize a cadre of conservative politicians to step up with ever bolder measures. The conservative movement could be on the cusp of new energy, so far unprecedented. That would truly be significant, given the already substantial inroads that have been made by conservatives among the electorate.

Scripture Memory Made Easy


Scripture Memory Made Easy is the title of a little book by Mark Waters. The method resembles the approach I was taught by Garry Friesen as a college student in the late 1970s. The 64-page booklet, dubbed an “easy-to-understand pocket reference guide,” is both a guide to Scripture memorization and “a plan for learning one hundred Bible verses in fifty-two weeks.”

The author stresses the importance of review and has built this crucial element into the method. He also advises the excellent practice of memorizing verses topically. Both of these components of a sound Scripture memory plan were part of the Navigator’s “Topical Memory System” that I used when I was a teenager.

I have always believed in the value of Scripture memorization. It’s never too early to begin. Nor is it ever too late. For all the enthusiasm we see today for new techniques of “spiritual formation,” there is almost no emphasis on the memorization of carefully selected passages from the Bible.

Scripture Memory Made Easy, by Mark Waters, is a useful remedy.

Order at Amazon

Happily, the Topical Memory System, by the Navigators, continues to be published. Today’s kit includes 60 verses cards with passages from several familiar English translations, a workbook, and a verse card holder.

If Scripture memorization is new to you, I urge you to begin now. God will reward your efforts with the supply of wisdom for life’s small and major moments.

Note: I welcome your response to this post. Other readers may be encouraged to know of how your own experience with Scripture memory has increased your faith, enabled you to follow God’s will, and fostered greater boldness as a believer living in a secular society.

This website is read by people of differing beliefs. This particular post is primarily for those who believe the Bible is the greatest source for wise living. Anyone who believes this should be especially open to the value of Scripture memorization.

Again, I look forward to hearing from you!

Page Numbers in Kindle


Cover of "Kindle Wireless Reading Device,...

Cover via Amazon

This week I ordered the new Kindle, upgrading from the original Kindle that I bought a few years ago. My new Kindle arrived in the mail today. I’ve already enjoyed its improved features.

Amazon has recently created a new firmware version that includes several new features. The most welcome feature is the possibility of determining the page numbers in hard copy for the Kindle ebook version of a book you happen to be reading. This is critical to readers like me who write and lecture and need to be able to document references to the reading we site.

There are things to know about this new feature and its availability:

  1. Even my brand new Kindle came with version 3.0.2 of the firmware. This was superseded by 3.0.3. Why my new Kindle is loaded with the older firmware is unclear to me. But more important, my new Kindle should have the very latest firmware—3.1. Why doesn’t it?
  2. Amazon provides a page of instructions about how to upgrade your Kindle firmware to version 3.1. But I found today that the link for downloading the software is not working. So for the time being, I’m not able to upgrade to 3.1. (This may have something to do with the browser I’m using, which is Firefox. I’ll try this download with a different browser later.)
  3. Not every book purchased for Kindle makes use of the page numbers feature.
  4. When you use the page numbers feature with your Kindle, the way to be sure which physical copy it corresponds with is to go to the product detail page for that book at Amazon and scroll down to find a line that gives the “Page Numbers Source ISBN” under the “Product Details” section of the page.

For Amazon’s own information about the page numbers feature on the Kindle, go here and here.

 

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