To beg the question does not mean “to invite the question.” Here’s a faulty use of the phrase: “Bill’s report shows too many returns on our Mark 20 widget, which begs the question, ‘How will we improve our manufacturing quality?’” Or, “The weeds in this lawn beg the question, ‘Why is it so hard to get a good gardener?’”
As a rule, if some variant of “beg the question” is used in a sentence with an embedded question, the phrase is used incorrectly.
Used properly, begging the question (petitio principia) is a logical fallacy that means to assume the conclusion in your premise.
For example: “(1) The Bible is the word of God; therefore (2) it’s correct.” This one leaves much unsaid:

1. God exists [unstated assumption, and the reason for the fallacy]
2. (1) the Bible comes from God [stated premise]
3. therefore (2) the Bible is correct [stated conclusion]
4. therefore the Bible is correct when it says, “God exists” [unstated conclusion].

Question begging often hides in convoluted prose. Wikipedia gives this example: “To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State, for it is highly conducive to the interests of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.” In other words: freedom of speech is essential because it is good. A simplifying restatement can often uncover this fallacy in both others’ arguments and our own.
Begging the question is similar to circular reasoning, but the difference is subtle. The flaw with begging the question is that it depends on an unstated premise. The flaw with circular logic is structural. It is an argument of the form “A, therefore A.” That is, the conclusion is a restatement of the premise.
An example of circular logic: “He is unattractive because he is so damn ugly.” “He is ugly” is just a restatement of “he is unattractive.” Or, “Dr. Smith’s Pink Pills are what you need because that’s the best treatment.”
“The Wheel of Power” illustrates an example of circular logic with more steps:

1. “How can you be sure it’s the word of God?” Because the Bible tells us so.
2. “But why believe the Bible?” The Bible is infallible.
3. “But how do you know?” The Bible is the word of God. (And repeat …)

You should know what “beg the question” means so that you can understand it when used correctly, but I recommend against using it. If you use it correctly, many people won’t understand, and if you follow the crowd and use it to mean “invite the question,” you’ll annoy those who understand the correct usage.
Photo credit: Wikimedia
Related posts:

• See all the definitions in the Cross Examined Glossary.

Related links:

• “Begging the Question,” Wikipedia.
• “Circular Reasoning,” Wikipedia.
• “Petitio principia,” Iron Chariots Wiki.
• “Begs the Question,” Grammar Girl, 8/19/08.