The study of logical and rhetorical fallacies dates back to the ancient Greeks, but for all that studying, we're still overrun by them—and for understandable reasons. Most fallacies derive from valid rules-of-thumb that are deeply ingrained in our thinking, but are hastily applied, or taken to be conclusive, rather than a good starting point. There are cases when there are only two choices to be had—but not always. In that case, it's the “false dilemma” or “false dichotomy” fallacy. It's valid to note that cause precedes effect, and to look for causes accordingly, to take another example. But it's the “rooster fallacy” (aka post hoc ergo proctor hoc) to assume that the rooster crowing caused the sun to rise. It's the very utility of the underlying rules-of-thumb that makes fallacies so hard for us to shake.

Fallacies pop up all the time in the course of specific arguments, but the most broadly damaging ones can shape an entire realm of public discourse. Two such fallacies are at war in American politics today, and they're making progress extremely hard to come by. They were at work in the recent government shutdown, and they haven't gone anywhere in its aftermath, either.

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Fallacy No. 1 is the false balance fallacy—also known as false compromise, argument to moderation ("argumentum ad temperantiam" in Latin), and the golden mean fallacy, among others. It is a major feature of our so-called serious politicians and media figures, who routinely position themselves in between “extremists on both sides.” It's often the case that two people in an argument each miss something valid in each other's point of view. So there's a valid rule-of-thumb here in trying to see both sides. But it becomes a fallacy when this starting point becomes the end, particularly when balance or moderation becomes so important that it's rigidly, even fanatically adhered to, and the clear preponderance of evidence is given no more weight than someone's uninformed opinion. As Cenk Uygur put it, "If CNN did sports reporting, every game would be a tie."

Fallacy No. 2 is the “no true Scotsman” fallacy. Unlike most fallacies, it doesn't derive from a valid rule-of-thumb, though it is connected to some more benign cognitive impulses. Typically, A says, "No Scotsman puts sugar on his porridge." B replies, "I am Scottish, and put sugar on my porridge." A responds: "Ah, then you are not a true Scotsman." This fallacy commonly involves attempts to preserve purity—as when Tea Party conservatives denounced those willing to compromise on shutting down the government as not being “true conservatives.” Appeals to purity can arise anywhere on the political spectrum, but for a variety of reasons they tend to be much more common on the right.

Let's look a little more closely at each of these fallacies in turn.

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The false balance fallacy lay at the heart of the media's deep reluctance to blame conservative Republicans for the recent government shutdown. As I recently wrote for Al Jazeera English, the media had to ignore nine bodies of evidence that clearly showed it was Republicans, not Democrats, who caused the shutdown. Thus, instead of reporting as much context and as many perspectives as possible, the media's embrace of false balance severely constricts the range of facts and viewpoints it explores—the exact opposite of what it's supposedly trying to achieve.

President Obama is a walking embodiment of this fallacy. He is so eager to embrace Republican ideas— Bush's TARP, tax cuts in his stimulus bill, the Heritage Foundation's individual mandate, ” "cap and trade,” fiscal austerity, making permanent the vast majority of Bush's tax cuts, etc.—that he embraces objectively bad ideas, divides his own base, and doesn't even get any political benefit from it. For one thing, he doesn't give Republicans an opportunity to fight for their own ideas—to demonstrate to their own base that they stand for something that is in dispute. Rather than make them more willing to compromise with him, this increases the pressure on them to fight. We've seen this over and over again throughout the Obama presidency, but Obama never seems to learn. His very zeal in seeking compromise only makes it that much harder for Republicans who need to fight him. So it's really not all that surprising when they turn around and accuse him of being “unwilling to negotiate,” however misleading that may be. Whatever else is involved in keeping Obama stuck where he is, the false balance fallacy is part of the equation.

The flip side of the false balance fallacy is the false dichotomy mentioned earlier—the assumption that there is no middle ground, and there are only two sides. “You're either with us or against us,” as George Bush said. In America today, however, these two fallacies work hand-in-hand. Condemning “extremists on both sides” is an integral part of maintaining the “balanced” “moderate” center. But this condemnation in defense of false balance depends on a false dichotomy—extremists vs. moderates.

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On the other hand, false dichotomy also works together with the “no true Scotsman” fallacy. You need the false dichotomy fallacy to form the “true Scotsman” notion in the first place.

The underlying logic here is, in a sense, the exact opposite of the balance fallacy: It's better not to hear both sides, it's better not to even think there's another side. Psychologist Jonathan Haidt cites substantial evidence that conservatives are much more concerned about purity (aka sanctity) than liberals are. (Haidt thinks this is a liberal deficiency, I tend to disagree.) So it's not that surprising that purity is a much bigger concern among conservatives than it is among liberals.

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The fallacy has several major manifestations. The broadest of those is perfectly captured in the title of a 2009 post by John Cole at Balloon Juice: "Conservatism Cannot Fail, Only We Can Fail Conservatism.” In it, he asks:

[D]o you remember all the mass protests organized by Freedom Works and the fiscal conservative teabaggers when Bush and DeLay were jamming through the Prescription Drug bill? You remember 60-100,000 wingnuts descending on D.C. screaming “I want my country back?” while wailing about out of control spending? Me either.”

And he's hardly alone when he concludes by saying, "I’ve said it before, and I’ll say it again- these 'conservatives' sound like the excuse makers for the Soviet Union who tell us communism didn’t fail, it just wasn’t properly implemented."

What Soviet Communism and U.S. conservatism share in common is the “no true Scotsman” logic, which dismisses all their failings, rather than learning from them, treating them as the fault of impurities, outside intrusions, or insufficient commitment by the community of true believers. In both cases, this logic is absolutely deadly. It scarcely matters whether either the Communists or the conservatives originally had any valid insights or ideas or not—their embrace of the “no true Scotsman” fallacy made it impossible for them to improve on what they started with, impossible to learn from their mistakes.

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In the course of the budget shutdown crisis, there was a layering effect as the media struck a false balance between Democrats and Republicans, while Democrats also adopted a balance-based pose, arguing repeatedly that they were just being reasonable and the Republicans were being extreme. Of course, what the Democrats were saying wasn't false at all. But they were so concerned with being “on message” that they didn't want to get into the messy details—the empirical facts that are utterly essential is you want to make a valid argument based on facts, rather than a specious argument based on assertion.

It's not as if there were only two choices here—no false dichotomy! They could have struck some sort of middle ground balance with a disciplined presentation of facts, such as endlessly repeating, “The budget level in the CR is already a compromise—it gives House Republicans 90 percent of what they want.” One thing they would apparently never consider was bringing their own independent ideas to the fore—such as raising the cap on payroll taxes to secure Social Security indefinitely. The balance ethos was so deeply internalized that only conservative ideas got a hearing, even as conservatives were losing badly. And so those ideas remain dominant, despite everything there is to discredit them.

Case in point: Now that the shutdown crisis is over, talk of a “grand bargain” has begun again, implicitly including Obama's willingness to cut Social Security and Medicare (“in order to save it,” just like George Bush and Paul Ryan!) as part of a “balanced approach”—a phrase he uses constantly. “The challenge we have right now are not short-term deficits. It's the long-term obligations that we have around things like Medicare and Social Security. We want to make sure those are there for future generations,” Obama said, with no mention of raising taxes on the super-wealthy to help do it.

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Thus it is that the “center-left” comes out as center-right—but never anywhere near right enough for conservatives to stop yelling “socialist!” As long as the logic of fallacies dominates, no amount of factual details matter—much less any sophisticated arguments based on them.

These two warring fallacies are flip sides of one another. The false balance fallacy assumed it's better to hear both sides—even if one side is fact free and deceitful. As a purity mechanism, the Scotsman fallacy has the exact opposite underlying logic: it's better not to hear both sides, it's better not to even think there's another side.

Both fallacies are wrong, and both are dangerous—but not equally so. The "no true Scotsman" fallacy creates a vicious cycle—anything that would argue against it gets rejected as impure. Thus, we have Tea Party true believers denouncing those who failed to fight to the bitter end, as well as that old standby, blaming the “liberal media.” The "false balance" has an inkling of a way out—if enough pressure is brought to bear to force another point of view to be balanced.

This is what gay rights activists have been able to do over the past few years—both in terms of marriage equality and in ending “don't ask, don't tell.” It's what immigration activists are struggling mightily to do as well. And it's what progressives need to do now to fight against Obama and the D.C. establishment sliding back into "grand bargain" mode. To do that, progressives will have to be willing to come in for a heavy dose of being labeled “extremist” and being compared to the Tea Party. It's not that they should go out of their way to invite this. They just shouldn't duck when the knee-jerk false-equivalence attacks begin. They should be prepared to counterpunch. Hard.