Nevertheless, we don’t have to be able to recognize which specific rules of logic are being violated to recognize that things are terribly wrong in the affairs of state—just as we don’t have to know that protanopic color blindness is missing something when it reports that orange and green are essentially the same color.  (It’s missing the red-sensitive cone on the retina.)  We see the difference between orange and green, and it’s undeniable.  But if we do understand how the eye sees color, we can go a lot further: we can, for example appreciate how a bird’s color vision is vastly superior to a human’s

Deeper understanding of logical errors should empower us.  This power is the power of education. 

In 1990, Newt Gingritch was awarded a well-deserved "Doublespeak Award" by the National Conference of English Teachers for a booklet, Language,  a Key Mechanism of Control.  It was based on two of "The seven tools of propaganda," the use of which renders communication useless as information but effective as persuasion.
 
 

Ignoring other viewpoints, perceptions, understandings, expertise, imperatives, needs, etc, even though they are essential elements of our problems.

Improper: "Putative experts from 'think tanks,' most of whom haven't been to those countries or speak the languages are regularly called upon to give their opinions.  The result...

Proper:  Experts supply well-researched and wide-ranging knowledge, then add careful reasoning.  Expert reasoning concentrates on disconfirming evidence recognizing that confirming evidence is all too easy to find and, by itself, doesn't discriminate between what will work and what won't.
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Good reasoning concentrates on disconfirmations and pays minimal attention to confirmations. Confirmations are necessary but their sufficiency is minimal. 

Look for easy-to-understand examples to compare with our issue.

Eureka! - "Once you see it you can never again not see it."  And you know you must not ignore it.

Find examples of such logical imperatives which are close to our issue.

When a new insight solves an old problem and gets added to college curricula, the understanding usually doesn't spread. Rather, a few individuals pick up the technique and solve problems with it while a majority learn words and rituals for the exams.  Newton's physics breakthroughs of the 17th century are today usefully understood by perhaps 5 - 15% of those who learn them.  Physics education research of the past 30 years has greatly improved this situation by developing inquiry education that directs its students into the mental weight-lifting mode.

Here's the same error where it's easier to see: Why not define vegetable, with, "A vegetable is a potato."  We object because a vegetable might not be a potato.  (Just as energy might not be capacity to do work.)  In the language of logic:  "If potato, then vegetable," is correct, but "If vegetable then potato," is not correct. 

These are implications (in the formal logic sense): "Potato implies vegetable" is true and "Vegetable implies potato" is false.  To use the false statement not noticing the difference between the two, is to improperly invert an implication.  "Energy is the capacity to do work" improperly inverts an implication.  Those text authors make a logical error--most of the other authors simply avoid giving any definition of energy.

It's a very common error.  Many statements and arguments that we sense to be wrong, although we can't quite say why,  have improperly inverted implications to support them. 

Here's a puzzle which demonstrates how that very simple relationship, implication, is also very subtle:

In a set of cards each card has a number on one side and a letter on the other.  Four cards are lying on a table.  They show an "I", an "N", a "6", and a "3".  Someone suggests the hypothesis: If a card has a vowel on one side then it has an odd  number on the other side.  The problem is to determine which cards must be turned over to test the hypothesis.  No card is to be turned over unless necessary to test the hypothesis.

Search for disconfirmations is necessary to establish truth and to justify actions.  The shortest route to disaster is to ignore the rest of the universe once we’ve found something we like.  Skepticism is essential to ward off the constant deluge of propaganda—and to sidestep self-deception.

Egocentrism, ethnocentrism, and anthropocentrism, each ignores too much about the “others” we interact with.  If we learn more about those “others,” we usually discover they are really another part of  “us.”  “We are all in this together.”  (Thom Hartmann is currently espousing these thoughts.)

Logical imperatives are often not recognized.  Most common is probably the inverted implication:  all confused with some, necessity confused with sufficiency, equivalence confused with implication or mutual exclusion, etc.

Sorting the relevant from the irrelevant is too often not done—an outcome of not recognizing those logical relationships.  (A theme from Piaget.)

Modern science concepts are not what they seem at first glance.  They are a bit more abstract than we expect and need a bit of mental weight-lifting before they are usefully understood.

Innumeracy: the failure to recognize which math is appropriate for which situations.  Never mind the higher math like solving second-order partial differential equations or solving problems in algebraic topology.  Simple ratios and proportions are very often handled incorrectly and exponential relationships are frequently beyond the point where the math gets too fuzzy to fiddle with.  Also, statistics is a dangerous trap for the mathematically naïve.  (And so a commentator recently suggested that Bush’s persistence in Iraq until “victory” is like the lottery addict who persists in putting in money until he wins.)

Multidimensional insight eludes most college students: its potential is so great that it’s worth the effort needed to gain some understanding.  Ordering athletes by size and ordering paint chips by color are good ways to get started.  Such insights are necessary for solutions to our educational problems and to lopsided distribution of wealth.  This is why many Nobel Prizes in Economic Sciences are primarily new multidimensional insight.