Understanding science concepts frequently requires that we see implication relationships and easily distinguish implication from other Boolean relationships–such as the inverse of the implication, mutual exclusion, and equivalence, for example.  These insights are needed if we are to sort through multiple variables, influences and hypotheses and find which are relevant and which are not.  They're important to statistical reasoning, too, and modern science knows—in fact understands—that the world is fundamentally statistical.  Science sees statistics.

The energy concept is widely misunderstood because such insights are too often obscure.  The word "energy," was coined by Aristotle from roots meaning "at work."  The human notion of work–and all that goes with it: fatigue and rest, hunger and food, engines and fuel, etc–didn't get worked out scientifically until the mid 19th  century.  Now we know that the scientific use and the colloquial (including Aristotle's) uses are vastly different.  The scientific "energy" is simple, abstract, and conserved.  The colloquial "energy" is complex, concrete, and not conserved.  It's profoundly statistical, too.  ("Once used you can't use it again," said the Oregon governor's energy advisor.  But he had invoked the laws of thermodynamics to prove his point, so he was clearly confusing the two meanings.)

Good, clear insight into the mysteries of multiple influences is rare enough that many physics textbook authors improperly define energy with,  "Energy is the capacity to do work." [What's that?]  That's impossible on at least two grounds:

Definition requires (logical) equivalence.  That is, if you have energy you must have capacity to do work, and if you have capacity to do work you must have energy.  However, the actual relationship here is (logical) implication.  If you have capacity to do work you must have energy.  True!  (Alternatively worded, "Capacity to do work implies energy.")  But energy can be unavailable for doing work.  (Energy does not imply capacity to do work.)  And so the actual relationship is implication, not equivalence.  The statement cannot, because of elementary logic, be a defintion. 

Furthermore, "Energy is the capacity to do work" improperly inverts an implication.  "Is" can mean "implies" or "is a kind of,"  because usage has established that meaning.  But the correct statement would then be "Capacity to do work is energy.  You would never say "A vegetable is a potato," but you know "A potato is a vegetable" is perfectly correct.

And you certainly wouldn't define "vegetable" with "A vegetable is a potato."  Those errant textbook authors are making the same error.  But the error is in a slightly more abstract setting; it's "at the edge of human comprehension."  Furthermore, they have even defended their faulty definition in the teaching literature when other physicists have explained the error.  Those who see the error are often embarrased by those who don't, embarrased for the profession.

The issue has "buzz-saw certainty" embeded in its logic.

And both must be woven into a fabric of scientific thinking.  Warp without woof is unraveled thought.
 
 

Establishing the nature of energy was a matter for experiment.  The ultimate goal of those experiments was to become able to use observation to anticipate some real-world outcomes of things we do in the real world.  This is scientific experiment and requires that we understand how to recognize and deal with multiple influences...and so keep straight those Boolean relationships.

It also requires that we understand how to deal simultaneously with many influences which are further complicated by uncertainty and randomness.  We must understand statistical reasoning.

However, buzz-saw certainty deals with another issue: logical consistency.  When we don't see the logical relationships we can appear ridiculous to those who do see.  Buzz-saw certainty alone doesn't deal with observation, so it can't prove or disprove a hypothesis, such as Laetrile as a cancer cure or the reality of extraterrestrial visits to Earth.  But the logical consistency is necessary, if not sufficient, for analyzing the observational data...and to avoid looking absurd.