The answer:

This is an example of how a) psychiatry has lost its way; b) multiple choice questions are useless.

First, the context of the bipolar question is a CME quiz based on an article: pass the quiz, get CME credits, which the State Board requires doctors to get.  I don't have to take this quiz; but this quiz is accredited as a legitimate means of getting CME, i.e. it is educational.

What multiple choice questions test is synthetic judgments.  It tests, "what is the universe like, actually?"

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An analytic proposition is definitional; a synthetic proposition connects two independent parts that are not contained within one another.

A synthetic truth is one which its opposite can be conceived.  The opposite of an analytic truth is illogical.  So "humans have one head" is synthetic; "humans" and "head" are independent parts, connected.  It's possible humans might have two heads, or none.  "Bald men have no hair" is analytic.  "Bald" means "no hair."

The sentence, "adult AML has higher lethality than childhood AML" is synthetic because "AML" means something concrete that does not contain the notion of higher lethality in adults vs. kids.  "AML has more myelocytes than lymphocytes" is analytic because myelocyte perdominance is contained within the definition of AML.

Saying childhood bipolar has more irritability than adult bipolar isn't synthetic; it isn't additional information about "bipolar."  It is the definition of childhood bipolar.

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Consider the relationship "if p then q."  Therefore, if not q, then not p (contrapositive.)

So which is it:

"If you see X symptoms, it's bipolar."

or:

"If it's bipolar, he has X symptoms."

?

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"If he has X symptoms, then he has bipolar" is logically equivalent to "If he is not bipolar, then he does not have X symptoms."

Or:

"If he has bipolar, then he has X symptoms" is logically equivalent to "If he does not have X symptoms, then he does not have bipolar." 


It's obvious that both pairs of statements are invalid, because on the one hand we are agreeing to label a collection of symptoms as "bipolar" (analytic), but on the other hand we are secretly allowing that we can intuit "bipolar" regardless of a previously agreed upon definition, i.e. the symptoms (synthetic).

Cleverly, we allow ourselves another opening: use the definition to make analytic judgments (he has bipolar therefore he will have manias) and use our experience to make synthetic judgments which alter to the definition (manias may indeed be absent, replaced by irritability), simultaneously.

And we do this because the real meaning of the term isn't what is meant by it, but how we intend to use it.

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"If we had to name anything, we should have to say that it was its use."  When a mathematician sees something that resembles "irritability" what does he call it?  But when a psychiatrist sees something that resembles "irritability," what could he call it?  The mathematician finds the dictionary word "irritability" quite suitable for his purposes; but the psychiatrist can do nothing with the word "irritable" except use it to imply something else.

The sly move is to consider "irritability" to be a modifier of the more general construct "bipolar."  But "bipolar"is actually the modifier of irritability. 

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Maybe you are confused, because your mind is stuck on viewing bipolar as a term independent of the agent who observes it; a term that we learn things ABOUT.  But the meaning of "bipolar" is recursive.

It's pornography, impossible to define except as "I know it when I see it."  But that statement does not mean pornography is "very hard to define, but easy to identify."  It means it is defined, ad lib, by me. 

Synthetic propositions can be learned to be true (or false): "the majority of married men are happier than the majority of single men."  But what can be learned about pornography that is independent of the one experiencing pornography?  "The majority of pornography depicts nudity."  Even the word "majority" is useless since it qualifies a word which is itself a personal judgment.   This is neither a true nor false statement; while I know what "nudity" is, we still don't know what pornography is except that you are now defining it as containing nudity.  But once you choose a definition, can you change it?  Well-- what about a magazine devoted to stocking fetishists that has no nudity-- indeed, possibly no actual people?   Statements about pornography can not be found true or false because the term pornography requires an active subject.  It isn't a noun, it is a judgment about its use.

You mean "community standards." No-- a nude woman in Playboy is "porn--" but the exact same photo in a Soho art gallery seen by the same people may be something else.

"But we all agree, at least, that certain things are pornographic."  But a consensus among individuals isn't truth, it's definition: "we agree to call this pornography."  Until, of course, someone disagrees.  But what is the basis of the disagreement? It is never content, it is always intent: pornography is that which is "intended to elicit sexual arousal."  We disagree about what the purpose of the images are.

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What is the intention of the diagnosis "bipolar?"  To describe something?    As a reason for something?  To imply treatment?

"But you have to agree that if I give a child with bipolar disorder bipolar meds, they get less irritable."  But why not call them "irritability" meds?  If you gave them to an irritable child without bipolar, would they not get less irritable?  Or is it that if you gave them to an irritable child and nothing happened, the child doesn't have bipolar?

"I have a map of an imaginary world in my mind; according to it, you should be able to get to my house in twenty minutes."  The map exists for him, but tells you nothing about the real state of affairs.  And can you rely on such a person to use the term "minutes" the way you expect?

 The term "bipolar"-- whether it exists (as a so far unknown physical pathology) or not-- isn't valid because it says nothing about the world; it only says what the person using it thinks about the world.