5. SCALING IT UP: WORDHOOD SQUARED?

(Part of a series based upon Stiles, The Anatomy of Medical Terminology (Radix Antiqua 2015; copyright 1993; ISBN 978-1-988941-240; to be revised by Stiles and Russell 2017)

            Before the invitation to controversy, the pragmatic conclusion to the third post was that we can generate real (but unattested) words in Medical Terminology by means of rules based upon well-established words:  "For example, since any word of the form X-ectopia means 'the displacement of x,' we might postulate a...rule:

                        If generic OSTE-ectopia is a real word

                                    (where OSTE- denotes 'a bone' or 'bones'),

                        then the set of all real words in Medical Terminology also includes

                        all words x-ectopia

                                    such that 'x' names any one (or several) of the (more than two hundred)

                                    specific bones found in the human body."

            From here on in, I am going to take it as given that you are at least willing to consider the wild idea that, "while the reality of the CONCEPT named by a specific word generated by one of our rules might be disputed by anatomists, or by logicians--or perhaps welcomed by surrealist painters--(what exactly would 'the displacement of the skull' look like, anyway?), no such dispute calls into question the reality of the WORD itself."

            Still reading?  Good, because these premises bring us, by a long way around, to consideration of the possibility of "meta-rules" that could generate much larger sets of words. To begin, the existence of a single rule like the one about generic oste-ectopia would seem to suggest that other rules could be formulated by an analogy that as it were takes us off in a direction which (by another, related analogy!) represents another dimension.

             To see this in action, consider that the combining form oste- meaning "a bone or bones" (as opposed to the substance "bone") begins at least 30 words listed as main entries in any large Medical Dictionary.  This means we should be able to postulate at least 30 additional rules, in each case replacing -ectopia in the previous rule by one of those 30 word-remnants; thus we should be able to write analogous rules introduced by, for example,

            OSTE-otomy                            the cutting of a bone; or

            OSTEO-neur-algia                    pain involving the nerves of a bone; or even

            OSTEO-lipo-chondr-oma         a tumor involving cartilage and fat, involving a bone.

            So far so good.  But perhaps we could better describe this much larger set of real words by one new "meta-rule," a much more abstract one formed again by analogy to those we have already derived:

                        If generic OSTE-Z  is a real word in Medical Terminology

                                    (where OSTE- denotes "a bone" or "bones" AND

                                    where "Z" stands for the word parts added to it to form a real word):

                        then the set of all real words in Medical Terminology also includes

                        all words x-Z such that "x" names any specific bone or bones.

This plan would save us writing out all the individual rules we would have otherwise been forced to generate separately.  Caution is required however; note that we have dramatically increased or "scaled up" the number of real but perhaps unattested words we are describing by our new rule, from something in the neighborhood of ("on the scale of") 200 words in the case of oste-ectopia to (very) approximately 200 times 30 = 6,000 words in the case of x-Z.  This is a difference in "order of magnitude"--a difference of scale.  The very number suggests caution, in that, by the act of changing scale, we make it difficult to spot any small or "local" constraints emanating from the smaller scale--at the scale of, say, oste-ectopia--while at the same time distortions or problems caused by such constraints might seem to be themselves "scaled up."

            But before I get us all any more confused, let's consider an actual example.  Can we substitute the name of just any bone at all for the generic osteo- in the case of

            OSTEO-arthri-tis          the inflammation of a joint, involving a bone or bones?

That is, would a simple rule made on the direct analogy of oste-ectopia generate a full complement of words on the scale of 200?   Or would the words in this particular subset be limited to those bones which can be said to be "involved" with other bones in the structures called "joints?"  Given our lack of expertise, we will have to leave such distinctions to the anatomists (and the logicians!).  But we can postulate the constraint, even if we can't specify the details of its real-world application; and (here is the really cool part) even though the number of words generated by the specific "level one" rule based on osteo-arthr-itis might be seriously affected by this constraint, the scale of the number of words in the subset generated by the "meta-rule" is not: if the rule predicts "around 200" words and observable constraints limit the number to (a guess, to make the point) 100 words, that is huge difference between hypothesis and "reality."  But if the rule predicts a number "on the scale of 6,000" words and observable constraints limit that number to, say, 5,900 words, the difference is not as important--the rule is not seriously challenged.  To put the finishing touches to the discussion at this point we would need to add a statistician to our pool of expert consultants; but the general point remains I think valid.

            A more serious objection might be made on the basis of an extant dictionary word (one of the 30 or so of the form oste-Z) like

            oste-otom-e                an instrument for cutting a bone.

The related word or "parallel" word, denoting the surgical operation which the instrument is used for, namely,

            oste-otom-y                 the cutting of a bone,

is an excellent individual example of our "meta-rule;" we can easily imagine a perfectly real word denoting "the cutting of x" where x names any specific bone or bones--if you can cut one bone, you can cut 'em all!  But can we say the same for the instrument used for that operation?  To perform an operation called

            femor-otom-y              the cutting of the femur

would we really need to go and find ourselves a clean

            femor-otom-e             an instrument for cutting the femur,

or would any old osteotome do the trick?

            Pretty clearly, we've just lost us another 200 or so words!  But one last time, at the scale at which our "meta-rule" is operating, does the loss of a few hundred words make much difference?

            And finally, can't you imagine an imaginary scenario in which the tense surgeon, after hours of careful cutting, and sawing, and filing away at a stubborn femor mutters to her aides, "pass me the damn femorotome!"--and, if someone else without a second thought reaches for the osteotome?  The only real test of the reality of a linguistic utterance, after all, is whether one of us might utter it and another of us understand it. 

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