logic of substitutes in ancient materia medica

Medical practice created a demand for knowledge of substitutes among materia medica.  A sphere of knowledge competition in ancient medicine stretched from southern Spain to India and from northern Greece to northern Africa.  Across this vast geographic expanse, a medicinal herb found in one location might not be readily available in another location.  More generally, the cost of medicines promoted demand for substitutes.  Some medicines, such as theriac, consisted of many exotic ingredients and were very expensive.  At the same time, physicians sought to provide medicine for the poor. Cheap substitutes for expensive medicines helped physicians to serve the poor.

Some ancient lists of substitutes among materia medica have a simple propositional form.  They consists of lists of pairs of medical substances.  A focal medical substance is paired with its substitute.[1]  The earliest surviving list of substitutes among materia medica has such a form.  It exists as a chapter in the influential, seventh-century Medical Compendium in Seven Books, by Paulus Aegineta.  In Baghdad early in the eighth century, the Jewish physician Māsarjawaih produced in Arabic a formally similar list of substitutes.  Māsarjawaih, thought to have been the first to translate a scientific book into Arabic, apparently was an important scholar.  His list of substitutes thus probably garnered considerable attention in the ancient world.

What is the logical structure of the substitute propositions individually and as a list?  A substitute might be equivalent to the focal medicine.  That’s often the case today for a brand-name drug and a generic drug.  But a substitute might also be a useful but inferior replacement for the focal medicine.  Expressed in logical formalism, if the substitute for A is B, does that mean A = B,  or does it mean A > B?  What about if the substitute for A is B, and the substitute for B is C, then is C also a substitute for A?

Paulus Aegineta’s substitute list shows no awareness of these logical issues of substitution.  Paulus Aegineta attributes to Galen the substitute list that he reproduces.  He introduces the list with the following text:

In Alexandria, he {Galen} says, wishing to obtain the campion (lychnis) for a certain woman who was in danger, and not having got it, if I had not found and used the seed of acanthium, the woman would have been soon lost.  Hence, having been requested by my companions, I made out a list of the medicines which may be substituted for one another, in order, beginning with this same article: [2]

After the list, Paulus Aegineta appends this commentary:

Commentary. This is taken from a work ascribed to Galen, the authenticity of which, however, is very doubtful.  Cornarius has attempted many corrections of the text, and we have found ourselves compelled to make other alterations.

The introductory text, with the exception of the apparently inserted “he says,”  seems to have come from Paulus Aegineta’s source.  Its claim “if I had not found and used the seed of acanthium, the woman would have been soon lost” has the ring of authentic Galenic self-promotion. More importantly, both Cornarius and Paulus Aegineta have critically reviewed the list.  Nonetheless, the first substitute pair listed is “Instead of  {for} the seed of acanthium, campion (lychnis).”[3] That substitute-pair statement suggests that seed of acanthium would be used if both seed of acanthium and campion are available (no need for a substitute).  Galen, in contrast, apparently would choose campion in such circumstances.  If seed of acanthium and campion are medically equivalent substitutes, then the choice of one or the other has no medical significance.

If the substitutes in Paulus Aegineta’s list are medical equivalents, then its materials would be more usefully placed in equivalence classes, rather than pairs.  Paulus Aegineta’s list contains 41 repeated materials.  These repeated materials imply equivalence classes with more than two members.  For example, Paulus Aegineta’s list includes these pairs (preceding number is the pair sequence number and  A => B indicates that the substitute for focal medicine A is B):

 45: diphryges => Phrygian stone
105: magnet => Phrygian stone
106: Phrygian stone => agerat
128: roasted misy => diphryges

If the substitute relation is an equivalence, then these pairs imply the equivalence class {diphryges, Phrygian stone, magnet, agerat, roasted misy}.  Presenting the substitutes as pairs obscures some of the facts, e.g. that a substitute for roasted misy is Phrygian stone.

Moreover, in Paulus Aegineta’s list, no materials repeat as the focal medicine in different pairs.  Materials are either a focal medicine and a substitute, or a substitute for two different focal medicines.  That lack of symmetry in the pairs is contrary to the symmetry of equivalence.[4]

Internal evidence in Māsarjawaih’s list suggests that its substitute pairs are not equivalences.  Māsarjawaih’s list contains 15 repeated materials.  All these repeated materials occur once as the focal medicine and once as the substitute medicine (except for oil of radish, which occurs twice as a substitute).  In Māsarjawaih’s list, as in Paulus Aegineta’s list, no material is repeated as the focal medicine.  Moreover, in Māsarjawaih’s list, the repeated elements are arranged in adjacent pairs, with the repeated element as the substitute in the first pair, and as the focal medicine in the second pair.[5]  That textual arrangement fosters an inference of transitivity and thus a substitute preference order.  For example, consider these pairs from Māsarjawaih’s list:

7: crystalline sugar => dry black plum
8: dry black plum => tamarind [6]

The arrangement of those pairs supports the inference that tamarind is a substitute for crystalline sugar, but an inferior substitute relative to dry black plum.

References to groups of medicines in Māsarjawaih’s list also suggests that the pairs are not equivalences.  Māsarjawaih’s list contains six instances of “all of these {with or without further specification}” and two instances of “both of these”.  All eight of these grouping occur in the focal position.  That’s consistent with the focal position being superior to the substitute position.  A physicians looking for a substitute chooses not among focal medicines, but among substitutes.  Specifying multiple inferior medicines would not instruct a physician’s choice among those inferior medicines.

Māsarjawaih’s list contains some inconsistencies.  Consider these pairs:

 98: leech => place cupping glass on the spot affected by a snake, scorpion, a kind of worm, and dalmukha
 99: inspissated juice of artichoke => nux vomica
100: both of these => borax and mustard

The grouping “both of these” most plausibly refers to “inspissated juice of artichoke” and “nux vomica.”  However, with the transitivity that the list suggests overall, pair 100 could be more simply specified as “nux vomica => borax and mustard.”  The transitive inference would generate the same substitute relation as the grouping “both of these.”  A more surprising specification is this:

49: caper => caper with pure honey or caper with oxymel or mountain mint

The substitute apparently encompass the focal medicine.  That makes no sense.

Specifying medical substitutes as a list of pairs of materials has weighty medical weaknesses.  Medicine is typically used to treat a specific sickness.  That specific sickness is likely to be relevant to the best substitute medicine.  Specifying substitutes without respect to quantities also seems irrational: the potencies of materia medica surely vary.  Other ancient specifications of substitutes provide details on the medical application and relative quantities.[7]

The systemic shortcomings of ancient medical substitute lists suggest a more general systemic problem.  Ibn Abi Usaibia’s History of Physicians indicates that ancient physicians commonly studied logic and could have applied it to lists of medical substitutes.  Nonetheless, even a highly sophisticated, extraordinarily comprehensive pharmacological treatise from the twelfth century seems not to have considered the logical relation between substitute claims.[8]  Systemic reasoning has less direct personal return than pursuing particular interests.  That’s as true in intellectual reasoning as it is in government budgeting.

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Data: substitutes among materia medica according to Paulus Aegineta and Māsarjawaih (Excel version)

Read more:

• the ancient pharmaceutical profession
• formulating medicines for the poor
• astrology and medicine closely related in the ancient world

Notes:

[1] Usually the medical substances are what’s called simple medicines — a single plant, animal, or inorganic material.

[2] Bk 7, Sec. 25, trans. Adams (1844) p. 604.  What the Galenic text means by “in order” isn’t clear.  The pairs in this list are much less ordered than in Māsarjawaih’s list.  In addition to the ordering of pairs with repeated materials (described above), Māsarjawaih’s list also groups pairs by non-medicinal characteristics, e.g. robs, electuaries, oils, clysters, galls, etc.

[3] Levey’s example translation of Paulus’ list is “For A, B.” Levey (1971b) p. 10.  That A is the focal medicine is consistent with the position of repeated materials across the lists of both Paulus and Māsarjawaih.

[4] Pythagoras’ list of substitutes, which was valued enough for Hunayn ibn Ishaq to translate in ninth-century Baghdad, explicitly identifies substitute equivalences with a separate pair and often the descriptive tag phrase “in turn.”  See Levey (1971b) pp. 24-5 (mugwort and camomile), pp. 28-9 (common germander and Hart’s Tongue fern; white mustard and gum ammoniac; black nightshade and knotweed) pp. 30-1 (gum of the olive and black cumin).

[5] Such pair adjacencies occur in Paulus’ list (see, e.g. above pairs 105 and 106 with Phrygian stone), but adjacent pairs with repeated materials are much less frequent than pairs with repeated materials that are widely separated in the pair list sequence.

[6] For Māsarjawaih’s list translated from Arabic into English, see Levey (1971b) pp. 35-45.  The list describes the pairs with sentences of the form, “The substitute for A is B.”

[7] See the substitute lists of Pythagoras and al-Rāzī  in Levey (1971b).

[8] Ibn Baklarish was a leader in compiling information on medicines.  According to Ibn Abi Usaybiah:

Ibn Baklārish was a Jew, one of the greatest medical savants in Andalusia, who possessed vast experience and knowledge in the field of simple medicines. He served the dynasty of Banū Hūd as physician. Among his books is a “Synopsis of Simple Medicaments” with an index; this was composed in Almeria for al-Musta`īh bi-Allāh Abū Ja`far Ahmad ibn al-Mu`amin bi-Allāh ibn Hūd.

HP p. 644.  Levey (1971a) reproduces a few pages from ibn Baklarish’s monumental twelfth-century book on simple medicines.  That book shows mace gum as a substitute for sarcocol, and sarcocol as a substitute for marine sponge.  These relations imply that mace gum is also a substitute for marine sponge.  But ibn Baklarish didn’t list mace gum as a substitute for marine sponge.

References:

Adams, Francis. 1844. The seven books of Paulus Aegineta, tr. from the Greek, with a commentary embracing a complete view of the knowledge possessed by the Greeks, Romans, and Arabians on all subjects connected with medicine and surgery. London: Sydenham Society.

HP: Ibn Abi Usaybi’ah, Ahmad ibn al-Qasim. English translation of History of Physicians (4 v.) Translated by Lothar Kopf. 1971. Located in: Modern Manuscripts Collection, History of Medicine Division, National Library of Medicine, Bethesda, MD; MS C 294.  Online transcription.

Levey, Martin. 1971a. “The pharmacological table of ibn Biklãrish”. Journal of the History of Medicine and Allied Sciences. 26 (4): 413-21.

Levey, Martin. 1971b. Substitute drugs in early Arabic medicine. With special reference to the texts of Māsarjawaih, al-Rāzī, and Pythagoras. Stuttgart: Wissenschaftliche Verlagsgesellschaft.

[image] Thanks to the Historical Collections & Services, Claude Moore Health Sciences Library, University of Virginia, for making the above image available on the web.