Saturday, February 28, 2009

Pope John XXI (Peter of Spain)

I know it does me no good to set up my day's discussion with a bunch of questions if I am going to give you the answer as the title of my posting. But it is fun, and perhaps you will be amused, and even amazed. Especially today.

Q: Who is the only Pope (besides Peter) mentioned as being in heaven in Dante's "Divine Comedy"?
Q: Who was a physician and taught at the University of Siena before he was elected Pope?
Q: Who was "archiater" = Physician to the Papal City, roughly corresponding to "Chief of the Department of Health" before he was elected Pope?
Q: Who wrote one of the first books in the Italian language - on the eye and its diseases and treatments?
Q: Whose poem from another of his books is behind the very strange line in Chesterton's poem "True Sympathy or Prevention Of Cruelty To Teachers" which states:
I wore my Soul's Awakening smile
I felt it was my duty:
Lo! Logic works by Barbara
And life is ruled by Beauty.
[GKC, CW10:486-7]
Huh? "Logic works by Barbara"? You'll see. It really does. But let's deal with these questions first.

Well, yes, you already know who it was. He was called Peter of Spain, though he was born in Lisbon, Portugal, of a man named Julianus, in the second decade of the 13th century (between 1210 and 1220). He studied in Paris and (apparently) also in Montpelier, and sometime between 1250 and 1260 he was invited to the Chair of "Physic" (the Medical school) of the University of Siena, and it was while he taught there that he wrote a book called Summulae Logicales, which became the textbook of logic at most of the Italian universities for the next two centuries.

It is in this book that (I am told) we find this very strange series of words:
Barbara, Celarent, Darii, Ferio.
Cesare, Camestres, Festino, Baroko.
Darapti, Disamis, Datisi, Felapton, Bokardo, Ferison.
Bramantip, Camenes, Dimaris, Fesapo, Fresison.
I may note that there are other versions, at least of the lines after the first, and the version I have may be truncated. But it's the first line that really matters.

Let us say these mystic words together. No, they are not nonsense; in fact, they are quite serious, as you will see in just a moment.

Barbara, Celarent, Darii, Ferio.

Yes, they sound like magic... You won't find them in those books about Hogwarts, but the great logician De Morgan says "They are magic words, more full of meaning than any that were ever made." (De Morgan is well known to computer scientists and all who use Boolean Algebra as well as logicians.) Let's say them again:

Barbara, Celarent, Darii, Ferio.

In these four words you hold the great Master Key of Logic, at least as far as concerns the very important form called the Syllogism. The whole little poem might be called an example of "microcode" (a cunning trick used deep within computers), as their precise spellings - in particular the order of the vowels - gives the specification of the various forms of the Syllogism, and for their reduction to the four forms of the "First Figure".

Barbara = aaa = "All M is S. All P is M. Therefore, All P is S."
Celarent = eae = "No M is S. All P is M. Therefore, No P is S."
Darii = aii = "All M is S. Some P is M. Therefore, Some P is S."
Ferio = eio = "No M is S. Some P is M. Therefore, Some P is not S."

But I do not have the time or space to explain all these very interesting device, since there's much more to tell. (All right, I will give it as a footnote.)

At some point Peter wrote a little book on the eye, Liber de oculo, written in Italian, which showed how much was already known about the anatomy and diseases of the eye in the 13th century.

Peter was made Archbishop of Portugal; after that he was summoned again to Rome to be consulting physician to the Papal Court. It was at this time (September 13, 1276) he was elected Pope and took the name John. He did not reign very long, not even a year, but he dealt with several political issues, yet still continued with his scientific work. You may find that hard to believe, even harder than imagining an ophthalmologist as Pope, but as the e-edition of the Catholic Encyclopedia states,
Amid the cares of the papacy John found time for his scientific studies, which were more congenial to him than the business of the Curia. To secure the necessary quiet for these studies, he had an apartment added to the papal palace at Viterbo, to which he could retire when he wished to work undisturbed. On 14 May, 1277, while the Pope was alone in this apartment, it collapsed; John was buried under the ruins, and died on 20 May in consequence of the serious injuries he had received.
and though he is not canonized, I think we might pray to him as well as for him...

O John XXI,
"...Peter of Spain,
Who through twelve volumes full of light descants."
[Dante, "Paradiso", Canto XII, 135]
You who were author, physician, ophthalmologist, logician, and Pope, beg God to give us light and logic.



For more information, please see here; I also used Walsh's Catholic Churchmen in Science, Second Series, The Popes and Science, and Shallo's Scholastic Philosophy.

And now, on the "microcode" of Barbara and the rest:

Meanings of the letters:

a = "All X is Y"
i = "Some X is Y"
e = "No X is Y"
o = "Some X is not Y"

(These are the vowels from affirmo = "I affirm, say yes", and nego = "I deny, say no".)

The initial letter of the word specifies which of the four forms of the "First Figure", which are valid syllogisms:

B (Barbara) = "All M is S. All P is M. Therefore, All P is S."
C (Celarent) = "No M is S. All P is M. Therefore, No P is S."
D (Darii) = "All M is S. Some P is M. Therefore, Some P is S."
F (Ferio) = "No M is S. Some P is M. Therefore, Some P is not S."

The other letters (in the second, third, and fourth lines) are the "instructions" which show how to convert each form into one of the First Figure.

m - transpose the premises (exchange S and P)
s - convert the preceding vowel "simply" (exchange the left side and right side of the "is" in that statement)
p - convert by "limitation"
k - apply "indirect reduction" (this means showing the trutb by assuming the contradictory, and showing that the assumption leads to absurdity)

Here's an example from Shallo:
S: All stars are self-luminous bodies.
P: No planets are self-luminous bodies.
Therefore, no planets are stars.

This is a syllogism in Camestres; it is reducible to Celarent. The first s indicates that the minor is to be simply converted; the m that this new minor is to change places with the former major; the last s that the conclusion is to be simply converted, thus:

S: No self-luminous bodies are planets.
P: All stars are self-luminous bodies.
Therefore, no stars are planets.


At 06 April, 2010 15:17, Blogger Pedro Beirao said...

John XXI was called "Petrus Hispanus". "Hispania" was the roman name for the whole Iberian Peninsula, and not only Spain, which exists as a country only since the 15th century. Portugal is much older, it was founded as a kingdom in the 12th century.


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