Margaret Masterman, George Boole and the Holy Trinity:

a brief intro to her article in Theoria to Theory

I know little about Margaret Masterman, beyond the fact that she was a Cambridge philosopher who wrote a fascinating piece, "Theism as a Scientific Hypothesis", which ran in four parts in a somewhat obscure and difficult to find journal, Theoria to Theory, Vol 1, 1-4, 1966-67. I believe this was intended as the first half of a longer work, but I haven't seen the rest of it, either in the jounral or in book form. If it exists, I would love to hear about it.

In the third part of her article, published in April 1967, she talks about George Boole's fascination with the idea of "three" -- he apparently wrote a "sonnet to the Number Three" which echoes the sentiments of St. Gregory Nazianzen on the Trinity: "the ineffable radiance common to the Three". And she also reproduces a variant on the Trinity "graph" shown below, which I tend to think of as a "mediaeval rendition of a HipBone Game played in heaven":

She proposes that this image (versions of which are commonly found in mediaeval churches) can be mapped onto a Boolean lattice / Hasse diagram of eight elements -- and that a "reading" of this diagram in terms of Boolean algebra "translates" into theological propositions concerning the persons of the Trinity which are remarkably coherent with those in the Athanasian Creed...

Masterman's article is part of a longer work, "Theism as a Scientific Hypothesis"... a very quirky and individual synthesis of zen koans and Boole, icons as the American philosopher Peirce used the term and icons in the Russian Orthodox sense... addressed to a mixed audience of theologians and scientists.

This is fascinating stuff, although she goes into enough different disciplines that it's hard for me to follow her.


Masterman's longer work is concerned with the philosophy of science, and argues (if I am reading her correctly) that at least some examples of scientific creativity can be considered "revelatory" in the same sense in which, say, Julian of Norwich's religious "Revelations of Divine Love" might be so considered.

This is an intriguing point, and goes to the heart of what we mean by the word "inspiration".

Masterman pursues it both because she feels this "revelatory" quality in science needs to be invited into the spiritual chorus, so to speak, and recognized as "valid revelation" in theological terms, and also because she feels that it needs to recognize itself as belonging there -- while also clarifying for the scientific side of her audience that the same quality in religion is necessarily "apophatic" and paradoxical, because it properly dwells in mystery, not in formulations.

Masterson cites Boole's Idempotency Laws, "xx = x" and "x to nth power = x", as an example of a possible "revelatory" insight, and suggests that they are in effect western "koans" -- meditative devices which use paradox as a springboard to insight.

She also writes of Boole himself:

Towards mathematical truth he had indeed a consciously religious attitude, which he sometimes expressed to himself by the phrase, 'For ever, O Lord, Thy word is settled in heaven.' Boole's behaviour during his last illness was characteristic of the man... When his mind had been wandering in fever, he told his wife that the whole universe seemed to be spread before him like a great black ocean, where there was nothing to see and nothing to hear, except that at intervals a silver trumpet seemed to sound across the waters, 'For ever, O Lord, Thy word is settled in heaven.' And as he lay in bed on the borders of delirium, all the little sounds of the house, such as the creaking of doors, resolved themselves into a chant of these words, which expressed for him the excellence of mathematical truth.


Her scheme for creating a Trinitarian "icon" out of Boolean algebra and medieval iconography can be found in pp 240-46, Theoria to Theory, Vol 1, 3rd Quarter, April 1967.

In the immediately preceding passages, she has been dealing with the idea of *icon* as it appears in the American philosopher Charles Sanders Peirce, and in Orthodox use as in the works of Vladimir Lossky.

When she discovered that Boole had written a sonnet on Three, Masterman apparently decided to play around with the triads (111; 110, 101, 011; 100, 010, 001; 000), and formed them into a Hasse Diagram (Hasse's Bead Game?), which tells us some things about the triads in Boolean terms.

Then a friendly nun, one Mother Geraldine Mary SSM -- (this must have been some conversation) -- suggested she look at a schematic of the Godhead and Three Persons in a 1914 Oxford University Press book on English Churches: Francis Bond, *Dedication of English Churches*. MGM further suggested that MM try mapping the "Trinity" schematic in Bond's book onto her Boolean lattice (Hasse diagram), which she did.

Then, just as if a series of algebraic equations were being given possible arithmetic equivalence, she found that the Hasse / Boole relations of "summum" and "infimum" of x and y (where x and y were triads) read out when translated into theological jargon into what are effectively "Athanasian" credal formulae describing the relationship between the three "Persons" of the Christian Godhead and the Godhead itself.

Consider: if "threeness" is present in both number theory and in theology, is there any reason why the Boolean "summum-atque-infimumness" derivable from threeness shouldn't be, also?

Finding that parts of the Athanasian Creed "correspond" in some way with a piece of elegant math is interesting of course, but at best -- from a theological perspective -- it reinforces what has already been envisoned and formulated in the creeds.

One particular aspect of the correspondence turned out to be of particular interest: the mathematics of the diagram when "translated" into theological terms clearly excluded the disputed "filioque" clause -- the "proceeding" of the Holy Spirit from *both* the Father and the Son. Finding that the Filioque doesn't "add up" in this translational system might -- if it's not circular reasoning -- provide an external-to-theology suggested answer to a within-theology vexed question, and that would be interesting in and of itself.

It should be noted, however, that Masterman herself allows that not all the relations permitted in her algebra make theological sense. In a comment towards the foot of p 342, Theoria to Theory, Vol 1 4th Quarter, July 1967, she admits that not all the logical conclusions that can be drawn from her Hasse diagram correspond to "valid" theological ideas.


For those who are interested in the theological side of all this, Masterman also compares the Trinity to a koan in zen, citing the Orthodox theologian V Lossky:

Theology will never be abstract, working through concepts, but contemplative: raising the mind to those realities which pass all understanding. This is why the dogmas of the Church often present themselves to the human reason as antinomies, the more difficult to resolve the more sublime the mystery which they express. It is not a question of suppressing the antinomy by adapting the dogma to our understanding, but of a change of heart and mind enabling us to attain to the contemplation of the reality which reveals itself to us as it raises us to God... The highest point of revelation, the dogma of the Holy Trinity, is preeminently an antinomy. To attain to the contemplation of this primordial reality in all its fullness, it is necessary to reach the goal which is set before us, to attain to the state of deification.

Incidentally, since Masterman's "triads" are also the familiar "trigrams" of the I Ching, it might be interesting to make a similar mapping of the "meanings" and "relations" of the trigrams onto Masterman's Hasse diagram, and see whether the results had a similar congruence with Chinese commentaries on that venerable work.

Charles Cameron

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