Thursday, March 12, 2009

Fuzzy Logic and the Church We Know (I)

There are two kinds of people in the world, those who believe there are two kinds of people in the world and those who don't.
Robert Benchley, Benchley's Law of Distinction
US actor, author, & humorist (1889 - 1945)
But there really are two kinds of people in the world when it comes to logic: those who use the traditional, Aristotelian kind, and those who use "fuzzy logic". Here are some examples:

Aristotelian logic:

The Anglican Curmudgeon is a member of the Episcopal Church (USA).

The Episcopal Church (USA) is Anglican.

Therefore, the Anglican Curmudgeon is Anglican.

Fuzzy logic:

The Anglican Curmudgeon says he is both Anglican and Episcopalian, but I don't like the Curmudgeon's binary logic---it's too "either/or".

Who's to say what it means to be Anglican? Or Episcopalian, for that matter?

That's why I am proud to be Episcopalian---and Anglican, too; just not the kind of Anglican that the Curmudgeon is.

Here is another set:

Aristotelian logic:

A covenant is a solemn agreement that is binding on those who sign it.

A covenant is being proposed for the member churches of the Anglican Communion.

Therefore, if the member churches of the Anglican Communion adopt the covenant, it will be binding on them.

Fuzzy logic:

A covenant is a fine thing, but who's to say what it means? And who's to enforce it?

Now, take the Covenant for Communion in Mission proposed by IASCOME---that's a covenant I could live with.

So let's all sign the Covenant for Communion in Mission---then we can go right on with what we are already doing.

As you can tell from these examples, fuzzy logic has no problem embracing what Aristotelians, in their binariness, would call "illogic". Traditional Aristotelians swear by "the Law of the Excluded Middle": something is either A or not-A; it cannot be both A and not-A at the same time. Those who are comfortable with fuzzy logic, however, do not recognize any such law; it bothers them not a whit, for example, that the Episcopal Church can claim to be Anglican while disregarding the Communion's advisory expressed in the 1998 Lambeth Conference's Resolution 1.10. "After all, it's not binding on us, it's only advisory." 

Fuzzy logic has always been with us (witness Adam and Eve's decision to taste the apple on the word of a talking serpent, or Pharaoh's thinking, after about the fifth or sixth plague, that he could continue to do as he had been doing, or the Buddhist teachings that a rose is empty, because it is made of non-rose elements, or that good is made of evil, and evil made of good). In recent years, however, fuzzy logic has (paradoxically) become more systematized, and has been harnessed to work in everything from washing machines to rice cookers.

The methods of fuzzy logic were first analyzed in depth by Lotfi A. Zadeh, a professor in the Department of Electrical Engineering at U. C. Berkeley, where he has taught since 1959. Beginning in the 1960s, he published a series of pathbreaking articles that explored the usefulness of assigning "truth-values" in electrical circuits that were between the binary off or on values of zero and one, respectively. As summarized in this article, the principles of fuzzy logic that he established are these:

  • In fuzzy logic, exact reasoning is viewed as a limiting case of approximate reasoning.
  • In fuzzy logic everything is a matter of degree.
  • Any logical system can be fuzzified
  • In fuzzy logic, knowledge is interpreted as a collection of elastic or, equivalently, fuzzy constraints on a collection of variables
  • Inference is viewed as a process of propagation of elastic constraints.
Don't worry if the technical jargon goes over your head. The most important principles which Professor Zadeh discovered are these: In fuzzy logic everything is a matter of degree, and: Any logical system can be fuzzified. (Meaning: any logical system can be modified to deal with truth-values between 0 and 1. Thus water can be 0.75 "hot", instead of just "hot", or 0.33 "cold", instead of just "cold". Think what kinds of possibilities this opens up for programming a washing machine.) With that discovery, the Law of the Excluded Middle was no longer a law, but only an axiom of one (non-fuzzified) type of logic, called quaintly, "Aristotelian".

I submit, after considerable research on the Web, that the difference between Aristotelian and fuzzy logic is what is largely responsible for the current divide between religious liberals and religious conservatives (to go back to some quaint old terms for a moment). Fuzzy logic developed in the 1960s, just in time to become part of the academic toolset (and later mindset) in the 1970s and 1980s, when many of our current clergy graduated from seminary (and our current lay deputies and officials graduated from college). In the process, the traditional truth-values of theology became "fuzzified"; this also happened to coincide with the spread of evolutionary theory to explain the entire spectrum of life, and to make "the God hypothesis" optional. (Please do not get me wrong: I am not a creationist; I believe in evolution. I am not convinced yet, however, that randomly guided evolution per se explains the emergence of life just 400 or so million years after the earth formed, to say nothing of the beginning, some nine or so billion years before that, of the universe in which we find ourselves.)

Science naturally resists binary truth, or I should say: welcomes fuzzy logic, because measurement rarely results in a whole number. (I remember a science cartoon by that master of the genre, Sidney Harris, which showed a group of white-jacketed technicians all standing next to a giant (old-style), room-filling computer with a long paper tape coming out of it. One technician is looking at the end of the tape, and announces to the rest: "It says the answer is '2'.") Kurt Gödel's famous proofs of his incompleteness theorems indeed removed the last basis for believing that scientific statements were either true or false, and in doing so undermined Karl Popper's entire doctrine of falsifiability

One subject which is antithetical to fuzzy logic is my own discipline: law. In law (unlike real life), a person has to be either guilty or not guilty of the offense as charged. The traffic light is either red, yellow, or green, and not any shade in between; and a declaration of trust is either signed and valid, or is invalid (for any of a number of possible reasons). The law is very uncomfortable in dealing with ambiguity: it is the court's task (and sometimes an extremely difficult one) to decide just what the words of a contract mean, based on the testimony and other evidence offered of what was going on at the time it was signed, and how the parties themselves interpreted it before they came to disagree. 

Present-day law itself developed out of the Roman church's canon law, which in turn grew out of the digests of Roman law prepared under Justinian. There is thus an intimate connection between law and religion, even though today the law goes to great lengths to deny it (witness how the Supreme Court is all over the map in deciding whether religious displays in civic places violate the First Amendment, and how suits are brought to challenge mottos like "In God We Trust"). And in the church itself, law finds its expression, as it has for centuries, in the system of canon law by which a church agrees to be governed. At the same time, churches have to observe and respect the system of secular law that governs the country in which they function. So it is simply not possible to divorce law from the church.

But what is a church to do with a canonical phrase like "If a Bishop abandons the communion of this Church . . ."? What does the canon (IV.9, as currently numbered; it will probably be renumbered as a result of changes proposed for General Convention this summer) mean by those words? (The definition which the canon itself gives has recently been entirely eroded, as I explain in detail here and here.)

With this particular Canon, we run into our first problem. In law, it would be the function of a judge to interpret the language and to rule what it means. If one party does not agree with the judge's ruling, that party has a right to appeal the decision to a higher court. (As one federal district judge once reminded me, long ago: "Counsel, I get paid just to make a decision. The Ninth Circuit [Court of Appeal] gets paid to make it right.") But there is no counterpart to a judge in proceedings under Canon IV.9, because there is no trial. So who interprets the Canon, in the case of a bishop charged with abandonment?

If you read the Canon, and its related provisions in Title IV, you will find that it is interpreted by no less than hundreds of people in the course of its being applied. First the Presiding Bishop receives a complaint and decides whether to forward it to the Title IV Review Committee. That Committee, consisting of five bishops, two priests, and two lay members of the Church, in turn decides by majority vote whether to certify a charge of abandonment to the Presiding Bishop, who then has to record it. The Presiding Bishop next refers the certification to the three senior bishops in the Church, who must all agree to inhibit the bishop in question, based on the charges.

Until very recently, therefore, there were thirteen people who reviewed any charge of abandonment of communion, and it took the approval of at least nine of them, including the Presiding Bishop and all three of the senior bishops, to refer a charge of abandonment to the full House of Bishops for consideration. (Recently, however, by applying fuzzy logic, the Presiding Bishop decided that the concurrence of the three senior bishops was unnecessary to the process, because three bishops should not be allowed to exercise a veto over what she and the other active bishops wanted to do.) 

Once the charges of abandonment are brought by the Presiding Bishop to the House of Bishops, the Canon then requires that a majority of all the bishops entitled to vote in the House---that is, a majority of all the active and resigned [retired] bishops in the Church, of which combined there are approximately 300---must vote to depose the bishop on the charge of abandonment before sentence of deposition may be pronounced by the Presiding Bishop. (Once again, however, the Presiding Bishop has applied fuzzy logic to the language of the Canon, and decided that all that is needed is a majority of the number of bishops who actually show up for a meeting of the House and are present on the floor at the time of the vote. Otherwise, you see, the Canon would be "unworkable" in the current state of the Church, where so many retired bishops do not bother to show up for meetings, and she could never get a majority to approve her deposing anyone.) 

Thus this process has no parallel in the law at all, unless it would be the impeachment of a sitting President---but that is not a judicial process, either. There is no one body in the Episcopal Church (USA) which has the power to interpret Canon IV.9 in a definitive and authoritative (binding) manner. General Convention does not sit in judgment on a bishop; all it can do is change or amend canons which practice shows are ambiguous. The House of Bishops might be considered as such a body in the case of Canon IV.9, except that it no longer meets with a full complement of bishops who are canonically entitled to vote. (The last time it did so meet to depose a bishop, in the case of Bishop McCoskry of Michigan in 1878, the meeting had to be adjourned several times until enough bishops could be brought back from their vacations to make the required majority of the whole number entitled to vote. See the description and links in this post.) The House of Bishops alone has no authority to amend a canon, nor has it attempted to issue any definitive "opinions" on the interpretation and application of canons since the early nineteenth century, when it numbered in the few dozens and was far more collegial than at present.

The situation is thus ripe for the intrusion of fuzzy logic, since there is no definitive authority to gainsay what the active minority of bishops, led by the Presiding Bishop, have decided they want to do, regardless of what the canons actually say. (They are a minority, because even the 88 who voted last September in favor of the deposition of Bishop Duncan fall well short of a majority of the 300 or so bishops who have a seat and a vote in the House.) And while fuzzy logic may work wonders in washing machines and rice cookers, it can only erode, and eventually destroy altogether, the binary certainty provided by the rule of law as it has traditionally been followed in the Church. 

There is so much more to say on this topic; I have barely scratched the surface. In future posts in this series, I will examine the effects of fuzzy logic as applied to the interpretation of Holy Scripture, and to the role of the Church in the Anglican Communion. I will also have more to say about the degradation that fuzzy logic is having on the ECUSA Constitution and on other canons, and the implications that degradation has for the polity of the Church itself. 

[UPDATE 03/12/2009:
The Anglican Communion Institute has now posted a statement on the degradation in the Church's polity which has resulted from the Presiding Bishop's decision to use her office to accomplish end-runs around the Constitution and canons:

. . . The complaint [in the Pittsburgh litigation---see this post for details] proffered by the Presiding Bishop’s chancellor seeks to turn The Episcopal Church’s governance on its head and asks the court to enshrine this reversal in civil law. It alleges that the polity of The Episcopal Church has as its highest tier of authority the central bodies of the Presiding Bishop, General Convention and Executive Council. Underneath this triumvirate on “the next level” are the dioceses and their bishops. Dioceses are explicitly characterized as “subordinate unit[s].”

These allegations could hardly be more incorrect. The Episcopal Church is after all called The Episcopal Church, not The Synodical Church, The Convention Church or The Executive Council Church. This name reflects both the legal reality of The Episcopal Church’s constitution and the ecclesiology of an apostolic church. The constitution of The Episcopal Church does not purport to define the authority of a bishop, who possesses the inherent authority of the office of successor to the apostles. The Historic Episcopate has long been recognized as an essential, non-negotiable element of Anglican identity. The polity of The Episcopal Church, clearly expressed in its name, its constitution and its history, is that of dioceses and bishops meeting in a general convention as equals. The Presiding Bishop and the Executive Council are the agents, not the superiors, of the dioceses.

As the ACI indicates, what is happening at the national level of ECUSA is a unilateral attempt by the agents of the dioceses to become their masters. In the short course of just 220 years, ECUSA will have gone from a voluntary association of equals to an involuntary and rigid hierarchy under the absolute power of a metropolitan. Dioceses which refuse to take note of what is happening will be swept along in the current, unable or unwilling to emerge from the fog of fuzzy logic now enveloping them.]


  1. Normally I tend to agree completely with your reasoning. Having employed "fuzzy logic" repeatedly, however, may I say that it is (rather non-intuitively) a way of creating deterministic algorithms to usefully extend Aristotelian logic to systems that are not necessarily binary, though any useful model can be reduced to binary, otherwise we couldn't model it with an algorithm that executes on a binary machine..
    It seems that those of a post-modernist outlook rely on the uncertainy principle, which, while experimentally provable, is only of application when the problem domain is vanishingly small, (within the region of quantum effect) and is completely inappropriate ( read, fails to create a useful model) for application to systems in the classical domain in which we interact.

  2. I have to admit that I didn't have time to read the entire post, but I will comment on the opening examples of Aristotelian and fuzzy logic, as well as the status of I.10.
    The first example puts me clearly in the Aristotelian camp although I would change the second statement to "The Episcopal Church (USA) belongs to the Anglican Communion." One can assert that being Anglican does not require being part of a Church that belongs to the Communion, but that makes "Anglican" a fuzzy word in my book.
    As to the second set of statements, I would also place myself in the Aristotelian camp, which may be why I would want Episcopalians to be honest about what sort of covenant we could accept as binding. I think the fuzzy logic statements about covenant are rather odd because they put into words, although not to well, some of the questions that anyone should have before entering into a covenant, i.e., questions about the exact meaning of a covenant and the enforcement procedures. I happen to be a fan of the proposal from IASCOME and i see nothing fuzzy about the 9 commitments in that covenant. While the Anglican Curmudgeon may not think these commitments are sufficient, that is another matter and not, I think, a matter of the conflict bewteen two kinds of logic.
    One final thought: covenants are "binding" and that means that they restrict the freedom of the parties. In this regard, the words of Jesus in John 11:44 come to mind, "Unbind him, and let him go." My hope is that whatever Anglican Covenant is proposed will free all of us so that we may share in the missio Dei.

  3. larnold, thank you so much for that comment, from someone who lives and works with fuzzy logic and knows its capabilities and limits.

    The "fuzzy logic" I allude to that is rampant in theology and the church today is not the same as what you work with. Yours is, as you say, a useful extension of Aristotelian (transistor) binary logic, through the application of deterministic algorithms. What the post-moderns (or maybe they have to be described as post-post-moderns) are doing with their own adapted variant of fuzzy logic is ignoring the strictures of logic altogether by constantly modifying the truth-values of their rules---not in a deterministic, algorithmic fashion, but in an outcome-based process that decides first on the result desired in any given situation, and then backs up to the problem of justifying that outcome. A fuzzy logic chip is still a programmed chip; there is no "program" at all to the fuzzy logic in the church's highest bureaucracy, but only an innate desire to control for the sake of turning what was formerly proscribed into the new orthodoxy, and turning the old orthodoxy into something now proscribed.

    The analogy to Heisenberg's uncertainty principle, as the misapplication of another tool of modern science to a situation for which it was never intended, is also apt. In direct contrast to the still rather small magnitude of the delta product of position and momentum applied to macroscopic objects, however, the degree of uncertainty resulting in the church's approach is simply incalculable. Whatever it uses to justify its approach today can be reinvented as necessary tomorrow, with no need to remain consistent, or on a continuum with, with what has been done before. That is uncertainty with a capital "U".

  4. I first wrote it the way you would have, Father Weir, but then I realized there was no Aristotelian parallel between the church being a member of the Anglican Communion and my being a member of the Church---that is, the latter does not make me a "member" of the AC, since only churches are members. So I had to settle for the somewhat less-than-perfect version in the post.

    I, too, have no problem with the Covenant for Communion in mission. Now if only those who want to sign up to it would recognize as well the St. John's version of the draft Anglican Covenant as equally valuable, we might get somewhere . . .

    However, since this is the AC, we will have to wait to see what the ACC does with the Covenant before deciding whether to sign on. I understand and agree with that.

    My feeling of illogic about the Communion in Mission "Covenant" is that it is more a credo than a covenant. Nothing in it is objectively measurable or, as a consequence, enforceable; the Covenant as a whole fairly teems with fuzzy logic (example: "3. Encourage expressions of our new life in Christ"). I would say that many Episcopalians would no doubt feel that they were already following what the Covenant says, even if they did not know about it beforehand.

  5. In the fields I work in (robotics and AI), fuzzy logic has largely been supplanted by Bayesian inference.

    Fuzzy logic makes statements like "A is 75% true", whereas Bayesian inference makes statements like "Given everything I know, I believe A to be true with 75% probability," and that turns out to be much more mathematically tractable and interesting than the fuzzy logic statement, as well as more philosophically acceptable (at least to me).

    This would not be the first case I've seen of academics latching on to a 30 year old half understood hard-science theory and using it as the base of their "philosophies."

  6. This is an overreach: Kurt Gödel's famous proofs of his incompleteness theorems indeed removed the last basis for believing that scientific statements were either true or false, and in doing so undermined Karl Popper's entire doctrine of falsifiability.

    It is most definitely not clear that the criteria for invocation of Gödel's theorems are satisfied for the topics in discussion. (They probably are not.)

    You might want to look at the video:

  7. As a Computer Science academic (and a graduate of UC Berkeley where Lofti Zadeh worked), I need to say that fuzzy logic bears no resemblance to the capricious "re-interpretation" of the canons by our presiding bishop. (However, RoboDoc is correct that Bayesian logic is far superior to fuzzy logic since it handles that fact that the probabilities may be dependent or independent, whereas fuzzy logic doesn't.)

  8. RoboDoc, BobbyMac and John Tang Boyland (you guys could be the name of a law firm), thank you so much for adding your perspectives here to my humble attempt to illustrate the logical freedom that characterizes both the older form of fuzzy logic as first systematized by Prof. Zadeh, and the thinking of the religious liberals whom I so frequently take to task on this blog.

    First of all, you will get no dispute from me that fuzzy logic as a tool for algorithmic reasoning has been surpassed and greatly improved by Bayesian inference methods. You put your finger on the reason, RoboDoc, when you explained that the latter makes a rational assumption about the probability that A is true, whereas fuzzy logic proceeds by assigning an arbitrary initial truth value and then works things out as best it can from there. As the article cited in the main post states: "In fuzzy logic, everything is a matter of degree."

    It is likewise with the relativism of religious and theological belief statements in post- (or postpost-) modern Episcopalianism, as I shall show in subsequent installments in this series. And it is only in that "every truth-value is a matter of degree" sense that I equate liberal fuzzy logic with Prof. Zadeh's fuzzy logic.

    The Bayesians among you might be interested by the misuse of that logic in a famous case, People v. Collins, involving a robbery witnesses saw committed by a couple---the man was black, the woman was white and blonde, with her hair in a ponytail---who drove off in a yellow car. It is discussed in this article (scroll to p. 4). (The expression "to uphold the appeal" is British for saying that the appellant couple was successful in getting their guilty verdict reversed on appeal.)

    BobbyMac, thank you very much also for that fascinating link---it must be fun to work at Google, where you get paid to attend such talks as part of your work. But I note that Prof. Calude says (at about 42:30 to 44:00 in the talk) that "what we can prove mathematically is very tiny compared to what we can not mathematically prove." This is all that I was saying---that the world is full of statements that we might well believe to be true, but which, Gödel showed, cannot be proved to be true. You might also be interested to know that it was the awareness of this consequence of the incompleteness theorems that caused no less a luminary than Stephen Hawking to give up on his attempt to find a Theory of Everything.

    Anyway, I love it when posts here draw interest from people who otherwise may not find all the legal analysis exactly their cup of tea. Thanks again to each of you for stimulating the discussion!

  9. The link on your update is broken; it goes to an amusing post about the "Asterisk Administration".

  10. Thanks, K-W---it's fixed. That was actually a link I used in this previous post, about how President Obama has been treating his campaign promises. I'm glad you found it amusing.

  11. Dear Mr. Haley,

    You state that "Those who are comfortable with fuzzy logic, however, do not recognize" the Aristotelian Law of the Excluded Middle." While this is true, it does not, IMHO, begin to limn the boundaries of what they do not recognize, which all too frequently includes the Law of Non-contradiction."

    This apparent oversight on your part leaves me wondering if you have been paying attention to the full spectrum of those whom are describe. ;-)

    Blessings and regards,
    Keith Toepfer