Fuzzy Logic and Theology

During my posts on gossip I repeatedly had this thought:

There are times when I think theological discourse could benefit from using fuzzy logic.

Shall I explain?

Most of us are familiar with Classical logic. Classical logic is bivalenced. That is, propositions are seen as either True or False. So, when we reason about propositions like "Richard Beck is a man." We can evaluate that proposition as either True or False. In set-theoretic terms, you are either in a set or not.

But fuzzy logic is multivalenced. That is, set-membership can vary along a continuum. "Truthfulness" can vary along a continuum from 100% True to 50% True to 0% True (and all values in between). This may seem strange, but examples are close at hand. For example, evaluate the following propositions. Are they True or False?

"Richard Beck is a good person."

"This conversation is gossip."

"Sam is a Christian."

"Bill loves God."

"That view is heresy."

"Susan believes in God."

"Pam is kind."

Are propositions like these, moral and theological propositions, best evaluated by classical, bivalenced logic? Can we cleanly say that a given proposition is True or False?

I don't think so. The reason is that sets such as "goodness," "gossip," Christian," "love," "heresy," "belief," and "kindness" are best viewed as fuzzy sets. Fuzzy sets don't have discrete boundaries. Thus, set-membership is not a discrete In versus Out. Extreme cases might be so easily classified, but generally we would evaluate set-membership as varying along a continuum.

My favorite biblical examples of fuzzy logic come from the following passages:

Matthew 22: 36-40
"Teacher, which is the greatest commandment in the Law?" Jesus replied: "'Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment. And the second is like it: 'Love your neighbor as yourself.' All the Law and the Prophets hang on these two commandments."

1 Corinthians 15: 3-8
For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures, and that he appeared to Peter, and then to the Twelve. After that, he appeared to more than five hundred of the brothers at the same time, most of whom are still living, though some have fallen asleep. Then he appeared to James, then to all the apostles, and last of all he appeared to me also, as to one abnormally born.

Lots of doctrinal and ethical propositions are True. But I like the examples above because they hint that doctrinal and ethical categories are fuzzy. That is, there are "greatest" commandments and things of "first" importance. Too often, in doctrinal and ethical discussions I get tangled in, people tend to reason and debate in bivalenced categories. Of course, if a proposition is in the bible it can lay a claim to truth. But these passages, and the example I offered above, suggest that debates and conversations may be better served if people employ fuzzy categories. Allowing some issues to be, I have no better words for this, "more true" or "more ethical."

Personally, I think the dominance of bivalenced logic is why the public discourse involving religion is so impoverished. Bivalenced logic is neat, clean, and easy to use. Everything is cut and dried. There is Good and there is Evil. And whose side are you on? There is Right and there is Wrong. Which will you choose? Etc.

Fuzzy categories, although common, are more clunky to reason with. It takes effort, wisdom, and discernment. Plus, fuzzy logic doesn't make a nice soundbite.

Maybe theology, at least in the public realm, needs a little more fuzz.

This entry was posted by Richard Beck. Bookmark the permalink.

4 thoughts on “Fuzzy Logic and Theology”

  1. I agree with this sentiment more and more - especially as a computer science person. Real logic knows it's limits. Logical systems are helpful if the input is true and the rules are appropriate to the situation. Logical systems are not infallible - they can lull you into a fall sense of security because they help you "make sense of" things. But logic is a tool, not the truth.

  2. Fuzzy logic might(!) be unnecessary. All you need is Bayesian reasoning. The mathematics of "degrees of belief" have been worked out for much longer than Kosko's mathematics of imprecise categories. Furthermore, Fuzzy Logic is not fuzzy. The logic and mathematics are quite precise. It's the assumptions or propositions that it deals with which are fuzzy.

    But I think what you're actually getting at in the first section (statements that might be true, but we aren't clear about their truth) is a little different from the latter section of your post, which I think is probably the real focus of your effort. That is, I think what you're getting at is that some truths are hierarchically more important than others. For example, "preserve innocent life" is usually accepted as an ethically desirable motivation derived from a belief that "life is valuable" is a true statement; likewise with "do not lie" (deriving from "lying is wrong"). However, I would argue that lying to preserve innocent life is justified. "Preserve innocent life" is more important than "do not lie." It takes wisdom to discern which ethical truths dominate others, and, when they bump into each other, how to relax one in favor of the other. In the case of the two ethical propositions I mentioned above, I would ask myself, "When would I ever face a situation in which it would be better to tell the truth and let innocent life be lost as a result?" Since I haven't yet conceived or encountered such a situation in which it is better to tell the truth and consequently let innocents die, I tend to believe that "preserve innocent life" dominates "do not lie." Ultimately, I think this is the message Matthew tells us about in Matthew 12:1-14.

  3. i love this discussion, the concept in general. I only found this while I was doing research for a body of material I'm working on called www.fuzzyhermeneutics.com. Thank you all for being so brilliant.

Leave a Reply