The Fuzzy Logic of Belief
The logic of belief is a big subject, which I am only just beginning to think about. The literature is vast, and I have read little of it, though I hope to rectify that.
Still, I've been thinking about this subject, and I figured that recording my thoughts would help me sort things out. I hope it might be interesting to others.
I continue to find the concepts belief and believe fascinating. It seems clear that you can believe only that which you are convinced is the case. To believe is to be convinced; to be convinced is to believe. Believing is not an additional step you take after being convinced. When you understand why the solution to an algebra problem is x=2, you don't then decide to believe it. It's the same with the conclusion of any syllogism. If you are convinced that the premises are true and you see that the logical inference is valid, then you automatically believe the conclusion.
Here's what follows: you can't believe something you don't take to be true. I don't understand someone's saying, "I have no idea if X is the case, but I believe it." I understand that people may wish to believe X, may tell people they believe X, may act as though they believe X. But that is different from actually believing X. You simply cannot believe X unless you are unconvinced that X is the case. Belief is not an act of will or a choice. You have no choice once you are convinced, and it makes no sense to say you don't know whether you believe or not. Maybe this is already obvious to everyone.
Of course, believing, like being convinced, is a matter of degree, not a binary yes or no. We'll get to this below.
I was thinking about this recently after I heard someone say on an atheist podcast that while the concept believe doesn't fit easily into Aristotelian logic, don't worry because "there are other logics out there."
Other logics? Really? Since Aristotelian logic begins with the axiomatic laws of identity, noncontradiction, and excluded middle, I wondered how the other logics began. I couldn't see how we could make sense of -- much less talk about -- a system of thought that began with A is not-A. As Ludwig Wittgenstein wrote, "What we cannot think, that we cannot think: we cannot therefore say what we cannot think."
What the "other logics" guy had in mind was what he called "doxastic logic," which is the logic of belief. (In Greek doxa means "common belief." Aristotle's wrote a great deal about the importance of endoxa, reputable belief, in our acquisition of knowledge.) As best as I can tell, doxastic logic is a kind of "fuzzy logic," which is discussed in books on logic. But don't be thrown by the term. As Deborah J. Bennett writes in Logic Made Easy: How to Know when Language Deceives You, "Fuzzy logic is a logic of fuzzy concepts; it is not a logic that is itself fuzzy." And apparently unbeknown to the "other logics" guy, Aristotle dealt with fuzzy concepts within his logical system 2,500 years ago. It's not new.
What a relief to know that logic is logic!
So what are fuzzy concepts? In everyday language we have common words that are vague, where the boundaries are fuzzy -- that is, words that admit of degree or shades. These ordinarily cause us no problem. It's 2020 after all, and we're coping (even with the pandemic). Men have walked on the moon, and we use GPS systems, which rely on Einstein's theory of relativity, every day.
Take the word tall. Outside of any context the word could be vague -- everyone is tall (and short) relative to something -- but it's not vague, or it's less vague, in a specified context. If I say, "He's tall for a jockey," you probably won't think I mean he's 6-foot-7. That would indeed be tall for a jockey, but everyone knows that someone that tall is not likely to be a jockey. And if I say, "He's tall for an NBA player," you also probably won't think I mean he's 6-foot-7 because a basketball player that size would not be unusual. (By the way, the shortest NBA player was Muggsy Bogues, 5-foot-3. He was not tall in almost any context.)
So context is crucial, and most of the time we can sort things out without difficulty. On those occasions when we can't, we often can ask questions for clarification or look for other clues regarding the context.
Is it the case that everyone is either tall or not-tall, as the classical Law of Excluded Middle would lead us to think? Sure, but that should then open a conversation about how tall was being defined and what the context was, or else we wouldn't know who belonged in which group. The boundary is fuzzy and can't be located independent of context. Any boundary we set will useful only if it serves a human purpose. It's not something we discover "out there."
What sounds just wrong is saying that everyone is either tall or short -- unless short is defined, oddly, as not-tall -- because that ignores the continuum; some people are in between. It's not black and white, but that is not a problem for logic.
It's pretty much the same with belief. It comes in degrees. We can believe strongly, weakly, or somewhere in between. This corresponds to how convinced we are, for convinced also comes in degrees depending on how much evidence we have and how much confidence we have in that evidence. If we have a small amount of credible evidence, we might say we are beginning to be convinced or that we are mildly convinced. The degree would increase as we saw more and more credible evidence, to the point where we felt confident enough to say, "I am convinced that such and such is the case." Then we could also say, "I believe that such and such is the case." (I'm not going to touch the red-herring word absolutely; the word is pretty useless in this context.)
So we can say that everyone either believes or does not believe such and such (to some extent). We could say more specifically that everyone either strongly (or weakly) believes or does not strongly (or weakly) believe such and such. That's the excluded middle.
What's this got to do with the God question? Obviously, we can say that everyone either believes in God or does not believe in God. (If someone said he didn't know if he believed or not, I'd wonder about his fluency in English.) The first group would include those with a belief to any extent, strong, middling, or weak, as long as it's greater than zero. We can also say that everyone either strongly believes in God or does not strongly believe in God. Here the second group would include everyone whose belief is less than strong (however that's defined) and all atheists, who obviously do not strongly (or weakly) believe in God.
Still, I've been thinking about this subject, and I figured that recording my thoughts would help me sort things out. I hope it might be interesting to others.
I continue to find the concepts belief and believe fascinating. It seems clear that you can believe only that which you are convinced is the case. To believe is to be convinced; to be convinced is to believe. Believing is not an additional step you take after being convinced. When you understand why the solution to an algebra problem is x=2, you don't then decide to believe it. It's the same with the conclusion of any syllogism. If you are convinced that the premises are true and you see that the logical inference is valid, then you automatically believe the conclusion.
Here's what follows: you can't believe something you don't take to be true. I don't understand someone's saying, "I have no idea if X is the case, but I believe it." I understand that people may wish to believe X, may tell people they believe X, may act as though they believe X. But that is different from actually believing X. You simply cannot believe X unless you are unconvinced that X is the case. Belief is not an act of will or a choice. You have no choice once you are convinced, and it makes no sense to say you don't know whether you believe or not. Maybe this is already obvious to everyone.
Of course, believing, like being convinced, is a matter of degree, not a binary yes or no. We'll get to this below.
I was thinking about this recently after I heard someone say on an atheist podcast that while the concept believe doesn't fit easily into Aristotelian logic, don't worry because "there are other logics out there."
Other logics? Really? Since Aristotelian logic begins with the axiomatic laws of identity, noncontradiction, and excluded middle, I wondered how the other logics began. I couldn't see how we could make sense of -- much less talk about -- a system of thought that began with A is not-A. As Ludwig Wittgenstein wrote, "What we cannot think, that we cannot think: we cannot therefore say what we cannot think."
What the "other logics" guy had in mind was what he called "doxastic logic," which is the logic of belief. (In Greek doxa means "common belief." Aristotle's wrote a great deal about the importance of endoxa, reputable belief, in our acquisition of knowledge.) As best as I can tell, doxastic logic is a kind of "fuzzy logic," which is discussed in books on logic. But don't be thrown by the term. As Deborah J. Bennett writes in Logic Made Easy: How to Know when Language Deceives You, "Fuzzy logic is a logic of fuzzy concepts; it is not a logic that is itself fuzzy." And apparently unbeknown to the "other logics" guy, Aristotle dealt with fuzzy concepts within his logical system 2,500 years ago. It's not new.
What a relief to know that logic is logic!
So what are fuzzy concepts? In everyday language we have common words that are vague, where the boundaries are fuzzy -- that is, words that admit of degree or shades. These ordinarily cause us no problem. It's 2020 after all, and we're coping (even with the pandemic). Men have walked on the moon, and we use GPS systems, which rely on Einstein's theory of relativity, every day.
Take the word tall. Outside of any context the word could be vague -- everyone is tall (and short) relative to something -- but it's not vague, or it's less vague, in a specified context. If I say, "He's tall for a jockey," you probably won't think I mean he's 6-foot-7. That would indeed be tall for a jockey, but everyone knows that someone that tall is not likely to be a jockey. And if I say, "He's tall for an NBA player," you also probably won't think I mean he's 6-foot-7 because a basketball player that size would not be unusual. (By the way, the shortest NBA player was Muggsy Bogues, 5-foot-3. He was not tall in almost any context.)
So context is crucial, and most of the time we can sort things out without difficulty. On those occasions when we can't, we often can ask questions for clarification or look for other clues regarding the context.
Is it the case that everyone is either tall or not-tall, as the classical Law of Excluded Middle would lead us to think? Sure, but that should then open a conversation about how tall was being defined and what the context was, or else we wouldn't know who belonged in which group. The boundary is fuzzy and can't be located independent of context. Any boundary we set will useful only if it serves a human purpose. It's not something we discover "out there."
What sounds just wrong is saying that everyone is either tall or short -- unless short is defined, oddly, as not-tall -- because that ignores the continuum; some people are in between. It's not black and white, but that is not a problem for logic.
It's pretty much the same with belief. It comes in degrees. We can believe strongly, weakly, or somewhere in between. This corresponds to how convinced we are, for convinced also comes in degrees depending on how much evidence we have and how much confidence we have in that evidence. If we have a small amount of credible evidence, we might say we are beginning to be convinced or that we are mildly convinced. The degree would increase as we saw more and more credible evidence, to the point where we felt confident enough to say, "I am convinced that such and such is the case." Then we could also say, "I believe that such and such is the case." (I'm not going to touch the red-herring word absolutely; the word is pretty useless in this context.)
So we can say that everyone either believes or does not believe such and such (to some extent). We could say more specifically that everyone either strongly (or weakly) believes or does not strongly (or weakly) believe such and such. That's the excluded middle.
What's this got to do with the God question? Obviously, we can say that everyone either believes in God or does not believe in God. (If someone said he didn't know if he believed or not, I'd wonder about his fluency in English.) The first group would include those with a belief to any extent, strong, middling, or weak, as long as it's greater than zero. We can also say that everyone either strongly believes in God or does not strongly believe in God. Here the second group would include everyone whose belief is less than strong (however that's defined) and all atheists, who obviously do not strongly (or weakly) believe in God.
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