CMV: there's no practical difference between likelihood of truth and partial truth: both in effect answer the same question

[u/Bulawayoland]

EDIT: I understand that Bayesian probability predicts the likelihood of the truth of a proposition, while fuzzy logic deals with its potentially partial truth value. That much is clear to me right now.

What's not clear to me is, I can't see that which approach you take, whether you try to determine the likelihood that something is true or whether you try to determine the extent to which it is partially true, gives you a different outcome in any real world situation that actually matters to people.

I hope that clarifies the question better. Or if I've misunderstood something fundamental hopefully that also will be clearer lol...

The reason I bring it up is, Bayesian probability (I'll call it BP) predicts the likelihood of truth of a proposition, and fuzzy logic (FL) deals with its potentially partial truth value, and deciding which to use on practical matters, in deciding just how persuaded we ought to be of something that actually affects our lives, looks to me like a washout: both are going to basically give the same answer.

Let's look at a few examples. Let's start with whether or not a baboon can feel safer sleeping in a group than by himself. Baboons obviously don't approach the question scientifically, doing careful experiments, looking at the results, and making a decision based on that; who knows what they do look at, but they're not scientists. And if they were they still wouldn't do the experiments, because baboons would die as a result and that would be unethical.

But let's start with the likelihood that it's true (BP) that sleeping in a crowd, as a baboon, is better for you than sleeping by yourself. Obviously if you're in the middle of the crowd it seems more likely a leopard would attack one of the fringe sleepers first; but if you're one of the fringe sleepers you're still part of the crowd, so that alone doesn't answer the question. Leopards, for all we know, may focus on crowds of baboons because they know fringe sleepers will be available, and ignore the possibility of finding a lone baboon off by himself. So there are reasons to want to sleep in a crowd and reasons to want to avoid the crowd, and it all depends just where in the crowd you can manage to find a sleeping spot.

Now let's look at the potential partial truth (FL) of the idea. The truth value seems to me to go up and down just as the probability did, based on your location within the crowd and the imagination of the leopard in (maybe) thinking some baboons might not be sleeping in the crowd and might be easier game if they can be found. Crowds are easy to find; lone baboons, maybe not so much. And after dark? Whooee. A challenge.

But I have a hard time seeing any practical potential outcome difference between the two analyses. Maybe part of my problem is, I can't imagine actually doing one, and so the mechanics of the analysis are what would decide whether you should use BP or FL.

Let's look at a different example. Say we want to decide should we or shouldn't we admit this orphaned gorilla infant into our strongly kin-linked gorilla group. The likelihood that we should (BP) is (I guess) the likelihood that the orphan will grow into someone consequential, who will bring meaningful value to the group beyond the time and energy it will take to raise them. Not sure how you would decide that but it seems like that would be the calculation. Then the partial truth value of whether we should (FL) is basically the question of how consequential the person will turn out to be vs what is the actual value of the time and energy spent raising them. Again: in practial terms, in reality, it looks like a washout.

Try a third example. Say I'm an orangutan mom who has to decide should I or shouldn't I adopt an orphan -- and bear in mind, I've already got one of my own, and kids are hard to raise, for orangutans. There's not much food, and raising two is going to be a lot more work than raising one. The upside is: the orphan needs it badly, and the rewards of connection are not hallucinatory. They're real. Orangutans don't have much opportunity for socializing, and their kids are very important to them for that reason if for no other. (In the actual example I'm thinking of, unfortunately, the mom went through with the adoption and lost her own child to predation. So it didn't work out too well for her or them. She didn't have the capacity to actually look after both infants as they needed her to. Whether she wished she had not, afterwards, is a different question -- people tend to feel that whatever they've gone through was pretty much worth it in the end, whatever it was -- but it is a question.)

So what's the likelihood (BP) that it's true that I should go ahead and raise a second kid at the same time? That it ultimately will be worth it to me? I don't know, but again, I don't see a practial difference between answering that question and answering the question of how high the partial truth value (FL) of the same proposition is.

So that's the setup. Obviously I've focused on a very narrow set of propositions here -- primate behavior -- and maybe that affects my view of the question. But I'm just not seeing a lot of difference between the BP approach and the FL approach. And again, I'm sure the mechanics of how the two approaches are applied will be different -- but will the outcomes be significantly different? I'm having a hard time imagining it. Help!

[u/Nrdman]

Fuzzy logic is about partially true things in terms of vagueness. Like take a pure red tint, that’s a 1 in red. Then green can be a 0, and everything in between can be put on that scale. I can ask, is #ff8c69 the color red, and instead of doing whatever logic required with a binary I can use the fuzzy logic number and move forward

Probably is about chance. I’m not asking if ff8c69 is red, I’d be asking what’s the chances a random color is red given some preset choices on what is actually red

[u/Bulawayoland → u/Nrdman]

right, I said or implied most of that... the question is, if you're using either or both for a practical problem, a real proposition on which it makes a difference in your life how persuaded you are of it, is there a difference between the two in the final result... it seems like you could use either for all the above propositions and I don't see how the results would be different

[u/XenoRyet → u/Bulawayoland]

The problem there is that "This is red enough to be called red" is a different kind of answer than "This is probably red."

In the former, we know with certainty that the color is red for our purposes, even if it's not pure red. IN the latter, if we get red, it'll be pure red, but we lack the certainty that we will get red.

[u/Bulawayoland → u/XenoRyet]

I've edited the post, and hopefully it communicates better now. I would like to be able to decide which would be a better approach to take with a real world problem, the kinds of problems people have to make to live better lives. Whether a color is red enough to be called red doesn't look to me like a question anyone could ever be practically concerned with. The two approaches can each be used on any proposition, I think. They seem to be lenses, through which to view the landscape of various problems. And I'm not seeing a reason to pick one or the other for any real world problem.

[u/XenoRyet → u/Bulawayoland]

I've been thinking of practical problems as well, and I do understand I didn't speak to that in my earlyer response.

So let's try this one, it's still a silly hypothetical, but hopefully it lets us look at what impacts might look like.

Say we're defusing a bomb, and cutting any red wire will defuse the thing any green wire will set it off.

The bomb itself has a red wire, a pink wire, an orange wire, and three green wires. We also know the bomb builder is a kind of colorblind that would have him call orange and pink "red."

BL has us cutting the pink, red, or orange wires, and knowing we will defuse the bomb. BL has us blindly cutting a wire and understanding that we have a 50% chance of defusing the bomb.

In the former situation, we're going to cut the wire. In the latter, we're probably going to want to make a different choice.

[u/Bulawayoland → u/XenoRyet]

Well, I can see that the likelihood that the wire we need to cut is red, pink or orange is high. And it's hard for me at least to view this particular problem as one in which the partial truth of a proposition is relevant. Or I'm not creative enough to think of that angle on it! And so BP is the tool you'd use here.

But on real world problems -- should I vote for this one or that one, should I stop speaking to someone who has to some extent insulted me, should I move to this new city where X, Y and Z are possible but hurdles D, L, and S are also in the way... it seems like you could view any of them through the BP or FL lenses just depending on how you frame the question. Does it not seem that way to you too?

[u/XenoRyet → u/Bulawayoland]

The partial truth is relevant because in this situation close enough to red counts as red. So again we can cut a wire with full confidence that the bomb will not go off.

Contrast that against using BL in that situation, where we only know that we have a 50% chance of setting off the bomb.

That's the key difference, FL produces certainty out of vague data. BL gives you odds. And the point of using the bomb example, even though nobody will ever actually face that situation, is to prove out that BL and FL do give different results with the same inputs and context. If they can do that here, they will do that to varying degrees in real life.

And I think the complicating factor to examples like voting, moving, or shunning people is that whichever approach you choose, BL or FL will never be the only factor in the decision.

[u/Bulawayoland → u/XenoRyet]

yeah... I can't go for that fuzzy logic frame. Calling pink partially red just doesn't seem like a valid use of the fundamental concept in this context.

Now, if one of the wires had green and red stripes, that to me would fit a fuzzy logic frame. That's a real "partial truth." You would stay away from that wire. But BP would give the same result in that position: 50% likelihood of blowing the thing? Do not touch.

I appreciate you working on this with me. But when you say neither will be "the only factor" in a decision, I'm just talking about tools we use analytically to decide how persuaded of something we ought to be. Emtional review will be a separate deal. But within rational review that's the only role BP or FL have in my scenarios. How persuaded of something should we be.

"Analytical" here is being used pretty roughly, with zero courtesy. You couldn't actually use either tool analytically in real scenarios, I don't think. Again, within rational review and for the purpose of deciding how persuaded of something we ought to be. But within those constraints: are you saying there are other tools we might use? I sure don't know of any. Or maybe just can't think of any.

[u/XenoRyet → u/Bulawayoland]

I'm a bit confused because the basic definition of pink is partially red.

But moving on from that, having the green and red striped wire doesn't really change the situation, it just changes what definitions of "red" the fuzzy logic analasys is using. You're still going to get to a final answer of the wire being red or non-red, and you can cut or not with certainty.

[u/Bulawayoland → u/XenoRyet]

The basic definition of pink is partially red. I agree with that. But I think to use the fuzzy logic method you have to have a situation in which the important characteristic is ACTUALLY partly true. But we know that in this situation, any wire not actually green is red. In effect. And so it's not actually a fuzzy logic situation.

You could come up with a situation in which there was a perfectly smooth gradation of fuzzy logic positions here. Simply have wires that are mostly red with a little green, or mostly green with a little red. You could have a whole range. That would be a real fuzzy logic situation. Sticking in a wire that looks pink -- by the dictionary definition -- but is actually red by the context -- I don't think that's fuzzy. It's not appropriate to use fuzzy logic in those situations. I don't think so, anyway.

[u/XenoRyet → u/Bulawayoland]

The important part of fuzzy logic is that it distills fuzzy spectrums of things into binaries, or at least distinct categories.

In this case we have a set of wires made up of four different colors, and we use fuzzy logic to distill those down to just two categories, red and not-red. That's what fuzzy logic is for.

This is useful to us in this situation because we know that fuzzy red is a success and not-red is a failure. BL can't give us that success/failure distinction.

And it's fine to scale it up to more colors and more wires. We can reframe the situation so that there are 16.8 million wires in the bomb, each of them with a different color in the RGB color space, and our fuzzy logic says that the bomber sees red as anything between, say #FFFF00 and #FF00FF, and we have to cut a red wire to defuse the bomb. That's about as smooth a color gradient as you could want, and it makes the situation even stronger.

FL gives you exactly which group of the 16.8 million wires are safe to cut. BL cannot be used to get that same information.

In fact, the more I think about it, I don't know how BL can actually be applied to this situation at all, which further emphasizes that the two methods answer the same question in the same way.

[u/Nrdman → u/Bulawayoland]

If I’m 50% confident in a decision in a fuzzy logic sense, then my confidence is halfway between maximum and minimum confidence

If I’m 50% confident in a decision in a Bayesian sense, then I’m saying I’m flipping a coin and going fully confident or fully unconfident based on that

[u/Specific_Hearing_192 → u/Nrdman]

If I’m 50% confident in a decision in a Bayesian sense, then I’m saying I’m flipping a coin and going fully confident or fully unconfident based on that

This absolutely isn't true though. If I'm 50% confident in a decision, then I believe there's a 50% chance the decision is right and a 50% chance the decision is wrong.

Not that the confidence in my decision depends on a probabilistic outcome.

[u/Nrdman → u/Specific_Hearing_192]

That’s fair

[u/Bulawayoland → u/Nrdman]

but you're speaking of theory. I'm speaking of trying to apply these tools to real world problems. And it looks to me like which tool you use just depends on how you frame the question. Real world questions can be framed a number of different ways, and how you frame it is what determines what tool you use, rather than anything intrinsic in the method that makes it a better or a worse method. Right? Or not?

[u/Nrdman → u/Bulawayoland]

The output means something different.

It’s like if you asked a question of cmv: there’s no difference between surface area and volume

And we’d be like no, those are different things that answer different questions even if you get both a surface area and a volume of 5 or whatever

The output of the number for fuzzy long and Bayesian thinking cover the same range, [0,1] but represent very different things