The implicit issue is whether the belief or non-belief matters. Whether you believe or don't believe in the subject of a fairly trivial thought experiment doesn't concern anything important - whether you believe or disbelieve in this case, doesn't make any difference. When it comes to some kinds of beliefs, however - most typically religious beliefs or belief in an economic or political ideology, then holding such beliefs are felt by their advocates to matter, to be important.

And that's where belief or unbelief is significant. It's not significant in respect of examples which have no import.

Actually the example is similar to the well-known 'Russell's Teapot'. This is an analogy used to illustrate that the philosophic burden of proof lies upon a person making a claim, specifically a claim about the existence of God, rather than shifting the burden of disproof to others.

He wrote that if he were to assert, without offering proof, that a teapot, too small to be seen by telescopes, orbits the Sun somewhere in space between the Earth and Mars, he could not expect anyone to believe him solely because his assertion could not be proven wrong.

The problem with this analogy is that, likewise, the existence or non-existence of an orbiting teapot matters not one whit. It's completely specious. Whereas, whether one believes in God or not, the belief might be consequential.

See Bill Vallicella, Russell's Teapot Revisited for a detailed discussion.

p can be false; p can be true.

One can believe; one can not believe.

Hence, four possibilities:

1) Bp
2) B~p
3) ~Bp
4) ~B~p

Six permutations:

1 contradicts 2.
1 contradicts 3.
2 contradicts 4.

2 implies 3.
1 implies 4.

3 is compatible with 4, in that one can have no beliefs about p. It's called agnosticism.

I agree that there is no contradiction between ~Bp and ~B~p.

Now, kindly answer: does B~p imply believing that the probability of p is 0, and/or vice versa?

No.

Interesting. Can I get an example where the non-equivalence holds?

Perhaps you can answer: I don't know the probability of the dolphin. This is admissible — Pneumenon

Not with Bayesian probability it isn't. You don't know if the coin will land on heads or tails. That makes the probability 50/50.

The error here is assuming that belief is some identifiable bit of data lodged in the brain somewhere, that of any given object (once described to me) I will create a byte of data corresponding binomially to whether I believe it or not (see ). There is very little evidence to support this theory of belief. Rather beliefs are dispositional states. My belief that there is an invisible miniature dolphin swimming in continuous circles around my head is a measure of the extent to which I'm going to act as if that were the case. This allows for (in fact necessitates) grades of belief - I can easily act as if it might rain today without having to form a belief that it will or won't.

Not only is belief graded this way, but it is constantly updated. The evidence from our perception becomes the prior for our next inference, so we rarely have a consistent state of belief about any given thing unless we're interacting with it, and even then our belief is changing all the while we're manipulating the object (works for concepts too).

Furthermore, our beliefs then affect our perception in turn. So a disposition to believe what I see is a tree will lead me to actively look for leaves, a trunk, branches... the things I'm expecting to see there because it's a tree. I will disregard parts that don't conform to 'tree'. Again, the same works for concepts.

So active disbelief is only really a verbal state with 99% of examples. to actively disbelieve the teapot is only to say that if someone asked me if there was a teapot orbiting mars I should be inclined to say no. If no-one asks I have no belief state about it at all. Not zero, just no state.

Likewise a belief in some object (or entity) is not the same for each person. To say "I believe in God" does not mean the same thing from the devout fanatic as it does from the social church-goer because the resulting behaviours are different.

You don't know if the coin will land on heads or tails. That makes the probability 50/50. — Isaac

Off topic - We don't have to assume 50/50, do we? Couldn't one start at assuming a 100% probability of heads, leaving it to the Bayesian process to level out at 50/50? I'm just wondering what the correct process is.

Otherwise, an agreeable reply.

We don't have to assume 50/50, do we? Couldn't one start at assuming a 100% probability of heads, leaving it to the Bayesian process to level out at 50/50? I'm just wondering what the correct process is. — Banno

Yeah. I'm no expert in Bayesian mathematics, so I couldn't say if the actual function is expected to carried out that way, but insofar as it applies to cognitive processes, the brain is remarkably confident about supplying us with priors and it will do so with only the slightest provocation (see sensory isolation experiments), so you're, right, it probably is more accurate to say we start off with something other than 50/50 - some past experience getting lucky with heads, some half-considered notion that heads are heavier, maybe even (as very young children) some simple misconception about how physics works. Something probably will bias our initial belief and we revise it down as we get an increasing number of errors using our 70/30 or 100/0 models.

You can see how supernatural beliefs get maintained this way though. By the time you've revised your model down to say 60/40, you're getting increasingly less likely to actually notice the errors in your model unless you really experiment in the abstract. Someone who had a prior belief that a coin was 60% likely to land heads and 40% likely to land tails (because 'God prefers heads' or whatever), will have little reason to update that prior unless they actually toss a thousand coins and plot the results (and believe in maths, of course)

Cheers.

Active disbelief is the belief that not-P.

Lack of belief is the absence of a belief that P.

I can be unaware that I lack belief in something. You lack belief in an invisible miniature dolphin swimming in continuous circles around your head right now. You were unaware that you lacked belief until you read that. You are now aware that you do not believe in the invisible miniature dolphin.

What is the probability of the invisible miniature dolphin's existence?

If you answer "0 or negligible," then you actively disbelieve in the dolphin. If you answer "non-negligible and non-0," then you simply lack belief in the dolphin. But, to simply lack belief in it, you must affirm a nonzero, non-negligible probability of its existence. To actively disbelieve in it, then you must affirm that the probability of the dolphin is 0 or negligible.

Perhaps you can answer: I don't know the probability of the dolphin. This is admissible. But, if you answer thus, you admit that you don't know whether or not you disbelieve in the dolphin. So, to avoid active disbelief while maintaining the absence of belief, you must claim ignorance about your own epistemic state. Whence this ignorance? — Pneumenon

I'd rephrase the underlined part in the last paragraph as "you know you can't either believe or disbelieve". Where is this "ignorance" you speak of? A verdict of true or false regarding any proposition maybe witheld pending conclusive evidence and in no way implies that the person doing this is ignorant of what it is that s/he believes in the sense that s/he's confused; all it means is that s/he is clear-headed enough to recognize "I don't know" is a completely acceptable response to any question at all and that not just because of ignorance but also because to say anything else amounts to overstepping the limits set by the available evidence.

We all know what this is about.

Here is what I have to say about it:

ATHEISM is as much a product of "belief" as is THEISM.

Theists "believe" there is a God...or "believe" it is more likely there is a God than that there are no gods.

Atheists "believe" there are no gods...or "believe" it is more likely that there are no gods than that there is at least one.

I repeat: Both ATHEISM and THEISM are the product of "belief."

I also there is nothing wrong with "believing" (or blindly guessing) in either direction.

That was supposed to read, I also acknowledge there is nothing wrong with "believing" (or blindly guessing) in either direction.

Not with Bayesian probability it isn't. You don't know if the coin will land on heads or tails. That makes the probability 50/50. — Isaac

I'm not a statistician by any means, but as I understand it, Bayesian theory defines probability by how strongly one believes that something is/will be true. If a consequence of this is that I cannot say, "I don't know the probability of that," then I'm not sure what to make of that. There are probabilities I don't know. The probability of a coin landing on heads is not exactly 50/50, but I don't know what the exact ratio is. Does Bayesian probability make it impossible for me to say that?

There are probabilities I don't know. If your Bayesian epistemology can't accommodate that, then so much the worse for your epistemology.

The error here is assuming that belief is some identifiable bit of data lodged in the brain somewhere, that of any given object (once described to me) I will create a byte of data corresponding binomially to whether I believe it or no — Isaac

Well, I don't see what I said that presupposes that. I can ask you whether you believe something, and I can ask you what the probability is. The presence of some piece of data in the brain is not implied by asking you either of those things, as far as I can see.

If you really want a dispositional analysis, then we can posit a disposition to say certain things, if that's how it has to work.

There are probabilities I don't know. The probability of a coin landing on heads is not exactly 50/50, but I don't know what the exact ratio is. — Pneumenon

You may not know what the exact ratio is, but that would only matter in frequentist probability. Your mental models appear to be better explained by Bayesian probability. So the ratio doesn't matter. If you'd bet no more on heads than you would on tails then the probability is 50/50. Your belief is that it is no more likely to land on heads than it is on tails.

It might help to think of it as two questions about your knowledge (priors).

Do you know something about heads which biases the coin in its favour? Do you know something about tails which biases the coin in its favour?

An answer of "I don't know" doesn't make any sense here because it's not a question about the world, it's a question about your knowledge of it.

Since you have no more reason to think it will land heads than you do to think it will land tails, the probability is 50/50.

The presence of some piece of data in the brain is not implied by asking you either of those things, as far as I can see. — Pneumenon

No, you're right, I was reading too much in to your comment. Most people, when they talk about belief, refer to it that way - "Jim believes in God", "Bob believes in UFOs"... As if there were some part of their brain in either an on or an off state for each posit.

Our brains just don't seem to work like that. Our beliefs are probabilities, not switches and they're tested and updated all the time depending on the stimuli we're trying to model. Your disposition toward God or UFOs or even where your front door is will not be the same tomorrow as it is today.

I also there is nothing wrong with "believing" (or blindly guessing) in either direction. — Frank Apisa

Apart from a certain intellectual dishonesty...

Perhaps this will help: which part of your argument is about Bayesian mathematics, and which part is an epistemology based on Bayesian mathematics?

I can believe that Bayesian statistics does not see questions about probability as sensible unless they're couched in terms of a person's beliefs/knowledge. What I don't believe is that any sensible epistemology of probability must be Bayesian, in that sense at least.

That is to say, it makes sense to me to say, "In Bayesian probability, you can't say that you don't know the probability of something." I can accept that as a feature of the formal system. But I can't accept an epistemology of probability that won't let me say that there are probabilities I don't know.

Apart from a certain intellectual dishonesty... — Banno

Whether or not one suspends disbelief in the face of equally-probably alternatives has to do with one's priorities. Is it more important to have true beliefs, or to avoid false ones?

Is it more important to have true beliefs, or to avoid false ones? — Pneumenon

Seems to be a theme here this morning.

My Master's thesis was about organisational decision making; it made the obvious observation that organisations have no choice but to act, and that hence organisations were inherently irrational.

But we can be silent.

You're saying it's more rational to suspend judgment than to flip a coin. But why?

Not quite. I'm saying that one might do either, that the choice of to flip or stand is not rational.

The body of the thesis was an explanation of how management theory builds a pretence of rationality as a sort of callus over its embarrassment.

THat's what much of philosophy is, but for individuals rather than for organisations.

Not quite. I'm saying that one might do either, that the choice of to flip or stand is not rational. — Banno

I agree. It's outside the scope of this thread, but I think there's a point to be made here about epistemic relativism. Maybe elsewhere....

can't accept an epistemology of probability that won't let me say that there are probabilities I don't know. — Pneumenon

Why not? Put it like this. If you want to insert a frequentist theory of probability into your epistemology - how many trials does it take until you do know the probability? If after a thousand trials the proportion of heads to tails is 501:499 do you now know the probability is 50.1/49.9? Because if you do, I'd say you were wrong.

You already channeled the discussion towards Bayesianism when you identified beliefs with probabilities. If you want to have a broader, less theory-laden first approach, you might want to step back from that. Do you want to talk about a specific theory or family of theories, or about phenomenology, or word usage? (I realize that these subjects are not entirely separate.)

Bayesianism though has many varieties, including austere ones that eschew prior probabilities. @Isaac is appealing to a thoroughgoing, Dutch book subjective Bayesianism, in which there is no such thing as being uncommitted: you can't decline a bet. His identification of beliefs with dispositions makes this position more plausible, but I suppose such an identification is itself contentious. In any event, if we are considering the way we actually think, then it is fair to caution that we are not perfect Bayesian computers.

Banno
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I also there is nothing wrong with "believing" (or blindly guessing) in either direction.
— Frank Apisa

Apart from a certain intellectual dishonesty... — Banno

Agreed.

My personal feeling is that the "intellectual dishonesty" comes mostly from making a guess...and then calling that guess a "belief." Seems to me it would be much more honest to make a guess of "There is 'at least one god'" or "There are no gods"...and call the guesses...guesses.

But I acknowledge that is just a bugaboo with me.

You already channeled the discussion towards Bayesianism when you identified beliefs with probabilities. — SophistiCat

Did I? I think you can always ask a person what they believe a probability to be, but that doesn't make their belief a probability.

But, to simply lack belief in it, you must affirm a nonzero, non-negligible probability of its existence. — Pneumenon

Here is where I have a problem. Implicit is that I "must" affirm a "non-zero" & etc. probability of what I am not aware of. Why must I? Or even, how can I - how is that even possible? Once aware, I presumably am careful to identify just exactly what I am aware of, and that even by itself resolves most confusions.

So, to avoid active disbelief while maintaining the absence of belief, you must claim ignorance about your own epistemic state. — Pneumenon

Let me try a version of this: If I think about invisible dolphins swimming at this moment about my head, I assign to that a zero chance of being an accurate representation of reality. In ignorance, however - in saying, "I dunno" - I am (you say) affirming possibility. It would seem to evolve to the question of how someone who is aware can make stupid assertions. Answers: 1) there's no accounting for stupidity, and 2) that, or they're trying to sell you something.

And this would seem to apply in areas where people have trouble keeping apart reality from their ideas about reality. Sense? Or did I miss it?

What is the probability of the invisible miniature dolphin's existence? — Pneumenon

Please tick one:

• Zero or negligible
• Non-negligible but doubtful
• Certain, or negligible degree of doubt

Did I? I think you can always ask a person what they believe a probability to be, but that doesn't make their belief a probability. — Pneumenon

If you did not, then what is this question supposed to mean?

What is the probability of the invisible miniature dolphin's existence? — Pneumenon

Probability estimates are like statistics. 92% of each is made up right on the spot.

ARE

If you did not, then what is this question supposed to mean? — SophistiCat

A picture of a pipe is not a pipe. A belief that a probability is 50/50 is not a probability.

I can believe that a squirrel is an animal. That does not mean that my belief is an animal. I can use my brain to think about a chair. My brain is not a chair. And so on.