If 100% is simply unattainable given that Descartes Deceiver is not logically impossible, then it surely makes sense to gauge one’s “strength” of belief. One could surely rank the following:
There is a reality external to my mind
The universe began before I was born
Intelligent life exists outside Earth.
Intelligent life exists outside Earth but within 10 light years.
Liverpool will win the Premiership next season.
Santa Claus exists.
I have a problem with the idea that a 51% confidence that a statement is true is the same as believing that statement, and I think that is at the root of the debate here. For any statement we hear we have some assessment of whether it is true. If a person says the stock market is going to go up tomorrow, and I know from experience that it goes up 52% of the time, does that mean I believe him? That isn’t how I hear people use the word belief.
If we do use the 50% rule, since it is infinitessimally likely that our intuition about the truth of a statement would be at exactly 50.000…%, then not being on the positive side would pretty much guarantee being on the negative side, so with that rule, absence of belief would imply disbelief, or belief in the opposite.
However I think common usage would imply that I have to have upwards of 80% confidence before I say something is a belief. In that case the fact that my confidence falls short of 80% certainly does not imply disbelief. From 20% to 80% is reasonably characterized as “don’t know”.
I call myself an atheist. That doesn’t mean I’m 100% sure there isn’t a god. I would say I’m about 99% sure there isn’t. Thus it is fair to say I believe god does not exist. If I told people I was an agnostic, most would assume I was near the 50% mark. Then it would be fair to say I neither believe nor disbelieve.
For God’s sake don’t get any books out on measure theory! It’s last year undergraduate/postgraduate maths stuff. It’ll put you off statistics for life!
Just take on board this fundamental principle:
In order to talk about probabilities in any meaningful (i.e. non-rhetorical) way, there has to be a probabilistic event being measured.
The confusion arises in part because people do use probabilities in a rhetorical fashion all the time. But when you’re debating the finer points and your arguments begin to rest on such probabilities, you really need to make sure that you understand exactly what you’re talking about.
So identify what is probabilistic and what isn’t. As a start: the existence or not of something is definitely not probabilistic! It is the results of random tests given such an existence that is where you want to be focussing.
In a way it’s all related to the Monty Hall problem (that old chestnut about choosing a box and either changing your mind and otherwise) in that such an argument is based on conditional probability. And human beings are notoriously awful at understanding conditional probability (again, see the Monty Hall problem!)
Anyway, back to the OP. Focus now on assessing the existence of God not as a sloppy “50% chance he exists” statement but a “Given he exists, 50% chance that the universe is such” statement instead, as per my earlier post. Do you now agree with me that ¬B(G) ¬= B(¬G)?
pan
Let’s stick with that dice example, kabbes.
Now, a child who knew nothing about probabilities might simply believe she was going to throw a 3 every time. I am not arguing that one can know the actual probabilities, merely that this is the way our minds work (given that our minds are all we have and any appeal to external reality is merely pretending that something very likely - the existence of an external reality - is actually 100% certain.
To back off from the theoretical and symbolic logic versions, I propose that there are at least this many classes of human beings:
Thus the scale that flips a switch at 50% from belief to disbelief is ignoring the real population of human beings and their relationship to a belief structure.
Related to what Bullfighter said: traditionally in statistics we require the data to have less than a 5% chance of occurring before we reject a postulate.
I don’t think that is exactly the point though. Even if you take a 50% chance as sufficient to change your mind, that doesn’t change the fact that “absence of belief” simply means that the evidence tipping the 50% just hasn’t come along yet.
In my die example above, the chance of the 6 was in both cases less than 30%. That doesn’t stop you either believing in it being loaded or not believing in it being loaded. And neither version is the same as believing in it being not loaded.
Meat - if one talks about “strength of belief”, then one is still talking about the probability of the evidence given the postulate and not the probability of the postulate. As I said, the difference is subtle but crucial.
Pharmaceutical companies, for example, will start off with the hypothesis that a drug is harmful. They must collect evidence to show that the drug is not harmful. Would you be happy for them to instead start of with the hypothesis that the drug is not harmful and be allowed to continue so long as evidence doesn’t contradict this?
If not, why not?
In either case, is the drug ACTUALLY harmful or not?
Does this tell you anything about the difference between absence of a belief and the belief of an absence?
pan
I’m not sure what is taught in “measure theory” but I personally find there is great utility in thinking of something as “probabilistic” any time our knowledge of something is incomplete (which is all the time). If I roll a die, it normally would have a 1/6 chance of coming up 3. If I roll it behind a screen so I can’t see it, it may definitely 3 or not 3, but since I don’t know, the probability in my mind is still 1/6. Probability can be different for the same event depending on what you know about it.
No worries mate, I’ve a PhD in acoustics: My psychoacoustical experiments put me off statistics for life in the first place.
I don’t see where you’re going with this. Suppose she believes that she’s going to throw a 3 every time. She throws a 6. Now she either has to reject that belief or keep it. If she rejects it, it says nothing about her further belief as to whether or not the die is loaded in favour of sixes.
pan
And what of the probability that Descartes’ Deceiver is watching me swallow this imaginary “evidence” as my brain sits in its jar of nonsense? How can one arrive at a figure of 5% statistical significance for such a theory?
Good question. Our analysis of the available data is definitely not rigorous! But that is where we tiptoe into the realms of epistiomology – the study of how we know what we know.
My personal epistiomological model is one of falsification, otherwise known as the scientific method. I start from a position of accepting nothing and will accept a postulate only if I am persuaded to do so. However this says nothing about what my criteria for persuasion are and I’d certainly not put a percentage chance on something I can’t measure!
This is irrelevant to the question in the OP, however. Just because my criteria of being persuaded are nebulous, doesn’t mean that I don’t still have to be persuaded. And being persuaded is not the same thing as starting from the opposite stance and rejecting the thing.
(A final appeal: imagine a world in which you were assumed guilty and your lawyer had to prove otherwise…)
pan
Measure Theory (large .pdf file). Don’t say that you weren’t warned…
(Of course, such highly technical course notes in themselves will show you nothing. It’s the professor’s commentary and discussion that surrounds such concepts that tends to illuminate the rather more “fluffy” concepts such as this one).
pan
Whoa, OK, give me a while to read that mother of all pdf’s.
Can you, then, falsify the proposition that you are in a Jar of Deception? No? Do you, then, believe it? Surely you ascribe to it a tiny probability, even though it explains every phenomonological datum in the universe perfectly well?
I would say not, which is why I specifically mentioned Descartes’ Deceiver in the OP and multiple times thereafter.
The classic response to Descartes’ Deceiver is that the truth or otherwise of the statement makes no difference. Either way, I must either continue with my life as if it is not true, so I will ignore the question completely.
Now: how does that fit within your B(¬G) stroke ¬B(G) model? The response is actually one of enlightened ambivelence!
But on the falsification score: my default position is that I am that which I appear to be, i.e. a corporal being living on Earth. Present me with some evidence to the contrary and I will consider it. In the meantime, I reject the proposition that I am otherwise.
That doesn’t mean that I categorically state it to be not true.
pan
And why should my “default” not be that I am in a jar, such that I must be presented with evidence that there is an external reality?
Here we have two theories which fit the data perfectly. Any “evidence” can be used to support both theories just as strongly.
Altogether now: They are both possible. Altogether now: I believe I am not in a jar.
Now, I admit outright that I ascribe a small probability to one and, consequently, a large probability to the other. Surely, in order to avoid doing so, you must explain why one is logically impossible?
No, no, no. If you believe that you are not in a jar, you B(¬J). I, however, ¬B(J). You are starting from the “given that I am in a jar…” proposition and rejecting it, I am starting from the “given that I am not in a jar” proposition and not rejecting it. It’s exactly the same as the B(¬G)/¬B(G) dichotomy!
Note that I’m not saying that either position is the “correct” one - that would be a whooooole other debate. I’m just pointing out that the positions are different.
pan
You quoted a tiny piece of my argument, but not all of it.
It is nothing but sheer failure to understand plain English that would hold that the lack of a particular belief is itself a form of belief.
Percentages are used for measures of CERTAINTY in either knowledge or belief. But belief and knowledge are themselves both binary: either you have knowledge of something, or you don’t. Either you believe something or you don’t. Either you are willing to concede the truth of an offered assumption, or you are not, and it will have to be proven further to you. Either you’ve jumped off the cliff or you haven’t.
Only if you conclude that the statement is either definitively true or definitively false. If you conclude that there is no good evidence for the statement, you are perfectly justified in simply not believing it is true, which is not itself the same thing as having a belief that the statement is false. As far as you are concerned, the statement could be true or false, but there is no reason to believe it is true, so it cannot be conceeded. The same is true for any claim that the statement is false. Any person advancing EITHER claim will have to present evidence and argument for their case.
SM, you are right to realize that negative claims are not different than positive claims, and neither is inherently “stronger” than the other as an assumption. But you are wrong about the nature of making assumptions. Not making an assumption is not the same thing as making an assumption not.
Lack of belief is NOT identical to active disbelief. Hasn’t anyone else ever heard of ίσοσθηνια. Great day in the morning! What passes for “philosophy” or “critical thinking” in this “modern” education that children get? Is it really nothing more than presuming that to not accept a dogma is and must be utterly identical to actively rejecting that dogma?
There is a difference between nescio (I do not know) and nullo (it is false). Indeed, the heart of skepticism is not running around activtely dogmatizing about situations “This is false. That is false. This is false. That is false.” Skepticism is “Is this true?” It is not “This cannot be true because…”
Likewise, are people actually permitted to graduate from school with the belief that if something is factual ones belief in it is no longer a matter of belief? Great night in the evening! I know people who believe things that are not true and people who refuse to believe things that are true. Their belief, or lack does not alter the truth value of the principles in question, but nevertheless, the truth value likewise does not seem to alter their belief or lack. Thus, to say “I don’t need to believe in something because I know it’s true.” reveals magnificent, indeed truly wondrous ignorance regarding the nature of belief vs. truth.
Kabbes
While it may be important for scientific purposes to compute the probability that a certain experimental observation would be made given the truth of a proposition, I don’t feel this reflects what we ordinarily mean by “belief”. I think you object to assigning a probability to a claim (a potential belief) because it cannot be rigorously defined what this means, or possibly because there is no well defined way to compute it.
Nevertheless, I think the human brain must compute something of this nature because it is essential for all decision making. We could define the probability based on the best odds you would be willing to give on a bet that the belief was true. If you believe that George W. will win the election in 2004, the strength of that belief would be reflected in the odds you would be willing to give on that bet.
I say such estimates are necessary for decision making because we are constantly faced with choices. If I were deciding whether to call a girl for a date (purely hypothetical - I’m married) I would need to estimate the probability of success in order to judge whether the pleasure of success would outweigh the pain of rejection. I recently decided that I wouldn’t read your “measure theory” paper because I estimated the probability of it being valuable to me was not great enough to offset the effort of reading it. These mental estimates are not explicitly numerical of course, but there must be quantitative comparisons going on in our heads.
Apos
You acknowledge that degree of certainty can vary yet you state that belief must be binary. Does that mean that once you have reached a particular degree of certainty something goes from being a non-belief to a belief? I have lots of opinions which have enough uncertainty so that it’s not clear that I should call them beliefs. This is not the sort of thing that can have a hard borderline. On the other hand, I feel we should never call 60% certainty a belief, but we should always call 99.9% certainty a belief.
I have a serious problem with that whole scenario.
TRUE is 100%
FALSE is 0%
Anything in between is uncertainty and an estimate of probability, like 80% probability of TRUE is also a 20% probability of FALSE.
BELIEF == to accept something as TRUE without sufficient evidence, therefore belief is stupid by definition.
of course that is not the dictionary definition but it implies there is a difference between a PROOF and an ABSOLUTE PROOF which is mathematical nonsense.
Dal Timgar