We’ve actually covered this before. It is a matter of epistemic logic (or doxastic logic), which is too weak to tie ~BG with B~G.
To simply matters, think of it this way: B is a specialized symbol for the general modal symbol . Thus, we would have ~G along with ~G. It can be seen at a glance that these are NOT mutal implications.
Niggle away good sir. I will, however, continue to choose my phrasing with care.
It isn’t that I believe in an external reality, rather it is that it is my default assumption and I don’t reject it. I am not sufficiently convinced by the jar to put my eggs in it, so to speak.
pan
Many thanks Lib - they’re the type of keywords I can get my teeth into. (BTW, a hearty welcome back. This electronic landscape is indeed more arid and lifeless without you).
I think RaftPeople (welcome also!) characterised the OP well: That taking a position in the first place follows the exact same process as taking on a belief, a non-belief or a belief-not, and confusion arising from sloppy use of English (mine!) is bound to arise.
kabbes, if I may point to some of the words and phrases you have used: “sufficiently convinced”, “but she may exist”, “allow for the possibility”, “I [don’t] categorically state it to be not true”.
Would you say, then, that you personally ascribe in your mind a small probability to the statement “I am in a jar” being true, given that it is not necessarily false?
Is there a name for a phrase which demonstrates itself in this manner?!
If the assertion of the OP is correct then we all have an infinite number of beliefs, not only the “positive” beliefs:
[ul][li]I am sat at my desk[]I am posting to the SDMB[]etc[/ul] but then an uncountable myriad of “negative” beliefs:[/li][ul][li]I am not sat on Alice’s desk[]I am not sat on Bob’s desk[]…[]There is no Invisible Pink Unicorn[]There is no Invisible Lilac Unicorn[]There is no Invisible Pink and Lilac Striped Unicorn[]…etc[/ul][/li]To my mind this has a 51% chance of being crazy…
This is so obviously false that I do not know how anyone can believe it for more than 30 seconds.
So the reasoning is that since I believe God must either exist or not exist, if I do not believe he exists I must believe he does not exist. Which is patently false.
I believe Poster X must be either a man or a woman but I have no belief as to whether that poster is, in fact, a man OR a woman. If you ask me whether I believe it is a man I will say “No, I do not believe it is a man” and if you ask me if I believe it is a woman I will answer “NO, I do not believe it is a woman”. Saying that if I do not believe it is a man then I HAVE to believe it is a woman is plain silly.
Saying that if I do not believe in God then I have to believe in the only other alternative (the non existence of God) is just silly. The answer is that I do not have enough knowledge to believe anything one way or another.
Kind of – I ascribe a small probability to the chance that the evidence presented to me by the universe has arisen due to the jar possibility.
How can I suggest otherwise? To say that there is a zero chance is to say that this universe could not possibly be as it appears to be if I am actually a brain-in-a-jar. That would be a palpably false statement.
When I came into this world, I had no concept of any kind of “God”. At some point, the concept was introduced to me. As of this time, I am yet to be convinced. I therefore lack belief in God.
On the other hand, I have not proved that God doesn’t exist either. I therefore lack belief in no-God either.
The latter statement is not the point though, is it?. The world doesn’t seem much to care about my belief in no-God. What it cares about is my belief in God. Well, my answer to that question is, “I don’t believe in God”. See? The statement says nothing about my belief in no-God.
pan
A person who has never bothered much about the idea of God is asked: Do you believe in God? I.e. do you think B(G) is true. He listens to what the questioner considers evidence, and isn’t convinced of the existence of God. So his state of mind can be described as ¬B(G).
If he then becomes interested in the ‘big questions’, reads everything he comes over on religion, science and everything, he can still end up in the state ¬B(G), but he can combine that with ¬B(¬G), or he can end up with B(¬G)
¬B(G) is the default. I don’t care, or ‘who is this god person anyway?’
¬B(G) & ¬B(¬G) is agnostisism. There could be a god, or not, I can’t decide.
B(¬G) is atheism. I believe there is no need for God, and all evidence points to him being an invention of man.
I personally, ended up with B(¬G), but it’s not something that’s an important part of me, it’s just the answer to the question “Do you believe in God?”. When no one asks (including me), my state of mind is ¬B(G), which isn’t a belief.
Mascaroni said:
Which is impossible. The idea of atheism is linked to the idea of the existence or non-existence of a god. If you don’t care, you don’t need a word to use on yourself. If no one else cares, you don’t need a word to give to them. Then you have non-belief, and no description is needed. The moment you ask yourself the question, you alter the reference frame.
Why so small? Given that the evidence supports both positions equally well, whay not ascribe an equal probability to the two?
Given that the two are mutually exclusive, ie. jar = ¬(external reality) and external reality = ¬ jar, then if your ascribed probability of jar is small, then your ascribed probability of external reality is very high.
How is the statement “I ascribe external reality to be very likely” different to the statement “I believe in an external reality”?
If the two are equivalent, and given the aforementioned mutual exclusitvity, surely this is further equivalent to “I believe I am not in a jar”?
naita, I agree with your post, mostly, but must pull you up on your use of terms.
Strictly, “a-gnosticism” means “one who does not follow the gnostic philosophy”. Gnosticism is “the conviction that matter is evil and that emancipation comes through gnosis”, which basically means that Gnostics think that it is possible (and necessary) to understand the nature of God. By contrast, a-gnostics (or agnostics) believe that the nature of God is fundamentally not knowable.
That’s nothing to do with a belief or otherwise in the existence of God.
On the other hand, a-theism (or atheism) is the opposite of theism, which is a simple belief in some form of God. An atheist lacks such belief.
Someone who’s philosophy is ¬B(G) is therefore an atheist. Someone who is ¬B(¬G) may or may not be an atheist.
Popular usage of the word “agnostic” has come to mean “one who is undecided as to whether or not God exists”. This is sloppy and, in my opinion, doesn’t even make any sense. You either believe in God or you don’t (just like you either believe there is no God or you don’t). Belief isn’t “partial”. If you aren’t sure then you don’t believe.
To differentiate, the term “weak atheist” has been employed to describe someone who is ¬B(G). The term “strong atheist” has been employed to describe someone who is B(¬G).
The best way to think about true agnosticism and atheism is as two scales on a belief axis. You can have an agnostic theist and (I suppose) a gnostic atheist and everything in between.
pan
If we consider the set of possibilities to be { Live in jar, Live in “real” world } SentientMeat’s rule says ascribe equal probabilities – Probability that we live in the real world = 50%
Yet if we consider the set of possibilities to be { Live in a jar, Live in “The Matrix”, Live in “real” world }, SentientMeat’s rule says ascribe equal probabilities – Probability that we live in the real world = 33%
And that’s “why not”, your decision theory is sensitive to the addition of irrelevant criteria.
Meat, get rid of the word “small” if it bothers you. The point is that under my epistimiological system I require strong evidence for the jar option.
And talk of “50%” is
(a) pointless, since I have no way of objectively measuring such a probability; and
(b) irrelevant, since I am more than capable of stubbornly clinging to my default position even in the face of strong evidence.
The key is that I have so far not accepted the jar reality, because evidence has not swayed me.
But I’m not sure what the purpose of this tangent is. Why are we now talking about brains in a jar rather than God? What’s wrong with your original question in the OP – why shift to this rather first-year-philosophy-student analogy?
And this:
… reveals that you still have confusion about probabilities. I have not not not ascribed a probability to the jar, I have ascribed a probability to the data given the jar’s existence. The alternative is ascribing a probability to the data given the jar’s non-existence. These aren’t mutually exhaustive probabilities! They can both be 99%, they can both be 1%. Symbolically, they are as follows:
P(D|J); and
P(D|¬J)
There is nothing to say that P(D|J) + P(D|¬J) must equal 1!
pan
To add in The Great Unwashed’s point, the “matrix” option is represented by:
P(D|M)
ie “Probability of data given we live in Matrix” and NOT “Probability of living in the Matrix”. That’s why things apparently go screwy with your reasoning when you bring in other options.
pan
kabbes: yes, I’m getting through your file - I thought I’d just get these sophomoric whinings out of my system before the true incandescence of my glaring ignorance filters through my slowly-opening eyes:
I do not why you arbitraily choose one option as “default”.
Were I to choose a situation excluding external reality (let us call all such situations “jar”) as my “default”, all evidence provided to me by my mind and senses would serve simply to reinforce that default. I would find no evidence which suggested an external reality. I would have no reason to switch my default.
And yet, I haven’t. And neither have you. Why not?
You have already accepted an external reality based on no evidence which distinguished it from the jar, agreed?
Cheerfully agreed. It is my own preconceptions that lead me to the ¬B(J) state. As stated though, I most emphatically do not B(¬J).
I can’t believe that you’ve decided to read that Measure Theory file. Seriously. I remember about 0.2% of that stuff. I just have a particular recollection of its application to statistics because statistics is my field and it was nice to know that there was a rigorous underpinning to the whole thing. When the lecturer started talking about probabilistic events, my ears pricked up. By the next lecture, they’d slumped back again 
pan
I am merely surprised that you are unwilling to say “If I really had to make a guess, it would be that I was not in a jar”. I cannot distinguish this sentence from “I believe I am not in a jar”.
Well, so far as I can see:
I) P(D|J) = 1
II) P(D|¬J) = 1
So no help there, which is why the Deceiver problem is ultimately bunk – you can’t resolve it either way and it makes no difference even if you decide it’s true.
Given this, it’s a matter of pure gut feel. From that, I can say that I ¬B(J) but I cannot say that B(¬J), since that would be at odds with (I).
pan
And you would not be willing to say “I reckon I’m not in a jar” based solely on gut feel? (Which, I admit, is what governs most of the decisions, guesses and positions I take every day, even though I strive to base them on appropriate evidence.)
Vacuum: the absence of matter.
Therefore, by Sentient Meat’s definition, the absence of matter is itself matter. A vacuum is therefore not an actual vacuum?
Don’t buy it.
Nahtanoj
Might I have the sheer gall and outright temerity to request that anyone tempted to throw in a drive-by witticism based solely on the thread’s title might actually read the thread before doing so?