 | | | Subject: Richard Dawkins on C4 (UK)
Posted Jan 23, 2006 by Pattern-chaser
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  | | <the question is meaningless. Pattern chaser - it isn't the lack of proof, and that was (part of) my point. It's the impossibility of proof.>
 You say this like you are responding to something I said with which you disagree. And yet you focus exactly on my point: <the impossibility of proof>.
<an agnostic position [...] requires that you accept the possibility that there is a logical proof for an illogical premise>
surely an agnostic position acknowledges a non-zero probability that something which seems very unlikely might actually prove to be so?
If a claim concerning the real world seems vanishingly unlikely, but subsequently turns out to be the case, then it *is*, just as things in the real world *are*. The real world doesn't read the books we read, and knows nothing of logic or cheese. It just is; everything else must conform to it. Whether humans classify it as logical, or not, has no relevance.
Pattern-chaser
"Who cares, wins"
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| | | Subject: Richard Dawkins on C4 (UK)
Posted Jan 24, 2006 by 2_short_plancks
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| | um... impossibility of proof is not a "non-zero probability". It is a zero probability. Hence impossible.
Also, the "real world" is not, as you seem to be implying, divorced from logic. All logic is based on the way things work in the real world. It is simply a way of determining whether something is "true" or an illusion based on or own biases, whether in terms of correlation, causation or (in this case) actual existence. If something cannot logically exist, it doesn't. If an opinion is not logical, it is meaningless; it can only be objectively "true" by random chance.
Which is all sort of beside the point; I very much doubt whether you have 100% unshakeable definite proof for anything you believe to be true- that doesn't mean you consider nothing to be true. I very much doubt you could function if that were the case.
Consider it like this- if all the evidence points to x being true, if logic validates x, and there is no credible evidence to the contrary, would you hold the position that x is true; or that x may or may not be true? Because if you opt for the second you could not have knowledge of anything. Science becomes meaningless because you couldn't even accept empirical first principles. You couldn't even have an opinion, and you certainly seem to have those...
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| | | Subject: Richard Dawkins on C4 (UK)
Posted Jan 24, 2006 by Pattern-chaser
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| | <impossibility of proof is not a "non-zero probability". It is a zero probability. Hence impossible.>
Good sound bite. What does it mean? "impossibility of proof" and "non-zero probability" were used to describe different things. You compare them as though they were used to describe the same thing.
<the "real world" is not, as you seem to be implying, divorced from logic>
Not divorced, no. The degree to which the real world is independent of logic is much more than this.
<logic is based on the way things work in the real world>
Exactly. Logic is based on the world, not the other way around. The world just *is*. Logic is a human invention we overlay onto the world, and hope it fits. The world is wholly unaltered whether or not it does.
<If something cannot logically exist, it doesn't. If an opinion is not logical, it is meaningless>
I observe that (for example) human behaviour is sometimes illogical and irrational. I need a way of thinking and acting that will allow me to deal with other humans. Your exclusive focus on logic appears to me to lack value.
Pattern-chaser
"Who cares, wins"
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| | | Subject: Richard Dawkins on C4 (UK)
Posted Mar 30, 2006 by Fathom
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That's clever, Dogster, but not strictly true.
By definition zero probability means impossible while unit probability means inevitable.
In your example there is an infinite number of (real) numbers between 0 and 1 so if I choose any one it appears to have probability 0. In practice however I would have to choose a number with a finite number of decimal places; so I must choose, say, 0.5 or 0.335 or 0.123456789... I cannot offer as my choice any number having an infinite string of digits (unless it can be defined as a fraction or a known constant such as pi). Consequently I don't really have an infinity of choices at all and the probability of any one choice is much better than zero.
A similar argument can be used to show that the universe cannot logically be infinitely old - since if an infinity of time has passed already then the probability of the Earth existing at this particular point in its history is exactly zero.
F
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| | | Subject: Richard Dawkins on C4 (UK)
Posted Mar 30, 2006 by Dogster
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| | It's not only clever, it's actually correct as well. Zero probability only means 'impossible' on finite (or countably infinite) sample spaces. Zero probability = impossible is a convenient falsehood used to make teaching the idea of probability easier and more intuitive.
You're right that a human can't make a choice from an infinite sample space (at least, he couldn't report that choice because in a finite lifetime you could only report a finite number of symbols), but the universe can and (if quantum mechanics is correct) does.
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| | | Subject: Richard Dawkins on C4 (UK)
Posted Mar 31, 2006 by Fathom
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I'll take your word for it that "Zero probability only means 'impossible' on finite (or countably infinite) sample spaces" and since the set of real numbers between 0 and 1 is (arguably) a continuum it falls outside this definition. However your example calls for me to "pick a number" and plainly that leaves me with a finite set to choose from.
Whether the universe has access to a genuine continuum or is, as recent theories suggest, essentially digital; being limited to minimum values of time and length is an interesting question. Can there ever be a real, as opposed to mathematical, infinity?
F
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| | | Subject: Richard Dawkins on C4 (UK)
Posted Mar 31, 2006 by Pattern-chaser
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| | <Zero probability = impossible is a convenient falsehood used to make teaching the idea of probability easier and more intuitive.>
I note what has already been said about choosing from infinite or non-infinite spaces, and conclude that zero probability, as it applies to the real world, *does* mean 'impossible', just like a probability of 1 means 'certain'.
...
Except now I'm confusing myself, because neither (objective) impossibility or certainty - as they concern the real physical universe - can be recognised or verified by human beings. 
Sometimes thinking is just plain hard. 
Pattern-chaser
"Who cares, wins"
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| | | Subject: Richard Dawkins on C4 (UK)
Posted Mar 31, 2006 by Dogster
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| | Fathom,
"Can there ever be a real, as opposed to mathematical, infinity?"
Well, not even all mathematicians agree on 'mathematical infinity'. There are the ultrafinitists for example, who deny all sorts of infinity. Of course you're right we don't know whether or not the universe is discrete or continuous. I don't know whether or not this relates to the original question about whether or not god exists though. I was mostly pointing out that probalistic arguments are irrelevant in deciding this. My real reasons for saying this are more complicated, but I thought I'd illustrate it by pointing out that this one use of it is misleading.
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