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Old 08-13-2003, 11:43 AM   #11
Bill Snedden
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I'm not sure that many theists would regard HUP as a serious threat to the concept of omniscience. It could be the case that our inability to detect both position and momentum simultaneously is an epistemic problem vs. an ontological one. If that's the case, God's ability to know both is not an issue as his knowledge is perfect and he has no epistemic issues.

Not to intentially hijack the thread, but I think a more serious challenge to omniscience as a concept is Cantor's set theorem:

Quote:
Suppose there were a set T of all truths, and consider all subsets of T --all members of the power set T. To each element of this power set will correspond a truth. To each set of the power set, for example, a particular truth T1 either will or will not belong as a member. In either case we will have a truth: that T1 is a member of that set, or that it is not.

There will then be at least as many truths as there are elements of the power set T. But by Cantor's power set theorem we know that the power set of any set will be larger than the original. There will then be more truths than there are members of T, and for any set of truths T there will be some truth left out. There can be no set of all truths.

One thing this gives us, I said, is "a short and sweet Cantorian argument against omniscience." Were there an omniscient being, what that being would know would constitute a set of all truths. But there can be no set of all truths, and so can be no omniscient being.
From Patrick Grim in Logic and Limits of Knowledge and Truth (Nos 22 (1988), 341-367).

There is an exchange between Grim and Alvin Plantinga discussing this argument here

I think it's been discussed before in this forum (?).

Regards,

Bill Snedden
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Old 08-13-2003, 05:55 PM   #12
Jobar
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Quite some time ago, Albert Cipriani the Traditional Catholic attempted to address the HUP by claiming that, in a sense, God *is* every particle, and since the particle itself has a distinct position and momentum, it may be said that God 'knows' both simultaneously. It's only external observers that are limited by quantum uncertainty.

Rather a good argument, but when I demonstrated that it required him to embrace pantheism, he dropped it.
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Old 08-15-2003, 10:17 PM   #13
spacer1
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Hi HRG. Thanks for the response.
Quote:
In a general state, neither x nor p have any sharp value; thus even an omnipotent deity could not "know" the value of x.
What do you mean by neither having a "sharp value"? Why must HUP be inherent in the nature of the matter, rather than merely a limitation of our knowledge of that matter?

Also, perhaps you (or anyone here) could tell me where I am going wrong on this thread?
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Old 08-16-2003, 09:43 AM   #14
HRG
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Quote:
Originally posted by spacer1
[B]Hi HRG. Thanks for the response.

What do you mean by neither having a "sharp value"?
If E(X) denotes the expected value of X in a particular state, then you can form the mean square deviation of X from its expected value: E((X - E(X)2). If it is zero, then X has a sharp value in this particular state; otherwise, X has only a distribution of possible values.

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Why must HUP be inherent in the nature of the matter, rather than merely a limitation of our knowledge of that matter?
Because commutators (like xp - px) can be measured in many cases, and non-zero commutators imply generalized HUPs.

Regards,
HRG.
]
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Old 08-16-2003, 01:40 PM   #15
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Ladies & Bentlemen,

Is the probability of this great being limited by our intelligence? Suppose the being is not limited by human intellect, then I only have to realise Quanta and Quantum principles are based on the limiting value of c, the speed of light. Planck et al. .

At 2c or 3c, embedded in this external being all the probabilities change.

Thus your proposed omniGOD is not limited to c, but omniGOD >> c.

Repeat for effect : a possible omniGOD >> c..
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Old 08-16-2003, 01:55 PM   #16
Howard
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I must say, sophie, you always bring a unique perspective to these debates. Im not entirely sure what that perspective is, but it certainly makes for interesting reading. Alas, I must yield to greater minds that mine to decipher and respond to your post.
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Old 08-18-2003, 08:20 AM   #17
the_cave
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Quote:
Originally posted by Bill Snedden
Not to intentially hijack the thread, but I think a more serious challenge to omniscience as a concept is Cantor's set theorem:
Fascinating. I think the problem is Cantor sets things up to fail, if you see what I mean. First he posulates a set of all truths--but then he proves that there can be no such set. Uh...

(For that matter, what does Cantor's paradox prove about numbers? It seems it would prove there is no set of all numbers...)
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Old 08-18-2003, 09:15 AM   #18
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the_cave,
Quote:
(For that matter, what does Cantor's paradox prove about numbers? It seems it would prove there is no set of all numbers...)
I agree with your evaluation of Cantor's sets (although I'm no expert). Regarding the above quote, I think the analogy to Cantor's sets could be made more accurate by representing "the set of all numbers" by some "number", let's say the number "$". Now, if $ represents the set of all numbers, but is a number itself, then $ cannot represent the set of all numbers for it cannot inculde itself in that set. The problem arises because of the creation of the power - the $ which represents all numbers and is supposedly a number itself.

Regarding God's omniscience, I always took God's omniscience as true, such that any logical laws would not apply to such an entity. Therefore, God's knowledge would encompass the set of all truths. Could God know that He knows everything? It seems that by simply asking the question (i.e. by creating a new power, or meta-perspective), we simultaneously create the paradox. Obviously, the set of all numbers exists, and we do not need to define such a set by another "number". Whether the same can apply to truth may be a different story, but I think the result should be the same.
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Old 08-18-2003, 09:29 AM   #19
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Upon further reflection, perhaps the issue could be resolved by taking the definition of a "set" more seriously. By definition a set is bounded by some characteristic(s) and is closed when we define it by such a grouping. If we maintain such a stringency, then we should not allow for any "new" additions to the set, such as those created to describe or label the set, which are also inclusive in the set, e.g., $ (the number which represents the set of all numbers).
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