Logic: How is this question different from the Omnipotence paradox?

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Discussion Overview

The discussion revolves around the comparison between two versions of the Omnipotence paradox: the traditional question of whether God can create a rock so heavy that He cannot lift it, and a new question regarding whether God can will His own non-existence. Participants explore the implications of these questions, their logical foundations, and the nature of God as it relates to omnipotence and omnipresence.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants question how the second version of the paradox differs from the first, particularly in terms of logical implications.
  • There is a suggestion that aspects of nature may be illogical yet possible, challenging the reliance on common sense in philosophical discussions.
  • One participant argues that if God's existence is not logically necessary, then the question of His non-existence may not be logically impossible.
  • Another participant asserts that many phenomena in physics, such as entanglement and black holes, do not violate logic but rather challenge previous axioms.
  • Some participants propose that the definitions of God influence the logical structure of the arguments, with materialistic and idealistic viewpoints leading to different conclusions about God's nature.
  • There is a discussion about the potential for logical contradictions in various formulations of God, depending on how God is defined.
  • One participant emphasizes that the universe may not yield to human logic, suggesting that foundational science could be flawed if causality and dynamism do not hold true.
  • Concerns are raised about the adequacy of logical definitions of God in constructing sound arguments, with some arguing that theological arguments often rely on common sense rather than strict logic.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the nature of the paradoxes, the definitions of God, and the relationship between logic and common sense. The discussion remains unresolved, with no consensus on the implications of the arguments presented.

Contextual Notes

Participants highlight the limitations of definitions and assumptions in their arguments, noting that the lack of a clear logical definition of God complicates the discussion. There are also references to unresolved mathematical and philosophical steps in the reasoning.

BenVitale
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We're all too familiar with the version of the Omnipotence paradox, the so-called paradox of the stone :

Can God create a rock so heavy that even he cannot lift it? ... (1)

... which has been discussed ad nauseam in philosophy classes and on the web.

Now, how about this version:

Can God will his own non-existence? ......... (2)

How is question (#2) different from question (#1) ?

Can we make a sound argument for (#2)? Is it even possible?

Does the version (#2) avoid to do the the logically impossible?
 
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Some aspects of nature are illogical, yet possible. (Human) common sense is largely over-rated and often naive.
 
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Does the version (#2) avoid to do the the logically impossible?

As long as God's existence is not logically necessary (as defined in modal logic), the answer is yes. But most theists will probably answer in the negative to the above, which negates the paradox (as far as I can tell).
 
GeorgCantor said:
Some aspects of nature are illogical, yet possible.
Such as?

(Human) common sense is largely over-rated and often naive.
This is a non sequitur. Logic and (human) common sense are two completely different things.
 
Gokul43201 said:
Such as?



Relative spacetime, entanglement, time passing at different rates in different inertial frames, GR's general covariance, black holes, SQUID experiments, self-awareness, freewill, dark matter, etc. etc.

What's your point?


This is a non sequitur. Logic and (human) common sense are two completely different things.


Where did i say they were not different? Did you read my post(esp. in light of the question i was replying to)?
 
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GeorgCantor said:
Relative spacetime, entanglement, time passing at different rates in different inertial frames, GR's general covariance, black holes, SQUID experiments, self-awareness, freewill, dark matter, etc. etc.

I don't see how these phenomena are illogical. Logic is a connective between axioms or observations and statements that preserve the truth value of the original axioms/observations. With the proper axioms, most of these phenomena and their logically connected phenomena are studied in depth.
In short, they do not violate logic; they violate previous axioms/observations that were not true (ie., the previous generation of "common sense" in physics), and as such revealed the correct axioms and/or new expected observations, derived logically.
If, in fact, any of these phenomena that have not yet yielded to being embedded in a logical structure pointed to illogic, the scientific method would have to be abandoned, as it depends on logical connection between true statements and predictions.
 
GeorgCantor said:
Relative spacetime, entanglement, time passing at different rates in different inertial frames, GR's general covariance, black holes, SQUID experiments, self-awareness, freewill, dark matter, etc. etc.
None of these things are illogical (i.e., entail an internal inconsistency within some logical framework). Some of them may be ill-defined (eg: self-awareness, freewill) but that's a different matter.

What's your point?
My point is to obtain further elucidation for your claim. Is it really inconceivable to you that someone reading a broad assertion such as the one you made might want to know what exactly you have in mind?

Where did i say they were not different? Did you read my post(esp. in light of the question i was replying to)?
Yes, I read your post. It wasn't particularly long and hard to read. Your statement about the naivete of (human) common sense is still a non sequitur.

I recommend we try to keep discussion limited to the questions raised by Ben, and not let it drift too far afield.
 
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Logic depends on the viewpoint you choose, from materialistic viewpoint there is a paradox, from idealistic there is not.

Materialism:
God creates a rock no one can destroy -> He is now a Demi-God, because he depends on this rock
God wills his own non-existence -> He cease to exist

Idealism:
God's will creates a rock no one can destroy -> He is still God, because he still depends only on his will, and not the rock, thus he's will can destroy it
God's will brings him to non-existence -> He cease to exist for as long as he wants

In other words, idealism is beyond logic, God is beyond idealism.

"I cannot conceive of a God who rewards and punishes his creatures, or has a will of the kind that we experience in ourselves." - Einstein
 
BenVitale said:
Can God create a rock so heavy that even he cannot lift it? ... (1)
Can God will his own non-existence? ......... (2)

How is question (#2) different from question (#1) ?
Question 1 relies on omnipotence.
Question 2 relies on omnipresense.

Both may, or may not be aspects of a defined god.
Can we make a sound argument for (#2)? Is it even possible?
Depends on how you define god. If god is simply 'the creator', then suicide is prefectly possible. If god is something more eternal and pervasive then you would have a logical contradiction. Bear in mind, most formulations of god run into logical contradiction, largely because we are trying to conceptualize something that by definition defies limits...
Does the version (#2) avoid to do the the logically impossible?
Neither is logically impossible, given the right premises...

Question 1 contrasts an omnipotent god with an anthropomorphic god.
Question 2 contrasts a omnipotent god with an eternal god.

The reason these examples are a good intro to questions in philosophy is because they force the student to examine their premises... their definitions of things, more closely than they might otherwise.
 
  • #10
Gokul43201 said:
None of these things are illogical (i.e., entail an internal inconsistency within some logical framework). Some of them may be ill-defined (eg: self-awareness, freewill) but that's a different matter.

My point is to obtain further elucidation for your claim. Is it really inconceivable to you that someone reading a broad assertion such as the one you made might want to know what exactly you have in mind?

Yes, I read your post. It wasn't particularly long and hard to read. Your statement about the naivete of (human) common sense is still a non sequitur.

I recommend we try to keep discussion limited to the questions raised by Ben, and not let it drift too far afield.


Umm, ok. Let me make a statement that may ellucidate my point further - given the deep conceptual problems in physics, there is no guarantee whatsoever that the universe will yield to human logic. The deep internal workings of the universe MAY forever remain in the twilight zone(the universe as a whole is beyond logic).

Our logic hinges on the ideas of causality and dynamism, if those 2 assumptions don't hold till the end - foundational science(as we know it) is a hopeless endeavor.


It's been assumed for centuries that the universe behaved logically and consistently, but the last century gives also support to the view that the universe might simply be illogical. If this is the case(it's quite possible!), the internal logic that the OP ascribes to God, may aslo be part of a 'defective' and incomplete logic(i.e. ours).
 
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  • #11
Gokul43201 said:
Such as?

This is a non sequitur. Logic and (human) common sense are two completely different things.
Yes, but the stone argument is not logic, but common sense too. As are most theological arguments, pro or con, as there is no logical definition of 'a god' at hand to play logic over.
 
  • #12
ZQrn said:
Yes, but the stone argument is not logic, but common sense too. As are most theological arguments, pro or con, as there is no logical definition of 'a god' at hand to play logic over.
It is one thing to say that there is "no logical definition of 'a god' at hand", but that does not prevent the contruction of a logical argument involving a god. A more pertinent objection would be if you were saying that there can be no logical definition of a god to be used for this argument. Or is that what you are saying?
 
  • #13
Gokul43201 said:
It is one thing to say that there is "no logical definition of 'a god' at hand", but that does not prevent the contruction of a logical argument involving a god. A more pertinent objection would be if you were saying that there can be no logical definition of a god to be used for this argument. Or is that what you are saying?
I can define:

\forall x : agod(x)[/itex]<br /> <br /> That seems to be a logical definition of &#039;a god&#039;, quite formal I dare say, and from that we can prove that assuming:<br /> <br /> \exists x : x = x[/itex]&lt;br /&gt; &lt;br /&gt; that:&lt;br /&gt; &lt;br /&gt; \exists x : agod(x)&lt;br /&gt; &lt;br /&gt; There, a god exists, logical like Principia Mathematica.&lt;br /&gt; &lt;br /&gt; What I&amp;#039;m trying to illustrate is that definitions work the other way around. Saying &amp;#039;there can be no logical definition of a god&amp;#039; isn&amp;#039;t really logical in nature, you can&amp;#039;t play logic over a thing until you defined it, so you can never prove that a thing can&amp;#039;t be defined, you need to define it for that namely. (Look up on &amp;#039;defining definability&amp;#039;).&lt;br /&gt; &lt;br /&gt; To illustrate it, this logic is completely isomorphic with:&lt;br /&gt; &lt;br /&gt; \forall x : cow(x)[/itex]&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; What I name this predicates hardly matters, what&amp;amp;#039;s important is how I close over them. To illustrate it with programming, what you call your variables isn&amp;amp;#039;t relevant, as long as you use the names consistently, &amp;amp;#039;descriptive variable&amp;amp;#039; names, in logic, as they are in programming, are merely to make things easier on the human reader, as long as define the relationships between your variables in the same way, what you name them isn&amp;amp;#039;t relevant.
 
  • #14
Thanks to all of you for your insights.

We cannot use, here, the known rational arguments for why God does not and cannot exist.

In this exercise, we suppose that God exists, and He merely wills his non-existence.

Yes, we need to define God, and try to figure out whether 'willing its non-existence' makes any sense?

We could define God as one unit, the most fundamental unit that exists, which has 2 properties: it is infinite and eternal. And, that unit causes and connects things we all commonly experience.

Modern physics (Relativity and Quantum theory) confirms this unity of reality, the basic oneness of the universe.

If that fundamental unit disappears or ceases to exist, then what?

Collapse of universe(s)?

Am I on the right track, here?
 
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  • #15
You lost me, but then, I'm not a philosopher.
 
  • #16
Just my thoughts...

That God could will his own non-existence is totally nonsensical and does not allude to an attribute necessary for omnipotence.
A capacity for self-destruction actually alludes to non-omnipotence, in my opinion.
 
  • #17
pallidin said:
Just my thoughts...

That God could will his own non-existence is totally nonsensical and does not allude to an attribute necessary for omnipotence.
A capacity for self-destruction actually alludes to non-omnipotence, in my opinion.

If He cannot will it, then he's not omnipotent ... same argument used in (#1), i.e. if he cannot lift the rock, then ...
 
  • #18
Put another way, to consider a lack of capacity to be an indicator of non-omnipotence is illogical in this context.
For example, assuming God has zero sexual desire for humans or animals, does this "lack of sexual desire" degrade the omnipotence of GOD? No, of course not.
Omnipotence is ALWAYS coupled with WISDOM.
 
  • #19
BenVitale said:
If He cannot will it, then he's not omnipotent ... same argument used in (#1), i.e. if he cannot lift the rock, then ...
The point where this debate stops being logical is 'to be able to'.

How do we define if someone is 'able to do' something? Some philosophers would indeed say that we do all we were able to do. Like, if I didn't get up to make a sandwich, then I wasn't able to do so at that moment.

Provided we take this definition, then for God to be omnipotent, he does all at every time.

Provided we take a loser, and logically harder to formalize definition, as in, one could still do a thing one doesn't do, we can just say he could lift up the stone, even though he doesn't do it.
 
  • #20
On page 1 of this thread, I posted...

BenVitale said:
We cannot use, here, the known rational arguments for why God does not and cannot exist.
In this exercise, we suppose that God exists, and He merely wills his non-existence.

Yes, we need to define God, and try to figure out whether 'willing its non-existence' makes any sense?

We could define God as one unit, the most fundamental unit that exists, which has 2 properties: it is infinite and eternal. And, that unit causes and connects things we all commonly experience.

Modern physics (Relativity and Quantum theory) confirms this unity of reality, the basic oneness of the universe.

If that fundamental unit disappears or ceases to exist, then what? Collapse of universe(s)?
Am I on the right track, here?

But, I'm not clear on what physicists are saying about this unit of reality

Could anyone clarify what physicists are talking about?
 
  • #21
BenVitale said:
On page 1 of this thread, I posted...



But, I'm not clear on what physicists are saying about this unity of reality

Could anyone clarify what physicists are talking about?



Ummmmm, they don't strictly know what they are talking about(YET) beyond the usual - "subject and object are one and the same", "the measurement apparatus is not separate from the object being measured". Have a look at the possibilities here:



"Holism and Nonseparability in Physics"


http://plato.stanford.edu/entries/physics-holism/


Taken at face value, the non-separability issue(if it's true) hints that the fundamental constituent of the universe is... observations.


The issue becomes even more bewildering if one considers that the wavefunction specifying a system is real and a sub-part of a non-separable 'environment'.
 
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  • #22
BenVitale said:
We're all too familiar with the version of the Omnipotence paradox, the so-called paradox of the stone :

Can God create a rock so heavy that even he cannot lift it? ... (1)

... which has been discussed ad nauseam in philosophy classes and on the web.

Now, how about this version:

Can God will his own non-existence? ......... (2)

How is question (#2) different from question (#1) ?

Can we make a sound argument for (#2)? Is it even possible?

Does the version (#2) avoid to do the the logically impossible?

This type of questions falls into the category "how many angels can dance on the tip of a pencil".

Such discussions are totally irrelevant, if you ask me.
 

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