The Roles of Logic and Science in Questions of Theology

[_marg]

Ok just a quick note. I'm bowing out of the discussion for 2 days until Sunday. There are some other things I need to focus on. If I spend any time on this I'll use it to read the replies I haven't read yet, but not much point replying because that might generate more replies which I can't focus on now.

[_Calculus Crusader]

marg,

Previously you asked me what I thought Kurt Gödel meant by God or God-like. I suspect he had something like the following in mind
(excerpted from a paper by Brian Leftow):

* God has no material parts.
* God is not distinct from his essential attributes.
* God's essential attributes are not distinct from one another.
* God is not distinct from His existence.

[_JAK]

marg,

Previously you asked me what I thought Kurt Gödel meant by God or God-like. I suspect he had something like the following in mind
(excerpted from a paper by Brian Leftow):

* God has no material parts.
* God is not distinct from his essential attributes.
* God's essential attributes are not distinct from one another.
* God is not distinct from His existence.

Thus, in your view and/or Brian Leftow’s, Gödel assumed God. Exactly my analysis early on in this thread.

But Christian pundits wanted even more from Gödel which they did not get.

Christian History Institute.

Notice the title first:
“Christian History Institute Presents More Stories: Kurt Godel Proved Truth Higher than Logic © 2007”

Then the final statement:

“In other words, no finite system, even one as vast as the universe, can satisfy the questions it raises. Godel recognized this and tried to find a watertight proof of God's existence. He failed. Sadly, the evidence of his life suggests he failed to find a personal relationship with Christ either.” (bold added for focus)

JAK here:
The assertion that Gödel proved truth of any kind and particularly as it relates to religion was not established. Naturally, an organization such as this would have been ecstatic if they could have their position proved.

Their Christian position appears never to have been asserted by Gödel.

Now you cite Brian Leftow as representing Gödel (in your view).

He would appear to be qualified to characterize Gödel.

In three of the four statements made, Brian Leftow recognizes that Gödel assumes God.

What is the subject in three of the four sentences?
All sentences have a verb.

In the one sentence in which “attributes” is subject what possessive noun possesses “attributes”?

As if that were not ambiguous enough, “attributes” are “essential.” Does this mean there are non-essential attributes? What are those? Does Gödel make the distinction? If no distinction, why further muddy the statement?

Does it change the meaning one iota to drop “essential”?
If so, specifically how is the meaning changed?

Notice that multiple assumptions taking place here. In addition we have ambiguous words nullifying meaning wherever those ambiguities are present.

Now let’s look at that 1st sentence. It’s a negative statement. “* God has no material parts.”

That’s a claim. (This is assuming that you accurately represent Leftow, and that he accurately represents Gödel. I’m not challenging that in this analysis. Keep that in mind. This is not pejorative toward either you or Leftow.)

Based on that 1st sentence, one must inquire.
What are the “parts”? If not “material” they’re what? -- not stated.

2nd sentence: “* God is not distinct from his essential attributes.”

We have a second negative statement. Yet we have no answer to inquiry regarding the 1st sentence -- “no material parts.”

3rd sentence: “* God's essential attributes are not distinct from one another.” The ambiguity worsens. But the claims continue.

4th sentence: “* God is not distinct from His existence.”
This sentence could just as well have been first. If we move from the general (major premise) to the specific (conclusion), the 4th sentence is more general than the 1st. It’s also vague and circular. What is “distinct” from its “existence”? What’s an example?

Why is “His” capitalized? It refers to “God” which is assumed.

“...no material parts” is both an extraordinary claim as well as a specific claim. Yet that was 1st.

It’s easy to understand why critics of Gödel characterized this particular material as “fuzzy” and a “ruse” and “sleight of hand.” Those were not my words, but they are correct.

It’s my impression that those adherents to religious (particularly Christian) doctrine wanted some highly regarded individual in mathematics and logic to make the case for God. Gödel tried, but as the Christian History Institute acknowledged, he did not satisfy them as they had hoped.

In no way do I intrude on comments which marg may wish to make. You addressed her.

JAK

[_Calculus Crusader]

Give it a rest JAK. It is painfully obvious that you never knew what you were talking about and that has not changed. Brian Leftow's paper has nothing to do with Kurt Gödel. I was merely conjecturing as to what Gödel's conception of God might have been.

[_JAK]

Give it a rest JAK. It is painfully obvious that you never knew what you were talking about and that has not changed. Brian Leftow's paper has nothing to do with Kurt Gödel. I was merely conjecturing as to what Gödel's conception of God might have been.

Quite non-responsive to analysis and questions before you.

Calculus Crusader stated:
marg,

Previously you asked me what I thought Kurt Gödel meant by God or God-like. I suspect he had something like the following in mind
(excerpted from a paper by Brian Leftow):

* God has no material parts.
* God is not distinct from his essential attributes.
* God's essential attributes are not distinct from one another.
* God is not distinct from His existence.

I responded to that statement.

Now Calculus Crusader states:
Brian Leftow's paper has nothing to do with Kurt Gödel. I was merely conjecturing as to what Gödel's conception of God might have been.


Read your two statements together. You contradict yourself. First you “thought Kurt Gödel meant by God...”

Now you claim: “Brian Leftow's paper has nothing to do with Kurt Gödel.”

If Leftow’s paper has “nothing to do with Kurt Gödel," why did you make the first statement? You refer to “Kurt Gödel.” You also state that: “I suspect he (Kurt Gödel) had something like the following in mind
(excerpted from a paper by Brian Leftow):...”

Following that you state the above four sentences as you consider was Leftow’s “had something like the following in mind.”

As I stated in my post Sun Sep 09, 2007 1:12 pm, my remarks were addressed to the four statements about which you said: “I suspect he (Kurt Gödel) had something like the following in mind
(excerpted from a paper by Brian Leftow):...”

Your statement was that Brian Leftow “had something like the following in mind” regarding Kurt Gödel.

I took at face value your statement and accepted that Brian Leftow thought just what you stated.

You have made no refutation of my analysis here or otherwise in previous posts. You appear to contradict yourself here as you state: “Brian Leftow's paper has nothing to do with Kurt Gödel.”

If that were the case, why did you cite “Brian Leftow” as commenting on what Gödel had “in mind”?

Most inconsistent, CC.

JAK

[_marg]

marg,

Previously you asked me what I thought Kurt Gödel meant by God or God-like. I suspect he had something like the following in mind
(excerpted from a paper by Brian Leftow):

* God has no material parts.
* God is not distinct from his essential attributes.
* God's essential attributes are not distinct from one another.
* God is not distinct from His existence.

I intend to address other posts in this thread and get back to ones I said I would respond to.

CC you stated that logic is essential to theology and then said your reasoning was that you accept Godel's logic argument for God and worked from there. Gad I believe supported you in the premise that "logic was essential to theology". My understanding of theology is that it includes a study of God/Gods.

The practical purpose of using logic both formal and informal is to reach conclusions which can be relied upon.

Your statement above regarding what Godel meant by God and God-like illustrates you do not employ logic as a basis in theology, because you acknowledge you don't even know what Godel meant. You say "I suspect he had something like the following in mind... " If you don't have a clear understanding of Godel's God you can't reach reliable conclusions which follow from that poor understanding.


What I have been attempting in this thread and I believe JAK as well has, is to get you, Gad and Tarski to support the argument "logic is essential to theology".

Not one of you seems to be able to explain what Godel's God is. And once Godel's God is explained then show that Godel's God links to or relates to theology...the crux of this argument.

Personally, I believe Godel's God has nothing to do with theology. Whaty I believe Godel God is differs to what you think. Tarksi mentioned in a post that Godel's God is a "being". I'd like to know where Godel's ever makes claim symbolically or using words that the God in his argument is an entity/being.

I will try in the next week to spend more time on this thread. My priorities have shifted away from message boards. But this thread still interests me, because critical thinking is what I am most interested in.

[_A Light in the Darkness]

Yesterday, an event happened. My stepdaughter cried. I suppose science would be helpless to decipher the cause of that event. It seems to me a good starting hypothesis would be the ice cream truck passed by before I could grab my wallet and get out the door. But in "to John history" all I can say is that the ice cream truck drove by. A lot of dots, with no lines.

I just started reading this thread, but you're already off on the wrong foot. I doubt the poster was saying that science cannot speak to causes of events. That's most of what science is. Rather, what he was attempting to get across likely was the idea that science can describe events without eliminating supernatural cases. So the idea that the ice cream truck incident was caused by a series of events set in motion by God is not something science can speak to. But then charity was never one of your virtues.

[_A Light in the Darkness]

Gadianton -

A common criticism of Ontological arguments, including Godel's, is that they are question-begging or invalid depending on how they are read. The charge is usually of sneaking the property of existence somewhere to prove existence. (see: http://plato.stanford.edu/entries/ontol ... arguments/) If I were to guess, that's why I imagine Jak made the criticism. Now it is true one wouldn't expect Godel to make an elementary error, but I don't think anyone with a sophisticated view on the subject makes that accusation. Jak seems like he is, so I think your critique is apt. However, that does not mean that someone's reasoning cannot in a more subtle way reduce into a simple fallacy. A great logician isn't going to commit simple logical fallacies, but he or she very well might make errors that ultimately reduce into those fallacies. It is not absurd to charge Godel with begging the question somewhere as long as that is understood. As for the success or failure of ontological arguments, it's generally common knowledge that they are susceptible to parodies that tell us they are going wrong somewhere, but one of the things that makes them worthy of academic study is that it isn't as simple of a matter to figure out exactly how they are going wrong. They really don't have much to do with LDS faith or the thinking behind it.

[_marg]

As I said though rereading last night the thread and JAK's post again, made me appreciate just how brilliant he is.

You've been bamboozled.

by the way, here is where you can read about the mandelbot set.
http://www.ipod.org.uk/reality/reality_ ... iverse.asp

Tell me if you think no new information can be discovered about it since it is a purely analytically defined object?
Hint: We discover profound things about this set all the time. Knowledge is gained.

I only briefly looked at the mandlebot set ..computer pattern simulation. I'm not certain if this is providing new information. I'll assume a pattern can be created infinitely, but if so that is already imbedded in the mathematical formulation. That would be similar to dividing 10 by 3 and the answer is an infinite 3.333 etc. If there is a loop it can go on indefinitely.

But Tarski, mathematical arguments/formulations do not equate into word arguments cleanly and necessarily. When a deductive word argument is formulated such as this Godel one for "God" in which it does not link to an actual world, then the conclusion is a created assumed one. The word God in the conclusion loops back to the word God of the def'n. In both the conclusion and the def'n, the existence of this "God" whatever that God is ..is assumed.

But if we can link to the actual world then the argument makes sense. If Godel or if whomever translated Godel's symbols into word format had been more specific in the def'n of the word God-like..and described/defined God as a (platonic) ultimate eternal knowledge, the argument would make sense, because everyone can appreciate that conceptually. But by using the value laden word "God" people such as CC are misinterpreting and assuming that Godel's argument can be lifted and applied to the God concept in theology. And as in this case, CC has erroneously assumed that because the argument appears to be presented logically then theology must be logically based.

by the way I took this from your link:

Note the conclusion: "Only in a stable, 4-dimensional universe such as our universe would mathematics be useful for analysing physical reality. Hence, the reason why we find mathematics such as useful tool."


"Why does Physics follow Mathematics?
The principle of axioms might go some way to explain the almost uncanny match between mathematics and physics. Mathematics has been almost uncannily useful in explaining the natural sciences. It is almost weird the way that developments in mathematics, and the discovery of new mathematical structures, has been later matched by discoveries in physics which involve the similar structures in the physical world (see The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner, and the entertaining short story Unreasonable Effectiveness by Alex Kasman). For example, in 1931 Paul Dirac predicted the existence of the positron purely by considering mathematics - the first time a particle had been predicted from purely mathematical considerations. For this reason, mathematics has been called the "language of nature".

In order to get a better understanding of this apparently uncanny match, we should consider the origin of mathematics. Right back when man first started counting physical objects and discovered the usefulness of numbers and arithmetic for commerce, mathematics has been developed as a useful tool when it is used as an abstraction from physical reality. Maybe we now find a situation whereby developments in mathematics are later being shown to have equivalent counterparts in physics, but we would do well to remember that at the start it was physical reality that provided the motive for developments in mathematics.


It should also be realised that physical structures and processes are axiomatic systems - at their most fundamental level they are themselves also subject to physical axioms, self-evident truths. The axioms can be combined to describe the behaviour of larger, more complex physical systems: macroscopic behaviour results from microscopic behaviour (read about the building of a ladder of effective theories on the It's a Small World page). Indeed, David Hilbert wanted to see a full mathematical treatment of the axioms of physics (see here). In particular, he considered the kinetic theory of gases in which the pressure, temperature, or volume of gases could be found by considering the statistical mathematical behaviour of smaller constituent molecules. Paul Benioff has described a framework for linking physics and mathematics: "The basic properties of the physical and mathematical universes and a coherent theory are emergent together and mutually determined and entwined" (arXiv paper quant-ph/0201093).

If mathematics was developed as a model of the behaviour of physical reality, and if physical reality is an axiomatic system, then it should be no surprise that the resultant mathematics turned out to be an axiomatic system. From the very start, mathematics was designed to match physics, to be an effective tool. Developments in physics provided the motive and inspiration for developments in mathematics. As developments in physics are now stalling (with the requirement for ever-larger particle accelerators) it's little wonder that developments in mathematics have forged ahead and are later found to mirror developments in physics. The use of symmetry in discovering new elementary particles has been especially remarkable, but it should be remembered that the initial inspiration for exploring mathematical symmetry came from exploring the natural beauty of the macroscopic physical world.

So we should not forget that the strength of mathematics lies in its ability as an abstracted tool for describing physical reality, which was its initial function. Hence, mathematics emerges as an epiphenomenon - see here. It could be said that mathematics has moved away from this role to consider structures which have reduced roles in physical reality, such as Gödel's Theorem and Cantor's "uncountable infinities". As explained in the previous "White Christmas" discussion, it might be possible to find uses for these results in physical reality, but that would prove a difficult task. Indeed, the mathematical principle of "infinity" appears to have no manifestation in physical reality, and the presence of infinity in physics theories is generally taken to represent a flaw in the theory (the elimination of troublesome infinities is a major reason behind the popularity of string theory). And the discovery of some logical paradoxes involving circular reasoning would also appear unable to correspond to any situation in the real world - see Russell's paradox (physical reality contains no such circular paradoxes: only if time travel was ever discovered might we see the emergence of "killing your own grandfather"-type circular paradoxes). As mathematics continues down this esoteric path, it might be considered to be "disappearing up its own backside": mathematics for mathematics' sake.

Mathematics in the Multiverse

Andrei Linde has considered the development of mathematics in different universes of a "multiverse" structure (Section 11 of arXiv paper hep-th/0211048).

Each "bubble" universe in an eternally inflating multiverse can have different values for the physical constants, and even different numbers of spatial dimensions (see the page on The Anthropic Principle for a discussion of eternal inflation and the multiverse).
In the discussion of Andrei Linde there is once again an implicit acknowledgement of the importance of mathematics as being first and foremost an abstraction from physical reality (no Platonic realms in Linde's world). Hence, the different physical conditions in each universe would result in different mathematical systems. Many universes (maybe possessing more or less than 3 spatial dimensions) would have physical conditions completely averse to the formation of stable structures (such as galaxies and planets) and the evolution of life would be impossible. Many universes would be unable to expand, or would rapidly shrink back to nothing. Mathematics, being an abstraction from physical reality, would be of no use in such a degenerate universe. Only in a stable, 4-dimensional universe such as our universe would mathematics be useful for analysing physical reality. Hence, the reason why we find mathematics such as useful tool."

[_JAK]

Yesterday, an event happened. My stepdaughter cried. I suppose science would be helpless to decipher the cause of that event. It seems to me a good starting hypothesis would be the ice cream truck passed by before I could grab my wallet and get out the door. But in "to John history" all I can say is that the ice cream truck drove by. A lot of dots, with no lines.

I just started reading this thread, but you're already off on the wrong foot. I doubt the poster was saying that science cannot speak to causes of events. That's most of what science is. Rather, what he was attempting to get across likely was the idea that science can describe events without eliminating supernatural cases. So the idea that the ice cream truck incident was caused by a series of events set in motion by God is not something science can speak to. But then charity was never one of your virtues.

ALITD stated in part:
I doubt the poster was saying that science cannot speak to causes of events. That's most of what science is. Rather, what he was attempting to get across likely was the idea that science can describe events without eliminating supernatural cases. (bold emphasis added)

“Supernatural cases” have not been established. Science ignores claims absent evidence. But you, it would appear, wish to assert “supernatural.”

If that’s the case, the burden of proof lies with those who make claims. Science makes no claims regarding supernatural mythologies.

You make up a story here:

ALITD stated:
So the idea that the ice cream truck incident was caused by a series of events set in motion by God is not something science can speak to. But then charity was never one of your virtues.

You are not speaking to it unless you can establish reliable evidence for a claim God. You have not done that. You speculate absent the presentation of evidence. The ice cream truck incident in no way speaks to any elucidation of a God claim.

You make it up as you go. Absent evidence for a God claim, such a claim is irrelevant. Psychology and psychiatry can speak to the story of the ice cream truck. And both are aspects of science not religion.

Absent affirmative evidence for a claim, the negative is assumed. Hence, the burden of proof and evidence to support that lies with the affirmative claim.

JAK