The Roles of Logic and Science in Questions of Theology

[_marg]

marg,

Am I understanding this post correctly?

Did presently “Gadianton” previously posted as “Grayskull” on this same forum?

JAK

Correct. Some time ago Gad was going through some personal problems and notified the board he was leaving. I believe about a year ago. He came back posting as grayskull but didn't tell the board who he was. Then more recently Gad started posting again and mentioned he had been posting as someone else but didn't give the name. It was Tarski who revealed who he was. You might remember grayskull as the logically impaired individual who sided with Aquinas, the fellow who started the thread "Logic lessons for marg and Jak.

I've come across Gad in the past on this board. He was critical of a post by Bob McCue (who was also philo on 2 think..he didn't post much there) which Bob wrote on the Mormon apologetic board FAIR now called MADD. Gad's forté is philosophical lingo. That's probably more information than you wanted to know.

[_JAK]

marg,

Am I understanding this post correctly?

Did presently “Gadianton” previously posted as “Grayskull” on this same forum?

JAK

Correct. Some time ago Gad was going through some personal problems and notified the board he was leaving. I believe about a year ago. He came back posting as grayskull but didn't tell the board who he was. Then more recently Gad started posting again and mentioned he had been posting as someone else but didn't give the name. It was Tarski who revealed who he was. You might remember grayskull as the logically impaired individual who sided with Aquinas, the fellow who started the thread "Logic lessons for marg and Jak.

I've come across Gad in the past on this board. He was critical of a post by Bob McCue (who was also philo on 2 think..he didn't post much there) which Bob wrote on the Mormon apologetic board FAIR now called MADD. Gad's forté is philosophical lingo. That's probably more information than you wanted to know.

I’m for information :-) and it’s not more than I wanted to know. It’s more than I expected to learn.

What is your view on why anyone is motivated to do what you have described? (more information, please)

JAK

[_marg]

I asked you previously regarding Godel's ontological conclusion: Does the conclusion conclude that a God exists as an actual entity, by actual I mean a thing which exists in reality.


You replied : Yes, but "actual entities" in philosophy are slippery. Does "truth" actually exist? Does the number "5" actually exist?

I specified the type of reality I was referring to..actualities ..entities identifiable or potentially identifiable. I'm clearly not talking about platonic truth, platonic reality or numbers in mathematical games, so don't bother setting up strawmen to argue against.

Your answer contradicts Tarski who said "So it seems that an existence proof in an axiomatic system only establishes existence relative to that system." Therefore Tarski does not say the conclusion concludes an actual God exists and you are in disagreement with him.

So please don't disingenously attempt to piggy back onto Tarski's post, as if you have been thinking the same thing all along as what he presented.

As I said before everything JAK said appears to me to coincide with Tarski, I see no contradictions, whereas I do see major contradiction between Tarski's point and the anemic bits of argument you have presented.

[_marg]

I’m for information :-) and it’s not more than I wanted to know. It’s more than I expected to learn.

What is your view on why anyone is motivated to do what you have described? (more information, please)

JAK

I don't think Gad meant anything devious by posting as grayskull. I think perhaps he wasn't sure he wanted to get involved much again, and by posting incognito it would be easier.

[_Calculus Crusader]

Gad wrote (among other things):

While the world's most significant logician might have been wrong, he probably wasn't merely begging the question.

I think you're just a wee bit outclassed by Godel...(and he almost surely never published anything containing a clear logical fallacy nor simply did he ever reason in circles)

As for the Ontological Argument on its own, even if true, it doesn't tell us very much. But let's be clear on a few things:

1) the Ontological argument existed long before "modal logic" so JAK's list of sources hoping to show that there isn't agreement on formalizing modal logic is only slightly more interesting than the fact that there is no exhaustive formal list of rules for writing in English and one may, write in English, on many different topics, just like one can use modal logic to pursue many things other than the Ontological Argument which most philosophers today probably have little interest in.
2) modal logic could at least potentially tell us many things about the world without "empirical evidence". There are those on the ultra skeptical side about that like say, Daniel Dennett, but he holds a very minority view and plenty of atheists committed to a purely physical and natural world, as an example for the other side of the extreme, David Lewis (who was a modal realist, which is possibly even more extreme than being a Platonist), make strong arguments about the way the world is using modal logic without actually engaging any "evidence". So you can shout all you like about the need for empirical evidence, and I sure do like evidence myself, but all the emperical evidence in the world isn't going to tell you whether numbers are real or not, or whether moral statements are real. "God" in theism reasoned from ontology, similarly, isn't something empirical evidence will ever say much about.


3) sorry, but JAK has not, nor will he ever find a simple logical fallacy in Godel's thinking, no matter what Godel was thinking about.

This is congruent with what Dr. Tarski wrote. I am the only one here who fully supports Gödel's argument. Gad merely objected to a pretentious know-nothing putting on airs and having the temerity to disparage one of the greatest, if not the greatest, logicians of all time.

[_Tarski]

I asked you previously regarding Godel's ontological conclusion: Does the conclusion conclude that a God exists as an actual entity, by actual I mean a thing which exists in reality.


You replied : Yes, but "actual entities" in philosophy are slippery. Does "truth" actually exist? Does the number "5" actually exist?

I specified the type of reality I was referring to..actualities ..entities identifiable or potentially identifiable. I'm clearly not talking about platonic truth, platonic reality or numbers in mathematical games, so don't bother setting up strawmen to argue against.

Your answer contradicts Tarski who said "So it seems that an existence proof in an axiomatic system only establishes existence relative to that system." Therefore Tarski does not say the conclusion concludes an actual God exists and you are in disagreement with him.

So please don't disingenously attempt to piggy back onto Tarski's post, as if you have been thinking the same thing all along as what he presented.

As I said before everything JAK said appears to me to coincide with Tarski, I see no contradictions, whereas I do see major contradiction between Tarski's point and the anemic bits of argument you have presented.

Marg,
First of all I am no authority and I used the word "seems" on purpose. I think that in the setting of Godel's ontological proof words like "real" and 'actual" are tricky as Gad says. I have been puzzling over it for a while. Also, while I agree that it seems overwhelmingly likely that Godel's argument does not do what Christian theists hope it does, it is also not the case that I think that Godel is just making a silly logic 101 mistake. Even if he is in the end, it would take a very close look and a trained person to discern it. This is what Gad is getting at.

There is a difference between saying that Godel just simplemindedly begged the question and recognizing that not only do we usually take truths in axiomatic system to be based on the assumed truth of the axioms, it is also the case that the ontology of the entities derived in existential proofs must lean on the ontology of the axioms in some way also; but this seems tricky to me.

This type of thing does not interfere with the work of (most) mathematicians and scientists.

I have to admit to being puzzled by the adversarial thing between you and Gad.

I think there is a kind of personality conflict going on that prevents communication.

My take on Gad is that he does have some good background. In fact, he hints a lot at arguments familiar to people like Richard Rorty, Hilary Putnam, Hubert Dreyfus, Nelson Goodman etc. that while variously flawed, cause real problems for simplistic versions of empiricism, falsificationism and other traditional positions, and call into question any formulaic idea of what science is.

Having read some of the same stuff, I can often catch what he is hinting at.
So why doesn't he come out with a definitive argument? Well, because he is touching on issues that are pretty subtle and are still causing turmoil in philosophy. He is hinting at book length arguments and discussions--discussions that often end not in positive conclusions but in heightened awareness of often unnoticed issues.

I don't blame him for not launching on a 50 page explanation of why 'actual" is touchy etc.

The funny thing is that we all agree that Godel has not given a proof of God's existence in any sense that would be useful to mainstream Christians and probably not even in a sense that would ultimately be useful in philosophy.

Despite his awareness of and refusal to dismiss the ideas of many philosophers (including those in the continental tradition), I guess that at the end of the day and in practice, Gad is a supporter of mainstream science and basic skeptical attitudes.

So even when he agrees with someones basic conclusions he does not like to let it just be if he thinks that it was all to easy and if certain subtleties were missed.

Do I wish he would say more and argue it out a bit more?
Yes.
Do I think he is faking it and just throwing out lingo?
No I don't.

[_JAK]

I asked you previously regarding Godel's ontological conclusion: Does the conclusion conclude that a God exists as an actual entity, by actual I mean a thing which exists in reality.


You replied : Yes, but "actual entities" in philosophy are slippery. Does "truth" actually exist? Does the number "5" actually exist?

I specified the type of reality I was referring to..actualities ..entities identifiable or potentially identifiable. I'm clearly not talking about platonic truth, platonic reality or numbers in mathematical games, so don't bother setting up strawmen to argue against.

Your answer contradicts Tarski who said "So it seems that an existence proof in an axiomatic system only establishes existence relative to that system." Therefore Tarski does not say the conclusion concludes an actual God exists and you are in disagreement with him.

So please don't disingenously attempt to piggy back onto Tarski's post, as if you have been thinking the same thing all along as what he presented.

As I said before everything JAK said appears to me to coincide with Tarski, I see no contradictions, whereas I do see major contradiction between Tarski's point and the anemic bits of argument you have presented.

Marg,
First of all I am no authority and I used the word "seems" on purpose. I think that in the setting of Godel's ontological proof words like "real" and 'actual" are tricky as Gad says. I have been puzzling over it for a while. Also, while I agree that it seems overwhelmingly likely that Godel's argument does not do what Christian theists hope it does, it is also not the case that I think that Godel is just making a silly logic 101 mistake. Even if he is in the end, it would take a very close look and a trained person to discern it. This is what Gad is getting at.

There is a difference between saying that Godel just simplemindedly begged the question and recognizing that not only do we usually take truths in axiomatic system to be based on the assumed truth of the axioms, it is also the case that the ontology of the entities derived in existential proofs must lean on the ontology of the axioms in some way also; but this seems tricky to me.

This type of thing does not interfere with the work of (most) mathematicians and scientists.

I have to admit to being puzzled by the adversarial thing between you and Gad.

I think there is a kind of personality conflict going on that prevents communication.

My take on Gad is that he does have some good background. In fact, he hints a lot at arguments familiar to people like Richard Rorty, Hilary Putnam, Hubert Dreyfus, Nelson Goodman etc. that while variously flawed, cause real problems for simplistic versions of empiricism, falsificationism and other traditional positions, and call into question any formulaic idea of what science is.

Having read some of the same stuff, I can often catch what he is hinting at.
So why doesn't he come out with a definitive argument? Well, because he is touching on issues that are pretty subtle and are still causing turmoil in philosophy. He is hinting at book length arguments and discussions--discussions that often end not in positive conclusions but in heightened awareness of often unnoticed issues.

I don't blame him for not launching on a 50 page explanation of why 'actual" is touchy etc.

The funny thing is that we all agree that Godel has not given a proof of God's existence in any sense that would be useful to mainstream Christians and probably not even in a sense that would ultimately be useful in philosophy.

Despite his awareness of and refusal to dismiss the ideas of many philosophers (including those in the continental tradition), I guess that at the end of the day and in practice, Gad is a supporter of mainstream science and basic skeptical attitudes.

So even when he agrees with someones basic conclusions he does not like to let it just be if he thinks that it was all to easy and if certain subtleties were missed.

Do I wish he would say more and argue it out a bit more?
Yes.
Do I think he is faking it and just throwing out lingo?
No I don't.

Tarski & marg,

At this point in this thread, I decided to return to page 1 of the first comments. There, it seemed as if there was some effort to address the issue: The Roles of Logic and Science in Questions of Theology. However, as discussion turned to ambiguity of language and use of terminology or implied narrow definition, the discussion appeared to get farther and farther from an address of the initial question.

Given just the Wikipedia extended definition of that term and the various links, the “roles” are ambiguous as your post here would seem to confirm.

You, Tarski, observed:
I think that in the setting of Godel's ontological proof words like "real" and 'actual" are tricky...

I agree and tricky words make for complex if not failed communication as people who use such words mean different things by them.

You, Tarski, observed:
Also, while I agree that it seems overwhelmingly likely that Godel's argument does not do what Christian theists hope it does, it is also not the case that I think that Godel is just making a silly logic 101 mistake. Even if he is in the end, it would take a very close look and a trained person to discern it.

I also agree with your “while” subordinate clause (as my previous analysis has shown). Whether we have a “silly logic...mistake” is a judgment from a perspective removed from the source of the construction. However, it’s irrelevant if we agree with your “while” subordinate clause.

On page 2 (at the bottom) in this thread, Calculus Crusader (CC) posted definitions, axioms, theorems, and corollaries which he attributed to Gödel.

Supposing that to be accurate, “Definition 1” assumes God.

The definition as quoted by CC reads:
“Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive”

Regardless of any debate over “properties” vs. “essential properties” and regardless of consensus or lack thereof on “positive,” the definition itself makes assumption. That assumption is repeated in “Axiom 3,” “Corollary 1,” “Theorem 2,” and “Theorem 3.”

Your last sentence in the above comment states:

... it is also not the case that I think that Godel is just making a silly logic 101 mistake. Even if he is in the end, it would take a very close look and a trained person to discern it.

Assuming that which has not been established is certainly flawed science. It’s also flawed logic in the broader context of logic than merely form or mathematical consistency or argument from syllogism.

I don’t see essential disagreement with you in this extension.

The stated topic contains several terms which are clearly open to interpretation and contextual application. In the pages of discussion which followed, that factor was overlooked or abandoned entirely.

I find this comment puzzling:

[color=#3CB371] You observed:
I have to admit to being puzzled by the adversarial thing between you and Gad.

I think there is a kind of personality conflict going on that prevents communication.

Rather than address issues in the topic with intent to discuss controversy or problem in the topic, Gad instead chose ad hominem. It was not marg who began that, but she pointed it out and challenged Gad to address the topic. He continued with what marg regarded as off-topic, spurious comment. That does not seem a puzzle.

[color=#3CB371] You stated:
My take on Gad is that he does have some good background.


It was not well demonstrated to either marg or me.

[color=#3CB371] You stated:
So why doesn't he (Gad) come out with a definitive argument? Well, because he is touching on issues that are pretty subtle and are still causing turmoil in philosophy.

I’m skeptical of that reason.

Why not do as you have done here: recognize we are addressing “issues” which are “subtle” and cause “turmoil in philosophy”? You have a clear, articulate expression.

[color=#3CB371] You stated:
He (Gad) is hinting at book length arguments and discussions--discussions that often end not in positive conclusions but in heightened awareness of often unnoticed issues.

If these are “book length arguments” (and I agree), why waste time in limited space with specious, bogus language?

[color=#3CB371] You stated:
The funny thing is that we all agree that Godel has not given a proof of God's existence in any sense that would be useful to mainstream Christians and probably not even in a sense that would ultimately be useful in philosophy.

Again, I’m skeptical that “we all agree...” If that were the case, Gad could have easily expressed that (as you have) and could have addressed points of issue related to the initial topic.

[color=#3CB371] You stated:
...I guess that at the end of the day and in practice, Gad is a supporter of mainstream science and basic skeptical attitudes.

So even when he agrees with someones basic conclusions he does not like to let it just be if he thinks that it was all to easy and if certain subtleties were missed.

An interesting defense

JAK

[_Tarski]

The definition as quoted by CC reads:
“Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive”

Regardless of any debate over “properties” vs. “essential properties” and regardless of consensus or lack thereof on “positive,” the definition itself makes assumption. That assumption is repeated in “Axiom 3,” “Corollary 1,” “Theorem 2,” and “Theorem 3.”

You need to explain this better. How does merely making a technical definition amount to assuming the outcome of the argument??

For example, suppose I make the following definition.

Definition: A Riemannian manifold is ghost-like if it is geodesically complete but not metrically complete.

Now if I make an argument showing that ghost-like manifolds exist, then I will have certainly made a mistake, because in fact, it can be proved that all geodesically complete manifolds are metrically complete. So ghost-like manifolds do not exist. But the definition is OK as it stands until the existential question is settled rendering it empty (and it is settled in this case; they don't exist).

I have not made a mistake in the very definition have I? I can define whatever I want as long as the definition is clear and refers to only understood ideas and entities.
If Godel makes a mistake here, it is either in that the definition is not clear (referring to unclear notions of positive etc). Otherwise the mistake comes later in the argument.

Notice that the argument would be the same even if he used the word G-like or even H-like or Q-like in the definition.

To my eye, definition 3 looks suspicious. What word or concept is being defined? exists?
On the face of it 3 looks more like a claim than a definition.

I suspect that it boils down to the usual issue over whether existence (or necessary existence) is a property (or in this case a positive property-whatever that is!).

Now you also see the word "God" in axiom 3 and so you seem to conclude that God's existence is assumed there. But again this can't be the problem.
The axiom reads "Axiom 3: The property of being God-like is positive". This doesn't assume the existence of a God-like being and God-like is still so far just coinage for what is defined in definition 1 (we didn't need to use the word "God" at all).

The question for axioms is whether they are clear and whether they can usefully be regarded as true. Well, is Axiom 3 true and clear?
Not to me. First, I am unclear on the term "positive". Where is it defined?
Second, even after having settled on a sense for the word positive it still seems unlikely that I would consider the axiom to be obviously true.

[_marg]

Marg,
First of all I am no authority and I used the word "seems" on purpose. I think that in the setting of Godel's ontological proof words like "real" and 'actual" are tricky as Gad says.

Tarski, I agree real and reality are tricky words and I'll forego explanation. I don't think actual and actualities are tricky word. You Tarksi actually exist. You are a scientific object which exists as an actuality. You can be studied, there can be consensus agreement on what you are, at whatever level is under study.

I have been puzzling over it for a while. Also, while I agree that it seems overwhelmingly likely that Godel's argument does not do what Christian theists hope it does, it is also not the case that I think that Godel is just making a silly logic 101 mistake. Even if he is in the end, it would take a very close look and a trained person to discern it. This is what Gad is getting at.

I appreciate and have expressed this, that Godel's God argument is a closed system. That argument with its conclusion may be valid, but the conclusion is contingent upon the game. You can not take that conclusion outside the game. Just like in Euclidean geometry conclusions regarding triangles are contingent upon the Euclidean system, not outside it with other systems. So as long as one is honest and acknowledges that Godels' god is contingent upon his axioms and definitions and says nothing reliable logically about an actual God outside the system, I don't have a problem with Godel. I have a problem with those who attempt to argue that Godel provides logical proof of a god. Without a link to the actual world, what reliable information to us re a God or Gods,can it possibly offer? And by the way I asked both Gad and CC, where is the link and neither responded.

There is a difference between saying that Godel just simplemindedly begged the question and recognizing that not only do we usually take truths in axiomatic system to be based on the assumed truth of the axioms, it is also the case that the ontology of the entities derived in existential proofs must lean on the ontology of the axioms in some way also; but this seems tricky to me.

I really can not see how any ontological proof can possibly logically establish the existence of an entity. It seems to me that if one creates a definition, assumes axioms which bear no direct relation to the actual world, that it has to be a matter of begging the question. As I pointed out to Gad, all deductive arguments are circular to some extent, and this modal proof for God seems deductive to me. Deductive within the system. With science the natural physical laws are assumed because they have been found to hold true, should one ever be found to not hold true the assumption will change. But science doesn't willy nilly simply assume whatever it wishes to for (axiomatic) natural physical laws.

This type of thing does not interfere with the work of (most) mathematicians and scientists.

I have to admit to being puzzled by the adversarial thing between you and Gad.



I think there is a kind of personality conflict going on that prevents communication.

Gad had plenty of opportunity to communicate on the main issue at hand, he chose disingenuous diversionary tactic (re K. Armstrong) and plenty of ad hominem. I'm not going to psychoanalyze him.

My take on Gad is that he does have some good background. In fact, he hints a lot at arguments familiar to people like Richard Rorty, Hilary Putnam, Hubert Dreyfus, Nelson Goodman etc. that while variously flawed, cause real problems for simplistic versions of empiricism, falsificationism and other traditional positions, and call into question any formulaic idea of what science is.

Having read some of the same stuff, I can often catch what he is hinting at.
So why doesn't he come out with a definitive argument? Well, because he is touching on issues that are pretty subtle and are still causing turmoil in philosophy. He is hinting at book length arguments and discussions--discussions that often end not in positive conclusions but in heightened awareness of often unnoticed issues.

Again I'm not going to comment.

I don't blame him for not launching on a 50 page explanation of why 'actual" is touchy etc.

Tarski it's not that complicated. Does Godel's proof offer a reliable conclusion that an actual God exists. We don't have to appreciate the reality of a God to answer that.

The funny thing is that we all agree that Godel has not given a proof of God's existence in any sense that would be useful to mainstream Christians and probably not even in a sense that would ultimately be useful in philosophy.

Why do you only mention Christianity? Let's just assume a God exists which we have no knowledge of, we can not appreciate any sort of reality of this god..but it exists just the same as an actuality which we don't currently comprehend. Does Godel's proof help us in anyway logically? Is there any connection between Godel's proof and that actual God? It really would be just a coincidence that Godel's conclusion god exists, is right. It's like if you wrote a multiple choice test and got 85% but answered based on a predetermined formula. You may have guessed right, the formula was successful but the 85% has no connection to your knowledge about the subject, you just happened to pick the right formula. And so it is with Godel's formula it doesn't offer a reliable conclusion, and hence it's not logical to assume God based on it.

Despite his awareness of and refusal to dismiss the ideas of many philosophers (including those in the continental tradition), I guess that at the end of the day and in practice, Gad is a supporter of mainstream science and basic skeptical attitudes.

So even when he agrees with someones basic conclusions he does not like to let it just be if he thinks that it was all to easy and if certain subtleties were missed.

Gad was arrogant and disrespectful to JAK who was undeserving of Gad's behavior.

Do I wish he would say more and argue it out a bit more?
Yes.
Do I think he is faking it and just throwing out lingo?
No I don't.

Well Gad has indicated to me previously on this board his logic appreciation is suspect. I think he's studied philosophy and I note he loves to use philosphical terms to whomever he's discussing with, even if they are not familiar with that language.

[_Tarski]

That argument with its conclusion may be valid, but the conclusion is contingent upon the game. You can not take that conclusion outside the game. Just like in Euclidean geometry conclusions regarding triangles are contingent upon the Euclidean system, not outside it with other systems.

And yet if I draw a conclusion about Euclidean triangles a surveyor might actually care and trust that certain physical consequences follow even without specifically testing them, while if I draw a conclusion about hyperbolic triangles she/he would not. We both no there is a reason for that.

I really can not see how any ontological proof can possibly logically establish the existence of an entity. It seems to me that if one creates a definition, assumes axioms which bear no direct relation to the actual world, that it has to be a matter of begging the question. As I pointed out to Gad, all deductive arguments are circular to some extent, and this modal proof for God seems deductive to me. Deductive within the system. With science the natural physical laws are assumed because they have been found to hold true, should one ever be found to not hold true the assumption will change. But science doesn't willy nilly simply assume whatever it wishes to for (axiomatic) natural physical laws.

Then one must argue about how Godel's axioms are willy-nilly. He did not just assume God exists. Read my reply to JAK.

A couple of questions (don't assume what my answers may be):

1. Are prime numbers actual? real? (We do use primeness in the real world for cryptography). What have I accomplished if I show that there exists an infinite number of primes and does this have real world consequences?

2. Is the real number system (which gives rise to the possibility of the mathematics of general relativity) a closed system based on willy-nilly assumptions completely unconnected to the actual world? Can I use the mathematics to arrive at likely truths about the real cosmos (positive mass conjecture etc.)?

3. How can we ever use deductive reason about the actual real world?

4. Can I use arithmetic to arrive at conclusions about the real world (like my finances or whether my digital secrets are secure)?

5. Are all axioms equally unrelated or related to the actual world?

6. Is there a difference between actual, real and physical?

Finally

7. Do you agree with JAK that the existence of God is assumed in definition 1? (see my response to him)