The Roles of Logic and Science in Questions of Theology

[Guest]

Tarski,

Not only are you repeating, you continue to evade the issues which I have raised.

You, Tarski, stated:
You are starting to repeat yourself and yet you are clearly not really reading and thinking about what I write.

I have addressed the point about connotations of the word God in the coinage God-like.

Use of mathematical examples are perfect for the task because here we have a fertile ground for formal deductive structures. The whole point about a formal deductive argument is that its validity depends only on its form (while soundness depends also on the truth of the axioms).

JAK:
Why are terms like “x” used in the construction of deductive structures?

I submit they are used so that the focus is upon the structure. Mixing emotionally loaded, religious/theological terms contaminates that focus.

I have no objection to use of deductive structures. However, beyond simply instruction in the syllogism as a tool, deductive structures, no matter how well constructed, generate flawed conclusions if their generalizations (premises) are false, ambiguous, or lack support.

Your obsession with math here has taken you away from the question at hand “The Roles of Logic and Science in Questions of Theology.”

What’s “the task” in your above statement?

Your opening:
“Use of mathematical examples are perfect for the task...”

The issues in “The Roles of Logic and Science in Questions of Theology” are not addressed by “mathematical examples” alone.

“Formal deductive structures” are useful.

Absent reliable premises (flawed or ambiguous) they are of no practical benefit. I think that has been a point of marg in her discussion with you.

Surely you would agree that a flawed or ambiguous premise in a “formal deductive structure” will yield false or unreliable conclusion.

Perhaps not. In any case, your obsession with math over logic, science, and theology appears to make it impossible for you to address the topic.

Your posts seem to make it clear that you have no intention of addressing the fundamental questions which I have raised regarding Godel’s word choices.

To wit:

Tarski stated:
Let me try one last time.

First, Godel defines a term. He is not simply applying a common term or trying to merely expand on a common notion.

He does not use in his argument anything beyond what is in the definition. Can you pinpoint exactly where you think he does that? One sentence should do.

In particular, he doesn't insert anything that people normally associate with the word God but sticks to his own definition. Show otherwise if you can.

Tarski stated:
The formal argument is unaltered if he replaces the word god-like with dog-like.

JAK:
The topic: “The Roles of Logic and Science in Questions of Theology”

Your defense of word-games continues, just as before, to beg the question.

Do you defend use of “God-like”? If not and if “God-like” is equal to “dog-like,” why would Godel not have used “dog-like”?

I submit he did not because the entire construction would have appeared an absurdity to anyone who took the language as meaningful or useful beyond a formula for construction.

The formal argument is contaminated with other ambiguous words regardless of the issues raised by Godel’s selection of “God-like.”

Tarski stated:
However, he does use the word God in his coinage "God-like" for a reason-- just not the reason you think. He uses it because he feels, and so do I, that his definition does define something which is intuitively fitting.

JAK:
“Intuitively fitting” exactly and of what?

That means that “dog-like” would not have sufficed in his construction. “God-like” implies something quite different from “dog-like.” So you admit that “dog-like” would not have worked in the total of the construction to any benefit. Exactly my point. There was a reason to use “God” in the construction which had nothing to do with the formal argument at all.

“Intuitively fitting” -- another weasel phrase to cover the intent as Christian History Institute expressed: “Kurt Godel Proved Truth Higher than Logic.” But of course Godel proved no such thing as even that partisan website recognized.

Tarski stated:
He hopes not only to show that something exists which fits his definition, but eventually he hopes that the properties which adhere logically to his defined notion will answer to the readers intuitions about God.

JAK:
Exactly. So “God-like” is a “ruse” a “sleight of hand” as critics observed. He did not select “God-like” as a random, willie nilly, any-old-word-will-do since we are constructing formal logic.

Tarski stated:
But as far as the validity of the formal argument goes, the choice of the word "God-like" is utterly irrelevant.

JAK:
You have just admitted it’s relevant to the total construction which Godel makes. That any term could be substituted in a word-game is what is irrelevant to the total construction and intent which you admit and which for which Christian History Institute expressed compliment.

Finally, you support exactly my points regarding word-choice and the entirety of the Godel construction. And you knew that all along.

Tarski stated:
Just as is the case with the definition of the word smooth in mathematics. The word smooth has a precise meaning that would be the same and would not affect conclusions if it were called something else. Indeed, it is sometimes called C-infinity. But also the word smooth is used because of the intuitive connection between the ordinary use and the precise definition given.

JAK:
Entirely irrelevant to the issues which I raised. With the possible exception of university course work in deductive construction, words convey meaning within context. And the context here was not “merely definition” or “coinage” as you fallaciously attempted to defend previously.

Tarski stated:
So the reasons Godel used "G-o-d" in "God-like" is the same as the reason that Whitney (or whoever) chose the word smooth in the definition of smooth manifold and in both cases the connotations do not interfere with or enter the logic at all! (noticed that it is right here that I just addressed the question about word choice that you claim I don't address)

JAK:
A false claim based on your just made previous admission regarding Godel’s intent. It is not the same in application and intent as you admitted that: “He (Godel) hopes not only to show that something exists which fits his definition, but eventually he hopes that the properties which adhere logically to his defined notion will answer to the readers intuitions about God.”

The use of “God-like” and the use of “smooth” are comparatively dissimilar in the total application of the construction.

What does “smooth” attempt “to show” about “God”?
You admit that Godel intended to make a religious/theological proof. The word-game does not address my questions regarding word-choice.

You appear to be looking at a grain of sugar while ignoring the pie in which that grain appears.

Again, I have no objection to formal reasoning per se and for purposes greater than merely a study of form. In the context of this discussion the topic remains: “The Roles of Logic and Science in Questions of Theology.”

Despite the repeated use of “God-like,” Godel failed to connect logic to theology. That transcends your argument that “dog-like” could just as easily have been used as “God-like.” And for Godel’s purposes and the entire construction, “dog-like” would have made Godel appear absurd if we leave all other statements and substitute only “dog-like” for the phrase Godel in fact used -- “God-like.”

Tarski stated:
Godel clearly hopes that his readers will agree that definition he gives for God-like are intuitive and that the properties he shows follow from the definitions and axioms will be worthy of his choice of words.


JAK:
Of course he does and it’s a clear reason why he did not use “dog-like” or any other word phrase in his construction.

Previously, I asked you about “intuitive.” I some cases it might seem one thing, while in other cases, a different conclusion might result.

We already know that there is ambiguity in the construction of definitions. And “...worthy of his choice of words” clearly is an admission by you that word choice is not only important, it’s critical. Not just any old word will do. “Dog-like” will not do.

So the construction is about much more than a deductive format as you admit here. And you are finally addressing, in part, the issues which I raised.

Tarski stated:
He does not however, try do anything but prove that something satisfying definition 1 must exist (assuming the axioms of course).


JAK:
You never challenged that definition 1 was ambiguous. It is. As a result, nothing is proved despite the “try.”

Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive

Tarski stated:
The reader is free to deny that such a thing should be worshipped or thought of as identical with a pregiven notion of God already found in society. The reader is also free to deny the truth of the axioms.

JAK:
Yes

Tarski stated:
One thing he does not do is draw conclusions that derive inappropriately from any connotations that exceed his definition of the notion of God-like.

JAK:
And his construction assumes God-like Do you see ambiguity in “God-like”? What is “God-like”? Let’s consider your parallel which you claimed it was the same as “dog-like.” What is “dog-like”? Is it like dog? --Similar to “dog” If so, “dog” just as “God” is a noun and in Godel’s construction “God” as assumed, not “dog.” And the two in the context of any reading along with the complete construction do not and would not be the same in the mind of any rational reader of the construction.

Contrary to your claim, definition 1 assumes “God.” What does “is” mean? If it means exists (the general understanding of that word), the definition assumes “God.” Or, like God.

Definition 1: x is God-like... (bold is mine for emphasis).

How do we interpret “like” in the definition?

If we interpret it as a preposition, “God” is a noun object of the preposition. If we interpret it as description “God” is still a noun. The author chose the words. You admit the author intended to prove “God”. But we can see by definition 1 that “God” is assumed.

Definition 1: x is God-like... Clearly “x” is a noun and the subject of “is” (the linking verb).

Or x is like God. The “if” part of the construction is ambiguous. How relevant is ambiguous characterization? Not very. We don’t know what the author means, but we can guess that it’s ameliorative not pejorative.

Tarski stated:
The one caveat is that the Definition 1 employs the notion of positiveness which is insufficiently clarified. Indeed, the plausibility of the axioms applying to something in real seems to depend on the connotations of that word. But that is an issue with the axioms not the formal validity of the argument.

JAK:
Yes. Are you sure you agree with yourself? If “God” could just as well be “dog” and you deny difference because of formal structure, why not do the same thing with “positive”? It then means anything just as “God-like” equals “dog-like.” If that were really correct/true, “positive” could mean anything as well. It makes no difference what positive means.

I am not advocating the above, but rather pointing out that if one reduces all language (symbols) to meaningless, one could argue the above.

Tarski stated:
Godel's argument fails but for much more subtle reasons than most of what you have suggested (e.g. def 1 doesn't assume the existence of God). This should not be surprising since Godel is perhaps the greatest mathematical logician of modern times.

JAK:
As I articulated just above, definition 1 does assume. You have nowhere refuted the my analysis of construction as a whole and the analysis of definition 1. He connects “x” with a linking verb to “God-like.” We do not have, in Godel’s construction, purity of form with meaningless symbols. In the total construction of what was replicated, “God” is assumed in “God-like.” You are simply incorrect.

Attempting to void language and thought fails.

Formal logic is a set of rules for making deductions that seem self evident. It does not address the disciplines relevant to establish the premises. Absent reliable premises, conclusions are unreliable or false. It seems to me that you disregard this latter aspect of evidence.

i. e.
All humans are mortal
Tarski is a human
Therefore: Tarski is mortal

We can with meaning attach definition here.

While syllogisms like the following occur in every day conversation, they often are flawed because of ambiguity and unestablished premises.

Failure to articulate clear, transparent definition of any terms may result in a flawed syllogism. Godel has such flaws in the complete construction which we have before us. It’s not his math expertise which is in question. What’s in question is the construction which we have before us.

I agree with your analysis regarding “subtle,” but there is more than that as my analysis has shown. Your “subtle” fits with another critic who used terms like “fuzzy,” and “sleight of hand.”

An argument supports a conclusion. If you agree, what is Godel’s conclusion as replicated by CC?

Can you please state that conclusion?
----------------------------------------
Tarski stated:
Your wildly ungracious and flippant reading of him is annoying.

JAK:
Your opinion which was not my intent. Rather, the intent was to address what appeared on the screen directly, with thoughtful consideration, and with analysis.

Tarski stated:
It is now clear that you, JAK, are simply garnering pseudo-understanding about logic from googling etc.
You give a rather clear example of why real training and maturity in an exact science such as logic and/or mathematics is needed for an understanding of Godel.

JAK:
It appears clear that you, Tarski, understand little about the inductive processes which generate reliable premises from which deductive logic can be or may be constructed. And you give a clear example of why the scientific method of accumulating information and knowledge is essential before construction of deductive logic if those deductions are to also have reliability.

You have not demonstrated or documented your opinions but merely asserted them. No direct quotes were made to document your opinions.

The central issue here from the start has been: “The Roles of Logic and Science in Questions of Theology.”

Tarski stated:
Your analysis sounds quite inauthentic and sophomoric. One clearly senses someone using words not deeply understood.

You also use a shotgun approach pointing the finger of fallacy of all types at every point of the argument hoping that something will stick.
It makes for tedious reading.

JAK:
You appear to have little comprehension of ad hominem or assertion absent evidence.

Fallacious Arguments are quite specific, and I have identified only some of yours. Opinion does not constitute fact. And specific examples of Fallacious Arguments were directed minimally to your flawed arguments/reasoning.

You appear to favor mindless deduction over academically honest, intellectual inquiry prior to the set-up of premises.

You appear to fail recognition that a statement being supported is the conclusion of the argument, and the statements that support it must be from premises which are reliable and established.
A correct form does not make for a reliable conclusion.

i.e.

Major Premise: All men are stupid.
Minor Premise: Tarski is a man.
Conclusion: Tarski is stupid.

We have perfect form which is unreliable. Why? It’s because the 1st Premise is flawed and can be demonstrated to be flawed by inductive accumulation of information and evidence.

You appear to argue that if the form is correct, we have valid conclusion. It’s a narrow, false, shrunken, and erroneous notion of the word. So, in deference to that misguided notion, I have used unreliable to avoid confusion on that term. And in that context, you appear to have little understanding of grammatical construction as it’s accuracy is inherently conjoined to deductive development.

JAK

[_Tarski]

Do you defend use of “God-like”? If not and if “God-like” is equal to “dog-like,” why would Godel not have used “dog-like”?

Because then nut jobs who know nothing about logic would accuse him of assuming that dogs exist? LOL

godel only tries to prove that there exists an entity that "has as essential properties those and only those properties which are positive".

Is that God? Call it what you like JAK. Call such an entity a dog-like entity if you think that is a better word choice. It matters not for the validity of the formal argument.



Criticise this version:

http://upload.wikimedia.org/math/3/2/3/ ... 788b38.png

[_Tarski]

I.e.

Major Premise: All men are stupid.
Minor Premise: Tarski is a man.
Conclusion: Tarski is stupid.

We have perfect form which is unreliable. Why? It’s because the 1st Premise is flawed and can be demonstrated to be flawed by inductive accumulation of information and evidence.

You appear to argue that if the [b]form is correct, we have valid conclusion[/b]. [/color]

No, I certainly never argued that or thought it. LOL
How could you be so freaking confused over the simple point about definition 1?

After all your bloviating, it turns out you don't know the difference between valid and sound? Priceless!
An argument can be valid without being sound. http://www.iep.utm.edu/v/val-snd.htm


I have never once argued that Godel's axioms are true or even plausible. I have never argued that his conclusions are correct or that he had proved that God exists.
I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid. I am right about that and you are wrong (I am sure that you think that just me saying this fact is a fallacy but once again I am making a true statement not trying to prove it--a distinction you do not comprehend).

The argument of Godel is unsound to the extent that the premises (in this case axioms) are not true. The validity of the argument is not the same as its soundness. Despite your assertion above, validity is about form.


by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument.

I never once said that something about you had a logical consequence for Godel's argument or anything else for that matter.

So it turns out again that it is rather you that have little understanding of the issues.

[_JAK]

Misrepresentation

Tarski, stated:
This definition does not beg the question of God's existence but it does have another more subtle problem. Namely, it appeals to a notion of positiveness that has not been clarified or shown to be exemplified.

JAK just scanned through and looked for the letters g-o-d and assumed that the question was begged at every such point. But he misunderstands what is going on as I hope you now see.

JAK:
Misrepresentation of JAK. I did not state Definition 1 begged the question.. In regard to your evasion of specific questions and analysis I said you begged the question -- the very questions I put before you as questions or analysis.

Definition 1 is a claim

Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive

Regardless of the problems in the “if” clause, “x is God-like...”
That is a God claim. It’s that x is like God. To argue that there is no claim here is to misread.

What do we consider the meaning of “is” connecting “x” to God-like”? We either have “God” a noun in which we have a clear claim and link to “x” or we have a statement about the noun “God.”

Answer the question regarding “is.”

What is before it?. What is after it?

And to underscore this, your previous claim that we could just as well substitute “dog-like” will not stand along with the remainder of the construction.

Again, the definition 1 does not beg the question, it makes a declaration with a subject, linking verb, and predicate nominative.

The construction assumes “God-like” or like God.

Your continued denial that there is an assumption of that which has not been established is flawed.

God or “God-like” is assumed in definition 1.

I agree with your challenge to the “if” clause. But you misrepresent.

You further state:
“The theorems cannot be expected to be shown to be true unless the truth of the axioms is assumed or self evident.”

This is directly related to my analysis. “The truth of the axioms is assumed...” It is not self evident in this construction.

Axiom 1: If a property is positive, then its negation is not positive.

Axiom 2: Any property entailed by — I.e., strictly implied by — a positive property is positive

Axiom 3: The property of being God-like is positive

What’s the “property of being God-like”?

Not only is it ambiguous it claims “God-like.”

Both Axioms 1 & 2 contain ambiguous words which can mean anything one wishes to imagine as “positive” or “positive property”

And “Positive property is positive” is a circular statement.

The flaws are numerous as well as “subtle” as you characterize.

You have in no way refuted this analysis and the Fallacy: Muddy the Water is employed by you as you attempt analogy that fails to sustain your own claims on the matter.

Tarski, stated:
To me the axioms are not self evident and do not clearly map onto anything familiar the way the axioms of arithmetic do.

Exactly. The structure of the whole is flawed as we identify a variety of flaws inherent in various parts of that construction.

Fundamentally, I don’t have disagreement with other aspects of your analysis.

What is missing in the attempt at a deductive construction is what is essential -- that which precedes the deductive construction.

We require evidence from the inductive processes.
We require evidence to establish Definition 1.

Lacking that, no formal construction has reliability.

JAK

[_JAK]

Tarski, stated:
After all your bloviating, it turns out you don't know the difference between valid and sound? Priceless!
An argument can be valid without being sound.

I understand both terms. One can use a narrow notion for purposes of describing form only. However, that is not a general understanding of the word “valid.”

And so in deference to you, I used the word reliable. I suspect you would be unmoved by a dictionary definition. It was my intent to communicate.

However a dictionary:

valid Part of Speech: adjective Definition: genuine Synonyms: accurate, attested, authentic, authoritative, binding, bona fide, cogent, compelling, conclusive, confirmed, convincing, credible, determinative, efficacious, efficient, good, in force, irrefutable, just, kosher*, lawful, legal, legit*, legitimate, logical, official, original, persuasive, potent, powerful, proven, pure, right, solid, sound, stringent, strong, substantial, telling, tested, true, trustworthy, ultimate, unadulterated, unanswerable, uncorrupted, weighty, well-founded, well-grounded

Given the appropriate context, all these terms are definitions/synonyms for the word valid.

Given the same understanding of terminology, I agree with your statement: “An argument can be valid without being sound.”

However, in that application/context the meaning is restricted to refer to form only. So long as everyone truly understands that is the way “valid” is intended, communication results (or can).

Why such insecurity?

Tarski, stated:
The validity of the argument is not the same as its soundness. Despite your assertion above, validity is about form.

Only if all agree that form is the only thing being characterized by a specific application of the term.

The above definitions obviously do not refer to form only. Yet they are terms synonymous with valid in various applications.

Your narrow perception is at odds with standard meanings implied or intended by the use of that single word.

Do you have a dictionary all your own which you have published?

I would be skeptical.

JAK

[_Tarski]

Misrepresentation

Tarski, stated:
This definition does not beg the question of God's existence but it does have another more subtle problem. Namely, it appeals to a notion of positiveness that has not been clarified or shown to be exemplified.

JAK just scanned through and looked for the letters g-o-d and assumed that the question was begged at every such point. But he misunderstands what is going on as I hope you now see.

JAK:
Misrepresentation of JAK. I did not state Definition 1 begged the question.. In regard to your evasion of specific questions and analysis I said you begged the question -- the very questions I put before you as questions or analysis.
Definition 1 is a claim

Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive

Regardless of the problems in the “if” clause, “x is God-like...”
That is a God claim. It’s that x is like God. To argue that there is no claim here is to misread.

What do we consider the meaning of “is” connecting “x” to God-like”? We either have “God” a noun in which we have a clear claim and link to “x” or we have a statement about the noun “God.”

Answer the question regarding “is.”

What is before it?. What is after it?

And to underscore this, your previous claim that we could just as well substitute “dog-like” will not stand along with the remainder of the construction.

Again, the definition 1 does not beg the question, it makes a declaration with a subject, linking verb, and predicate nominative.

So now I also see that you don't know what "begging the question" means. On the one hand, you claim that definition1 assumes the existence of God. Since that is what is supposed to be the final outcome, this would be a case of begging the question.

Behold:

begging the question describes a type of logical fallacy, petitio principii, in which the conclusion of an argument is implicitly or explicitly assumed in one of the premises

Secondly, definitions are not claims.

Look at the construction below:

Definition: A a smooth function is a function that is continuously differentiable k-times for all k.

This may look like claim to you but it is not at all. It is a definition and makes no claims despite grammatical similarity.
This is the proper grammatical construction for definitions (not claims).

Here are a few more standard definitions from the literature. Note the grammatical pattern:

Definition: A real or complex Hilbert space is a real or complex inner product space that is a complete normed space (Banach space) under the norm defined by the inner product.

Definition: A topological vector space X is a vector space over a topological field K (most often the real or complex numbers with their standard topologies) which is endowed with a topology such that vector addition X × X → X and scalar multiplication K × X → X are continuous functions.

Definition: A differentiable manifold is a topological manifold equipped with an atlas whose transition maps are all differentiable. More generally a Ck-manifold is a topological manifold with an atlas whose transition maps are all k-times continuously differentiable.

You are so far of base it is stunning JAK.

[_marg]

I.e.

Major Premise: All men are stupid.
Minor Premise: Tarski is a man.
Conclusion: Tarski is stupid.

We have perfect form which is unreliable. Why? It’s because the 1st Premise is flawed and can be demonstrated to be flawed by inductive accumulation of information and evidence.

You appear to argue that if the [b]form is correct, we have valid conclusion[/b]. [/color]

No, I certainly never argued that or thought it. LOL
How could you be so freaking confused over the simple point about definition 1?

After all your bloviating, it turns out you don't know the difference between valid and sound? Priceless!
An argument can be valid without being sound. http://www.iep.utm.edu/v/val-snd.htm


I have never once argued that Godel's axioms are true or even plausible. I have never argued that his conclusions are correct or that he had proved that God exists.
I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid. I am right about that and you are wrong (I am sure that you think that just me saying this fact is a fallacy but once again I am making a true statement not trying to prove it--a distinction you do not comprehend).

The argument of Godel is unsound to the extent that the premises (in this case axioms) are not true. The validity of the argument is not the same as its soundness. Despite your assertion above, validity is about form.


by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument.

I never once said that something about you had a logical consequence for Godel's argument or anything else for that matter.

So it turns out again that it is rather you that have little understanding of the issues.

Tarski you are incorrect to think JAK doesn't understand sound, valid form, and what ad hominem fallacy is.

When JAK says "You appear to argue that if the form is correct, we have valid conclusion", his use of the word "valid" is descriptive of the word "conclusion ", not descriptive of the word "argument" and in that case he is using the term to mean "correct."

JAK is also correct that to have a valid conclusion in a sound argument, true unambiguous premises are essential.

You say the following "I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid." I don't follow why the form of the argument would be altered if one assumes something in the definition?

You also say this "by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument."

An ad hominem is not a fallacy if it is legitimate and is argued as part of an argument. For example if someone claims or needs particular expertise, it is legitmate to criticize that person for their lack of credentials or expertise which has a bearing on the argument. You though have not established JAK doesn't understand logic. You assume that but you've not demonstrated it. And I might add, your "LOL" peppered in your arguments, meant to be condescending detract from your argument.

I note you replied to my questions from last night. Thank you. I still have to read your answers before I respond.

One of the things which bothers me in this whole discussion, is that no one who respects Godel has explained what are the properties of Godel's god.

[_Tarski]

I.e.

Major Premise: All men are stupid.
Minor Premise: Tarski is a man.
Conclusion: Tarski is stupid.

We have perfect form which is unreliable. Why? It’s because the 1st Premise is flawed and can be demonstrated to be flawed by inductive accumulation of information and evidence.

You appear to argue that if the [b]form is correct, we have valid conclusion[/b]. [/color]

No, I certainly never argued that or thought it. LOL
How could you be so freaking confused over the simple point about definition 1?

After all your bloviating, it turns out you don't know the difference between valid and sound? Priceless!
An argument can be valid without being sound. http://www.iep.utm.edu/v/val-snd.htm


I have never once argued that Godel's axioms are true or even plausible. I have never argued that his conclusions are correct or that he had proved that God exists.
I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid. I am right about that and you are wrong (I am sure that you think that just me saying this fact is a fallacy but once again I am making a true statement not trying to prove it--a distinction you do not comprehend).

The argument of Godel is unsound to the extent that the premises (in this case axioms) are not true. The validity of the argument is not the same as its soundness. Despite your assertion above, validity is about form.


by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument.

I never once said that something about you had a logical consequence for Godel's argument or anything else for that matter.

So it turns out again that it is rather you that have little understanding of the issues.

Tarski you are incorrect to think JAK doesn't understand sound, valid form, and what ad hominem fallacy is.

When JAK says "You appear to argue that if the form is correct, we have valid conclusion", his use of the word "word" is descriptive of the word conclusion , not descriptive of the word argument and in that case he is using the term to mean "correct." How he is using the word "valid" is correct.

JAK is also correct that to have a valid conclusion in a sound argument, true unambiguous premises are essential.

You say the following "I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid." I don't follow why the form of the argument would be altered if one assumes something in the definition?

Because it is improper and invalid in deductive form to assume the existence of something as part of it's very definition when the goal is to prove existence.

For example, the following is an improper definition. Just make it clear that it is indeed the logical form at issue, I will state it somewhat symbolically:

Definition (improper): An "H" is defined to be a G that is larger than the first H.

This definition is bad.
However, Definition 1 in the Godel argument makes no such error.

You also say this "by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument."

An ad hominem is not a fallacy if it is legitimate and is argued as part of an argument.

To say "you are incompetent" is not a logical fallacy.
To say "you are incompetent therefore you conclusions are false" is a logical fallacy. I did not commit such a fallacy. JAK claims that I did. That is evidence that he doesn't understand the fallacy.

[_JAK]

I.e.

Major Premise: All men are stupid.
Minor Premise: Tarski is a man.
Conclusion: Tarski is stupid.

We have perfect form which is unreliable. Why? It’s because the 1st Premise is flawed and can be demonstrated to be flawed by inductive accumulation of information and evidence.

You appear to argue that if the [b]form is correct, we have valid conclusion[/b]. [/color]

No, I certainly never argued that or thought it. LOL
How could you be so freaking confused over the simple point about definition 1?

After all your bloviating, it turns out you don't know the difference between valid and sound? Priceless!
An argument can be valid without being sound. http://www.iep.utm.edu/v/val-snd.htm


I have never once argued that Godel's axioms are true or even plausible. I have never argued that his conclusions are correct or that he had proved that God exists.
I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid. I am right about that and you are wrong (I am sure that you think that just me saying this fact is a fallacy but once again I am making a true statement not trying to prove it--a distinction you do not comprehend).

The argument of Godel is unsound to the extent that the premises (in this case axioms) are not true. The validity of the argument is not the same as its soundness. Despite your assertion above, validity is about form.


by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument.

I never once said that something about you had a logical consequence for Godel's argument or anything else for that matter.

So it turns out again that it is rather you that have little understanding of the issues.

Tarski you are incorrect to think JAK doesn't understand sound, valid form, and what ad hominem fallacy is.

When JAK says "You appear to argue that if the form is correct, we have valid conclusion", his use of the word "word" is descriptive of the word conclusion , not descriptive of the word argument and in that case he is using the term to mean "correct." How he is using the word "valid" is correct.

JAK is also correct that to have a valid conclusion in a sound argument, true unambiguous premises are essential.

You say the following "I only argued that definition 1 does not assume the existence of God. If it did, then the form itself would be invalid." I don't follow why the form of the argument would be altered if one assumes something in the definition?

Because it is improper and invalid in deductive form to assume the existence of something as part of it's very definition when the goal is to prove existence.

For example, the following is an improper definition. Just make it clear that it is indeed the logical form at issue, I will state it somewhat symbolically:

Definition (improper): An "H" is defined to be a G that is larger than the first H.

This definition is bad.
However, Definition 1 in the Godel argument makes no such error.

You also say this "by the way JAK, Ad Hominem is not fallacious if the insult is not presented as part of a logical argument but is rather just an observation. In this case an observation about your competence. Merely insulting someone or commenting negatively on their competence is not a logical fallacy if it is not part of a logical argument."

An ad hominem is not a fallacy if it is legitimate and is argued as part of an argument.

To say "you are incompetent" is not a logical fallacy.
To say "you are incompetent therefore you conclusions are false" is a logical fallacy. I did not commit such a fallacy. JAK claims that I did. That is evidence that he doesn't understand the fallacy.

Tarski, stated:
To say "you are incompetent" is not a logical fallacy.
To say "you are incompetent therefore you conclusions are false" is a logical fallacy. I did not commit such a fallacy. JAK claims that I did. That is evidence that he doesn't understand the fallacy.

JAK:
I should like to see a direct quotation of my words in context to which this refers.

And by the way, the "Quote" above which has "JAK" above it does not look like the real statement which I in fact wrote. So, it's a misquote. What I actually stated stands in my original statement.

Let's see an accurate quotation of your statement (in green) just above.

JAK

[_JAK]

Misrepresentation

Tarski, stated:
This definition does not beg the question of God's existence but it does have another more subtle problem. Namely, it appeals to a notion of positiveness that has not been clarified or shown to be exemplified.

JAK just scanned through and looked for the letters g-o-d and assumed that the question was begged at every such point. But he misunderstands what is going on as I hope you now see.

JAK:
Misrepresentation of JAK. I did not state Definition 1 begged the question.. In regard to your evasion of specific questions and analysis I said you begged the question -- the very questions I put before you as questions or analysis.
Definition 1 is a claim

Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive

Regardless of the problems in the “if” clause, “x is God-like...”
That is a God claim. It’s that x is like God. To argue that there is no claim here is to misread.

What do we consider the meaning of “is” connecting “x” to God-like”? We either have “God” a noun in which we have a clear claim and link to “x” or we have a statement about the noun “God.”

Answer the question regarding “is.”

What is before it?. What is after it?

And to underscore this, your previous claim that we could just as well substitute “dog-like” will not stand along with the remainder of the construction.

Again, the definition 1 does not beg the question, it makes a declaration with a subject, linking verb, and predicate nominative.

So now I also see that you don't know what "begging the question" means. On the one hand, you claim that definition1 assumes the existence of God. Since that is what is supposed to be the final outcome, this would be a case of begging the question.

Behold:

begging the question describes a type of logical fallacy, petitio principii, in which the conclusion of an argument is implicitly or explicitly assumed in one of the premises

Secondly, definitions are not claims.

Look at the construction below:

Definition: A a smooth function is a function that is continuously differentiable k-times for all k.

This may look like claim to you but it is not at all. It is a definition and makes no claims despite grammatical similarity.
This is the proper grammatical construction for definitions (not claims).

Here are a few more standard definitions from the literature. Note the grammatical pattern:

Definition: A real or complex Hilbert space is a real or complex inner product space that is a complete normed space (Banach space) under the norm defined by the inner product.

Definition: A topological vector space X is a vector space over a topological field K (most often the real or complex numbers with their standard topologies) which is endowed with a topology such that vector addition X × X → X and scalar multiplication K × X → X are continuous functions.

Definition: A differentiable manifold is a topological manifold equipped with an atlas whose transition maps are all differentiable. More generally a Ck-manifold is a topological manifold with an atlas whose transition maps are all k-times continuously differentiable.

You are so far of base it is stunning JAK.

Fallacious Argument: Appeal To Complexity
Fallacious Argument: Argument By Prestigious Jargon
Fallacious Argument: Argument From Spurious Similarity

JAK