[MySiddhi]

Originally Posted by gareth

I'm sure you realise that your idea of God is very different from the idea of God that many people have in the West, which is probably why certain people in this forum have such an unhelpful knee-jerk reaction to what you are trying to do.

For the common mind the whole issue revolves around semantics. Theists don't like the word natural and atheists don't like the word intelligence.

But to the surprise of both camps.... it is natural for their to be a Supreme Being and consciousness is a fundamental property of reality (not some epiphenomena of material structures).

[Buffy]

Originally Posted by MySiddhi

(idA: A → A)

This formula is called the Identity Morphism... feel free to look it up.

Ah, you're misusing it. You are trying to say that (A → A) is a property of A, whereas Identity Morphism--if it is included in your formal system at all--is the simple statement that (A → A) for any given A. It most clearly does not say that it is a *property* of A itself. Your formula is correct, however your interpretation is not, thus calling into question any of the deductions based upon it.

Originally Posted by MySiddhi

Gödel's theorems are only relevant to axiomatic deduction systems. I only have one deduction and it is natural (needing no axioms).

You do have an axiom, and it would appear that you need further ones, or your proof is incomplete. The reason I have directed you to Doctordick's thread is that what you are trying to create is what he would identify as a "flaw free epistemological construct," and the discussion in that thread deals with the fundamental attributes of such constructs, and it would behoove you to examine many of the topics raised there which are relevant to understanding why theories such as yours are not "flaw free."

Now attempting to use Natural Deduction as your mechanism of defining your proof is fully valid, however it is merely an alternative to Axiomatic Systems. Gentzen's goal in defining the most widely accepted version of it was to seek a way to reduce the use and dependence upon axioms in the most fundamental mathematical theorems. Thus your claim that Gödel does not apply is in fact false, because Natural Deductive theorems are onto with respect to the set of Axiomatic theorems. Gödel claims incompleteness applies even in the case where zero axioms are included in a system.

Unfortunately Natural Deduction does not fully replace the need for axioms especially when using them to define epistemological constructs. let alone ontological ones.

Indeed a fundamental element of Natural Deduction is the notion of "judgment" under which we ask the linked questions, "is a a valid proposition" "can A be assigned a truth value."

This is where you need to start making statements about the nature of "nothing" and "something."

Without these the rest of your dissertation is unfortunately completely unintelligible. For now I will resist the temptation to find fault with your Tautologies, and ask that you expound a bit more on the definitions of "nothing" and "something."

So, take a careful look at this statement:

Originally Posted by MySiddhi

Nothing can be true and false in the same respect at the same time.

Do you see more than one way to read this statement?

Time flies like a banana,
Buffy

[MySiddhi]

Ah, you're misusing it. You are trying to say that (A → A) is a property of A, whereas Identity Morphism--if it is included in your formal system at all--is the simple statement that (A → A) for any given A. It most clearly does not say that it is a *property* of A itself. Your formula is correct, however your interpretation is not, thus calling into question any of the deductions based upon it.

Reflexivity of Implication (A → A) is not Identity Morphism (idA: A → A) dear.

One deals with implication and the other deals with predication.

You do have an axiom, and it would appear that you need further ones, or your proof is incomplete.

You are welcome to prove that I need more axioms besides the sole axiom of non-contradiction that I use.

The only way you can go about proving such a thing is by demonstrating that my DEDUCTION does not follow without adding more axioms.

it would behoove you to examine many of the topics raised there which are relevant to understanding why theories such as yours are not "flaw free."

The word theory has many distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. In science a theory is a testable model...

However given the foundational nature of my proof it is more than just a theory (having a model) but also a theorem from which all models have to derive their essence.

And, any theory or model that does not fit in my theorem is a prior FALSE by necessity!

Gödel claims incompleteness applies even in the case where zero axioms are included in a system.

Gödel's theorems only apply to systems that are used as their own proof systems.

My single axiom of non-contradiction is my proof system and is not proven in my system.

[Buffy]

Originally Posted by MySiddhi

Reflexivity of Implication (A → A) is not Identity Morphism (idA: A → A) dear.

One deals with implication and the other deals with predication.

Yes, I understand that. The problem is not the notation and their formal definition, it is your insistence on translating the latter into:

Originally Posted by MySiddhi

idA: A → A “nothing has the property of nothing” Identity Morphism

...which is claiming the ability to bootstrap by saying that A is a *property* of itself, whereas Identity Morphism is simply the statement that "A is A."

You are the one using the language "is a property of," not me nor any definition of Identity Morphism. Since you are explicit carefully using this clearly unconventional claim concerning the meaning of Identity Morphism, it begs the question of why you do so!

As to whether this particular Tautology (T1) has an impact on your Deduction, well, as far as what you have published in your initial post, T1 is not referenced anywhere else in your proof, and would thus appear on the surface to be redundant.

OTOH, in looking at your mappings and implications of your usage of the terms "nothing" and "something" it appears you are trying to make the distinction between these terms mutually exclusive in T1, however because you have not bothered to address any of my questions concerning them, its unclear how they are relevant.

Originally Posted by MySiddhi

However given the foundational nature of my proof it is more than just a theory (having a model) but also a theorem from which all models have to derive their essence.

Cool! You'll need to take us through it, and so far you've got so many leaps to go over involving the aforementioned lack of specificity of terminology and its application that its really just gibberish so far.

Its quite apparent that you've had some good book learning on in logic. However you are indeed straying into epistemology, and you'll have to start addressing the concerns expressed so far, because you have integrated them tightly into your "theorem" rather than first trying to prove its abstract validity before then trying to map it onto specific instances of your proposition A.

If you need some help with this, I'd be glad to assist you!

We'll get back to Gödel when we've got enough to work with. For now, let's talk about the nature of "nothing."

Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which carry them out?
Buffy

[Overdog]

MySiddhi:

Even if there were nothing wrong with your logic (which I don't conceed), you would still face profound philosophical challenges against asserting that it says anything about any unobservable phenomenon, such as god.

2. The Empiricist Challenge: Knowledge Empiricism and the Underdetermination Argument
It is easy to characterize the basic empiricist underdetermination argument against scientific realism. Call two theories empirically equivalent just in case exactly the same conclusions about observable phenomena can be deduced from each. Let T be any theory which posits unobservable phenomena. There will always be infinitely many theories which are empirically equivalent to T but which are such that each differs from T, and from all the rest, in what it says about unobservable phenomena (for formalized theories, this is an elementary theorem of mathematical logic). Evidence in favor of T's conception of unobservable phenomena ("theoretical entities") would have to rule out the conceptions represented by each of those other theories. But, since T is empirically equivalent to each of them, they all make exactly the same predictions about the results of observations or experiments. So, no evidence could favor one of them over the others. Thus, at best, we could have evidence in favor of what all these theories have in common--their consequences about "observables"--we could confirm that they are all empirically adequate--but we could not have any evidence favoring T's conception of unobservable theoretical entities. Since T was any theory about unobservables, knowledge of unobservable phenomena is impossible; choice between competing but empirically equivalent conceptions of theoretical entities is underdetermined by all possible observational evidence.

Scientific Realism (Stanford Encyclopedia of Philosophy)

[MySiddhi]

Originally Posted by Overdog

MySiddhi:

Even if there were nothing wrong with your logic (which I don't conceed), you would still face profound philosophical challenges against asserting that it says anything about any unobservable phenomenon, such as god.

You assume that God is unobservable and yet I see God everywhere I look.

[MySiddhi]

...which is claiming the ability to bootstrap by saying that A is a *property* of itself, whereas Identity Morphism is simply the statement that "A is A."

You haven't refuted anything by saying Identity Morphism is a statement of A "is" A.

"IS" can be interpreted four different ways including PREDICATION. lol .... which I highlight via Identity Morphism.

The other three different ways of interpreting "is" are; of identity, of implication, and of existence.

I hope we are on the same page now. lol

Predication deals with attribution or properties or MORPHISM.

blue has the property of blue

gold has the properties of gold

the dead have the property of being dead

It's a logical tautology dear, deal with it.

As to whether this particular Tautology (T1) has an impact on your Deduction, well, as far as what you have published in your initial post, T1 is not referenced anywhere else in your proof, and would thus appear on the surface to be redundant.

If one were to even concede but a few of my logical tautologies I would be able to deduce all of the other attributes of God from them that would have been otherwise covered by any denied tautologies. Redundant yes, robust for sure.

Its quite apparent that you've had some good book learning on in logic.

My book learning in logic is from arguing with atheists for years (getting destroyed by them for years until I learned propositional calculus) and reading the work of Christopher Langan's CTMU and Spinoza's Ethics.

Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which carry them out?
Buffy

We can see our face through a reflection... and we can see our mental structures clearly through reflexive relations... i.e. logical tautologies.

[MySiddhi]

Originally Posted by MySiddhi

You assume that God is unobservable and yet I see God everywhere I look.

In fact, it is a necessity that God is observable from the endomorphism. And I verify this empirically for you.

I have even added the peer reviewed research papers at the end of my proof.

[Overdog]

Originally Posted by MySiddhi

You assume that God is unobservable and yet I see God everywhere I look.

Well, why don't you just drop all this ill-concieved attempt to prove it with flawed logic and just show him to us?

[Overdog]

I know, YOU CAN'T!!!