Disproof of Gödel Theorem

FrumiousBandersnatch said:

joinfree said:

... Gödel is plain wrong!

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Good grief... Dunning & Kruger would be proud.

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That certainly appears to be the inescapable conclusion when going up against Gödel's Incompleteness theorem whilst simultaneously demonstrating total ignorance of the depth of thinking behind it!

Wrangler said:

High probability is future. Proof is past.

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The future somehow appears to 'exist' when memories of the past are mysteriously combined with other human mind functions.
The evidence for this is that 'existence' is whatever we choose it to mean.
It would seem that 'the future' is no exception.

SelfSim said:

.. or in other words, truth 'exists' .. and therein lies a major flaw..

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Utter nonsense. One of these statements are true:
1. Truth exists
2. Truth does NOT exist.

If you examine #2, you'll find the contradiction. That truth exists is not an unassumption but rather an undeniable axiom.

Wrangler said:

Utter nonsense. One of these statements are true:
1. Truth exists
2. Truth does NOT exist.

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.. depends entirely on what you mean by 'exists'.
Understanding what we mean when we use the concept of 'reality' (or the term: 'exists') is pretty fundamental and hence, is hardly 'nonsense'.

Wrangler said:

That truth exists is not an unassumption but rather an undeniable axiom.

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.. an axiom holding what as its posit?

SelfSim said:

.. depends entirely on what you mean by 'exists'.

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Yea, refer to your favorite lexicon. Does it depend on what you mean by depend?

Wrangler said:

Yea, refer to your favorite lexicon. Does it depend on what you mean by depend?

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That rather depends.

Wrangler said:

Yea, refer to your favorite lexicon. Does it depend on what you mean by depend?

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Cutting to the chase, scientific thinking avoids using 'truth' as the sole basis for establishing its Objective Reality.
Put more succinctly, there is no truth needed in the scientific process .. (However, I'll grant that the thread is all about formal logic and math proofs .. and thus the existence of 'truth' is fundamental to its axioms).

It takes a human mind to conceive the meaning of 'truth' however.

Ophiolite said:

That rather depends.

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Circular arguments are frowned upon in logic, no?

By definition a theory cannot be proven. That is because theories are broad explanations of observable phenomena. That does not mean that there is evidence that a theory is wrong, which would invalidate the theory in part or in whole, but because we don’t know what will be discovered tomorrow.

Science operates by trying to invalidate theories. As a results of testing a theory it may be supported or invalidated but never proven.

As to whether or not G-d exists that is not a matter of proof, but belief. Either you believe or you do not. There is no empirical evidence that allows for a scientific theory to be posited as to the existence of G-d. Science does not concern itself with that question. A scientist who believes in G-d will get the same results from an experiment as one who does not.

SelfSim said:

Cutting to the chase, scientific thinking avoids using 'truth' as the sole basis for establishing its Objective Reality.

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Again, total nonsense. Science avoids using any evidence as the final conclusion of truth, not denying even the very concept of truth as you seem to be doing here.

Wrangler said:

Again, total nonsense. Science avoids using any evidence as the final conclusion of truth,

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The scientific process specifies objective testing.

Can you please cite the objective test supporting your claim of: 'Science avoids using any evidence as the final conclusion of truth'?

I've never seen any valid science which commences with 'avoidance' of 'a final conclusion'.
You seem to have that back-to-front!

Wrangler said:

... not denying even the very concept of truth as you seem to be doing here.

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'Truth' is untestable (objectively) if that's what you're getting at(?)
Very loosely, the closest science gets to holding something as being 'true' is (generally) consistent, objective, independently verifiable observations.

SelfSim said:

Circular arguments are frowned upon in logic, no?

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Axioms beg the questions, so logic is naturally self referential!

SelfSim said:

'Truth' is untestable (objectively)

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LOL. If you walk off a cliff, you may test the truth of gravity.

Wrangler said:

LOL. If you walk off a cliff, you may test the truth of gravity.

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No .. all that'll happen there is scientific minds will test what they mean when they use the term 'dead' (or 'injured', or 'gravity' etc) .. no truth needed in any of that.

Selfism,

Congratulations! You are the 1st person I put on my ignore list.


Wrangler

Some elaboration/clarification/wrapping up may be called for here .. I'll use the word 'truth' here, as far as it can be legitimately applied in science .. as an aid to clarfying the scientific perspective.

Typically I see many people, (note: not necessarily those in this thread), thinking that what science wants to say is something like:
"If theory X is true then outcome Y is true. The outcome Y is true. Therefore theory X is true".

That's actually a completely backward description of how science works. Science never needs to say "assume theory X is true", or "if theory X is true," those word formations have no use at all in science. This is because the whole reason we might say a theory is true, or not true, is because we have already verified the outcome Y.
It's crucial to understand that this is all a scientist can mean when they refer to the 'truth' or 'not-truth' of any theory.

It's a complete misunderstanding that science is a logical process that starts by assuming its theories are 'true'. That's how logic works, but logic never does anything but find the tautological equivalences of its predicates and postulates. Science isn't like that at all!

What a scientist might say, may be similar to:
"I have no idea whether to regard theory X as true, but it predicts Y, so we'll see if Y is true. If it is, we'll say theory X has some usefulness. Going further, we may also say that with enough different Y we will start to regard theory X as true contextually and provisionally".

See how extremely different that is from saying "science wants to say that if theory X is true, then outcome Y will be true"? In science, the only thing theory X ever does is organize, unify, and convey understanding in relation to a set of observations, Y. Then we take theory X and extend it to observation Y' that has not happened yet, but that we regard as sufficiently similar to the existing set of Y that theory X is used to understand, that we expect to understand Y' the same way.

We don't know until we try, but that is how science builds expectations. At no point is it ever necessary to say "if theory X is true", because the truth of theory X is already established by the existing set of Y ... there's no "if" involved, it's an inference not an assumption.
We never assume we'll get, for example, the gold in say, a gold prospecting exercise using science, and we never assume, (for eg), the electron definition is a good one, we test these things. And on the basis of these tests, we build expectations, and we live and die, (literally sometimes .. as in the above 'cliff' test), by those expectations ... because science is the worst way to form objective expectations except for every other way to do it.

The 'word meaning' sub-topic outlined above, can be objectively tested, (via a properly formed hypothesis), and produces its own objective evidence. The assumed existence of some 'truth' completely independent from human language meanings however, is provisionally untestable and can be treated as being nothing more than a belief, which science then handles with indifference (meaning it has zero impact).

Wrangler said:

Selfism,

Congratulations! You are the 1st person I put on my ignore list.

Wrangler

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Hmm .. 'excluded', eh?
Seems a pity for you when there's lots to learn on such topics.
I'd suggest looking into what stops you.
(Its always your choice however ...)
Cheers

Ophiolite said:

SelfSim said:

Ophiolite said:

Wrangler said:

SelfSim said:

Wrangler said:

:
Utter nonsense. One of these statements are true:
1. Truth exists
2. Truth does NOT exist.

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.. depends entirely on what you mean by 'exists'.

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Yea, refer to your favorite lexicon. Does it depend on what you mean by depend?

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That rather depends.

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Circular arguments are frowned upon in logic, no?

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Axioms beg the questions, so logic is naturally self referential!

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Not sure what you meant here ...(?)

@essentialsaltes is right: Gödel's Incompleteness Theorem is about the limits of systems in which one reasons deductively from a set of axioms. It is not about the kind of inductive reasoning one does in science, nor is it about the kind of reasoning one normally sees in theology. Gödel's theorem tells us nothing about the existence of God or the accuracy of the theory of evolution.