Do you believe in God/god(s)/a "higher power"?

[Jnyusa]

.. each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.

I just recently acquainted myself with the fact that one of the big unsolved questions in mathematics today is whether the set of true statements is larger than the set of provable statements? ... not sure I even phrased that correctly.

I expect that someone will come up with the proof one way or the other, but I have to say that I have a queasy feeling when I read lemmas whose purpose is to eliminate infinity from the equation.

There was a mathematician some twenty years ago (forgot his name) who published a mathematical definition for the term 'large,' because in things like 'the law of large numbers' there really is a question of how large is large. This guy said he thought up the definition while standing in the shower ... and I suppose that other mathematicians ended up accepting his definition, but that little twinkle in the pit of my stomach never went away ... 'large compared to what?' I thought, and he did define what 'large' was being compared to, but did not define how 'large' that second thing was ...

Anyway ... getting back to Goedel ... I suppose his proof is important to mathematicians for certain things they want to do, but it always seemed to me just another way of saying that most proofs begins with an axiom. And I thought ... well, yeah, you've got to start somewhere ...


Jn

[Lidless]

I think it is impossible to answer those questions without a convenient, unproveable theory that transcends the universe and is based on faith, not logic. Just as molecules leads to atoms lead to elementary particles leads to quanta leads to M-Theory leads to...? It's an onion skin.

[yovargas]

If there is no higher power or afterlife, Then where and how is it that we exist?

Even if there is a higher power, how did it come into existence? The higher power doesn't solve the problem, merely shifts the focus from us to it.

And if there is no purpose to this life, or meaning, then what does it all matter?

Even if there is a higher power, what does it all matter? The higher power doesn't solve the problem, merely shifts the focus from us to it.

There are no consequences to your actions.

Of course there are. The might not be eternal consequences but they're consequences nonetheless.

Quite simply, I believe that (nearly by definition) a moral life is a happier life.

[Holbytla]

How can morality exist in a vacuum?

[Lidless]

I just recently acquainted myself with the fact that one of the big unsolved questions in mathematics today is whether the set of true statements is larger than the set of provable statements? ... not sure I even phrased that correctly.

The definition of 'true' in a logical system is that it is provable from the basic axioms that have been designated as true, and if it is proveable, it is true. Whether the logic has been fully paved to designate something as true or not is another thing. Thus the two are equivalent - at least "officially true". There will be "intrinsically true" statements we haven't pathed the logic for yet, so "intrinsically true" will always be greater or equal to the the number of proveable statements - the difference being a function of time.

Goedel showed that there were statements in any system that could never be proved as true or false.

Poor Cantor.

[yovargas]

How can morality exist in a vacuum?

Highly simplified version of yov's moral system: Morality is defined as that which betters the well-being of mankind.

That's how.


PS - How could morality exist with a higher power? What part of the morality equation does the higher power change? None, as far as I can tell, except, perhaps, the set of good and bad consequences.

[Jnyusa]

... provable from the basic axioms ...

Yes ... the problem they're working on has something to do with the efficiency of the proof, and I have to confess that I don't fully understand the question, or why everyone finds it so intriguing ...

Let me see if I can find a better statement of the problem.

Jn

[Jnyusa]

Excuse me, the question does not concern provable theorems but soluable problems. Here the Wikipedia entry:

Computational complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. The most common resources are time (how many steps it takes to solve a problem) and space (how much memory it takes to solve a problem).

In this theory, the class P consists of all those decision problems that can be solved on a deterministic sequential machine in an amount of time that is polynomial in the size of the input; the class NP consists of all those decision problems whose positive solutions can be verified in polynomial time given the right information, or equivalently, whose solution can be found in polynomial time on a non-deterministic machine. Arguably, the biggest open question in theoretical computer science concerns the relationship between those two classes:
Is P equal to NP?

In a 2002 poll of 100 researchers, 61 believed the answer is no, 9 believed the answer is yes, 22 were unsure, and 8 believed the question may be independent of the currently accepted axioms, and so impossible to prove or disprove.[1] The Clay Mathematics Institute has offered a USD 1,000,000 prize for a correct solution.

http://en.wikipedia.org/wiki/Complexity ... s_P_and_NP

I got it in my head that P stood for 'provable'

[Holbytla]

If there were a higher power, then one could extrapolate that into some type of meaning or purpose.
Then from that you can determine right/wrong or good/bad.

I don't see how right and wrong can exist with the existence of a higher power.
Certainly each of us has a different interpretation of right and wrong.
How do you then arrive at some type of universal right and wrong, and if you can't then who cares? Who is there to care?

[Lidless]

Excuse me, the question does not concern provable theorems but soluable problems. Here the Wikipedia entry:

Computational complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. The most common resources are time (how many steps it takes to solve a problem) and space (how much memory it takes to solve a problem).

In this theory, the class P consists of all those decision problems that can be solved on a deterministic sequential machine in an amount of time that is polynomial in the size of the input; the class NP consists of all those decision problems whose positive solutions can be verified in polynomial time given the right information, or equivalently, whose solution can be found in polynomial time on a non-deterministic machine. Arguably, the biggest open question in theoretical computer science concerns the relationship between those two classes:
Is P equal to NP?

In a 2002 poll of 100 researchers, 61 believed the answer is no, 9 believed the answer is yes, 22 were unsure, and 8 believed the question may be independent of the currently accepted axioms, and so impossible to prove or disprove.[1] The Clay Mathematics Institute has offered a USD 1,000,000 prize for a correct solution.

http://en.wikipedia.org/wiki/Complexity ... s_P_and_NP

I got it in my head that P stood for 'provable'

Jny, you're a lifesaver! God knows, no pun intended, I need the cash.

If the action table has at most one entry for each combination of symbol and state then the machine is a deterministic Turing machine (DTM). If the action table contains multiple entries for a combination of symbol and state then the machine is a non-deterministic Turing machine (NDTM). The two are computationally equivalent, that is, it is possible to turn any NDTM into a DTM (and vice versa).

Thus N=NP.

Me wants my USD 1m, and have sent off my solution to the Clay Institute.

[yovargas]

If there were a higher power, then one could extrapolate that into some type of meaning or purpose.

Such as?

Then from that you can determine right/wrong or good/bad.

Such as?

How do you then arrive at some type of universal right and wrong, and if you can't then who cares? Who is there to care?

Who is there to care with the higher power? The higher power? Why is what it cares about more meaningful then what you care about?

[Jnyusa]

Lidless, Good luck.

Jn

[Lidless]

I'll make sure you get some sort of commission. Don't you worry.

[TheEllipticalDisillusion]

How do you then arrive at some type of universal right and wrong, and if you can't then who cares? Who is there to care?

I believe with our ten commandments, code of hammurabi, and such, we've somehow arrived at a near-universal right and wrong. So the how is useless since it has been close to done, but then it doesn't matter anyway, because humans are the only ones who care. Once we go, there truly will be no one left to care.

[Alatar]

Yova, do you ever post anything except questions? What do YOU think and why?

[yovargas]

Quite simply, I believe that (nearly by definition) a moral life is a happier life.

How could morality exist with a higher power? What part of the morality equation does the higher power change? None, as far as I can tell, except, perhaps, the set of good and bad consequences.

What do YOU think and why?

God's existance or non-existance doesn't create or change morality, only its consequences. With or without God, morality is about improving our happiness and well-being.

[Cerin]

With or without God, morality is about improving our happiness and well-being.

With God, the improvement of our well being is a by-product of morality, which is a reflection and exercise of the character of God.

Without God, morality is about improving our happiness and well-being.

[yovargas]

With or without God, morality is about improving our happiness and well-being.

With God, the improvement of our well being is a by-product of morality, which is a reflection and exercise of the character of God.

With God, what is the point of being moral?

[Cerin]

It is an aspect of worship. It is a consequence of fellowship.

That's kind of like asking, without God, what is the point of breathing?

[yovargas]

That's kind of like asking, without God, what is the point of breathing?

All these questions sound like that to my ears.