Is There Life Elsewhere in the Universe? Is There a God?

[winoman]

You are very much confusing the point I was making which is, you cannot prove or disprove the existence of God or gods or whichever. There is a course offered in my school called Imperfect Rationality. You ought to take it.

From my perspective there is no need to waste ones time on such a question that is beyond knowing and whose impact on one is seemingly negligible. For all practical purposes there is/are no god/gods - no afterlife or such - nor any of the various machinations assocaoated with religious belief - as one cannot produce any conclusive evidence that choice of belief in any one versus another makes any material (supernatural) difference. And as there are vast possibilities for existance (and non-existance) of dieties - and to choose one seems to automatically negate all the rest - it is only logical to assume the none of the above - as to pick one would seem to induce a critical paradox of asuming that ones personal choice of belief is necessarily true versus all of the other held beliefs that at the same time negate your own.

[Anonymouse]

Perhaps but these supposed beliefs and theoretical phenomenon that are not explainable by science may either be due to lack of proper sensory aparatus or understanding (that one day can be surmounted) or they plain and simple are abberations or false perceptions in the first place. I don't happen to believe in spiritual existance outside any physical/chemical phenomenon and I can't see any reason to believe in such nor can you (aparetly) prove to me that such is the case - so in my mind I find such highly doubtful - and for your part you have no menchanism to properly convey the truth of such - so where does that leave us? We can believe in unprovable things - but these seemingly cannot be recreated or properly percieved - etc etc - thus speculation - that perhaps may be interesting to contemplate - has very little real bearing upon reality as we know and experience it. And still this is no basis for doubting what we can percieve and understand through science (including Evolution)....

You are committing the same error I said one cannot commit when dealing these concepts, essentially you cannot ask evidence of that which is not physical because evidence by its very nature is physical and confined to the physical world. But this is precisely the distinction I was making, that there are two different realms: belief in science and the physical, or belief in the intangible and the two are mutually exclusive. You cannot use one or other to prove or disprove either.

There is no such thing as Scientism that I am at all aware of - can it found in the dictionary?

Yes

[Anonymouse]

From my perspective there is no need to waste ones time on such a question that is beyond knowing and whose impact on one is seemingly negligible. For all practical purposes there is/are no god/gods - no afterlife or such - nor any of the various machinations assocaoated with religious belief - as one cannot produce any conclusive evidence that choice of belief in any one versus another makes any material (supernatural) difference. And as there are vast possibilities for existance (and non-existance) of dieties - and to choose one seems to automatically negate all the rest - it is only logical to assume the none of the above - as to pick one would seem to induce a critical paradox of asuming that ones personal choice of belief is necessarily true versus all of the other held beliefs that at the same time negate your own.

That is illogical. If you state that there are no evidences that can be produced to prove the existence of God or Gods, it means that you already know all that there is to know, and all possible evidences for God or Gods' existence. Since no one can know everything then you can't logically proclaim there is no evidence for God or Gods. Hence why I said, one cannot prove or disprove the existence of God. If one attempts to do so one runs the risk of committing these fallacies.

[Siamanto]

"the beauty of the fascinating work of Godel" lies in the fact that no formal theory (strong and full enough to support theory of numbers) can be used to prove/disprove every sentence in that theory. Another "beauty" is that the consistency of a (strong enough) formal theory cannot be proven within the limits of that theory.

For lack of time, I will have to be brief . I apologize for it.
Most of all, I don't think that we disagree!

Godel's work was an attempt to answer the following question, raised many centuries ago - among others - by La Mettrie:
"Cam Mathematics be reduced to a simpler formal system?" (A form of reductionism!)
Once reduced to Arithmetic, Peano suggested an axiomatic.
Godel showed that the above question cannot be answered positively. In fact, he proved - as you know:
1- No axiomatic system is complete
2- As you have mentioned, if the Mathematical System is consistent, we can't prove it using Mathematical Logic

In other words, you can't logically - i.e. using Mathematical Logic - construct and validate the Mathematical System.
You need to make assumptions that cannot be proved - such as the ones that were made by Set Theorists.

As you see, the above in no way means that "Mathematical System cannot be logically constructed or validated", it only means that you can never get along with one formal theory to solve all your questions, you will need further refinements and generalizations to prove more intricate facts. That's all.

Yes! That was my point: I don't think we disagree!

I cannot see the link with God or his existence.

The point was:
If we cannot logically construct and validate a formal/deductive system such as Mathematics - without making fundamental assumptions that cannot be proven how can we expect to validate experimental/empirical/inductive systems that model the Universe?
In other words, we can't "scientifically" prove or disprove the existence - or non-existence - of God. The question has nothing to do with Sciences!

Again, I apologize for a rushed answer, but I hope that I have somehow clarified my initial statement!

[Anonymouse]

The point was:
If we cannot logically construct and validate a formal/deductive system such as Mathematics - without making fundamental assumptions that cannot be proven how can we expect to validate experimental/empirical/inductive systems that model the Universe?
In other words, we can't "scientifically" prove or disprove the existence - or non-existence - of God. The question has nothing to do with Sciences!

Again, I apologize for a rushed answer, but I hope that I have somehow clarified my initial statement!

Whenever I get bogged down in long boring language Siamanto is always there to clear it up.

[rabinovich]

For lack of time, I will have to be brief . I apologize for it.
Most of all, I don't think that we disagree!

Godel's work was an attempt to answer the following question, raised many centuries ago - among others - by La Mettrie:
"Cam Mathematics be reduced to a simpler formal system?" (A form of reductionism!)
Once reduced to Arithmetic, Peano suggested an axiomatic.
Godel showed that the above question cannot be answered positively. In fact, he proved - as you know:
1- No axiomatic system is complete
2- As you have mentioned, if the Mathematical System is consistent, we can't prove it using Mathematical Logic

In other words, you can't logically - i.e. using Mathematical Logic - construct and validate the Mathematical System.
You need to make assumptions that cannot be proved - such as the ones that were made by Set Theorists.

We DO disagree.

You say "As you have mentioned, if the Mathematical System is consistent, we can't prove it using Mathematical Logic" while I haven't mentioned such a thing. What I have mentioned is that having ONE formal theory is not enough, you need more and higher-level theories as your questions become more intricate. No one puts an equal sign between mathematics and a formal theory. Math is a discipline, while formal theory represents a particular subject of study, which in turn is a mathematical object and can be studied by higher-level theories.

You say "you can't logically - i.e. using Mathematical Logic - construct and validate the Mathematical System." I don't know what background are you coming from, but I'm a math graduate and never heard of such thing as "Mathematical System", capitalized and presented as one theory. There's no such thing, you see, math is a discipline, not a single theory.

As far as theories inside that discipline go - all of them are logically constructed, all of them serve their goals, and the results of Godel only say that none of those theories can give answer to every question - which means there will always be a need of new theories. That's all.

[rabinovich]

In other words, you can't logically - i.e. using Mathematical Logic - construct and validate the Mathematical System.
You need to make assumptions that cannot be proved - such as the ones that were made by Set Theorists.

First, you have to base on something to construct a theory. I will remind you the simple fact from mathematical logic - Axioms (what you base your theory on) are NOT the unprovable statements Godel talks about. Each axiom is immediately provable, actually, in one step: just state the axiom. You see, the formal concept of proof needs a basis (such as axioms) and inference rules (such as "if A and A=>B then B"). So axioms can be viewed as atomic constructs in a theory, pretty much like variables and constants - they just must be there to start talking about a theory.

So again, your example of set theory postulates is irrelevant and has nothing to do with Godel. The need for basic objects (i.e. sets) and a basic set of axioms (i.e. set axioms) is just necessary to start doing any work in the theory.

You do have unprovable statements in each theory though, that is agreed upon. But not in math in general, because math is not a closed and finite set of theories, it's a word to denote a wide area of continuing studies.

[CatWoman]

You think its cool to be an Atheist now a days??? I would love that, but no. Its only in certain circles, not within the general public (in this country anyway).

I have taken so much crap for being an Atheist from different people here. Its really sad how determined people are to bring independent thinking down.

I said COOL not EASY!

[ArmoBarbi]

I said COOL not EASY!

Oh ok!



It is only cool in certain circles, like most things...

[Siamanto]

We DO disagree.
You say "As you have mentioned, if the Mathematical System is consistent, we can't prove it using Mathematical Logic" while I haven't mentioned such a thing. What I have mentioned is that having ONE formal theory is not enough, you need more and higher-level theories as your questions become more intricate. No one puts an equal sign between mathematics and a formal theory. Math is a discipline, while formal theory represents a particular subject of study, which in turn is a mathematical object and can be studied by higher-level theories.

You seem to be willing to disagree! That's not of logical nature and I can' debate it!

1- Mathematics or the "Mathematical System" IS a formal system. Surprising that a "math graduate" ignores such an elementary truth! Do you understand what is a formal system?
2- As I have already stated, Godel's work was an attempt to answer the following question, raised many centuries ago - among others - by La Mettrie:
"Can Mathematics be reduced to a simpler formal system?" (A form of reductionism!)
Godel showed that the above question cannot be answered positively.

Godel's work applies to the Mathematical System in particular! "That's all" - as you say!

We DO disagree.
Math is a discipline, while formal theory represents a particular subject of study, which in turn is a mathematical object and can be studied by higher-level theories.

Again, do you have the slightest understanding of what is a formal system? The following is a simplified definition - hopefully you can understand it!

http://encyclopedia.laborlawtalk.com/Formal_system

You say "you can't logically - i.e. using Mathematical Logic - construct and validate the Mathematical System." I don't know what background are you coming from, but I'm a math graduate

I see it's about who has a "phallus" and/or who has the biggest "phallus?" Or maybe who's "mother is the most beautiful?"
By the way, you may be surprised to learn that my 'phallus" may be a couple of inches longer?
Let's focus on the subject and stop behaving such an adolescent! Thanks!

never heard of such thing as "Mathematical System", capitalized and presented as one theory. There's no such thing, you see, math is a discipline, not a single theory.

By the way, for many centuries, Mathematicians tried to reduce the Mathematical System or Mathematics to a more elementary system as as Arithmetic. Hoping to reduce it to Mathematical Logic!

Yes , because it can be reduced to a simpler - and more elementary - system; I can consider it as one formal system!
Sorry, I can say "Mathematical System! "That's all" - as you say!

As far as theories inside that discipline go - all of them are logically constructed, all of them serve their goals, and the results of Godel only say that none of those theories can give answer to every question - which means there will always be a need of new theories. That's all.

You have a confused mind and sloppy "thinking" - at least the expression of it! You still need to fully digest what you were fed!
But those many sub-systems can be reduced to more elementary one such as Arithmetic etc. etc. "That's all" - as you say!